A Highly Efficient Approach to Protein Interactome Mapping Based on Collaborative Filtering Framework

PubMed Central

Luo, Xin; You, Zhuhong; Zhou, Mengchu; Li, Shuai; Leung, Hareton; Xia, Yunni; Zhu, Qingsheng

2015-01-01

The comprehensive mapping of protein-protein interactions (PPIs) is highly desired for one to gain deep insights into both fundamental cell biology processes and the pathology of diseases. Finely-set small-scale experiments are not only very expensive but also inefficient to identify numerous interactomes despite their high accuracy. High-throughput screening techniques enable efficient identification of PPIs; yet the desire to further extract useful knowledge from these data leads to the problem of binary interactome mapping. Network topology-based approaches prove to be highly efficient in addressing this problem; however, their performance deteriorates significantly on sparse putative PPI networks. Motivated by the success of collaborative filtering (CF)-based approaches to the problem of personalized-recommendation on large, sparse rating matrices, this work aims at implementing a highly efficient CF-based approach to binary interactome mapping. To achieve this, we first propose a CF framework for it. Under this framework, we model the given data into an interactome weight matrix, where the feature-vectors of involved proteins are extracted. With them, we design the rescaled cosine coefficient to model the inter-neighborhood similarity among involved proteins, for taking the mapping process. Experimental results on three large, sparse datasets demonstrate that the proposed approach outperforms several sophisticated topology-based approaches significantly. PMID:25572661

A Highly Efficient Approach to Protein Interactome Mapping Based on Collaborative Filtering Framework

NASA Astrophysics Data System (ADS)

Luo, Xin; You, Zhuhong; Zhou, Mengchu; Li, Shuai; Leung, Hareton; Xia, Yunni; Zhu, Qingsheng

2015-01-01

The comprehensive mapping of protein-protein interactions (PPIs) is highly desired for one to gain deep insights into both fundamental cell biology processes and the pathology of diseases. Finely-set small-scale experiments are not only very expensive but also inefficient to identify numerous interactomes despite their high accuracy. High-throughput screening techniques enable efficient identification of PPIs; yet the desire to further extract useful knowledge from these data leads to the problem of binary interactome mapping. Network topology-based approaches prove to be highly efficient in addressing this problem; however, their performance deteriorates significantly on sparse putative PPI networks. Motivated by the success of collaborative filtering (CF)-based approaches to the problem of personalized-recommendation on large, sparse rating matrices, this work aims at implementing a highly efficient CF-based approach to binary interactome mapping. To achieve this, we first propose a CF framework for it. Under this framework, we model the given data into an interactome weight matrix, where the feature-vectors of involved proteins are extracted. With them, we design the rescaled cosine coefficient to model the inter-neighborhood similarity among involved proteins, for taking the mapping process. Experimental results on three large, sparse datasets demonstrate that the proposed approach outperforms several sophisticated topology-based approaches significantly.

An efficient sparse matrix multiplication scheme for the CYBER 205 computer

NASA Technical Reports Server (NTRS)

Lambiotte, Jules J., Jr.

1988-01-01

This paper describes the development of an efficient algorithm for computing the product of a matrix and vector on a CYBER 205 vector computer. The desire to provide software which allows the user to choose between the often conflicting goals of minimizing central processing unit (CPU) time or storage requirements has led to a diagonal-based algorithm in which one of four types of storage is selected for each diagonal. The candidate storage types employed were chosen to be efficient on the CYBER 205 for diagonals which have nonzero structure which is dense, moderately sparse, very sparse and short, or very sparse and long; however, for many densities, no diagonal type is most efficient with respect to both resource requirements, and a trade-off must be made. For each diagonal, an initialization subroutine estimates the CPU time and storage required for each storage type based on results from previously performed numerical experimentation. These requirements are adjusted by weights provided by the user which reflect the relative importance the user places on the two resources. The adjusted resource requirements are then compared to select the most efficient storage and computational scheme.

The application of nonlinear programming and collocation to optimal aeroassisted orbital transfers

NASA Astrophysics Data System (ADS)

Shi, Y. Y.; Nelson, R. L.; Young, D. H.; Gill, P. E.; Murray, W.; Saunders, M. A.

1992-01-01

Sequential quadratic programming (SQP) and collocation of the differential equations of motion were applied to optimal aeroassisted orbital transfers. The Optimal Trajectory by Implicit Simulation (OTIS) computer program codes with updated nonlinear programming code (NZSOL) were used as a testbed for the SQP nonlinear programming (NLP) algorithms. The state-of-the-art sparse SQP method is considered to be effective for solving large problems with a sparse matrix. Sparse optimizers are characterized in terms of memory requirements and computational efficiency. For the OTIS problems, less than 10 percent of the Jacobian matrix elements are nonzero. The SQP method encompasses two phases: finding an initial feasible point by minimizing the sum of infeasibilities and minimizing the quadratic objective function within the feasible region. The orbital transfer problem under consideration involves the transfer from a high energy orbit to a low energy orbit.

beachmat: A Bioconductor C++ API for accessing high-throughput biological data from a variety of R matrix types

PubMed Central

Pagès, Hervé

2018-01-01

Biological experiments involving genomics or other high-throughput assays typically yield a data matrix that can be explored and analyzed using the R programming language with packages from the Bioconductor project. Improvements in the throughput of these assays have resulted in an explosion of data even from routine experiments, which poses a challenge to the existing computational infrastructure for statistical data analysis. For example, single-cell RNA sequencing (scRNA-seq) experiments frequently generate large matrices containing expression values for each gene in each cell, requiring sparse or file-backed representations for memory-efficient manipulation in R. These alternative representations are not easily compatible with high-performance C++ code used for computationally intensive tasks in existing R/Bioconductor packages. Here, we describe a C++ interface named beachmat, which enables agnostic data access from various matrix representations. This allows package developers to write efficient C++ code that is interoperable with dense, sparse and file-backed matrices, amongst others. We evaluated the performance of beachmat for accessing data from each matrix representation using both simulated and real scRNA-seq data, and defined a clear memory/speed trade-off to motivate the choice of an appropriate representation. We also demonstrate how beachmat can be incorporated into the code of other packages to drive analyses of a very large scRNA-seq data set. PMID:29723188

beachmat: A Bioconductor C++ API for accessing high-throughput biological data from a variety of R matrix types.

PubMed

Lun, Aaron T L; Pagès, Hervé; Smith, Mike L

2018-05-01

Biological experiments involving genomics or other high-throughput assays typically yield a data matrix that can be explored and analyzed using the R programming language with packages from the Bioconductor project. Improvements in the throughput of these assays have resulted in an explosion of data even from routine experiments, which poses a challenge to the existing computational infrastructure for statistical data analysis. For example, single-cell RNA sequencing (scRNA-seq) experiments frequently generate large matrices containing expression values for each gene in each cell, requiring sparse or file-backed representations for memory-efficient manipulation in R. These alternative representations are not easily compatible with high-performance C++ code used for computationally intensive tasks in existing R/Bioconductor packages. Here, we describe a C++ interface named beachmat, which enables agnostic data access from various matrix representations. This allows package developers to write efficient C++ code that is interoperable with dense, sparse and file-backed matrices, amongst others. We evaluated the performance of beachmat for accessing data from each matrix representation using both simulated and real scRNA-seq data, and defined a clear memory/speed trade-off to motivate the choice of an appropriate representation. We also demonstrate how beachmat can be incorporated into the code of other packages to drive analyses of a very large scRNA-seq data set.

Semi-automatic sparse preconditioners for high-order finite element methods on non-uniform meshes

NASA Astrophysics Data System (ADS)

Austin, Travis M.; Brezina, Marian; Jamroz, Ben; Jhurani, Chetan; Manteuffel, Thomas A.; Ruge, John

2012-05-01

High-order finite elements often have a higher accuracy per degree of freedom than the classical low-order finite elements. However, in the context of implicit time-stepping methods, high-order finite elements present challenges to the construction of efficient simulations due to the high cost of inverting the denser finite element matrix. There are many cases where simulations are limited by the memory required to store the matrix and/or the algorithmic components of the linear solver. We are particularly interested in preconditioned Krylov methods for linear systems generated by discretization of elliptic partial differential equations with high-order finite elements. Using a preconditioner like Algebraic Multigrid can be costly in terms of memory due to the need to store matrix information at the various levels. We present a novel method for defining a preconditioner for systems generated by high-order finite elements that is based on a much sparser system than the original high-order finite element system. We investigate the performance for non-uniform meshes on a cube and a cubed sphere mesh, showing that the sparser preconditioner is more efficient and uses significantly less memory. Finally, we explore new methods to construct the sparse preconditioner and examine their effectiveness for non-uniform meshes. We compare results to a direct use of Algebraic Multigrid as a preconditioner and to a two-level additive Schwarz method.

Visual Tracking Based on Extreme Learning Machine and Sparse Representation

PubMed Central

Wang, Baoxian; Tang, Linbo; Yang, Jinglin; Zhao, Baojun; Wang, Shuigen

2015-01-01

The existing sparse representation-based visual trackers mostly suffer from both being time consuming and having poor robustness problems. To address these issues, a novel tracking method is presented via combining sparse representation and an emerging learning technique, namely extreme learning machine (ELM). Specifically, visual tracking can be divided into two consecutive processes. Firstly, ELM is utilized to find the optimal separate hyperplane between the target observations and background ones. Thus, the trained ELM classification function is able to remove most of the candidate samples related to background contents efficiently, thereby reducing the total computational cost of the following sparse representation. Secondly, to further combine ELM and sparse representation, the resultant confidence values (i.e., probabilities to be a target) of samples on the ELM classification function are used to construct a new manifold learning constraint term of the sparse representation framework, which tends to achieve robuster results. Moreover, the accelerated proximal gradient method is used for deriving the optimal solution (in matrix form) of the constrained sparse tracking model. Additionally, the matrix form solution allows the candidate samples to be calculated in parallel, thereby leading to a higher efficiency. Experiments demonstrate the effectiveness of the proposed tracker. PMID:26506359

Multi scales based sparse matrix spectral clustering image segmentation

NASA Astrophysics Data System (ADS)

Liu, Zhongmin; Chen, Zhicai; Li, Zhanming; Hu, Wenjin

2018-04-01

In image segmentation, spectral clustering algorithms have to adopt the appropriate scaling parameter to calculate the similarity matrix between the pixels, which may have a great impact on the clustering result. Moreover, when the number of data instance is large, computational complexity and memory use of the algorithm will greatly increase. To solve these two problems, we proposed a new spectral clustering image segmentation algorithm based on multi scales and sparse matrix. We devised a new feature extraction method at first, then extracted the features of image on different scales, at last, using the feature information to construct sparse similarity matrix which can improve the operation efficiency. Compared with traditional spectral clustering algorithm, image segmentation experimental results show our algorithm have better degree of accuracy and robustness.

On-Chip Neural Data Compression Based On Compressed Sensing With Sparse Sensing Matrices.

PubMed

Zhao, Wenfeng; Sun, Biao; Wu, Tong; Yang, Zhi

2018-02-01

On-chip neural data compression is an enabling technique for wireless neural interfaces that suffer from insufficient bandwidth and power budgets to transmit the raw data. The data compression algorithm and its implementation should be power and area efficient and functionally reliable over different datasets. Compressed sensing is an emerging technique that has been applied to compress various neurophysiological data. However, the state-of-the-art compressed sensing (CS) encoders leverage random but dense binary measurement matrices, which incur substantial implementation costs on both power and area that could offset the benefits from the reduced wireless data rate. In this paper, we propose two CS encoder designs based on sparse measurement matrices that could lead to efficient hardware implementation. Specifically, two different approaches for the construction of sparse measurement matrices, i.e., the deterministic quasi-cyclic array code (QCAC) matrix and -sparse random binary matrix [-SRBM] are exploited. We demonstrate that the proposed CS encoders lead to comparable recovery performance. And efficient VLSI architecture designs are proposed for QCAC-CS and -SRBM encoders with reduced area and total power consumption.

Efficient ICCG on a shared memory multiprocessor

NASA Technical Reports Server (NTRS)

Hammond, Steven W.; Schreiber, Robert

1989-01-01

Different approaches are discussed for exploiting parallelism in the ICCG (Incomplete Cholesky Conjugate Gradient) method for solving large sparse symmetric positive definite systems of equations on a shared memory parallel computer. Techniques for efficiently solving triangular systems and computing sparse matrix-vector products are explored. Three methods for scheduling the tasks in solving triangular systems are implemented on the Sequent Balance 21000. Sample problems that are representative of a large class of problems solved using iterative methods are used. We show that a static analysis to determine data dependences in the triangular solve can greatly improve its parallel efficiency. We also show that ignoring symmetry and storing the whole matrix can reduce solution time substantially.

Solving large sparse eigenvalue problems on supercomputers

NASA Technical Reports Server (NTRS)

Philippe, Bernard; Saad, Youcef

1988-01-01

An important problem in scientific computing consists in finding a few eigenvalues and corresponding eigenvectors of a very large and sparse matrix. The most popular methods to solve these problems are based on projection techniques on appropriate subspaces. The main attraction of these methods is that they only require the use of the matrix in the form of matrix by vector multiplications. The implementations on supercomputers of two such methods for symmetric matrices, namely Lanczos' method and Davidson's method are compared. Since one of the most important operations in these two methods is the multiplication of vectors by the sparse matrix, methods of performing this operation efficiently are discussed. The advantages and the disadvantages of each method are compared and implementation aspects are discussed. Numerical experiments on a one processor CRAY 2 and CRAY X-MP are reported. Possible parallel implementations are also discussed.

Partitioning Rectangular and Structurally Nonsymmetric Sparse Matrices for Parallel Processing

DOE Office of Scientific and Technical Information (OSTI.GOV)

B. Hendrickson; T.G. Kolda

1998-09-01

A common operation in scientific computing is the multiplication of a sparse, rectangular or structurally nonsymmetric matrix and a vector. In many applications the matrix- transpose-vector product is also required. This paper addresses the efficient parallelization of these operations. We show that the problem can be expressed in terms of partitioning bipartite graphs. We then introduce several algorithms for this partitioning problem and compare their performance on a set of test matrices.

Sparse non-negative matrix factorizations via alternating non-negativity-constrained least squares for microarray data analysis.

PubMed

Kim, Hyunsoo; Park, Haesun

2007-06-15

Many practical pattern recognition problems require non-negativity constraints. For example, pixels in digital images and chemical concentrations in bioinformatics are non-negative. Sparse non-negative matrix factorizations (NMFs) are useful when the degree of sparseness in the non-negative basis matrix or the non-negative coefficient matrix in an NMF needs to be controlled in approximating high-dimensional data in a lower dimensional space. In this article, we introduce a novel formulation of sparse NMF and show how the new formulation leads to a convergent sparse NMF algorithm via alternating non-negativity-constrained least squares. We apply our sparse NMF algorithm to cancer-class discovery and gene expression data analysis and offer biological analysis of the results obtained. Our experimental results illustrate that the proposed sparse NMF algorithm often achieves better clustering performance with shorter computing time compared to other existing NMF algorithms. The software is available as supplementary material.

A performance study of sparse Cholesky factorization on INTEL iPSC/860

NASA Technical Reports Server (NTRS)

Zubair, M.; Ghose, M.

1992-01-01

The problem of Cholesky factorization of a sparse matrix has been very well investigated on sequential machines. A number of efficient codes exist for factorizing large unstructured sparse matrices. However, there is a lack of such efficient codes on parallel machines in general, and distributed machines in particular. Some of the issues that are critical to the implementation of sparse Cholesky factorization on a distributed memory parallel machine are ordering, partitioning and mapping, load balancing, and ordering of various tasks within a processor. Here, we focus on the effect of various partitioning schemes on the performance of sparse Cholesky factorization on the Intel iPSC/860. Also, a new partitioning heuristic for structured as well as unstructured sparse matrices is proposed, and its performance is compared with other schemes.

An efficient gridding reconstruction method for multishot non-Cartesian imaging with correction of off-resonance artifacts.

PubMed

Meng, Yuguang; Lei, Hao

2010-06-01

An efficient iterative gridding reconstruction method with correction of off-resonance artifacts was developed, which is especially tailored for multiple-shot non-Cartesian imaging. The novelty of the method lies in that the transformation matrix for gridding (T) was constructed as the convolution of two sparse matrices, among which the former is determined by the sampling interval and the spatial distribution of the off-resonance frequencies and the latter by the sampling trajectory and the target grid in the Cartesian space. The resulting T matrix is also sparse and can be solved efficiently with the iterative conjugate gradient algorithm. It was shown that, with the proposed method, the reconstruction speed in multiple-shot non-Cartesian imaging can be improved significantly while retaining high reconstruction fidelity. More important, the method proposed allows tradeoff between the accuracy and the computation time of reconstruction, making customization of the use of such a method in different applications possible. The performance of the proposed method was demonstrated by numerical simulation and multiple-shot spiral imaging on rat brain at 4.7 T. (c) 2010 Wiley-Liss, Inc.

GPU-accelerated element-free reverse-time migration with Gauss points partition

NASA Astrophysics Data System (ADS)

Zhou, Zhen; Jia, Xiaofeng; Qiang, Xiaodong

2018-06-01

An element-free method (EFM) has been demonstrated successfully in elasticity, heat conduction and fatigue crack growth problems. We present the theory of EFM and its numerical applications in seismic modelling and reverse time migration (RTM). Compared with the finite difference method and the finite element method, the EFM has unique advantages: (1) independence of grids in computation and (2) lower expense and more flexibility (because only the information of the nodes and the boundary of the concerned area is required). However, in EFM, due to improper computation and storage of some large sparse matrices, such as the mass matrix and the stiffness matrix, the method is difficult to apply to seismic modelling and RTM for a large velocity model. To solve the problem of storage and computation efficiency, we propose a concept of Gauss points partition and utilise the graphics processing unit to improve the computational efficiency. We employ the compressed sparse row format to compress the intermediate large sparse matrices and attempt to simplify the operations by solving the linear equations with CULA solver. To improve the computation efficiency further, we introduce the concept of the lumped mass matrix. Numerical experiments indicate that the proposed method is accurate and more efficient than the regular EFM.

Compressed sensing for energy-efficient wireless telemonitoring of noninvasive fetal ECG via block sparse Bayesian learning.

PubMed

Zhang, Zhilin; Jung, Tzyy-Ping; Makeig, Scott; Rao, Bhaskar D

2013-02-01

Fetal ECG (FECG) telemonitoring is an important branch in telemedicine. The design of a telemonitoring system via a wireless body area network with low energy consumption for ambulatory use is highly desirable. As an emerging technique, compressed sensing (CS) shows great promise in compressing/reconstructing data with low energy consumption. However, due to some specific characteristics of raw FECG recordings such as nonsparsity and strong noise contamination, current CS algorithms generally fail in this application. This paper proposes to use the block sparse Bayesian learning framework to compress/reconstruct nonsparse raw FECG recordings. Experimental results show that the framework can reconstruct the raw recordings with high quality. Especially, the reconstruction does not destroy the interdependence relation among the multichannel recordings. This ensures that the independent component analysis decomposition of the reconstructed recordings has high fidelity. Furthermore, the framework allows the use of a sparse binary sensing matrix with much fewer nonzero entries to compress recordings. Particularly, each column of the matrix can contain only two nonzero entries. This shows that the framework, compared to other algorithms such as current CS algorithms and wavelet algorithms, can greatly reduce code execution in CPU in the data compression stage.

A method of vehicle license plate recognition based on PCANet and compressive sensing

NASA Astrophysics Data System (ADS)

Ye, Xianyi; Min, Feng

2018-03-01

The manual feature extraction of the traditional method for vehicle license plates has no good robustness to change in diversity. And the high feature dimension that is extracted with Principal Component Analysis Network (PCANet) leads to low classification efficiency. For solving these problems, a method of vehicle license plate recognition based on PCANet and compressive sensing is proposed. First, PCANet is used to extract the feature from the images of characters. And then, the sparse measurement matrix which is a very sparse matrix and consistent with Restricted Isometry Property (RIP) condition of the compressed sensing is used to reduce the dimensions of extracted features. Finally, the Support Vector Machine (SVM) is used to train and recognize the features whose dimension has been reduced. Experimental results demonstrate that the proposed method has better performance than Convolutional Neural Network (CNN) in the recognition and time. Compared with no compression sensing, the proposed method has lower feature dimension for the increase of efficiency.

Doubly Nonparametric Sparse Nonnegative Matrix Factorization Based on Dependent Indian Buffet Processes.

PubMed

Xuan, Junyu; Lu, Jie; Zhang, Guangquan; Xu, Richard Yi Da; Luo, Xiangfeng

2018-05-01

Sparse nonnegative matrix factorization (SNMF) aims to factorize a data matrix into two optimized nonnegative sparse factor matrices, which could benefit many tasks, such as document-word co-clustering. However, the traditional SNMF typically assumes the number of latent factors (i.e., dimensionality of the factor matrices) to be fixed. This assumption makes it inflexible in practice. In this paper, we propose a doubly sparse nonparametric NMF framework to mitigate this issue by using dependent Indian buffet processes (dIBP). We apply a correlation function for the generation of two stick weights associated with each column pair of factor matrices while still maintaining their respective marginal distribution specified by IBP. As a consequence, the generation of two factor matrices will be columnwise correlated. Under this framework, two classes of correlation function are proposed: 1) using bivariate Beta distribution and 2) using Copula function. Compared with the single IBP-based NMF, this paper jointly makes two factor matrices nonparametric and sparse, which could be applied to broader scenarios, such as co-clustering. This paper is seen to be much more flexible than Gaussian process-based and hierarchial Beta process-based dIBPs in terms of allowing the two corresponding binary matrix columns to have greater variations in their nonzero entries. Our experiments on synthetic data show the merits of this paper compared with the state-of-the-art models in respect of factorization efficiency, sparsity, and flexibility. Experiments on real-world data sets demonstrate the efficiency of this paper in document-word co-clustering tasks.

Securing image information using double random phase encoding and parallel compressive sensing with updated sampling processes

NASA Astrophysics Data System (ADS)

Hu, Guiqiang; Xiao, Di; Wang, Yong; Xiang, Tao; Zhou, Qing

2017-11-01

Recently, a new kind of image encryption approach using compressive sensing (CS) and double random phase encoding has received much attention due to the advantages such as compressibility and robustness. However, this approach is found to be vulnerable to chosen plaintext attack (CPA) if the CS measurement matrix is re-used. Therefore, designing an efficient measurement matrix updating mechanism that ensures resistance to CPA is of practical significance. In this paper, we provide a novel solution to update the CS measurement matrix by altering the secret sparse basis with the help of counter mode operation. Particularly, the secret sparse basis is implemented by a reality-preserving fractional cosine transform matrix. Compared with the conventional CS-based cryptosystem that totally generates all the random entries of measurement matrix, our scheme owns efficiency superiority while guaranteeing resistance to CPA. Experimental and analysis results show that the proposed scheme has a good security performance and has robustness against noise and occlusion.

Sparse subspace clustering for data with missing entries and high-rank matrix completion.

PubMed

Fan, Jicong; Chow, Tommy W S

2017-09-01

Many methods have recently been proposed for subspace clustering, but they are often unable to handle incomplete data because of missing entries. Using matrix completion methods to recover missing entries is a common way to solve the problem. Conventional matrix completion methods require that the matrix should be of low-rank intrinsically, but most matrices are of high-rank or even full-rank in practice, especially when the number of subspaces is large. In this paper, a new method called Sparse Representation with Missing Entries and Matrix Completion is proposed to solve the problems of incomplete-data subspace clustering and high-rank matrix completion. The proposed algorithm alternately computes the matrix of sparse representation coefficients and recovers the missing entries of a data matrix. The proposed algorithm recovers missing entries through minimizing the representation coefficients, representation errors, and matrix rank. Thorough experimental study and comparative analysis based on synthetic data and natural images were conducted. The presented results demonstrate that the proposed algorithm is more effective in subspace clustering and matrix completion compared with other existing methods. Copyright © 2017 Elsevier Ltd. All rights reserved.

A Fast Gradient Method for Nonnegative Sparse Regression With Self-Dictionary

NASA Astrophysics Data System (ADS)

Gillis, Nicolas; Luce, Robert

2018-01-01

A nonnegative matrix factorization (NMF) can be computed efficiently under the separability assumption, which asserts that all the columns of the given input data matrix belong to the cone generated by a (small) subset of them. The provably most robust methods to identify these conic basis columns are based on nonnegative sparse regression and self dictionaries, and require the solution of large-scale convex optimization problems. In this paper we study a particular nonnegative sparse regression model with self dictionary. As opposed to previously proposed models, this model yields a smooth optimization problem where the sparsity is enforced through linear constraints. We show that the Euclidean projection on the polyhedron defined by these constraints can be computed efficiently, and propose a fast gradient method to solve our model. We compare our algorithm with several state-of-the-art methods on synthetic data sets and real-world hyperspectral images.

Convex Banding of the Covariance Matrix

PubMed Central

Bien, Jacob; Bunea, Florentina; Xiao, Luo

2016-01-01

We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an estimator which tapers the sample covariance matrix by a Toeplitz, sparsely-banded, data-adaptive matrix. As a result of this adaptivity, the convex banding estimator enjoys theoretical optimality properties not attained by previous banding or tapered estimators. In particular, our convex banding estimator is minimax rate adaptive in Frobenius and operator norms, up to log factors, over commonly-studied classes of covariance matrices, and over more general classes. Furthermore, it correctly recovers the bandwidth when the true covariance is exactly banded. Our convex formulation admits a simple and efficient algorithm. Empirical studies demonstrate its practical effectiveness and illustrate that our exactly-banded estimator works well even when the true covariance matrix is only close to a banded matrix, confirming our theoretical results. Our method compares favorably with all existing methods, in terms of accuracy and speed. We illustrate the practical merits of the convex banding estimator by showing that it can be used to improve the performance of discriminant analysis for classifying sound recordings. PMID:28042189

Convex Banding of the Covariance Matrix.

PubMed

Bien, Jacob; Bunea, Florentina; Xiao, Luo

2016-01-01

We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an estimator which tapers the sample covariance matrix by a Toeplitz, sparsely-banded, data-adaptive matrix. As a result of this adaptivity, the convex banding estimator enjoys theoretical optimality properties not attained by previous banding or tapered estimators. In particular, our convex banding estimator is minimax rate adaptive in Frobenius and operator norms, up to log factors, over commonly-studied classes of covariance matrices, and over more general classes. Furthermore, it correctly recovers the bandwidth when the true covariance is exactly banded. Our convex formulation admits a simple and efficient algorithm. Empirical studies demonstrate its practical effectiveness and illustrate that our exactly-banded estimator works well even when the true covariance matrix is only close to a banded matrix, confirming our theoretical results. Our method compares favorably with all existing methods, in terms of accuracy and speed. We illustrate the practical merits of the convex banding estimator by showing that it can be used to improve the performance of discriminant analysis for classifying sound recordings.

Strategies for vectorizing the sparse matrix vector product on the CRAY XMP, CRAY 2, and CYBER 205

NASA Technical Reports Server (NTRS)

Bauschlicher, Charles W., Jr.; Partridge, Harry

1987-01-01

Large, randomly sparse matrix vector products are important in a number of applications in computational chemistry, such as matrix diagonalization and the solution of simultaneous equations. Vectorization of this process is considered for the CRAY XMP, CRAY 2, and CYBER 205, using a matrix of dimension of 20,000 with from 1 percent to 6 percent nonzeros. Efficient scatter/gather capabilities add coding flexibility and yield significant improvements in performance. For the CYBER 205, it is shown that minor changes in the IO can reduce the CPU time by a factor of 50. Similar changes in the CRAY codes make a far smaller improvement.

Implementation of hierarchical clustering using k-mer sparse matrix to analyze MERS-CoV genetic relationship

NASA Astrophysics Data System (ADS)

Bustamam, A.; Ulul, E. D.; Hura, H. F. A.; Siswantining, T.

2017-07-01

Hierarchical clustering is one of effective methods in creating a phylogenetic tree based on the distance matrix between DNA (deoxyribonucleic acid) sequences. One of the well-known methods to calculate the distance matrix is k-mer method. Generally, k-mer is more efficient than some distance matrix calculation techniques. The steps of k-mer method are started from creating k-mer sparse matrix, and followed by creating k-mer singular value vectors. The last step is computing the distance amongst vectors. In this paper, we analyze the sequences of MERS-CoV (Middle East Respiratory Syndrome - Coronavirus) DNA by implementing hierarchical clustering using k-mer sparse matrix in order to perform the phylogenetic analysis. Our results show that the ancestor of our MERS-CoV is coming from Egypt. Moreover, we found that the MERS-CoV infection that occurs in one country may not necessarily come from the same country of origin. This suggests that the process of MERS-CoV mutation might not only be influenced by geographical factor.

A sparse matrix-vector multiplication based algorithm for accurate density matrix computations on systems of millions of atoms

NASA Astrophysics Data System (ADS)

Ghale, Purnima; Johnson, Harley T.

2018-06-01

We present an efficient sparse matrix-vector (SpMV) based method to compute the density matrix P from a given Hamiltonian in electronic structure computations. Our method is a hybrid approach based on Chebyshev-Jackson approximation theory and matrix purification methods like the second order spectral projection purification (SP2). Recent methods to compute the density matrix scale as O(N) in the number of floating point operations but are accompanied by large memory and communication overhead, and they are based on iterative use of the sparse matrix-matrix multiplication kernel (SpGEMM), which is known to be computationally irregular. In addition to irregularity in the sparse Hamiltonian H, the nonzero structure of intermediate estimates of P depends on products of H and evolves over the course of computation. On the other hand, an expansion of the density matrix P in terms of Chebyshev polynomials is straightforward and SpMV based; however, the resulting density matrix may not satisfy the required constraints exactly. In this paper, we analyze the strengths and weaknesses of the Chebyshev-Jackson polynomials and the second order spectral projection purification (SP2) method, and propose to combine them so that the accurate density matrix can be computed using the SpMV computational kernel only, and without having to store the density matrix P. Our method accomplishes these objectives by using the Chebyshev polynomial estimate as the initial guess for SP2, which is followed by using sparse matrix-vector multiplications (SpMVs) to replicate the behavior of the SP2 algorithm for purification. We demonstrate the method on a tight-binding model system of an oxide material containing more than 3 million atoms. In addition, we also present the predicted behavior of our method when applied to near-metallic Hamiltonians with a wide energy spectrum.

Algorithms for solving large sparse systems of simultaneous linear equations on vector processors

NASA Technical Reports Server (NTRS)

David, R. E.

1984-01-01

Very efficient algorithms for solving large sparse systems of simultaneous linear equations have been developed for serial processing computers. These involve a reordering of matrix rows and columns in order to obtain a near triangular pattern of nonzero elements. Then an LU factorization is developed to represent the matrix inverse in terms of a sequence of elementary Gaussian eliminations, or pivots. In this paper it is shown how these algorithms are adapted for efficient implementation on vector processors. Results obtained on the CYBER 200 Model 205 are presented for a series of large test problems which show the comparative advantages of the triangularization and vector processing algorithms.

Technical note: Avoiding the direct inversion of the numerator relationship matrix for genotyped animals in single-step genomic best linear unbiased prediction solved with the preconditioned conjugate gradient.

PubMed

Masuda, Y; Misztal, I; Legarra, A; Tsuruta, S; Lourenco, D A L; Fragomeni, B O; Aguilar, I

2017-01-01

This paper evaluates an efficient implementation to multiply the inverse of a numerator relationship matrix for genotyped animals () by a vector (). The computation is required for solving mixed model equations in single-step genomic BLUP (ssGBLUP) with the preconditioned conjugate gradient (PCG). The inverse can be decomposed into sparse matrices that are blocks of the sparse inverse of a numerator relationship matrix () including genotyped animals and their ancestors. The elements of were rapidly calculated with the Henderson's rule and stored as sparse matrices in memory. Implementation of was by a series of sparse matrix-vector multiplications. Diagonal elements of , which were required as preconditioners in PCG, were approximated with a Monte Carlo method using 1,000 samples. The efficient implementation of was compared with explicit inversion of with 3 data sets including about 15,000, 81,000, and 570,000 genotyped animals selected from populations with 213,000, 8.2 million, and 10.7 million pedigree animals, respectively. The explicit inversion required 1.8 GB, 49 GB, and 2,415 GB (estimated) of memory, respectively, and 42 s, 56 min, and 13.5 d (estimated), respectively, for the computations. The efficient implementation required <1 MB, 2.9 GB, and 2.3 GB of memory, respectively, and <1 sec, 3 min, and 5 min, respectively, for setting up. Only <1 sec was required for the multiplication in each PCG iteration for any data sets. When the equations in ssGBLUP are solved with the PCG algorithm, is no longer a limiting factor in the computations.

Supercomputing on massively parallel bit-serial architectures

NASA Technical Reports Server (NTRS)

Iobst, Ken

1985-01-01

Research on the Goodyear Massively Parallel Processor (MPP) suggests that high-level parallel languages are practical and can be designed with powerful new semantics that allow algorithms to be efficiently mapped to the real machines. For the MPP these semantics include parallel/associative array selection for both dense and sparse matrices, variable precision arithmetic to trade accuracy for speed, micro-pipelined train broadcast, and conditional branching at the processing element (PE) control unit level. The preliminary design of a FORTRAN-like parallel language for the MPP has been completed and is being used to write programs to perform sparse matrix array selection, min/max search, matrix multiplication, Gaussian elimination on single bit arrays and other generic algorithms. A description is given of the MPP design. Features of the system and its operation are illustrated in the form of charts and diagrams.

Noniterative MAP reconstruction using sparse matrix representations.

PubMed

Cao, Guangzhi; Bouman, Charles A; Webb, Kevin J

2009-09-01

We present a method for noniterative maximum a posteriori (MAP) tomographic reconstruction which is based on the use of sparse matrix representations. Our approach is to precompute and store the inverse matrix required for MAP reconstruction. This approach has generally not been used in the past because the inverse matrix is typically large and fully populated (i.e., not sparse). In order to overcome this problem, we introduce two new ideas. The first idea is a novel theory for the lossy source coding of matrix transformations which we refer to as matrix source coding. This theory is based on a distortion metric that reflects the distortions produced in the final matrix-vector product, rather than the distortions in the coded matrix itself. The resulting algorithms are shown to require orthonormal transformations of both the measurement data and the matrix rows and columns before quantization and coding. The second idea is a method for efficiently storing and computing the required orthonormal transformations, which we call a sparse-matrix transform (SMT). The SMT is a generalization of the classical FFT in that it uses butterflies to compute an orthonormal transform; but unlike an FFT, the SMT uses the butterflies in an irregular pattern, and is numerically designed to best approximate the desired transforms. We demonstrate the potential of the noniterative MAP reconstruction with examples from optical tomography. The method requires offline computation to encode the inverse transform. However, once these offline computations are completed, the noniterative MAP algorithm is shown to reduce both storage and computation by well over two orders of magnitude, as compared to a linear iterative reconstruction methods.

Sparse Covariance Matrix Estimation With Eigenvalue Constraints

PubMed Central

LIU, Han; WANG, Lie; ZHAO, Tuo

2014-01-01

We propose a new approach for estimating high-dimensional, positive-definite covariance matrices. Our method extends the generalized thresholding operator by adding an explicit eigenvalue constraint. The estimated covariance matrix simultaneously achieves sparsity and positive definiteness. The estimator is rate optimal in the minimax sense and we develop an efficient iterative soft-thresholding and projection algorithm based on the alternating direction method of multipliers. Empirically, we conduct thorough numerical experiments on simulated datasets as well as real data examples to illustrate the usefulness of our method. Supplementary materials for the article are available online. PMID:25620866

Newmark-Beta-FDTD method for super-resolution analysis of time reversal waves

NASA Astrophysics Data System (ADS)

Shi, Sheng-Bing; Shao, Wei; Ma, Jing; Jin, Congjun; Wang, Xiao-Hua

2017-09-01

In this work, a new unconditionally stable finite-difference time-domain (FDTD) method with the split-field perfectly matched layer (PML) is proposed for the analysis of time reversal (TR) waves. The proposed method is very suitable for multiscale problems involving microstructures. The spatial and temporal derivatives in this method are discretized by the central difference technique and Newmark-Beta algorithm, respectively, and the derivation results in the calculation of a banded-sparse matrix equation. Since the coefficient matrix keeps unchanged during the whole simulation process, the lower-upper (LU) decomposition of the matrix needs to be performed only once at the beginning of the calculation. Moreover, the reverse Cuthill-Mckee (RCM) technique, an effective preprocessing technique in bandwidth compression of sparse matrices, is used to improve computational efficiency. The super-resolution focusing of TR wave propagation in two- and three-dimensional spaces is included to validate the accuracy and efficiency of the proposed method.

Sequential time interleaved random equivalent sampling for repetitive signal.

PubMed

Zhao, Yijiu; Liu, Jingjing

2016-12-01

Compressed sensing (CS) based sampling techniques exhibit many advantages over other existing approaches for sparse signal spectrum sensing; they are also incorporated into non-uniform sampling signal reconstruction to improve the efficiency, such as random equivalent sampling (RES). However, in CS based RES, only one sample of each acquisition is considered in the signal reconstruction stage, and it will result in more acquisition runs and longer sampling time. In this paper, a sampling sequence is taken in each RES acquisition run, and the corresponding block measurement matrix is constructed using a Whittaker-Shannon interpolation formula. All the block matrices are combined into an equivalent measurement matrix with respect to all sampling sequences. We implemented the proposed approach with a multi-cores analog-to-digital converter (ADC), whose ADC cores are time interleaved. A prototype realization of this proposed CS based sequential random equivalent sampling method has been developed. It is able to capture an analog waveform at an equivalent sampling rate of 40 GHz while sampled at 1 GHz physically. Experiments indicate that, for a sparse signal, the proposed CS based sequential random equivalent sampling exhibits high efficiency.

High-dimensional statistical inference: From vector to matrix

NASA Astrophysics Data System (ADS)

Zhang, Anru

Statistical inference for sparse signals or low-rank matrices in high-dimensional settings is of significant interest in a range of contemporary applications. It has attracted significant recent attention in many fields including statistics, applied mathematics and electrical engineering. In this thesis, we consider several problems in including sparse signal recovery (compressed sensing under restricted isometry) and low-rank matrix recovery (matrix recovery via rank-one projections and structured matrix completion). The first part of the thesis discusses compressed sensing and affine rank minimization in both noiseless and noisy cases and establishes sharp restricted isometry conditions for sparse signal and low-rank matrix recovery. The analysis relies on a key technical tool which represents points in a polytope by convex combinations of sparse vectors. The technique is elementary while leads to sharp results. It is shown that, in compressed sensing, delta kA < 1/3, deltak A+ thetak,kA < 1, or deltatkA < √( t - 1)/t for any given constant t ≥ 4/3 guarantee the exact recovery of all k sparse signals in the noiseless case through the constrained ℓ1 minimization, and similarly in affine rank minimization delta rM < 1/3, deltar M + thetar, rM < 1, or deltatrM< √( t - 1)/t ensure the exact reconstruction of all matrices with rank at most r in the noiseless case via the constrained nuclear norm minimization. Moreover, for any epsilon > 0, delta kA < 1/3 + epsilon, deltak A + thetak,kA < 1 + epsilon, or deltatkA< √(t - 1) / t + epsilon are not sufficient to guarantee the exact recovery of all k-sparse signals for large k. Similar result also holds for matrix recovery. In addition, the conditions delta kA<1/3, deltak A+ thetak,kA<1, delta tkA < √(t - 1)/t and deltarM<1/3, delta rM+ thetar,rM<1, delta trM< √(t - 1)/ t are also shown to be sufficient respectively for stable recovery of approximately sparse signals and low-rank matrices in the noisy case. For the second part of the thesis, we introduce a rank-one projection model for low-rank matrix recovery and propose a constrained nuclear norm minimization method for stable recovery of low-rank matrices in the noisy case. The procedure is adaptive to the rank and robust against small perturbations. Both upper and lower bounds for the estimation accuracy under the Frobenius norm loss are obtained. The proposed estimator is shown to be rate-optimal under certain conditions. The estimator is easy to implement via convex programming and performs well numerically. The techniques and main results developed in the chapter also have implications to other related statistical problems. An application to estimation of spiked covariance matrices from one-dimensional random projections is considered. The results demonstrate that it is still possible to accurately estimate the covariance matrix of a high-dimensional distribution based only on one-dimensional projections. For the third part of the thesis, we consider another setting of low-rank matrix completion. Current literature on matrix completion focuses primarily on independent sampling models under which the individual observed entries are sampled independently. Motivated by applications in genomic data integration, we propose a new framework of structured matrix completion (SMC) to treat structured missingness by design. Specifically, our proposed method aims at efficient matrix recovery when a subset of the rows and columns of an approximately low-rank matrix are observed. We provide theoretical justification for the proposed SMC method and derive lower bound for the estimation errors, which together establish the optimal rate of recovery over certain classes of approximately low-rank matrices. Simulation studies show that the method performs well in finite sample under a variety of configurations. The method is applied to integrate several ovarian cancer genomic studies with different extent of genomic measurements, which enables us to construct more accurate prediction rules for ovarian cancer survival.

LSRN: A PARALLEL ITERATIVE SOLVER FOR STRONGLY OVER- OR UNDERDETERMINED SYSTEMS*

PubMed Central

Meng, Xiangrui; Saunders, Michael A.; Mahoney, Michael W.

2014-01-01

We describe a parallel iterative least squares solver named LSRN that is based on random normal projection. LSRN computes the min-length solution to minx∈ℝn ‖Ax − b‖2, where A ∈ ℝm × n with m ≫ n or m ≪ n, and where A may be rank-deficient. Tikhonov regularization may also be included. Since A is involved only in matrix-matrix and matrix-vector multiplications, it can be a dense or sparse matrix or a linear operator, and LSRN automatically speeds up when A is sparse or a fast linear operator. The preconditioning phase consists of a random normal projection, which is embarrassingly parallel, and a singular value decomposition of size ⌈γ min(m, n)⌉ × min(m, n), where γ is moderately larger than 1, e.g., γ = 2. We prove that the preconditioned system is well-conditioned, with a strong concentration result on the extreme singular values, and hence that the number of iterations is fully predictable when we apply LSQR or the Chebyshev semi-iterative method. As we demonstrate, the Chebyshev method is particularly efficient for solving large problems on clusters with high communication cost. Numerical results show that on a shared-memory machine, LSRN is very competitive with LAPACK’s DGELSD and a fast randomized least squares solver called Blendenpik on large dense problems, and it outperforms the least squares solver from SuiteSparseQR on sparse problems without sparsity patterns that can be exploited to reduce fill-in. Further experiments show that LSRN scales well on an Amazon Elastic Compute Cloud cluster. PMID:25419094

Color normalization of histology slides using graph regularized sparse NMF

NASA Astrophysics Data System (ADS)

Sha, Lingdao; Schonfeld, Dan; Sethi, Amit

2017-03-01

Computer based automatic medical image processing and quantification are becoming popular in digital pathology. However, preparation of histology slides can vary widely due to differences in staining equipment, procedures and reagents, which can reduce the accuracy of algorithms that analyze their color and texture information. To re- duce the unwanted color variations, various supervised and unsupervised color normalization methods have been proposed. Compared with supervised color normalization methods, unsupervised color normalization methods have advantages of time and cost efficient and universal applicability. Most of the unsupervised color normaliza- tion methods for histology are based on stain separation. Based on the fact that stain concentration cannot be negative and different parts of the tissue absorb different stains, nonnegative matrix factorization (NMF), and particular its sparse version (SNMF), are good candidates for stain separation. However, most of the existing unsupervised color normalization method like PCA, ICA, NMF and SNMF fail to consider important information about sparse manifolds that its pixels occupy, which could potentially result in loss of texture information during color normalization. Manifold learning methods like Graph Laplacian have proven to be very effective in interpreting high-dimensional data. In this paper, we propose a novel unsupervised stain separation method called graph regularized sparse nonnegative matrix factorization (GSNMF). By considering the sparse prior of stain concentration together with manifold information from high-dimensional image data, our method shows better performance in stain color deconvolution than existing unsupervised color deconvolution methods, especially in keeping connected texture information. To utilized the texture information, we construct a nearest neighbor graph between pixels within a spatial area of an image based on their distances using heat kernal in lαβ space. The representation of a pixel in the stain density space is constrained to follow the feature distance of the pixel to pixels in the neighborhood graph. Utilizing color matrix transfer method with the stain concentrations found using our GSNMF method, the color normalization performance was also better than existing methods.

Representation-Independent Iteration of Sparse Data Arrays

NASA Technical Reports Server (NTRS)

James, Mark

2007-01-01

An approach is defined that describes a method of iterating over massively large arrays containing sparse data using an approach that is implementation independent of how the contents of the sparse arrays are laid out in memory. What is unique and important here is the decoupling of the iteration over the sparse set of array elements from how they are internally represented in memory. This enables this approach to be backward compatible with existing schemes for representing sparse arrays as well as new approaches. What is novel here is a new approach for efficiently iterating over sparse arrays that is independent of the underlying memory layout representation of the array. A functional interface is defined for implementing sparse arrays in any modern programming language with a particular focus for the Chapel programming language. Examples are provided that show the translation of a loop that computes a matrix vector product into this representation for both the distributed and not-distributed cases. This work is directly applicable to NASA and its High Productivity Computing Systems (HPCS) program that JPL and our current program are engaged in. The goal of this program is to create powerful, scalable, and economically viable high-powered computer systems suitable for use in national security and industry by 2010. This is important to NASA for its computationally intensive requirements for analyzing and understanding the volumes of science data from our returned missions.

Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners

DOE PAGES

Li, Ruipeng; Saad, Yousef

2017-08-01

This study presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits domain decomposition (DD) and low-rank corrections. The DD approach decouples the matrix and, once inverted, a low-rank approximation is applied by exploiting the Sherman--Morrison--Woodbury formula, which yields two variants of the preconditioning methods. The low-rank expansion is computed by the Lanczos procedure with reorthogonalizations. Numerical experiments indicate that, when combined with Krylov subspace accelerators, this preconditioner can be efficient and robust for solving symmetric sparse linear systems. Comparisonsmore » with pARMS, a DD-based parallel incomplete LU (ILU) preconditioning method, are presented for solving Poisson's equation and linear elasticity problems.« less

Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Ruipeng; Saad, Yousef

This study presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits domain decomposition (DD) and low-rank corrections. The DD approach decouples the matrix and, once inverted, a low-rank approximation is applied by exploiting the Sherman--Morrison--Woodbury formula, which yields two variants of the preconditioning methods. The low-rank expansion is computed by the Lanczos procedure with reorthogonalizations. Numerical experiments indicate that, when combined with Krylov subspace accelerators, this preconditioner can be efficient and robust for solving symmetric sparse linear systems. Comparisonsmore » with pARMS, a DD-based parallel incomplete LU (ILU) preconditioning method, are presented for solving Poisson's equation and linear elasticity problems.« less

Robust Principal Component Analysis Regularized by Truncated Nuclear Norm for Identifying Differentially Expressed Genes.

PubMed

Wang, Ya-Xuan; Gao, Ying-Lian; Liu, Jin-Xing; Kong, Xiang-Zhen; Li, Hai-Jun

2017-09-01

Identifying differentially expressed genes from the thousands of genes is a challenging task. Robust principal component analysis (RPCA) is an efficient method in the identification of differentially expressed genes. RPCA method uses nuclear norm to approximate the rank function. However, theoretical studies showed that the nuclear norm minimizes all singular values, so it may not be the best solution to approximate the rank function. The truncated nuclear norm is defined as the sum of some smaller singular values, which may achieve a better approximation of the rank function than nuclear norm. In this paper, a novel method is proposed by replacing nuclear norm of RPCA with the truncated nuclear norm, which is named robust principal component analysis regularized by truncated nuclear norm (TRPCA). The method decomposes the observation matrix of genomic data into a low-rank matrix and a sparse matrix. Because the significant genes can be considered as sparse signals, the differentially expressed genes are viewed as the sparse perturbation signals. Thus, the differentially expressed genes can be identified according to the sparse matrix. The experimental results on The Cancer Genome Atlas data illustrate that the TRPCA method outperforms other state-of-the-art methods in the identification of differentially expressed genes.

User's Manual for PCSMS (Parallel Complex Sparse Matrix Solver). Version 1.

NASA Technical Reports Server (NTRS)

Reddy, C. J.

2000-01-01

PCSMS (Parallel Complex Sparse Matrix Solver) is a computer code written to make use of the existing real sparse direct solvers to solve complex, sparse matrix linear equations. PCSMS converts complex matrices into real matrices and use real, sparse direct matrix solvers to factor and solve the real matrices. The solution vector is reconverted to complex numbers. Though, this utility is written for Silicon Graphics (SGI) real sparse matrix solution routines, it is general in nature and can be easily modified to work with any real sparse matrix solver. The User's Manual is written to make the user acquainted with the installation and operation of the code. Driver routines are given to aid the users to integrate PCSMS routines in their own codes.

Efficient Computation of Sparse Matrix Functions for Large-Scale Electronic Structure Calculations: The CheSS Library.

PubMed

Mohr, Stephan; Dawson, William; Wagner, Michael; Caliste, Damien; Nakajima, Takahito; Genovese, Luigi

2017-10-10

We present CheSS, the "Chebyshev Sparse Solvers" library, which has been designed to solve typical problems arising in large-scale electronic structure calculations using localized basis sets. The library is based on a flexible and efficient expansion in terms of Chebyshev polynomials and presently features the calculation of the density matrix, the calculation of matrix powers for arbitrary powers, and the extraction of eigenvalues in a selected interval. CheSS is able to exploit the sparsity of the matrices and scales linearly with respect to the number of nonzero entries, making it well-suited for large-scale calculations. The approach is particularly adapted for setups leading to small spectral widths of the involved matrices and outperforms alternative methods in this regime. By coupling CheSS to the DFT code BigDFT, we show that such a favorable setup is indeed possible in practice. In addition, the approach based on Chebyshev polynomials can be massively parallelized, and CheSS exhibits excellent scaling up to thousands of cores even for relatively small matrix sizes.

Sparse matrix methods based on orthogonality and conjugacy

NASA Technical Reports Server (NTRS)

Lawson, C. L.

1973-01-01

A matrix having a high percentage of zero elements is called spares. In the solution of systems of linear equations or linear least squares problems involving large sparse matrices, significant saving of computer cost can be achieved by taking advantage of the sparsity. The conjugate gradient algorithm and a set of related algorithms are described.

Efficient parallel linear scaling construction of the density matrix for Born-Oppenheimer molecular dynamics.

PubMed

Mniszewski, S M; Cawkwell, M J; Wall, M E; Mohd-Yusof, J; Bock, N; Germann, T C; Niklasson, A M N

2015-10-13

We present an algorithm for the calculation of the density matrix that for insulators scales linearly with system size and parallelizes efficiently on multicore, shared memory platforms with small and controllable numerical errors. The algorithm is based on an implementation of the second-order spectral projection (SP2) algorithm [ Niklasson, A. M. N. Phys. Rev. B 2002 , 66 , 155115 ] in sparse matrix algebra with the ELLPACK-R data format. We illustrate the performance of the algorithm within self-consistent tight binding theory by total energy calculations of gas phase poly(ethylene) molecules and periodic liquid water systems containing up to 15,000 atoms on up to 16 CPU cores. We consider algorithm-specific performance aspects, such as local vs nonlocal memory access and the degree of matrix sparsity. Comparisons to sparse matrix algebra implementations using off-the-shelf libraries on multicore CPUs, graphics processing units (GPUs), and the Intel many integrated core (MIC) architecture are also presented. The accuracy and stability of the algorithm are illustrated with long duration Born-Oppenheimer molecular dynamics simulations of 1000 water molecules and a 303 atom Trp cage protein solvated by 2682 water molecules.

Approximate method of variational Bayesian matrix factorization/completion with sparse prior

NASA Astrophysics Data System (ADS)

Kawasumi, Ryota; Takeda, Koujin

2018-05-01

We derive the analytical expression of a matrix factorization/completion solution by the variational Bayes method, under the assumption that the observed matrix is originally the product of low-rank, dense and sparse matrices with additive noise. We assume the prior of a sparse matrix is a Laplace distribution by taking matrix sparsity into consideration. Then we use several approximations for the derivation of a matrix factorization/completion solution. By our solution, we also numerically evaluate the performance of a sparse matrix reconstruction in matrix factorization, and completion of a missing matrix element in matrix completion.

A Semiparametric Approach to Simultaneous Covariance Estimation for Bivariate Sparse Longitudinal Data

PubMed Central

Das, Kiranmoy; Daniels, Michael J.

2014-01-01

Summary Estimation of the covariance structure for irregular sparse longitudinal data has been studied by many authors in recent years but typically using fully parametric specifications. In addition, when data are collected from several groups over time, it is known that assuming the same or completely different covariance matrices over groups can lead to loss of efficiency and/or bias. Nonparametric approaches have been proposed for estimating the covariance matrix for regular univariate longitudinal data by sharing information across the groups under study. For the irregular case, with longitudinal measurements that are bivariate or multivariate, modeling becomes more difficult. In this article, to model bivariate sparse longitudinal data from several groups, we propose a flexible covariance structure via a novel matrix stick-breaking process for the residual covariance structure and a Dirichlet process mixture of normals for the random effects. Simulation studies are performed to investigate the effectiveness of the proposed approach over more traditional approaches. We also analyze a subset of Framingham Heart Study data to examine how the blood pressure trajectories and covariance structures differ for the patients from different BMI groups (high, medium and low) at baseline. PMID:24400941

Technical note: an R package for fitting sparse neural networks with application in animal breeding.

PubMed

Wang, Yangfan; Mi, Xue; Rosa, Guilherme J M; Chen, Zhihui; Lin, Ping; Wang, Shi; Bao, Zhenmin

2018-05-04

Neural networks (NNs) have emerged as a new tool for genomic selection (GS) in animal breeding. However, the properties of NN used in GS for the prediction of phenotypic outcomes are not well characterized due to the problem of over-parameterization of NN and difficulties in using whole-genome marker sets as high-dimensional NN input. In this note, we have developed an R package called snnR that finds an optimal sparse structure of a NN by minimizing the square error subject to a penalty on the L1-norm of the parameters (weights and biases), therefore solving the problem of over-parameterization in NN. We have also tested some models fitted in the snnR package to demonstrate their feasibility and effectiveness to be used in several cases as examples. In comparison of snnR to the R package brnn (the Bayesian regularized single layer NNs), with both using the entries of a genotype matrix or a genomic relationship matrix as inputs, snnR has greatly improved the computational efficiency and the prediction ability for the GS in animal breeding because snnR implements a sparse NN with many hidden layers.

HYPOTHESIS TESTING FOR HIGH-DIMENSIONAL SPARSE BINARY REGRESSION

PubMed Central

Mukherjee, Rajarshi; Pillai, Natesh S.; Lin, Xihong

2015-01-01

In this paper, we study the detection boundary for minimax hypothesis testing in the context of high-dimensional, sparse binary regression models. Motivated by genetic sequencing association studies for rare variant effects, we investigate the complexity of the hypothesis testing problem when the design matrix is sparse. We observe a new phenomenon in the behavior of detection boundary which does not occur in the case of Gaussian linear regression. We derive the detection boundary as a function of two components: a design matrix sparsity index and signal strength, each of which is a function of the sparsity of the alternative. For any alternative, if the design matrix sparsity index is too high, any test is asymptotically powerless irrespective of the magnitude of signal strength. For binary design matrices with the sparsity index that is not too high, our results are parallel to those in the Gaussian case. In this context, we derive detection boundaries for both dense and sparse regimes. For the dense regime, we show that the generalized likelihood ratio is rate optimal; for the sparse regime, we propose an extended Higher Criticism Test and show it is rate optimal and sharp. We illustrate the finite sample properties of the theoretical results using simulation studies. PMID:26246645

The Use of Sparse Direct Solver in Vector Finite Element Modeling for Calculating Two Dimensional (2-D) Magnetotelluric Responses in Transverse Electric (TE) Mode

NASA Astrophysics Data System (ADS)

Yihaa Roodhiyah, Lisa’; Tjong, Tiffany; Nurhasan; Sutarno, D.

2018-04-01

The late research, linear matrices of vector finite element in two dimensional(2-D) magnetotelluric (MT) responses modeling was solved by non-sparse direct solver in TE mode. Nevertheless, there is some weakness which have to be improved especially accuracy in the low frequency (10-3 Hz-10-5 Hz) which is not achieved yet and high cost computation in dense mesh. In this work, the solver which is used is sparse direct solver instead of non-sparse direct solverto overcome the weaknesses of solving linear matrices of vector finite element metod using non-sparse direct solver. Sparse direct solver will be advantageous in solving linear matrices of vector finite element method because of the matrix properties which is symmetrical and sparse. The validation of sparse direct solver in solving linear matrices of vector finite element has been done for a homogen half-space model and vertical contact model by analytical solution. Thevalidation result of sparse direct solver in solving linear matrices of vector finite element shows that sparse direct solver is more stable than non-sparse direct solver in computing linear problem of vector finite element method especially in low frequency. In the end, the accuracy of 2D MT responses modelling in low frequency (10-3 Hz-10-5 Hz) has been reached out under the efficient allocation memory of array and less computational time consuming.

GPU-accelerated algorithms for compressed signals recovery with application to astronomical imagery deblurring

NASA Astrophysics Data System (ADS)

Fiandrotti, Attilio; Fosson, Sophie M.; Ravazzi, Chiara; Magli, Enrico

2018-04-01

Compressive sensing promises to enable bandwidth-efficient on-board compression of astronomical data by lifting the encoding complexity from the source to the receiver. The signal is recovered off-line, exploiting GPUs parallel computation capabilities to speedup the reconstruction process. However, inherent GPU hardware constraints limit the size of the recoverable signal and the speedup practically achievable. In this work, we design parallel algorithms that exploit the properties of circulant matrices for efficient GPU-accelerated sparse signals recovery. Our approach reduces the memory requirements, allowing us to recover very large signals with limited memory. In addition, it achieves a tenfold signal recovery speedup thanks to ad-hoc parallelization of matrix-vector multiplications and matrix inversions. Finally, we practically demonstrate our algorithms in a typical application of circulant matrices: deblurring a sparse astronomical image in the compressed domain.

Brief announcement: Hypergraph parititioning for parallel sparse matrix-matrix multiplication

DOE PAGES

Ballard, Grey; Druinsky, Alex; Knight, Nicholas; ...

2015-01-01

The performance of parallel algorithms for sparse matrix-matrix multiplication is typically determined by the amount of interprocessor communication performed, which in turn depends on the nonzero structure of the input matrices. In this paper, we characterize the communication cost of a sparse matrix-matrix multiplication algorithm in terms of the size of a cut of an associated hypergraph that encodes the computation for a given input nonzero structure. Obtaining an optimal algorithm corresponds to solving a hypergraph partitioning problem. Furthermore, our hypergraph model generalizes several existing models for sparse matrix-vector multiplication, and we can leverage hypergraph partitioners developed for that computationmore » to improve application-specific algorithms for multiplying sparse matrices.« less

Nonleachable Imidazolium-Incorporated Composite for Disruption of Bacterial Clustering, Exopolysaccharide-Matrix Assembly, and Enhanced Biofilm Removal.

PubMed

Hwang, Geelsu; Koltisko, Bernard; Jin, Xiaoming; Koo, Hyun

2017-11-08

Surface-grown bacteria and production of an extracellular polymeric matrix modulate the assembly of highly cohesive and firmly attached biofilms, making them difficult to remove from solid surfaces. Inhibition of cell growth and inactivation of matrix-producing bacteria can impair biofilm formation and facilitate removal. Here, we developed a novel nonleachable antibacterial composite with potent antibiofilm activity by directly incorporating polymerizable imidazolium-containing resin (antibacterial resin with carbonate linkage; ABR-C) into a methacrylate-based scaffold (ABR-modified composite; ABR-MC) using an efficient yet simplified chemistry. Low-dose inclusion of imidazolium moiety (∼2 wt %) resulted in bioactivity with minimal cytotoxicity without compromising mechanical integrity of the restorative material. The antibiofilm properties of ABR-MC were assessed using an exopolysaccharide-matrix-producing (EPS-matrix-producing) oral pathogen (Streptococcus mutans) in an experimental biofilm model. Using high-resolution confocal fluorescence imaging and biophysical methods, we observed remarkable disruption of bacterial accumulation and defective 3D matrix structure on the surface of ABR-MC. Specifically, the antibacterial composite impaired the ability of S. mutans to form organized bacterial clusters on the surface, resulting in altered biofilm architecture with sparse cell accumulation and reduced amounts of EPS matrix (versus control composite). Biofilm topology analyses on the control composite revealed a highly organized and weblike EPS structure that tethers the bacterial clusters to each other and to the surface, forming a highly cohesive unit. In contrast, such a structured matrix was absent on the surface of ABR-MC with mostly sparse and amorphous EPS, indicating disruption in the biofilm physical stability. Consistent with lack of structural organization, the defective biofilm on the surface of ABR-MC was readily detached when subjected to low shear stress, while most of the biofilm biomass remained on the control surface. Altogether, we demonstrate a new nonleachable antibacterial composite with excellent antibiofilm activity without affecting its mechanical properties, which may serve as a platform for development of alternative antifouling biomaterials.

Bundle block adjustment of large-scale remote sensing data with Block-based Sparse Matrix Compression combined with Preconditioned Conjugate Gradient

NASA Astrophysics Data System (ADS)

Zheng, Maoteng; Zhang, Yongjun; Zhou, Shunping; Zhu, Junfeng; Xiong, Xiaodong

2016-07-01

In recent years, new platforms and sensors in photogrammetry, remote sensing and computer vision areas have become available, such as Unmanned Aircraft Vehicles (UAV), oblique camera systems, common digital cameras and even mobile phone cameras. Images collected by all these kinds of sensors could be used as remote sensing data sources. These sensors can obtain large-scale remote sensing data which consist of a great number of images. Bundle block adjustment of large-scale data with conventional algorithm is very time and space (memory) consuming due to the super large normal matrix arising from large-scale data. In this paper, an efficient Block-based Sparse Matrix Compression (BSMC) method combined with the Preconditioned Conjugate Gradient (PCG) algorithm is chosen to develop a stable and efficient bundle block adjustment system in order to deal with the large-scale remote sensing data. The main contribution of this work is the BSMC-based PCG algorithm which is more efficient in time and memory than the traditional algorithm without compromising the accuracy. Totally 8 datasets of real data are used to test our proposed method. Preliminary results have shown that the BSMC method can efficiently decrease the time and memory requirement of large-scale data.

Using a multifrontal sparse solver in a high performance, finite element code

NASA Technical Reports Server (NTRS)

King, Scott D.; Lucas, Robert; Raefsky, Arthur

1990-01-01

We consider the performance of the finite element method on a vector supercomputer. The computationally intensive parts of the finite element method are typically the individual element forms and the solution of the global stiffness matrix both of which are vectorized in high performance codes. To further increase throughput, new algorithms are needed. We compare a multifrontal sparse solver to a traditional skyline solver in a finite element code on a vector supercomputer. The multifrontal solver uses the Multiple-Minimum Degree reordering heuristic to reduce the number of operations required to factor a sparse matrix and full matrix computational kernels (e.g., BLAS3) to enhance vector performance. The net result in an order-of-magnitude reduction in run time for a finite element application on one processor of a Cray X-MP.

Sparse PCA with Oracle Property.

PubMed

Gu, Quanquan; Wang, Zhaoran; Liu, Han

In this paper, we study the estimation of the k -dimensional sparse principal subspace of covariance matrix Σ in the high-dimensional setting. We aim to recover the oracle principal subspace solution, i.e., the principal subspace estimator obtained assuming the true support is known a priori. To this end, we propose a family of estimators based on the semidefinite relaxation of sparse PCA with novel regularizations. In particular, under a weak assumption on the magnitude of the population projection matrix, one estimator within this family exactly recovers the true support with high probability, has exact rank- k , and attains a [Formula: see text] statistical rate of convergence with s being the subspace sparsity level and n the sample size. Compared to existing support recovery results for sparse PCA, our approach does not hinge on the spiked covariance model or the limited correlation condition. As a complement to the first estimator that enjoys the oracle property, we prove that, another estimator within the family achieves a sharper statistical rate of convergence than the standard semidefinite relaxation of sparse PCA, even when the previous assumption on the magnitude of the projection matrix is violated. We validate the theoretical results by numerical experiments on synthetic datasets.

Sparse PCA with Oracle Property

PubMed Central

Gu, Quanquan; Wang, Zhaoran; Liu, Han

2014-01-01

In this paper, we study the estimation of the k-dimensional sparse principal subspace of covariance matrix Σ in the high-dimensional setting. We aim to recover the oracle principal subspace solution, i.e., the principal subspace estimator obtained assuming the true support is known a priori. To this end, we propose a family of estimators based on the semidefinite relaxation of sparse PCA with novel regularizations. In particular, under a weak assumption on the magnitude of the population projection matrix, one estimator within this family exactly recovers the true support with high probability, has exact rank-k, and attains a s/n statistical rate of convergence with s being the subspace sparsity level and n the sample size. Compared to existing support recovery results for sparse PCA, our approach does not hinge on the spiked covariance model or the limited correlation condition. As a complement to the first estimator that enjoys the oracle property, we prove that, another estimator within the family achieves a sharper statistical rate of convergence than the standard semidefinite relaxation of sparse PCA, even when the previous assumption on the magnitude of the projection matrix is violated. We validate the theoretical results by numerical experiments on synthetic datasets. PMID:25684971

An efficient optical architecture for sparsely connected neural networks

NASA Technical Reports Server (NTRS)

Hine, Butler P., III; Downie, John D.; Reid, Max B.

1990-01-01

An architecture for general-purpose optical neural network processor is presented in which the interconnections and weights are formed by directing coherent beams holographically, thereby making use of the space-bandwidth products of the recording medium for sparsely interconnected networks more efficiently that the commonly used vector-matrix multiplier, since all of the hologram area is in use. An investigation is made of the use of computer-generated holograms recorded on such updatable media as thermoplastic materials, in order to define the interconnections and weights of a neural network processor; attention is given to limits on interconnection densities, diffraction efficiencies, and weighing accuracies possible with such an updatable thin film holographic device.

Removing flicker based on sparse color correspondences in old film restoration

NASA Astrophysics Data System (ADS)

Huang, Xi; Ding, Youdong; Yu, Bing; Xia, Tianran

2018-04-01

In the long history of human civilization, archived film is an indispensable part of it, and using digital method to repair damaged film is also a mainstream trend nowadays. In this paper, we propose a sparse color correspondences based technique to remove fading flicker for old films. Our model, combined with multi frame images to establish a simple correction model, includes three key steps. Firstly, we recover sparse color correspondences in the input frames to build a matrix with many missing entries. Secondly, we present a low-rank matrix factorization approach to estimate the unknown parameters of this model. Finally, we adopt a two-step strategy that divide the estimated parameters into reference frame parameters for color recovery correction and other frame parameters for color consistency correction to remove flicker. Our method combined multi-frames takes continuity of the input sequence into account, and the experimental results show the method can remove fading flicker efficiently.

Sparse Covariance Matrix Estimation by DCA-Based Algorithms.

PubMed

Phan, Duy Nhat; Le Thi, Hoai An; Dinh, Tao Pham

2017-11-01

This letter proposes a novel approach using the [Formula: see text]-norm regularization for the sparse covariance matrix estimation (SCME) problem. The objective function of SCME problem is composed of a nonconvex part and the [Formula: see text] term, which is discontinuous and difficult to tackle. Appropriate DC (difference of convex functions) approximations of [Formula: see text]-norm are used that result in approximation SCME problems that are still nonconvex. DC programming and DCA (DC algorithm), powerful tools in nonconvex programming framework, are investigated. Two DC formulations are proposed and corresponding DCA schemes developed. Two applications of the SCME problem that are considered are classification via sparse quadratic discriminant analysis and portfolio optimization. A careful empirical experiment is performed through simulated and real data sets to study the performance of the proposed algorithms. Numerical results showed their efficiency and their superiority compared with seven state-of-the-art methods.

Tensor-GMRES method for large sparse systems of nonlinear equations

NASA Technical Reports Server (NTRS)

Feng, Dan; Pulliam, Thomas H.

1994-01-01

This paper introduces a tensor-Krylov method, the tensor-GMRES method, for large sparse systems of nonlinear equations. This method is a coupling of tensor model formation and solution techniques for nonlinear equations with Krylov subspace projection techniques for unsymmetric systems of linear equations. Traditional tensor methods for nonlinear equations are based on a quadratic model of the nonlinear function, a standard linear model augmented by a simple second order term. These methods are shown to be significantly more efficient than standard methods both on nonsingular problems and on problems where the Jacobian matrix at the solution is singular. A major disadvantage of the traditional tensor methods is that the solution of the tensor model requires the factorization of the Jacobian matrix, which may not be suitable for problems where the Jacobian matrix is large and has a 'bad' sparsity structure for an efficient factorization. We overcome this difficulty by forming and solving the tensor model using an extension of a Newton-GMRES scheme. Like traditional tensor methods, we show that the new tensor method has significant computational advantages over the analogous Newton counterpart. Consistent with Krylov subspace based methods, the new tensor method does not depend on the factorization of the Jacobian matrix. As a matter of fact, the Jacobian matrix is never needed explicitly.

Total variation-based method for radar coincidence imaging with model mismatch for extended target

NASA Astrophysics Data System (ADS)

Cao, Kaicheng; Zhou, Xiaoli; Cheng, Yongqiang; Fan, Bo; Qin, Yuliang

2017-11-01

Originating from traditional optical coincidence imaging, radar coincidence imaging (RCI) is a staring/forward-looking imaging technique. In RCI, the reference matrix must be computed precisely to reconstruct the image as preferred; unfortunately, such precision is almost impossible due to the existence of model mismatch in practical applications. Although some conventional sparse recovery algorithms are proposed to solve the model-mismatch problem, they are inapplicable to nonsparse targets. We therefore sought to derive the signal model of RCI with model mismatch by replacing the sparsity constraint item with total variation (TV) regularization in the sparse total least squares optimization problem; in this manner, we obtain the objective function of RCI with model mismatch for an extended target. A more robust and efficient algorithm called TV-TLS is proposed, in which the objective function is divided into two parts and the perturbation matrix and scattering coefficients are updated alternately. Moreover, due to the ability of TV regularization to recover sparse signal or image with sparse gradient, TV-TLS method is also applicable to sparse recovering. Results of numerical experiments demonstrate that, for uniform extended targets, sparse targets, and real extended targets, the algorithm can achieve preferred imaging performance both in suppressing noise and in adapting to model mismatch.

Signal Sampling for Efficient Sparse Representation of Resting State FMRI Data

PubMed Central

Ge, Bao; Makkie, Milad; Wang, Jin; Zhao, Shijie; Jiang, Xi; Li, Xiang; Lv, Jinglei; Zhang, Shu; Zhang, Wei; Han, Junwei; Guo, Lei; Liu, Tianming

2015-01-01

As the size of brain imaging data such as fMRI grows explosively, it provides us with unprecedented and abundant information about the brain. How to reduce the size of fMRI data but not lose much information becomes a more and more pressing issue. Recent literature studies tried to deal with it by dictionary learning and sparse representation methods, however, their computation complexities are still high, which hampers the wider application of sparse representation method to large scale fMRI datasets. To effectively address this problem, this work proposes to represent resting state fMRI (rs-fMRI) signals of a whole brain via a statistical sampling based sparse representation. First we sampled the whole brain’s signals via different sampling methods, then the sampled signals were aggregate into an input data matrix to learn a dictionary, finally this dictionary was used to sparsely represent the whole brain’s signals and identify the resting state networks. Comparative experiments demonstrate that the proposed signal sampling framework can speed-up by ten times in reconstructing concurrent brain networks without losing much information. The experiments on the 1000 Functional Connectomes Project further demonstrate its effectiveness and superiority. PMID:26646924

Uniform Recovery Bounds for Structured Random Matrices in Corrupted Compressed Sensing

NASA Astrophysics Data System (ADS)

Zhang, Peng; Gan, Lu; Ling, Cong; Sun, Sumei

2018-04-01

We study the problem of recovering an $s$-sparse signal $\\mathbf{x}^{\\star}\\in\\mathbb{C}^n$ from corrupted measurements $\\mathbf{y} = \\mathbf{A}\\mathbf{x}^{\\star}+\\mathbf{z}^{\\star}+\\mathbf{w}$, where $\\mathbf{z}^{\\star}\\in\\mathbb{C}^m$ is a $k$-sparse corruption vector whose nonzero entries may be arbitrarily large and $\\mathbf{w}\\in\\mathbb{C}^m$ is a dense noise with bounded energy. The aim is to exactly and stably recover the sparse signal with tractable optimization programs. In this paper, we prove the uniform recovery guarantee of this problem for two classes of structured sensing matrices. The first class can be expressed as the product of a unit-norm tight frame (UTF), a random diagonal matrix and a bounded columnwise orthonormal matrix (e.g., partial random circulant matrix). When the UTF is bounded (i.e. $\\mu(\\mathbf{U})\\sim1/\\sqrt{m}$), we prove that with high probability, one can recover an $s$-sparse signal exactly and stably by $l_1$ minimization programs even if the measurements are corrupted by a sparse vector, provided $m = \\mathcal{O}(s \\log^2 s \\log^2 n)$ and the sparsity level $k$ of the corruption is a constant fraction of the total number of measurements. The second class considers randomly sub-sampled orthogonal matrix (e.g., random Fourier matrix). We prove the uniform recovery guarantee provided that the corruption is sparse on certain sparsifying domain. Numerous simulation results are also presented to verify and complement the theoretical results.

Acceleration of GPU-based Krylov solvers via data transfer reduction

DOE PAGES

Anzt, Hartwig; Tomov, Stanimire; Luszczek, Piotr; ...

2015-04-08

Krylov subspace iterative solvers are often the method of choice when solving large sparse linear systems. At the same time, hardware accelerators such as graphics processing units continue to offer significant floating point performance gains for matrix and vector computations through easy-to-use libraries of computational kernels. However, as these libraries are usually composed of a well optimized but limited set of linear algebra operations, applications that use them often fail to reduce certain data communications, and hence fail to leverage the full potential of the accelerator. In this study, we target the acceleration of Krylov subspace iterative methods for graphicsmore » processing units, and in particular the Biconjugate Gradient Stabilized solver that significant improvement can be achieved by reformulating the method to reduce data-communications through application-specific kernels instead of using the generic BLAS kernels, e.g. as provided by NVIDIA’s cuBLAS library, and by designing a graphics processing unit specific sparse matrix-vector product kernel that is able to more efficiently use the graphics processing unit’s computing power. Furthermore, we derive a model estimating the performance improvement, and use experimental data to validate the expected runtime savings. Finally, considering that the derived implementation achieves significantly higher performance, we assert that similar optimizations addressing algorithm structure, as well as sparse matrix-vector, are crucial for the subsequent development of high-performance graphics processing units accelerated Krylov subspace iterative methods.« less

The fastclime Package for Linear Programming and Large-Scale Precision Matrix Estimation in R.

PubMed

Pang, Haotian; Liu, Han; Vanderbei, Robert

2014-02-01

We develop an R package fastclime for solving a family of regularized linear programming (LP) problems. Our package efficiently implements the parametric simplex algorithm, which provides a scalable and sophisticated tool for solving large-scale linear programs. As an illustrative example, one use of our LP solver is to implement an important sparse precision matrix estimation method called CLIME (Constrained L 1 Minimization Estimator). Compared with existing packages for this problem such as clime and flare, our package has three advantages: (1) it efficiently calculates the full piecewise-linear regularization path; (2) it provides an accurate dual certificate as stopping criterion; (3) it is completely coded in C and is highly portable. This package is designed to be useful to statisticians and machine learning researchers for solving a wide range of problems.

Sparse Matrices in MATLAB: Design and Implementation

NASA Technical Reports Server (NTRS)

Gilbert, John R.; Moler, Cleve; Schreiber, Robert

1992-01-01

The matrix computation language and environment MATLAB is extended to include sparse matrix storage and operations. The only change to the outward appearance of the MATLAB language is a pair of commands to create full or sparse matrices. Nearly all the operations of MATLAB now apply equally to full or sparse matrices, without any explicit action by the user. The sparse data structure represents a matrix in space proportional to the number of nonzero entries, and most of the operations compute sparse results in time proportional to the number of arithmetic operations on nonzeros.

Exact recovery of sparse multiple measurement vectors by [Formula: see text]-minimization.

PubMed

Wang, Changlong; Peng, Jigen

2018-01-01

The joint sparse recovery problem is a generalization of the single measurement vector problem widely studied in compressed sensing. It aims to recover a set of jointly sparse vectors, i.e., those that have nonzero entries concentrated at a common location. Meanwhile [Formula: see text]-minimization subject to matrixes is widely used in a large number of algorithms designed for this problem, i.e., [Formula: see text]-minimization [Formula: see text] Therefore the main contribution in this paper is two theoretical results about this technique. The first one is proving that in every multiple system of linear equations there exists a constant [Formula: see text] such that the original unique sparse solution also can be recovered from a minimization in [Formula: see text] quasi-norm subject to matrixes whenever [Formula: see text]. The other one is showing an analytic expression of such [Formula: see text]. Finally, we display the results of one example to confirm the validity of our conclusions, and we use some numerical experiments to show that we increase the efficiency of these algorithms designed for [Formula: see text]-minimization by using our results.

Smoothed low rank and sparse matrix recovery by iteratively reweighted least squares minimization.

PubMed

Lu, Canyi; Lin, Zhouchen; Yan, Shuicheng

2015-02-01

This paper presents a general framework for solving the low-rank and/or sparse matrix minimization problems, which may involve multiple nonsmooth terms. The iteratively reweighted least squares (IRLSs) method is a fast solver, which smooths the objective function and minimizes it by alternately updating the variables and their weights. However, the traditional IRLS can only solve a sparse only or low rank only minimization problem with squared loss or an affine constraint. This paper generalizes IRLS to solve joint/mixed low-rank and sparse minimization problems, which are essential formulations for many tasks. As a concrete example, we solve the Schatten-p norm and l2,q-norm regularized low-rank representation problem by IRLS, and theoretically prove that the derived solution is a stationary point (globally optimal if p,q ≥ 1). Our convergence proof of IRLS is more general than previous one that depends on the special properties of the Schatten-p norm and l2,q-norm. Extensive experiments on both synthetic and real data sets demonstrate that our IRLS is much more efficient.

HIGH DIMENSIONAL COVARIANCE MATRIX ESTIMATION IN APPROXIMATE FACTOR MODELS.

PubMed

Fan, Jianqing; Liao, Yuan; Mincheva, Martina

2011-01-01

The variance covariance matrix plays a central role in the inferential theories of high dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By assuming sparse error covariance matrix, we allow the presence of the cross-sectional correlation even after taking out common factors, and it enables us to combine the merits of both methods. We estimate the sparse covariance using the adaptive thresholding technique as in Cai and Liu (2011), taking into account the fact that direct observations of the idiosyncratic components are unavailable. The impact of high dimensionality on the covariance matrix estimation based on the factor structure is then studied.

AZTEC. Parallel Iterative method Software for Solving Linear Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hutchinson, S.; Shadid, J.; Tuminaro, R.

1995-07-01

AZTEC is an interactive library that greatly simplifies the parrallelization process when solving the linear systems of equations Ax=b where A is a user supplied n X n sparse matrix, b is a user supplied vector of length n and x is a vector of length n to be computed. AZTEC is intended as a software tool for users who want to avoid cumbersome parallel programming details but who have large sparse linear systems which require an efficiently utilized parallel processing system. A collection of data transformation tools are provided that allow for easy creation of distributed sparse unstructured matricesmore » for parallel solutions.« less

Fast and Adaptive Sparse Precision Matrix Estimation in High Dimensions

PubMed Central

Liu, Weidong; Luo, Xi

2014-01-01

This paper proposes a new method for estimating sparse precision matrices in the high dimensional setting. It has been popular to study fast computation and adaptive procedures for this problem. We propose a novel approach, called Sparse Column-wise Inverse Operator, to address these two issues. We analyze an adaptive procedure based on cross validation, and establish its convergence rate under the Frobenius norm. The convergence rates under other matrix norms are also established. This method also enjoys the advantage of fast computation for large-scale problems, via a coordinate descent algorithm. Numerical merits are illustrated using both simulated and real datasets. In particular, it performs favorably on an HIV brain tissue dataset and an ADHD resting-state fMRI dataset. PMID:25750463

Large Covariance Estimation by Thresholding Principal Orthogonal Complements

PubMed Central

Fan, Jianqing; Liao, Yuan; Mincheva, Martina

2012-01-01

This paper deals with the estimation of a high-dimensional covariance with a conditional sparsity structure and fast-diverging eigenvalues. By assuming sparse error covariance matrix in an approximate factor model, we allow for the presence of some cross-sectional correlation even after taking out common but unobservable factors. We introduce the Principal Orthogonal complEment Thresholding (POET) method to explore such an approximate factor structure with sparsity. The POET estimator includes the sample covariance matrix, the factor-based covariance matrix (Fan, Fan, and Lv, 2008), the thresholding estimator (Bickel and Levina, 2008) and the adaptive thresholding estimator (Cai and Liu, 2011) as specific examples. We provide mathematical insights when the factor analysis is approximately the same as the principal component analysis for high-dimensional data. The rates of convergence of the sparse residual covariance matrix and the conditional sparse covariance matrix are studied under various norms. It is shown that the impact of estimating the unknown factors vanishes as the dimensionality increases. The uniform rates of convergence for the unobserved factors and their factor loadings are derived. The asymptotic results are also verified by extensive simulation studies. Finally, a real data application on portfolio allocation is presented. PMID:24348088

Large Covariance Estimation by Thresholding Principal Orthogonal Complements.

PubMed

Fan, Jianqing; Liao, Yuan; Mincheva, Martina

2013-09-01

This paper deals with the estimation of a high-dimensional covariance with a conditional sparsity structure and fast-diverging eigenvalues. By assuming sparse error covariance matrix in an approximate factor model, we allow for the presence of some cross-sectional correlation even after taking out common but unobservable factors. We introduce the Principal Orthogonal complEment Thresholding (POET) method to explore such an approximate factor structure with sparsity. The POET estimator includes the sample covariance matrix, the factor-based covariance matrix (Fan, Fan, and Lv, 2008), the thresholding estimator (Bickel and Levina, 2008) and the adaptive thresholding estimator (Cai and Liu, 2011) as specific examples. We provide mathematical insights when the factor analysis is approximately the same as the principal component analysis for high-dimensional data. The rates of convergence of the sparse residual covariance matrix and the conditional sparse covariance matrix are studied under various norms. It is shown that the impact of estimating the unknown factors vanishes as the dimensionality increases. The uniform rates of convergence for the unobserved factors and their factor loadings are derived. The asymptotic results are also verified by extensive simulation studies. Finally, a real data application on portfolio allocation is presented.

SPARSKIT: A basic tool kit for sparse matrix computations

NASA Technical Reports Server (NTRS)

Saad, Youcef

1990-01-01

Presented here are the main features of a tool package for manipulating and working with sparse matrices. One of the goals of the package is to provide basic tools to facilitate the exchange of software and data between researchers in sparse matrix computations. The starting point is the Harwell/Boeing collection of matrices for which the authors provide a number of tools. Among other things, the package provides programs for converting data structures, printing simple statistics on a matrix, plotting a matrix profile, and performing linear algebra operations with sparse matrices.

Improved Estimation and Interpretation of Correlations in Neural Circuits

PubMed Central

Yatsenko, Dimitri; Josić, Krešimir; Ecker, Alexander S.; Froudarakis, Emmanouil; Cotton, R. James; Tolias, Andreas S.

2015-01-01

Ambitious projects aim to record the activity of ever larger and denser neuronal populations in vivo. Correlations in neural activity measured in such recordings can reveal important aspects of neural circuit organization. However, estimating and interpreting large correlation matrices is statistically challenging. Estimation can be improved by regularization, i.e. by imposing a structure on the estimate. The amount of improvement depends on how closely the assumed structure represents dependencies in the data. Therefore, the selection of the most efficient correlation matrix estimator for a given neural circuit must be determined empirically. Importantly, the identity and structure of the most efficient estimator informs about the types of dominant dependencies governing the system. We sought statistically efficient estimators of neural correlation matrices in recordings from large, dense groups of cortical neurons. Using fast 3D random-access laser scanning microscopy of calcium signals, we recorded the activity of nearly every neuron in volumes 200 μm wide and 100 μm deep (150–350 cells) in mouse visual cortex. We hypothesized that in these densely sampled recordings, the correlation matrix should be best modeled as the combination of a sparse graph of pairwise partial correlations representing local interactions and a low-rank component representing common fluctuations and external inputs. Indeed, in cross-validation tests, the covariance matrix estimator with this structure consistently outperformed other regularized estimators. The sparse component of the estimate defined a graph of interactions. These interactions reflected the physical distances and orientation tuning properties of cells: The density of positive ‘excitatory’ interactions decreased rapidly with geometric distances and with differences in orientation preference whereas negative ‘inhibitory’ interactions were less selective. Because of its superior performance, this ‘sparse+latent’ estimator likely provides a more physiologically relevant representation of the functional connectivity in densely sampled recordings than the sample correlation matrix. PMID:25826696

Dynamic Textures Modeling via Joint Video Dictionary Learning.

PubMed

Wei, Xian; Li, Yuanxiang; Shen, Hao; Chen, Fang; Kleinsteuber, Martin; Wang, Zhongfeng

2017-04-06

Video representation is an important and challenging task in the computer vision community. In this paper, we consider the problem of modeling and classifying video sequences of dynamic scenes which could be modeled in a dynamic textures (DT) framework. At first, we assume that image frames of a moving scene can be modeled as a Markov random process. We propose a sparse coding framework, named joint video dictionary learning (JVDL), to model a video adaptively. By treating the sparse coefficients of image frames over a learned dictionary as the underlying "states", we learn an efficient and robust linear transition matrix between two adjacent frames of sparse events in time series. Hence, a dynamic scene sequence is represented by an appropriate transition matrix associated with a dictionary. In order to ensure the stability of JVDL, we impose several constraints on such transition matrix and dictionary. The developed framework is able to capture the dynamics of a moving scene by exploring both sparse properties and the temporal correlations of consecutive video frames. Moreover, such learned JVDL parameters can be used for various DT applications, such as DT synthesis and recognition. Experimental results demonstrate the strong competitiveness of the proposed JVDL approach in comparison with state-of-the-art video representation methods. Especially, it performs significantly better in dealing with DT synthesis and recognition on heavily corrupted data.

An efficient classification method based on principal component and sparse representation.

PubMed

Zhai, Lin; Fu, Shujun; Zhang, Caiming; Liu, Yunxian; Wang, Lu; Liu, Guohua; Yang, Mingqiang

2016-01-01

As an important application in optical imaging, palmprint recognition is interfered by many unfavorable factors. An effective fusion of blockwise bi-directional two-dimensional principal component analysis and grouping sparse classification is presented. The dimension reduction and normalizing are implemented by the blockwise bi-directional two-dimensional principal component analysis for palmprint images to extract feature matrixes, which are assembled into an overcomplete dictionary in sparse classification. A subspace orthogonal matching pursuit algorithm is designed to solve the grouping sparse representation. Finally, the classification result is gained by comparing the residual between testing and reconstructed images. Experiments are carried out on a palmprint database, and the results show that this method has better robustness against position and illumination changes of palmprint images, and can get higher rate of palmprint recognition.

HIGH DIMENSIONAL COVARIANCE MATRIX ESTIMATION IN APPROXIMATE FACTOR MODELS

PubMed Central

Fan, Jianqing; Liao, Yuan; Mincheva, Martina

2012-01-01

The variance covariance matrix plays a central role in the inferential theories of high dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By assuming sparse error covariance matrix, we allow the presence of the cross-sectional correlation even after taking out common factors, and it enables us to combine the merits of both methods. We estimate the sparse covariance using the adaptive thresholding technique as in Cai and Liu (2011), taking into account the fact that direct observations of the idiosyncratic components are unavailable. The impact of high dimensionality on the covariance matrix estimation based on the factor structure is then studied. PMID:22661790

Computing sparse derivatives and consecutive zeros problem

NASA Astrophysics Data System (ADS)

Chandra, B. V. Ravi; Hossain, Shahadat

2013-02-01

We describe a substitution based sparse Jacobian matrix determination method using algorithmic differentiation. Utilizing the a priori known sparsity pattern, a compression scheme is determined using graph coloring. The "compressed pattern" of the Jacobian matrix is then reordered into a form suitable for computation by substitution. We show that the column reordering of the compressed pattern matrix (so as to align the zero entries into consecutive locations in each row) can be viewed as a variant of traveling salesman problem. Preliminary computational results show that on the test problems the performance of nearest-neighbor type heuristic algorithms is highly encouraging.

Sparse Matrix Software Catalog, Sparse Matrix Symposium 1982, Fairfield Glade, Tennessee, October 24-27, 1982,

DTIC Science & Technology

1982-10-27

are buried within * a much larger, special purpose package. We regret such omissions, but to have reached the practi- tioners in each of the diverse...sparse matrix (form PAQ ) 4. Method of solution: Distribution count sort 5. Programming language: FORTRAN g Precision: Single and double precision 7

SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

NASA Astrophysics Data System (ADS)

Ahlfeld, R.; Belkouchi, B.; Montomoli, F.

2016-09-01

A new arbitrary Polynomial Chaos (aPC) method is presented for moderately high-dimensional problems characterised by limited input data availability. The proposed methodology improves the algorithm of aPC and extends the method, that was previously only introduced as tensor product expansion, to moderately high-dimensional stochastic problems. The fundamental idea of aPC is to use the statistical moments of the input random variables to develop the polynomial chaos expansion. This approach provides the possibility to propagate continuous or discrete probability density functions and also histograms (data sets) as long as their moments exist, are finite and the determinant of the moment matrix is strictly positive. For cases with limited data availability, this approach avoids bias and fitting errors caused by wrong assumptions. In this work, an alternative way to calculate the aPC is suggested, which provides the optimal polynomials, Gaussian quadrature collocation points and weights from the moments using only a handful of matrix operations on the Hankel matrix of moments. It can therefore be implemented without requiring prior knowledge about statistical data analysis or a detailed understanding of the mathematics of polynomial chaos expansions. The extension to more input variables suggested in this work, is an anisotropic and adaptive version of Smolyak's algorithm that is solely based on the moments of the input probability distributions. It is referred to as SAMBA (PC), which is short for Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos. It is illustrated that for moderately high-dimensional problems (up to 20 different input variables or histograms) SAMBA can significantly simplify the calculation of sparse Gaussian quadrature rules. SAMBA's efficiency for multivariate functions with regard to data availability is further demonstrated by analysing higher order convergence and accuracy for a set of nonlinear test functions with 2, 5 and 10 different input distributions or histograms.

Solution of matrix equations using sparse techniques

NASA Technical Reports Server (NTRS)

Baddourah, Majdi

1994-01-01

The solution of large systems of matrix equations is key to the solution of a large number of scientific and engineering problems. This talk describes the sparse matrix solver developed at Langley which can routinely solve in excess of 263,000 equations in 40 seconds on one Cray C-90 processor. It appears that for large scale structural analysis applications, sparse matrix methods have a significant performance advantage over other methods.

Low-rank matrix decomposition and spatio-temporal sparse recovery for STAP radar

DOE PAGES

Sen, Satyabrata

2015-08-04

We develop space-time adaptive processing (STAP) methods by leveraging the advantages of sparse signal processing techniques in order to detect a slowly-moving target. We observe that the inherent sparse characteristics of a STAP problem can be formulated as the low-rankness of clutter covariance matrix when compared to the total adaptive degrees-of-freedom, and also as the sparse interference spectrum on the spatio-temporal domain. By exploiting these sparse properties, we propose two approaches for estimating the interference covariance matrix. In the first approach, we consider a constrained matrix rank minimization problem (RMP) to decompose the sample covariance matrix into a low-rank positivemore » semidefinite and a diagonal matrix. The solution of RMP is obtained by applying the trace minimization technique and the singular value decomposition with matrix shrinkage operator. Our second approach deals with the atomic norm minimization problem to recover the clutter response-vector that has a sparse support on the spatio-temporal plane. We use convex relaxation based standard sparse-recovery techniques to find the solutions. With extensive numerical examples, we demonstrate the performances of proposed STAP approaches with respect to both the ideal and practical scenarios, involving Doppler-ambiguous clutter ridges, spatial and temporal decorrelation effects. As a result, the low-rank matrix decomposition based solution requires secondary measurements as many as twice the clutter rank to attain a near-ideal STAP performance; whereas the spatio-temporal sparsity based approach needs a considerably small number of secondary data.« less

Parallel Conjugate Gradient: Effects of Ordering Strategies, Programming Paradigms, and Architectural Platforms

NASA Technical Reports Server (NTRS)

Oliker, Leonid; Heber, Gerd; Biswas, Rupak

2000-01-01

The Conjugate Gradient (CG) algorithm is perhaps the best-known iterative technique to solve sparse linear systems that are symmetric and positive definite. A sparse matrix-vector multiply (SPMV) usually accounts for most of the floating-point operations within a CG iteration. In this paper, we investigate the effects of various ordering and partitioning strategies on the performance of parallel CG and SPMV using different programming paradigms and architectures. Results show that for this class of applications, ordering significantly improves overall performance, that cache reuse may be more important than reducing communication, and that it is possible to achieve message passing performance using shared memory constructs through careful data ordering and distribution. However, a multi-threaded implementation of CG on the Tera MTA does not require special ordering or partitioning to obtain high efficiency and scalability.

Energy scaling advantages of resistive memory crossbar based computation and its application to sparse coding

DOE Office of Scientific and Technical Information (OSTI.GOV)

Agarwal, Sapan; Quach, Tu -Thach; Parekh, Ojas

In this study, the exponential increase in data over the last decade presents a significant challenge to analytics efforts that seek to process and interpret such data for various applications. Neural-inspired computing approaches are being developed in order to leverage the computational properties of the analog, low-power data processing observed in biological systems. Analog resistive memory crossbars can perform a parallel read or a vector-matrix multiplication as well as a parallel write or a rank-1 update with high computational efficiency. For an N × N crossbar, these two kernels can be O(N) more energy efficient than a conventional digital memory-basedmore » architecture. If the read operation is noise limited, the energy to read a column can be independent of the crossbar size (O(1)). These two kernels form the basis of many neuromorphic algorithms such as image, text, and speech recognition. For instance, these kernels can be applied to a neural sparse coding algorithm to give an O(N) reduction in energy for the entire algorithm when run with finite precision. Sparse coding is a rich problem with a host of applications including computer vision, object tracking, and more generally unsupervised learning.« less

Energy scaling advantages of resistive memory crossbar based computation and its application to sparse coding

DOE PAGES

Agarwal, Sapan; Quach, Tu -Thach; Parekh, Ojas; ...

2016-01-06

In this study, the exponential increase in data over the last decade presents a significant challenge to analytics efforts that seek to process and interpret such data for various applications. Neural-inspired computing approaches are being developed in order to leverage the computational properties of the analog, low-power data processing observed in biological systems. Analog resistive memory crossbars can perform a parallel read or a vector-matrix multiplication as well as a parallel write or a rank-1 update with high computational efficiency. For an N × N crossbar, these two kernels can be O(N) more energy efficient than a conventional digital memory-basedmore » architecture. If the read operation is noise limited, the energy to read a column can be independent of the crossbar size (O(1)). These two kernels form the basis of many neuromorphic algorithms such as image, text, and speech recognition. For instance, these kernels can be applied to a neural sparse coding algorithm to give an O(N) reduction in energy for the entire algorithm when run with finite precision. Sparse coding is a rich problem with a host of applications including computer vision, object tracking, and more generally unsupervised learning.« less

Immunohistochemical evidence of rapid extracellular matrix remodeling after iron-particle irradiation of mouse mammary gland

NASA Technical Reports Server (NTRS)

Ehrhart, E. J.; Gillette, E. L.; Barcellos-Hoff, M. H.; Chaterjee, A. (Principal Investigator)

1996-01-01

High-LET radiation has unique physical and biological properties compared to sparsely ionizing radiation. Recent studies demonstrate that sparsely ionizing radiation rapidly alters the pattern of extracellular matrix expression in several tissues, but little is known about the effect of heavy-ion radiation. This study investigates densely ionizing radiation-induced changes in extracellular matrix localization in the mammary glands of adult female BALB/c mice after whole-body irradiation with 0.8 Gy 600 MeV iron particles. The basement membrane and interstitial extracellular matrix proteins of the mammary gland stroma were mapped with respect to time postirradiation using immunofluorescence. Collagen III was induced in the adipose stroma within 1 day, continued to increase through day 9 and was resolved by day 14. Immunoreactive tenascin was induced in the epithelium by day 1, was evident at the epithelial-stromal interface by day 5-9 and persisted as a condensed layer beneath the basement membrane through day 14. These findings parallel similar changes induced by gamma irradiation but demonstrate different onset and chronicity. In contrast, the integrity of epithelial basement membrane, which was unaffected by sparsely ionizing radiation, was disrupted by iron-particle irradiation. Laminin immunoreactivity was mildly irregular at 1 h postirradiation and showed discontinuities and thickening from days 1 to 9. Continuity was restored by day 14. Thus high-LET radiation, like sparsely ionizing radiation, induces rapid-remodeling of the stromal extracellular matrix but also appears to alter the integrity of the epithelial basement membrane, which is an important regulator of epithelial cell proliferation and differentiation.

A Distributed-Memory Package for Dense Hierarchically Semi-Separable Matrix Computations Using Randomization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rouet, François-Henry; Li, Xiaoye S.; Ghysels, Pieter

In this paper, we present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use Hierarchically Semi-Separable (HSS) representations. Such matrices appear in many applications, for example, finite-element methods, boundary element methods, and so on. Exploiting this structure allows for fast solution of linear systems and/or fast computation of matrix-vector products, which are the two main building blocks of matrix computations. The compression algorithm that we use, that computes the HSS form of an input dense matrix, reliesmore » on randomized sampling with a novel adaptive sampling mechanism. We discuss the parallelization of this algorithm and also present the parallelization of structured matrix-vector product, structured factorization, and solution routines. The efficiency of the approach is demonstrated on large problems from different academic and industrial applications, on up to 8,000 cores. Finally, this work is part of a more global effort, the STRUctured Matrices PACKage (STRUMPACK) software package for computations with sparse and dense structured matrices. Hence, although useful on their own right, the routines also represent a step in the direction of a distributed-memory sparse solver.« less

A Distributed-Memory Package for Dense Hierarchically Semi-Separable Matrix Computations Using Randomization

DOE PAGES

Rouet, François-Henry; Li, Xiaoye S.; Ghysels, Pieter; ...

2016-06-30

In this paper, we present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use Hierarchically Semi-Separable (HSS) representations. Such matrices appear in many applications, for example, finite-element methods, boundary element methods, and so on. Exploiting this structure allows for fast solution of linear systems and/or fast computation of matrix-vector products, which are the two main building blocks of matrix computations. The compression algorithm that we use, that computes the HSS form of an input dense matrix, reliesmore » on randomized sampling with a novel adaptive sampling mechanism. We discuss the parallelization of this algorithm and also present the parallelization of structured matrix-vector product, structured factorization, and solution routines. The efficiency of the approach is demonstrated on large problems from different academic and industrial applications, on up to 8,000 cores. Finally, this work is part of a more global effort, the STRUctured Matrices PACKage (STRUMPACK) software package for computations with sparse and dense structured matrices. Hence, although useful on their own right, the routines also represent a step in the direction of a distributed-memory sparse solver.« less

Efficient spares matrix multiplication scheme for the CYBER 203

NASA Technical Reports Server (NTRS)

Lambiotte, J. J., Jr.

1984-01-01

This work has been directed toward the development of an efficient algorithm for performing this computation on the CYBER-203. The desire to provide software which gives the user the choice between the often conflicting goals of minimizing central processing (CPU) time or storage requirements has led to a diagonal-based algorithm in which one of three types of storage is selected for each diagonal. For each storage type, an initialization sub-routine estimates the CPU and storage requirements based upon results from previously performed numerical experimentation. These requirements are adjusted by weights provided by the user which reflect the relative importance the user places on the resources. The three storage types employed were chosen to be efficient on the CYBER-203 for diagonals which are sparse, moderately sparse, or dense; however, for many densities, no diagonal type is most efficient with respect to both resource requirements. The user-supplied weights dictate the choice.

A projected preconditioned conjugate gradient algorithm for computing many extreme eigenpairs of a Hermitian matrix [A projected preconditioned conjugate gradient algorithm for computing a large eigenspace of a Hermitian matrix

DOE PAGES

Vecharynski, Eugene; Yang, Chao; Pask, John E.

2015-02-25

Here, we present an iterative algorithm for computing an invariant subspace associated with the algebraically smallest eigenvalues of a large sparse or structured Hermitian matrix A. We are interested in the case in which the dimension of the invariant subspace is large (e.g., over several hundreds or thousands) even though it may still be small relative to the dimension of A. These problems arise from, for example, density functional theory (DFT) based electronic structure calculations for complex materials. The key feature of our algorithm is that it performs fewer Rayleigh–Ritz calculations compared to existing algorithms such as the locally optimalmore » block preconditioned conjugate gradient or the Davidson algorithm. It is a block algorithm, and hence can take advantage of efficient BLAS3 operations and be implemented with multiple levels of concurrency. We discuss a number of practical issues that must be addressed in order to implement the algorithm efficiently on a high performance computer.« less

Sparse Matrix for ECG Identification with Two-Lead Features.

PubMed

Tseng, Kuo-Kun; Luo, Jiao; Hegarty, Robert; Wang, Wenmin; Haiting, Dong

2015-01-01

Electrocardiograph (ECG) human identification has the potential to improve biometric security. However, improvements in ECG identification and feature extraction are required. Previous work has focused on single lead ECG signals. Our work proposes a new algorithm for human identification by mapping two-lead ECG signals onto a two-dimensional matrix then employing a sparse matrix method to process the matrix. And that is the first application of sparse matrix techniques for ECG identification. Moreover, the results of our experiments demonstrate the benefits of our approach over existing methods.

High efficient optical remote sensing images acquisition for nano-satellite: reconstruction algorithms

NASA Astrophysics Data System (ADS)

Liu, Yang; Li, Feng; Xin, Lei; Fu, Jie; Huang, Puming

2017-10-01

Large amount of data is one of the most obvious features in satellite based remote sensing systems, which is also a burden for data processing and transmission. The theory of compressive sensing(CS) has been proposed for almost a decade, and massive experiments show that CS has favorable performance in data compression and recovery, so we apply CS theory to remote sensing images acquisition. In CS, the construction of classical sensing matrix for all sparse signals has to satisfy the Restricted Isometry Property (RIP) strictly, which limits applying CS in practical in image compression. While for remote sensing images, we know some inherent characteristics such as non-negative, smoothness and etc.. Therefore, the goal of this paper is to present a novel measurement matrix that breaks RIP. The new sensing matrix consists of two parts: the standard Nyquist sampling matrix for thumbnails and the conventional CS sampling matrix. Since most of sun-synchronous based satellites fly around the earth 90 minutes and the revisit cycle is also short, lots of previously captured remote sensing images of the same place are available in advance. This drives us to reconstruct remote sensing images through a deep learning approach with those measurements from the new framework. Therefore, we propose a novel deep convolutional neural network (CNN) architecture which takes in undersampsing measurements as input and outputs an intermediate reconstruction image. It is well known that the training procedure to the network costs long time, luckily, the training step can be done only once, which makes the approach attractive for a host of sparse recovery problems.

BCYCLIC: A parallel block tridiagonal matrix cyclic solver

NASA Astrophysics Data System (ADS)

Hirshman, S. P.; Perumalla, K. S.; Lynch, V. E.; Sanchez, R.

2010-09-01

A block tridiagonal matrix is factored with minimal fill-in using a cyclic reduction algorithm that is easily parallelized. Storage of the factored blocks allows the application of the inverse to multiple right-hand sides which may not be known at factorization time. Scalability with the number of block rows is achieved with cyclic reduction, while scalability with the block size is achieved using multithreaded routines (OpenMP, GotoBLAS) for block matrix manipulation. This dual scalability is a noteworthy feature of this new solver, as well as its ability to efficiently handle arbitrary (non-powers-of-2) block row and processor numbers. Comparison with a state-of-the art parallel sparse solver is presented. It is expected that this new solver will allow many physical applications to optimally use the parallel resources on current supercomputers. Example usage of the solver in magneto-hydrodynamic (MHD), three-dimensional equilibrium solvers for high-temperature fusion plasmas is cited.

Salient Object Detection via Structured Matrix Decomposition.

PubMed

Peng, Houwen; Li, Bing; Ling, Haibin; Hu, Weiming; Xiong, Weihua; Maybank, Stephen J

2016-05-04

Low-rank recovery models have shown potential for salient object detection, where a matrix is decomposed into a low-rank matrix representing image background and a sparse matrix identifying salient objects. Two deficiencies, however, still exist. First, previous work typically assumes the elements in the sparse matrix are mutually independent, ignoring the spatial and pattern relations of image regions. Second, when the low-rank and sparse matrices are relatively coherent, e.g., when there are similarities between the salient objects and background or when the background is complicated, it is difficult for previous models to disentangle them. To address these problems, we propose a novel structured matrix decomposition model with two structural regularizations: (1) a tree-structured sparsity-inducing regularization that captures the image structure and enforces patches from the same object to have similar saliency values, and (2) a Laplacian regularization that enlarges the gaps between salient objects and the background in feature space. Furthermore, high-level priors are integrated to guide the matrix decomposition and boost the detection. We evaluate our model for salient object detection on five challenging datasets including single object, multiple objects and complex scene images, and show competitive results as compared with 24 state-of-the-art methods in terms of seven performance metrics.

Competition in high dimensional spaces using a sparse approximation of neural fields.

PubMed

Quinton, Jean-Charles; Girau, Bernard; Lefort, Mathieu

2011-01-01

The Continuum Neural Field Theory implements competition within topologically organized neural networks with lateral inhibitory connections. However, due to the polynomial complexity of matrix-based implementations, updating dense representations of the activity becomes computationally intractable when an adaptive resolution or an arbitrary number of input dimensions is required. This paper proposes an alternative to self-organizing maps with a sparse implementation based on Gaussian mixture models, promoting a trade-off in redundancy for higher computational efficiency and alleviating constraints on the underlying substrate.This version reproduces the emergent attentional properties of the original equations, by directly applying them within a continuous approximation of a high dimensional neural field. The model is compatible with preprocessed sensory flows but can also be interfaced with artificial systems. This is particularly important for sensorimotor systems, where decisions and motor actions must be taken and updated in real-time. Preliminary tests are performed on a reactive color tracking application, using spatially distributed color features.

Massively parallel sparse matrix function calculations with NTPoly

NASA Astrophysics Data System (ADS)

Dawson, William; Nakajima, Takahito

2018-04-01

We present NTPoly, a massively parallel library for computing the functions of sparse, symmetric matrices. The theory of matrix functions is a well developed framework with a wide range of applications including differential equations, graph theory, and electronic structure calculations. One particularly important application area is diagonalization free methods in quantum chemistry. When the input and output of the matrix function are sparse, methods based on polynomial expansions can be used to compute matrix functions in linear time. We present a library based on these methods that can compute a variety of matrix functions. Distributed memory parallelization is based on a communication avoiding sparse matrix multiplication algorithm. OpenMP task parallellization is utilized to implement hybrid parallelization. We describe NTPoly's interface and show how it can be integrated with programs written in many different programming languages. We demonstrate the merits of NTPoly by performing large scale calculations on the K computer.

Label consistent K-SVD: learning a discriminative dictionary for recognition.

PubMed

Jiang, Zhuolin; Lin, Zhe; Davis, Larry S

2013-11-01

A label consistent K-SVD (LC-KSVD) algorithm to learn a discriminative dictionary for sparse coding is presented. In addition to using class labels of training data, we also associate label information with each dictionary item (columns of the dictionary matrix) to enforce discriminability in sparse codes during the dictionary learning process. More specifically, we introduce a new label consistency constraint called "discriminative sparse-code error" and combine it with the reconstruction error and the classification error to form a unified objective function. The optimal solution is efficiently obtained using the K-SVD algorithm. Our algorithm learns a single overcomplete dictionary and an optimal linear classifier jointly. The incremental dictionary learning algorithm is presented for the situation of limited memory resources. It yields dictionaries so that feature points with the same class labels have similar sparse codes. Experimental results demonstrate that our algorithm outperforms many recently proposed sparse-coding techniques for face, action, scene, and object category recognition under the same learning conditions.

New algorithms for field-theoretic block copolymer simulations: Progress on using adaptive-mesh refinement and sparse matrix solvers in SCFT calculations

NASA Astrophysics Data System (ADS)

Sides, Scott; Jamroz, Ben; Crockett, Robert; Pletzer, Alexander

2012-02-01

Self-consistent field theory (SCFT) for dense polymer melts has been highly successful in describing complex morphologies in block copolymers. Field-theoretic simulations such as these are able to access large length and time scales that are difficult or impossible for particle-based simulations such as molecular dynamics. The modified diffusion equations that arise as a consequence of the coarse-graining procedure in the SCF theory can be efficiently solved with a pseudo-spectral (PS) method that uses fast-Fourier transforms on uniform Cartesian grids. However, PS methods can be difficult to apply in many block copolymer SCFT simulations (eg. confinement, interface adsorption) in which small spatial regions might require finer resolution than most of the simulation grid. Progress on using new solver algorithms to address these problems will be presented. The Tech-X Chompst project aims at marrying the best of adaptive mesh refinement with linear matrix solver algorithms. The Tech-X code PolySwift++ is an SCFT simulation platform that leverages ongoing development in coupling Chombo, a package for solving PDEs via block-structured AMR calculations and embedded boundaries, with PETSc, a toolkit that includes a large assortment of sparse linear solvers.

Improved collaborative filtering recommendation algorithm of similarity measure

NASA Astrophysics Data System (ADS)

Zhang, Baofu; Yuan, Baoping

2017-05-01

The Collaborative filtering recommendation algorithm is one of the most widely used recommendation algorithm in personalized recommender systems. The key is to find the nearest neighbor set of the active user by using similarity measure. However, the methods of traditional similarity measure mainly focus on the similarity of user common rating items, but ignore the relationship between the user common rating items and all items the user rates. And because rating matrix is very sparse, traditional collaborative filtering recommendation algorithm is not high efficiency. In order to obtain better accuracy, based on the consideration of common preference between users, the difference of rating scale and score of common items, this paper presents an improved similarity measure method, and based on this method, a collaborative filtering recommendation algorithm based on similarity improvement is proposed. Experimental results show that the algorithm can effectively improve the quality of recommendation, thus alleviate the impact of data sparseness.

Disentangling giant component and finite cluster contributions in sparse random matrix spectra.

PubMed

Kühn, Reimer

2016-04-01

We describe a method for disentangling giant component and finite cluster contributions to sparse random matrix spectra, using sparse symmetric random matrices defined on Erdős-Rényi graphs as an example and test bed. Our methods apply to sparse matrices defined in terms of arbitrary graphs in the configuration model class, as long as they have finite mean degree.

A High Performance Block Eigensolver for Nuclear Configuration Interaction Calculations

DOE PAGES

Aktulga, Hasan Metin; Afibuzzaman, Md.; Williams, Samuel; ...

2017-06-01

As on-node parallelism increases and the performance gap between the processor and the memory system widens, achieving high performance in large-scale scientific applications requires an architecture-aware design of algorithms and solvers. We focus on the eigenvalue problem arising in nuclear Configuration Interaction (CI) calculations, where a few extreme eigenpairs of a sparse symmetric matrix are needed. Here, we consider a block iterative eigensolver whose main computational kernels are the multiplication of a sparse matrix with multiple vectors (SpMM), and tall-skinny matrix operations. We then present techniques to significantly improve the SpMM and the transpose operation SpMM T by using themore » compressed sparse blocks (CSB) format. We achieve 3-4× speedup on the requisite operations over good implementations with the commonly used compressed sparse row (CSR) format. We develop a performance model that allows us to correctly estimate the performance of our SpMM kernel implementations, and we identify cache bandwidth as a potential performance bottleneck beyond DRAM. We also analyze and optimize the performance of LOBPCG kernels (inner product and linear combinations on multiple vectors) and show up to 15× speedup over using high performance BLAS libraries for these operations. The resulting high performance LOBPCG solver achieves 1.4× to 1.8× speedup over the existing Lanczos solver on a series of CI computations on high-end multicore architectures (Intel Xeons). We also analyze the performance of our techniques on an Intel Xeon Phi Knights Corner (KNC) processor.« less

A High Performance Block Eigensolver for Nuclear Configuration Interaction Calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aktulga, Hasan Metin; Afibuzzaman, Md.; Williams, Samuel

As on-node parallelism increases and the performance gap between the processor and the memory system widens, achieving high performance in large-scale scientific applications requires an architecture-aware design of algorithms and solvers. We focus on the eigenvalue problem arising in nuclear Configuration Interaction (CI) calculations, where a few extreme eigenpairs of a sparse symmetric matrix are needed. Here, we consider a block iterative eigensolver whose main computational kernels are the multiplication of a sparse matrix with multiple vectors (SpMM), and tall-skinny matrix operations. We then present techniques to significantly improve the SpMM and the transpose operation SpMM T by using themore » compressed sparse blocks (CSB) format. We achieve 3-4× speedup on the requisite operations over good implementations with the commonly used compressed sparse row (CSR) format. We develop a performance model that allows us to correctly estimate the performance of our SpMM kernel implementations, and we identify cache bandwidth as a potential performance bottleneck beyond DRAM. We also analyze and optimize the performance of LOBPCG kernels (inner product and linear combinations on multiple vectors) and show up to 15× speedup over using high performance BLAS libraries for these operations. The resulting high performance LOBPCG solver achieves 1.4× to 1.8× speedup over the existing Lanczos solver on a series of CI computations on high-end multicore architectures (Intel Xeons). We also analyze the performance of our techniques on an Intel Xeon Phi Knights Corner (KNC) processor.« less

Ordering Unstructured Meshes for Sparse Matrix Computations on Leading Parallel Systems

NASA Technical Reports Server (NTRS)

Oliker, Leonid; Li, Xiaoye; Heber, Gerd; Biswas, Rupak

2000-01-01

The ability of computers to solve hitherto intractable problems and simulate complex processes using mathematical models makes them an indispensable part of modern science and engineering. Computer simulations of large-scale realistic applications usually require solving a set of non-linear partial differential equations (PDES) over a finite region. For example, one thrust area in the DOE Grand Challenge projects is to design future accelerators such as the SpaHation Neutron Source (SNS). Our colleagues at SLAC need to model complex RFQ cavities with large aspect ratios. Unstructured grids are currently used to resolve the small features in a large computational domain; dynamic mesh adaptation will be added in the future for additional efficiency. The PDEs for electromagnetics are discretized by the FEM method, which leads to a generalized eigenvalue problem Kx = AMx, where K and M are the stiffness and mass matrices, and are very sparse. In a typical cavity model, the number of degrees of freedom is about one million. For such large eigenproblems, direct solution techniques quickly reach the memory limits. Instead, the most widely-used methods are Krylov subspace methods, such as Lanczos or Jacobi-Davidson. In all the Krylov-based algorithms, sparse matrix-vector multiplication (SPMV) must be performed repeatedly. Therefore, the efficiency of SPMV usually determines the eigensolver speed. SPMV is also one of the most heavily used kernels in large-scale numerical simulations.

Superresolution radar imaging based on fast inverse-free sparse Bayesian learning for multiple measurement vectors

NASA Astrophysics Data System (ADS)

He, Xingyu; Tong, Ningning; Hu, Xiaowei

2018-01-01

Compressive sensing has been successfully applied to inverse synthetic aperture radar (ISAR) imaging of moving targets. By exploiting the block sparse structure of the target image, sparse solution for multiple measurement vectors (MMV) can be applied in ISAR imaging and a substantial performance improvement can be achieved. As an effective sparse recovery method, sparse Bayesian learning (SBL) for MMV involves a matrix inverse at each iteration. Its associated computational complexity grows significantly with the problem size. To address this problem, we develop a fast inverse-free (IF) SBL method for MMV. A relaxed evidence lower bound (ELBO), which is computationally more amiable than the traditional ELBO used by SBL, is obtained by invoking fundamental property for smooth functions. A variational expectation-maximization scheme is then employed to maximize the relaxed ELBO, and a computationally efficient IF-MSBL algorithm is proposed. Numerical results based on simulated and real data show that the proposed method can reconstruct row sparse signal accurately and obtain clear superresolution ISAR images. Moreover, the running time and computational complexity are reduced to a great extent compared with traditional SBL methods.

Sparse graph regularization for robust crop mapping using hyperspectral remotely sensed imagery with very few in situ data

NASA Astrophysics Data System (ADS)

Xue, Zhaohui; Du, Peijun; Li, Jun; Su, Hongjun

2017-02-01

The generally limited availability of training data relative to the usually high data dimension pose a great challenge to accurate classification of hyperspectral imagery, especially for identifying crops characterized with highly correlated spectra. However, traditional parametric classification models are problematic due to the need of non-singular class-specific covariance matrices. In this research, a novel sparse graph regularization (SGR) method is presented, aiming at robust crop mapping using hyperspectral imagery with very few in situ data. The core of SGR lies in propagating labels from known data to unknown, which is triggered by: (1) the fraction matrix generated for the large unknown data by using an effective sparse representation algorithm with respect to the few training data serving as the dictionary; (2) the prediction function estimated for the few training data by formulating a regularization model based on sparse graph. Then, the labels of large unknown data can be obtained by maximizing the posterior probability distribution based on the two ingredients. SGR is more discriminative, data-adaptive, robust to noise, and efficient, which is unique with regard to previously proposed approaches and has high potentials in discriminating crops, especially when facing insufficient training data and high-dimensional spectral space. The study area is located at Zhangye basin in the middle reaches of Heihe watershed, Gansu, China, where eight crop types were mapped with Compact Airborne Spectrographic Imager (CASI) and Shortwave Infrared Airborne Spectrogrpahic Imager (SASI) hyperspectral data. Experimental results demonstrate that the proposed method significantly outperforms other traditional and state-of-the-art methods.

Crystallization of bFGF-DNA Aptamer Complexes Using a Sparse Matrix Designed for Protein-Nucleic Acid Complexes

NASA Technical Reports Server (NTRS)

Cannone, Jaime J.; Barnes, Cindy L.; Achari, Aniruddha; Kundrot, Craig E.; Whitaker, Ann F. (Technical Monitor)

2001-01-01

The Sparse Matrix approach for obtaining lead crystallization conditions has proven to be very fruitful for the crystallization of proteins and nucleic acids. Here we report a Sparse Matrix developed specifically for the crystallization of protein-DNA complexes. This method is rapid and economical, typically requiring 2.5 mg of complex to test 48 conditions. The method was originally developed to crystallize basic fibroblast growth factor (bFGF) complexed with DNA sequences identified through in vitro selection, or SELEX, methods. Two DNA aptamers that bind with approximately nanomolar affinity and inhibit the angiogenic properties of bFGF were selected for co-crystallization. The Sparse Matrix produced lead crystallization conditions for both bFGF-DNA complexes.

Sparse nonnegative matrix factorization with ℓ0-constraints

PubMed Central

Peharz, Robert; Pernkopf, Franz

2012-01-01

Although nonnegative matrix factorization (NMF) favors a sparse and part-based representation of nonnegative data, there is no guarantee for this behavior. Several authors proposed NMF methods which enforce sparseness by constraining or penalizing the ℓ1-norm of the factor matrices. On the other hand, little work has been done using a more natural sparseness measure, the ℓ0-pseudo-norm. In this paper, we propose a framework for approximate NMF which constrains the ℓ0-norm of the basis matrix, or the coefficient matrix, respectively. For this purpose, techniques for unconstrained NMF can be easily incorporated, such as multiplicative update rules, or the alternating nonnegative least-squares scheme. In experiments we demonstrate the benefits of our methods, which compare to, or outperform existing approaches. PMID:22505792

Multivariable frequency domain identification via 2-norm minimization

NASA Technical Reports Server (NTRS)

Bayard, David S.

1992-01-01

The author develops a computational approach to multivariable frequency domain identification, based on 2-norm minimization. In particular, a Gauss-Newton (GN) iteration is developed to minimize the 2-norm of the error between frequency domain data and a matrix fraction transfer function estimate. To improve the global performance of the optimization algorithm, the GN iteration is initialized using the solution to a particular sequentially reweighted least squares problem, denoted as the SK iteration. The least squares problems which arise from both the SK and GN iterations are shown to involve sparse matrices with identical block structure. A sparse matrix QR factorization method is developed to exploit the special block structure, and to efficiently compute the least squares solution. A numerical example involving the identification of a multiple-input multiple-output (MIMO) plant having 286 unknown parameters is given to illustrate the effectiveness of the algorithm.

A Sparsity-Promoted Method Based on Majorization-Minimization for Weak Fault Feature Enhancement

PubMed Central

Hao, Yansong; Song, Liuyang; Tang, Gang; Yuan, Hongfang

2018-01-01

Fault transient impulses induced by faulty components in rotating machinery usually contain substantial interference. Fault features are comparatively weak in the initial fault stage, which renders fault diagnosis more difficult. In this case, a sparse representation method based on the Majorzation-Minimization (MM) algorithm is proposed to enhance weak fault features and extract the features from strong background noise. However, the traditional MM algorithm suffers from two issues, which are the choice of sparse basis and complicated calculations. To address these challenges, a modified MM algorithm is proposed in which a sparse optimization objective function is designed firstly. Inspired by the Basis Pursuit (BP) model, the optimization function integrates an impulsive feature-preserving factor and a penalty function factor. Second, a modified Majorization iterative method is applied to address the convex optimization problem of the designed function. A series of sparse coefficients can be achieved through iterating, which only contain transient components. It is noteworthy that there is no need to select the sparse basis in the proposed iterative method because it is fixed as a unit matrix. Then the reconstruction step is omitted, which can significantly increase detection efficiency. Eventually, envelope analysis of the sparse coefficients is performed to extract weak fault features. Simulated and experimental signals including bearings and gearboxes are employed to validate the effectiveness of the proposed method. In addition, comparisons are made to prove that the proposed method outperforms the traditional MM algorithm in terms of detection results and efficiency. PMID:29597280

A Sparsity-Promoted Method Based on Majorization-Minimization for Weak Fault Feature Enhancement.

PubMed

Ren, Bangyue; Hao, Yansong; Wang, Huaqing; Song, Liuyang; Tang, Gang; Yuan, Hongfang

2018-03-28

Fault transient impulses induced by faulty components in rotating machinery usually contain substantial interference. Fault features are comparatively weak in the initial fault stage, which renders fault diagnosis more difficult. In this case, a sparse representation method based on the Majorzation-Minimization (MM) algorithm is proposed to enhance weak fault features and extract the features from strong background noise. However, the traditional MM algorithm suffers from two issues, which are the choice of sparse basis and complicated calculations. To address these challenges, a modified MM algorithm is proposed in which a sparse optimization objective function is designed firstly. Inspired by the Basis Pursuit (BP) model, the optimization function integrates an impulsive feature-preserving factor and a penalty function factor. Second, a modified Majorization iterative method is applied to address the convex optimization problem of the designed function. A series of sparse coefficients can be achieved through iterating, which only contain transient components. It is noteworthy that there is no need to select the sparse basis in the proposed iterative method because it is fixed as a unit matrix. Then the reconstruction step is omitted, which can significantly increase detection efficiency. Eventually, envelope analysis of the sparse coefficients is performed to extract weak fault features. Simulated and experimental signals including bearings and gearboxes are employed to validate the effectiveness of the proposed method. In addition, comparisons are made to prove that the proposed method outperforms the traditional MM algorithm in terms of detection results and efficiency.

On the efficiency of a randomized mirror descent algorithm in online optimization problems

NASA Astrophysics Data System (ADS)

Gasnikov, A. V.; Nesterov, Yu. E.; Spokoiny, V. G.

2015-04-01

A randomized online version of the mirror descent method is proposed. It differs from the existing versions by the randomization method. Randomization is performed at the stage of the projection of a subgradient of the function being optimized onto the unit simplex rather than at the stage of the computation of a subgradient, which is common practice. As a result, a componentwise subgradient descent with a randomly chosen component is obtained, which admits an online interpretation. This observation, for example, has made it possible to uniformly interpret results on weighting expert decisions and propose the most efficient method for searching for an equilibrium in a zero-sum two-person matrix game with sparse matrix.

A manual for PARTI runtime primitives

NASA Technical Reports Server (NTRS)

Berryman, Harry; Saltz, Joel

1990-01-01

Primitives are presented that are designed to help users efficiently program irregular problems (e.g., unstructured mesh sweeps, sparse matrix codes, adaptive mesh partial differential equations solvers) on distributed memory machines. These primitives are also designed for use in compilers for distributed memory multiprocessors. Communications patterns are captured at runtime, and the appropriate send and receive messages are automatically generated.

Recursive Factorization of the Inverse Overlap Matrix in Linear-Scaling Quantum Molecular Dynamics Simulations.

PubMed

Negre, Christian F A; Mniszewski, Susan M; Cawkwell, Marc J; Bock, Nicolas; Wall, Michael E; Niklasson, Anders M N

2016-07-12

We present a reduced complexity algorithm to compute the inverse overlap factors required to solve the generalized eigenvalue problem in a quantum-based molecular dynamics (MD) simulation. Our method is based on the recursive, iterative refinement of an initial guess of Z (inverse square root of the overlap matrix S). The initial guess of Z is obtained beforehand by using either an approximate divide-and-conquer technique or dynamical methods, propagated within an extended Lagrangian dynamics from previous MD time steps. With this formulation, we achieve long-term stability and energy conservation even under the incomplete, approximate, iterative refinement of Z. Linear-scaling performance is obtained using numerically thresholded sparse matrix algebra based on the ELLPACK-R sparse matrix data format, which also enables efficient shared-memory parallelization. As we show in this article using self-consistent density-functional-based tight-binding MD, our approach is faster than conventional methods based on the diagonalization of overlap matrix S for systems as small as a few hundred atoms, substantially accelerating quantum-based simulations even for molecular structures of intermediate size. For a 4158-atom water-solvated polyalanine system, we find an average speedup factor of 122 for the computation of Z in each MD step.

Background recovery via motion-based robust principal component analysis with matrix factorization

NASA Astrophysics Data System (ADS)

Pan, Peng; Wang, Yongli; Zhou, Mingyuan; Sun, Zhipeng; He, Guoping

2018-03-01

Background recovery is a key technique in video analysis, but it still suffers from many challenges, such as camouflage, lighting changes, and diverse types of image noise. Robust principal component analysis (RPCA), which aims to recover a low-rank matrix and a sparse matrix, is a general framework for background recovery. The nuclear norm is widely used as a convex surrogate for the rank function in RPCA, which requires computing the singular value decomposition (SVD), a task that is increasingly costly as matrix sizes and ranks increase. However, matrix factorization greatly reduces the dimension of the matrix for which the SVD must be computed. Motion information has been shown to improve low-rank matrix recovery in RPCA, but this method still finds it difficult to handle original video data sets because of its batch-mode formulation and implementation. Hence, in this paper, we propose a motion-assisted RPCA model with matrix factorization (FM-RPCA) for background recovery. Moreover, an efficient linear alternating direction method of multipliers with a matrix factorization (FL-ADM) algorithm is designed for solving the proposed FM-RPCA model. Experimental results illustrate that the method provides stable results and is more efficient than the current state-of-the-art algorithms.

Turbo-SMT: Parallel Coupled Sparse Matrix-Tensor Factorizations and Applications

PubMed Central

Papalexakis, Evangelos E.; Faloutsos, Christos; Mitchell, Tom M.; Talukdar, Partha Pratim; Sidiropoulos, Nicholas D.; Murphy, Brian

2016-01-01

How can we correlate the neural activity in the human brain as it responds to typed words, with properties of these terms (like ’edible’, ’fits in hand’)? In short, we want to find latent variables, that jointly explain both the brain activity, as well as the behavioral responses. This is one of many settings of the Coupled Matrix-Tensor Factorization (CMTF) problem. Can we enhance any CMTF solver, so that it can operate on potentially very large datasets that may not fit in main memory? We introduce Turbo-SMT, a meta-method capable of doing exactly that: it boosts the performance of any CMTF algorithm, produces sparse and interpretable solutions, and parallelizes any CMTF algorithm, producing sparse and interpretable solutions (up to 65 fold). Additionally, we improve upon ALS, the work-horse algorithm for CMTF, with respect to efficiency and robustness to missing values. We apply Turbo-SMT to BrainQ, a dataset consisting of a (nouns, brain voxels, human subjects) tensor and a (nouns, properties) matrix, with coupling along the nouns dimension. Turbo-SMT is able to find meaningful latent variables, as well as to predict brain activity with competitive accuracy. Finally, we demonstrate the generality of Turbo-SMT, by applying it on a Facebook dataset (users, ’friends’, wall-postings); there, Turbo-SMT spots spammer-like anomalies. PMID:27672406

Detection of Protein Complexes Based on Penalized Matrix Decomposition in a Sparse Protein⁻Protein Interaction Network.

PubMed

Cao, Buwen; Deng, Shuguang; Qin, Hua; Ding, Pingjian; Chen, Shaopeng; Li, Guanghui

2018-06-15

High-throughput technology has generated large-scale protein interaction data, which is crucial in our understanding of biological organisms. Many complex identification algorithms have been developed to determine protein complexes. However, these methods are only suitable for dense protein interaction networks, because their capabilities decrease rapidly when applied to sparse protein⁻protein interaction (PPI) networks. In this study, based on penalized matrix decomposition ( PMD ), a novel method of penalized matrix decomposition for the identification of protein complexes (i.e., PMD pc ) was developed to detect protein complexes in the human protein interaction network. This method mainly consists of three steps. First, the adjacent matrix of the protein interaction network is normalized. Second, the normalized matrix is decomposed into three factor matrices. The PMD pc method can detect protein complexes in sparse PPI networks by imposing appropriate constraints on factor matrices. Finally, the results of our method are compared with those of other methods in human PPI network. Experimental results show that our method can not only outperform classical algorithms, such as CFinder, ClusterONE, RRW, HC-PIN, and PCE-FR, but can also achieve an ideal overall performance in terms of a composite score consisting of F-measure, accuracy (ACC), and the maximum matching ratio (MMR).

Sparsistency and Rates of Convergence in Large Covariance Matrix Estimation.

PubMed

Lam, Clifford; Fan, Jianqing

2009-01-01

This paper studies the sparsistency and rates of convergence for estimating sparse covariance and precision matrices based on penalized likelihood with nonconvex penalty functions. Here, sparsistency refers to the property that all parameters that are zero are actually estimated as zero with probability tending to one. Depending on the case of applications, sparsity priori may occur on the covariance matrix, its inverse or its Cholesky decomposition. We study these three sparsity exploration problems under a unified framework with a general penalty function. We show that the rates of convergence for these problems under the Frobenius norm are of order (s(n) log p(n)/n)(1/2), where s(n) is the number of nonzero elements, p(n) is the size of the covariance matrix and n is the sample size. This explicitly spells out the contribution of high-dimensionality is merely of a logarithmic factor. The conditions on the rate with which the tuning parameter λ(n) goes to 0 have been made explicit and compared under different penalties. As a result, for the L(1)-penalty, to guarantee the sparsistency and optimal rate of convergence, the number of nonzero elements should be small: sn'=O(pn) at most, among O(pn2) parameters, for estimating sparse covariance or correlation matrix, sparse precision or inverse correlation matrix or sparse Cholesky factor, where sn' is the number of the nonzero elements on the off-diagonal entries. On the other hand, using the SCAD or hard-thresholding penalty functions, there is no such a restriction.

Novel Fourier-based iterative reconstruction for sparse fan projection using alternating direction total variation minimization

NASA Astrophysics Data System (ADS)

Zhao, Jin; Han-Ming, Zhang; Bin, Yan; Lei, Li; Lin-Yuan, Wang; Ai-Long, Cai

2016-03-01

Sparse-view x-ray computed tomography (CT) imaging is an interesting topic in CT field and can efficiently decrease radiation dose. Compared with spatial reconstruction, a Fourier-based algorithm has advantages in reconstruction speed and memory usage. A novel Fourier-based iterative reconstruction technique that utilizes non-uniform fast Fourier transform (NUFFT) is presented in this work along with advanced total variation (TV) regularization for a fan sparse-view CT. The proposition of a selective matrix contributes to improve reconstruction quality. The new method employs the NUFFT and its adjoin to iterate back and forth between the Fourier and image space. The performance of the proposed algorithm is demonstrated through a series of digital simulations and experimental phantom studies. Results of the proposed algorithm are compared with those of existing TV-regularized techniques based on compressed sensing method, as well as basic algebraic reconstruction technique. Compared with the existing TV-regularized techniques, the proposed Fourier-based technique significantly improves convergence rate and reduces memory allocation, respectively. Projected supported by the National High Technology Research and Development Program of China (Grant No. 2012AA011603) and the National Natural Science Foundation of China (Grant No. 61372172).

Convergence Speed of a Dynamical System for Sparse Recovery

NASA Astrophysics Data System (ADS)

Balavoine, Aurele; Rozell, Christopher J.; Romberg, Justin

2013-09-01

This paper studies the convergence rate of a continuous-time dynamical system for L1-minimization, known as the Locally Competitive Algorithm (LCA). Solving L1-minimization} problems efficiently and rapidly is of great interest to the signal processing community, as these programs have been shown to recover sparse solutions to underdetermined systems of linear equations and come with strong performance guarantees. The LCA under study differs from the typical L1 solver in that it operates in continuous time: instead of being specified by discrete iterations, it evolves according to a system of nonlinear ordinary differential equations. The LCA is constructed from simple components, giving it the potential to be implemented as a large-scale analog circuit. The goal of this paper is to give guarantees on the convergence time of the LCA system. To do so, we analyze how the LCA evolves as it is recovering a sparse signal from underdetermined measurements. We show that under appropriate conditions on the measurement matrix and the problem parameters, the path the LCA follows can be described as a sequence of linear differential equations, each with a small number of active variables. This allows us to relate the convergence time of the system to the restricted isometry constant of the matrix. Interesting parallels to sparse-recovery digital solvers emerge from this study. Our analysis covers both the noisy and noiseless settings and is supported by simulation results.

Efficient preconditioning of the electronic structure problem in large scale ab initio molecular dynamics simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schiffmann, Florian; VandeVondele, Joost, E-mail: Joost.VandeVondele@mat.ethz.ch

2015-06-28

We present an improved preconditioning scheme for electronic structure calculations based on the orbital transformation method. First, a preconditioner is developed which includes information from the full Kohn-Sham matrix but avoids computationally demanding diagonalisation steps in its construction. This reduces the computational cost of its construction, eliminating a bottleneck in large scale simulations, while maintaining rapid convergence. In addition, a modified form of Hotelling’s iterative inversion is introduced to replace the exact inversion of the preconditioner matrix. This method is highly effective during molecular dynamics (MD), as the solution obtained in earlier MD steps is a suitable initial guess. Filteringmore » small elements during sparse matrix multiplication leads to linear scaling inversion, while retaining robustness, already for relatively small systems. For system sizes ranging from a few hundred to a few thousand atoms, which are typical for many practical applications, the improvements to the algorithm lead to a 2-5 fold speedup per MD step.« less

Non-convex Statistical Optimization for Sparse Tensor Graphical Model

PubMed Central

Sun, Wei; Wang, Zhaoran; Liu, Han; Cheng, Guang

2016-01-01

We consider the estimation of sparse graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we assume the data follow a tensor normal distribution whose covariance has a Kronecker product structure. The penalized maximum likelihood estimation of this model involves minimizing a non-convex objective function. In spite of the non-convexity of this estimation problem, we prove that an alternating minimization algorithm, which iteratively estimates each sparse precision matrix while fixing the others, attains an estimator with the optimal statistical rate of convergence as well as consistent graph recovery. Notably, such an estimator achieves estimation consistency with only one tensor sample, which is unobserved in previous work. Our theoretical results are backed by thorough numerical studies. PMID:28316459

Efficient Implementation of an Optimal Interpolator for Large Spatial Data Sets

NASA Technical Reports Server (NTRS)

Memarsadeghi, Nargess; Mount, David M.

2007-01-01

Scattered data interpolation is a problem of interest in numerous areas such as electronic imaging, smooth surface modeling, and computational geometry. Our motivation arises from applications in geology and mining, which often involve large scattered data sets and a demand for high accuracy. The method of choice is ordinary kriging. This is because it is a best unbiased estimator. Unfortunately, this interpolant is computationally very expensive to compute exactly. For n scattered data points, computing the value of a single interpolant involves solving a dense linear system of size roughly n x n. This is infeasible for large n. In practice, kriging is solved approximately by local approaches that are based on considering only a relatively small'number of points that lie close to the query point. There are many problems with this local approach, however. The first is that determining the proper neighborhood size is tricky, and is usually solved by ad hoc methods such as selecting a fixed number of nearest neighbors or all the points lying within a fixed radius. Such fixed neighborhood sizes may not work well for all query points, depending on local density of the point distribution. Local methods also suffer from the problem that the resulting interpolant is not continuous. Meyer showed that while kriging produces smooth continues surfaces, it has zero order continuity along its borders. Thus, at interface boundaries where the neighborhood changes, the interpolant behaves discontinuously. Therefore, it is important to consider and solve the global system for each interpolant. However, solving such large dense systems for each query point is impractical. Recently a more principled approach to approximating kriging has been proposed based on a technique called covariance tapering. The problems arise from the fact that the covariance functions that are used in kriging have global support. Our implementations combine, utilize, and enhance a number of different approaches that have been introduced in literature for solving large linear systems for interpolation of scattered data points. For very large systems, exact methods such as Gaussian elimination are impractical since they require 0(n(exp 3)) time and 0(n(exp 2)) storage. As Billings et al. suggested, we use an iterative approach. In particular, we use the SYMMLQ method, for solving the large but sparse ordinary kriging systems that result from tapering. The main technical issue that need to be overcome in our algorithmic solution is that the points' covariance matrix for kriging should be symmetric positive definite. The goal of tapering is to obtain a sparse approximate representation of the covariance matrix while maintaining its positive definiteness. Furrer et al. used tapering to obtain a sparse linear system of the form Ax = b, where A is the tapered symmetric positive definite covariance matrix. Thus, Cholesky factorization could be used to solve their linear systems. They implemented an efficient sparse Cholesky decomposition method. They also showed if these tapers are used for a limited class of covariance models, the solution of the system converges to the solution of the original system. Matrix A in the ordinary kriging system, while symmetric, is not positive definite. Thus, their approach is not applicable to the ordinary kriging system. Therefore, we use tapering only to obtain a sparse linear system. Then, we use SYMMLQ to solve the ordinary kriging system. We show that solving large kriging systems becomes practical via tapering and iterative methods, and results in lower estimation errors compared to traditional local approaches, and significant memory savings compared to the original global system. We also developed a more efficient variant of the sparse SYMMLQ method for large ordinary kriging systems. This approach adaptively finds the correct local neighborhood for each query point in the interpolation process.

Large-scale two-photon imaging revealed super-sparse population codes in the V1 superficial layer of awake monkeys.

PubMed

Tang, Shiming; Zhang, Yimeng; Li, Zhihao; Li, Ming; Liu, Fang; Jiang, Hongfei; Lee, Tai Sing

2018-04-26

One general principle of sensory information processing is that the brain must optimize efficiency by reducing the number of neurons that process the same information. The sparseness of the sensory representations in a population of neurons reflects the efficiency of the neural code. Here, we employ large-scale two-photon calcium imaging to examine the responses of a large population of neurons within the superficial layers of area V1 with single-cell resolution, while simultaneously presenting a large set of natural visual stimuli, to provide the first direct measure of the population sparseness in awake primates. The results show that only 0.5% of neurons respond strongly to any given natural image - indicating a ten-fold increase in the inferred sparseness over previous measurements. These population activities are nevertheless necessary and sufficient to discriminate visual stimuli with high accuracy, suggesting that the neural code in the primary visual cortex is both super-sparse and highly efficient. © 2018, Tang et al.

Method and apparatus for optimized processing of sparse matrices

DOEpatents

Taylor, Valerie E.

1993-01-01

A computer architecture for processing a sparse matrix is disclosed. The apparatus stores a value-row vector corresponding to nonzero values of a sparse matrix. Each of the nonzero values is located at a defined row and column position in the matrix. The value-row vector includes a first vector including nonzero values and delimiting characters indicating a transition from one column to another. The value-row vector also includes a second vector which defines row position values in the matrix corresponding to the nonzero values in the first vector and column position values in the matrix corresponding to the column position of the nonzero values in the first vector. The architecture also includes a circuit for detecting a special character within the value-row vector. Matrix-vector multiplication is executed on the value-row vector. This multiplication is performed by multiplying an index value of the first vector value by a column value from a second matrix to form a matrix-vector product which is added to a previous matrix-vector product.

A manual for PARTI runtime primitives, revision 1

NASA Technical Reports Server (NTRS)

Das, Raja; Saltz, Joel; Berryman, Harry

1991-01-01

Primitives are presented that are designed to help users efficiently program irregular problems (e.g., unstructured mesh sweeps, sparse matrix codes, adaptive mesh partial differential equations solvers) on distributed memory machines. These primitives are also designed for use in compilers for distributed memory multiprocessors. Communications patterns are captured at runtime, and the appropriate send and receive messages are automatically generated.

Adaptive OFDM Waveform Design for Spatio-Temporal-Sparsity Exploited STAP Radar

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sen, Satyabrata

In this chapter, we describe a sparsity-based space-time adaptive processing (STAP) algorithm to detect a slowly moving target using an orthogonal frequency division multiplexing (OFDM) radar. The motivation of employing an OFDM signal is that it improves the target-detectability from the interfering signals by increasing the frequency diversity of the system. However, due to the addition of one extra dimension in terms of frequency, the adaptive degrees-of-freedom in an OFDM-STAP also increases. Therefore, to avoid the construction a fully adaptive OFDM-STAP, we develop a sparsity-based STAP algorithm. We observe that the interference spectrum is inherently sparse in the spatio-temporal domain,more » as the clutter responses occupy only a diagonal ridge on the spatio-temporal plane and the jammer signals interfere only from a few spatial directions. Hence, we exploit that sparsity to develop an efficient STAP technique that utilizes considerably lesser number of secondary data compared to the other existing STAP techniques, and produces nearly optimum STAP performance. In addition to designing the STAP filter, we optimally design the transmit OFDM signals by maximizing the output signal-to-interference-plus-noise ratio (SINR) in order to improve the STAP performance. The computation of output SINR depends on the estimated value of the interference covariance matrix, which we obtain by applying the sparse recovery algorithm. Therefore, we analytically assess the effects of the synthesized OFDM coefficients on the sparse recovery of the interference covariance matrix by computing the coherence measure of the sparse measurement matrix. Our numerical examples demonstrate the achieved STAP-performance due to sparsity-based technique and adaptive waveform design.« less

Exploiting Multiple Levels of Parallelism in Sparse Matrix-Matrix Multiplication

DOE PAGES

Azad, Ariful; Ballard, Grey; Buluc, Aydin; ...

2016-11-08

Sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many high-performance graph algorithms as well as for some linear solvers, such as algebraic multigrid. The scaling of existing parallel implementations of SpGEMM is heavily bound by communication. Even though 3D (or 2.5D) algorithms have been proposed and theoretically analyzed in the flat MPI model on Erdös-Rényi matrices, those algorithms had not been implemented in practice and their complexities had not been analyzed for the general case. In this work, we present the first implementation of the 3D SpGEMM formulation that exploits multiple (intranode and internode) levels of parallelism, achievingmore » significant speedups over the state-of-the-art publicly available codes at all levels of concurrencies. We extensively evaluate our implementation and identify bottlenecks that should be subject to further research.« less

Learning Low-Rank Class-Specific Dictionary and Sparse Intra-Class Variant Dictionary for Face Recognition.

PubMed

Tang, Xin; Feng, Guo-Can; Li, Xiao-Xin; Cai, Jia-Xin

2015-01-01

Face recognition is challenging especially when the images from different persons are similar to each other due to variations in illumination, expression, and occlusion. If we have sufficient training images of each person which can span the facial variations of that person under testing conditions, sparse representation based classification (SRC) achieves very promising results. However, in many applications, face recognition often encounters the small sample size problem arising from the small number of available training images for each person. In this paper, we present a novel face recognition framework by utilizing low-rank and sparse error matrix decomposition, and sparse coding techniques (LRSE+SC). Firstly, the low-rank matrix recovery technique is applied to decompose the face images per class into a low-rank matrix and a sparse error matrix. The low-rank matrix of each individual is a class-specific dictionary and it captures the discriminative feature of this individual. The sparse error matrix represents the intra-class variations, such as illumination, expression changes. Secondly, we combine the low-rank part (representative basis) of each person into a supervised dictionary and integrate all the sparse error matrix of each individual into a within-individual variant dictionary which can be applied to represent the possible variations between the testing and training images. Then these two dictionaries are used to code the query image. The within-individual variant dictionary can be shared by all the subjects and only contribute to explain the lighting conditions, expressions, and occlusions of the query image rather than discrimination. At last, a reconstruction-based scheme is adopted for face recognition. Since the within-individual dictionary is introduced, LRSE+SC can handle the problem of the corrupted training data and the situation that not all subjects have enough samples for training. Experimental results show that our method achieves the state-of-the-art results on AR, FERET, FRGC and LFW databases.

Learning Low-Rank Class-Specific Dictionary and Sparse Intra-Class Variant Dictionary for Face Recognition

PubMed Central

Tang, Xin; Feng, Guo-can; Li, Xiao-xin; Cai, Jia-xin

2015-01-01

Face recognition is challenging especially when the images from different persons are similar to each other due to variations in illumination, expression, and occlusion. If we have sufficient training images of each person which can span the facial variations of that person under testing conditions, sparse representation based classification (SRC) achieves very promising results. However, in many applications, face recognition often encounters the small sample size problem arising from the small number of available training images for each person. In this paper, we present a novel face recognition framework by utilizing low-rank and sparse error matrix decomposition, and sparse coding techniques (LRSE+SC). Firstly, the low-rank matrix recovery technique is applied to decompose the face images per class into a low-rank matrix and a sparse error matrix. The low-rank matrix of each individual is a class-specific dictionary and it captures the discriminative feature of this individual. The sparse error matrix represents the intra-class variations, such as illumination, expression changes. Secondly, we combine the low-rank part (representative basis) of each person into a supervised dictionary and integrate all the sparse error matrix of each individual into a within-individual variant dictionary which can be applied to represent the possible variations between the testing and training images. Then these two dictionaries are used to code the query image. The within-individual variant dictionary can be shared by all the subjects and only contribute to explain the lighting conditions, expressions, and occlusions of the query image rather than discrimination. At last, a reconstruction-based scheme is adopted for face recognition. Since the within-individual dictionary is introduced, LRSE+SC can handle the problem of the corrupted training data and the situation that not all subjects have enough samples for training. Experimental results show that our method achieves the state-of-the-art results on AR, FERET, FRGC and LFW databases. PMID:26571112

Efficient Kriging Algorithms

NASA Technical Reports Server (NTRS)

Memarsadeghi, Nargess

2011-01-01

More efficient versions of an interpolation method, called kriging, have been introduced in order to reduce its traditionally high computational cost. Written in C++, these approaches were tested on both synthetic and real data. Kriging is a best unbiased linear estimator and suitable for interpolation of scattered data points. Kriging has long been used in the geostatistic and mining communities, but is now being researched for use in the image fusion of remotely sensed data. This allows a combination of data from various locations to be used to fill in any missing data from any single location. To arrive at the faster algorithms, sparse SYMMLQ iterative solver, covariance tapering, Fast Multipole Methods (FMM), and nearest neighbor searching techniques were used. These implementations were used when the coefficient matrix in the linear system is symmetric, but not necessarily positive-definite.

Two-stage sparse coding of region covariance via Log-Euclidean kernels to detect saliency.

PubMed

Zhang, Ying-Ying; Yang, Cai; Zhang, Ping

2017-05-01

In this paper, we present a novel bottom-up saliency detection algorithm from the perspective of covariance matrices on a Riemannian manifold. Each superpixel is described by a region covariance matrix on Riemannian Manifolds. We carry out a two-stage sparse coding scheme via Log-Euclidean kernels to extract salient objects efficiently. In the first stage, given background dictionary on image borders, sparse coding of each region covariance via Log-Euclidean kernels is performed. The reconstruction error on the background dictionary is regarded as the initial saliency of each superpixel. In the second stage, an improvement of the initial result is achieved by calculating reconstruction errors of the superpixels on foreground dictionary, which is extracted from the first stage saliency map. The sparse coding in the second stage is similar to the first stage, but is able to effectively highlight the salient objects uniformly from the background. Finally, three post-processing methods-highlight-inhibition function, context-based saliency weighting, and the graph cut-are adopted to further refine the saliency map. Experiments on four public benchmark datasets show that the proposed algorithm outperforms the state-of-the-art methods in terms of precision, recall and mean absolute error, and demonstrate the robustness and efficiency of the proposed method. Copyright © 2017 Elsevier Ltd. All rights reserved.

Sparse image reconstruction for molecular imaging.

PubMed

Ting, Michael; Raich, Raviv; Hero, Alfred O

2009-06-01

The application that motivates this paper is molecular imaging at the atomic level. When discretized at subatomic distances, the volume is inherently sparse. Noiseless measurements from an imaging technology can be modeled by convolution of the image with the system point spread function (psf). Such is the case with magnetic resonance force microscopy (MRFM), an emerging technology where imaging of an individual tobacco mosaic virus was recently demonstrated with nanometer resolution. We also consider additive white Gaussian noise (AWGN) in the measurements. Many prior works of sparse estimators have focused on the case when H has low coherence; however, the system matrix H in our application is the convolution matrix for the system psf. A typical convolution matrix has high coherence. This paper, therefore, does not assume a low coherence H. A discrete-continuous form of the Laplacian and atom at zero (LAZE) p.d.f. used by Johnstone and Silverman is formulated, and two sparse estimators derived by maximizing the joint p.d.f. of the observation and image conditioned on the hyperparameters. A thresholding rule that generalizes the hard and soft thresholding rule appears in the course of the derivation. This so-called hybrid thresholding rule, when used in the iterative thresholding framework, gives rise to the hybrid estimator, a generalization of the lasso. Estimates of the hyperparameters for the lasso and hybrid estimator are obtained via Stein's unbiased risk estimate (SURE). A numerical study with a Gaussian psf and two sparse images shows that the hybrid estimator outperforms the lasso.

SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ahlfeld, R., E-mail: r.ahlfeld14@imperial.ac.uk; Belkouchi, B.; Montomoli, F.

2016-09-01

A new arbitrary Polynomial Chaos (aPC) method is presented for moderately high-dimensional problems characterised by limited input data availability. The proposed methodology improves the algorithm of aPC and extends the method, that was previously only introduced as tensor product expansion, to moderately high-dimensional stochastic problems. The fundamental idea of aPC is to use the statistical moments of the input random variables to develop the polynomial chaos expansion. This approach provides the possibility to propagate continuous or discrete probability density functions and also histograms (data sets) as long as their moments exist, are finite and the determinant of the moment matrixmore » is strictly positive. For cases with limited data availability, this approach avoids bias and fitting errors caused by wrong assumptions. In this work, an alternative way to calculate the aPC is suggested, which provides the optimal polynomials, Gaussian quadrature collocation points and weights from the moments using only a handful of matrix operations on the Hankel matrix of moments. It can therefore be implemented without requiring prior knowledge about statistical data analysis or a detailed understanding of the mathematics of polynomial chaos expansions. The extension to more input variables suggested in this work, is an anisotropic and adaptive version of Smolyak's algorithm that is solely based on the moments of the input probability distributions. It is referred to as SAMBA (PC), which is short for Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos. It is illustrated that for moderately high-dimensional problems (up to 20 different input variables or histograms) SAMBA can significantly simplify the calculation of sparse Gaussian quadrature rules. SAMBA's efficiency for multivariate functions with regard to data availability is further demonstrated by analysing higher order convergence and accuracy for a set of nonlinear test functions with 2, 5 and 10 different input distributions or histograms.« less

Sparse/DCT (S/DCT) two-layered representation of prediction residuals for video coding.

PubMed

Kang, Je-Won; Gabbouj, Moncef; Kuo, C-C Jay

2013-07-01

In this paper, we propose a cascaded sparse/DCT (S/DCT) two-layer representation of prediction residuals, and implement this idea on top of the state-of-the-art high efficiency video coding (HEVC) standard. First, a dictionary is adaptively trained to contain featured patterns of residual signals so that a high portion of energy in a structured residual can be efficiently coded via sparse coding. It is observed that the sparse representation alone is less effective in the R-D performance due to the side information overhead at higher bit rates. To overcome this problem, the DCT representation is cascaded at the second stage. It is applied to the remaining signal to improve coding efficiency. The two representations successfully complement each other. It is demonstrated by experimental results that the proposed algorithm outperforms the HEVC reference codec HM5.0 in the Common Test Condition.

Embedded sparse representation of fMRI data via group-wise dictionary optimization

NASA Astrophysics Data System (ADS)

Zhu, Dajiang; Lin, Binbin; Faskowitz, Joshua; Ye, Jieping; Thompson, Paul M.

2016-03-01

Sparse learning enables dimension reduction and efficient modeling of high dimensional signals and images, but it may need to be tailored to best suit specific applications and datasets. Here we used sparse learning to efficiently represent functional magnetic resonance imaging (fMRI) data from the human brain. We propose a novel embedded sparse representation (ESR), to identify the most consistent dictionary atoms across different brain datasets via an iterative group-wise dictionary optimization procedure. In this framework, we introduced additional criteria to make the learned dictionary atoms more consistent across different subjects. We successfully identified four common dictionary atoms that follow the external task stimuli with very high accuracy. After projecting the corresponding coefficient vectors back into the 3-D brain volume space, the spatial patterns are also consistent with traditional fMRI analysis results. Our framework reveals common features of brain activation in a population, as a new, efficient fMRI analysis method.

Iris recognition based on robust principal component analysis

NASA Astrophysics Data System (ADS)

Karn, Pradeep; He, Xiao Hai; Yang, Shuai; Wu, Xiao Hong

2014-11-01

Iris images acquired under different conditions often suffer from blur, occlusion due to eyelids and eyelashes, specular reflection, and other artifacts. Existing iris recognition systems do not perform well on these types of images. To overcome these problems, we propose an iris recognition method based on robust principal component analysis. The proposed method decomposes all training images into a low-rank matrix and a sparse error matrix, where the low-rank matrix is used for feature extraction. The sparsity concentration index approach is then applied to validate the recognition result. Experimental results using CASIA V4 and IIT Delhi V1iris image databases showed that the proposed method achieved competitive performances in both recognition accuracy and computational efficiency.

Optical coherence tomography retinal image reconstruction via nonlocal weighted sparse representation

NASA Astrophysics Data System (ADS)

Abbasi, Ashkan; Monadjemi, Amirhassan; Fang, Leyuan; Rabbani, Hossein

2018-03-01

We present a nonlocal weighted sparse representation (NWSR) method for reconstruction of retinal optical coherence tomography (OCT) images. To reconstruct a high signal-to-noise ratio and high-resolution OCT images, utilization of efficient denoising and interpolation algorithms are necessary, especially when the original data were subsampled during acquisition. However, the OCT images suffer from the presence of a high level of noise, which makes the estimation of sparse representations a difficult task. Thus, the proposed NWSR method merges sparse representations of multiple similar noisy and denoised patches to better estimate a sparse representation for each patch. First, the sparse representation of each patch is independently computed over an overcomplete dictionary, and then a nonlocal weighted sparse coefficient is computed by averaging representations of similar patches. Since the sparsity can reveal relevant information from noisy patches, combining noisy and denoised patches' representations is beneficial to obtain a more robust estimate of the unknown sparse representation. The denoised patches are obtained by applying an off-the-shelf image denoising method and our method provides an efficient way to exploit information from noisy and denoised patches' representations. The experimental results on denoising and interpolation of spectral domain OCT images demonstrated the effectiveness of the proposed NWSR method over existing state-of-the-art methods.

Fast Compressive Tracking.

PubMed

Zhang, Kaihua; Zhang, Lei; Yang, Ming-Hsuan

2014-10-01

It is a challenging task to develop effective and efficient appearance models for robust object tracking due to factors such as pose variation, illumination change, occlusion, and motion blur. Existing online tracking algorithms often update models with samples from observations in recent frames. Despite much success has been demonstrated, numerous issues remain to be addressed. First, while these adaptive appearance models are data-dependent, there does not exist sufficient amount of data for online algorithms to learn at the outset. Second, online tracking algorithms often encounter the drift problems. As a result of self-taught learning, misaligned samples are likely to be added and degrade the appearance models. In this paper, we propose a simple yet effective and efficient tracking algorithm with an appearance model based on features extracted from a multiscale image feature space with data-independent basis. The proposed appearance model employs non-adaptive random projections that preserve the structure of the image feature space of objects. A very sparse measurement matrix is constructed to efficiently extract the features for the appearance model. We compress sample images of the foreground target and the background using the same sparse measurement matrix. The tracking task is formulated as a binary classification via a naive Bayes classifier with online update in the compressed domain. A coarse-to-fine search strategy is adopted to further reduce the computational complexity in the detection procedure. The proposed compressive tracking algorithm runs in real-time and performs favorably against state-of-the-art methods on challenging sequences in terms of efficiency, accuracy and robustness.

Optimization Algorithm for Kalman Filter Exploiting the Numerical Characteristics of SINS/GPS Integrated Navigation Systems.

PubMed

Hu, Shaoxing; Xu, Shike; Wang, Duhu; Zhang, Aiwu

2015-11-11

Aiming at addressing the problem of high computational cost of the traditional Kalman filter in SINS/GPS, a practical optimization algorithm with offline-derivation and parallel processing methods based on the numerical characteristics of the system is presented in this paper. The algorithm exploits the sparseness and/or symmetry of matrices to simplify the computational procedure. Thus plenty of invalid operations can be avoided by offline derivation using a block matrix technique. For enhanced efficiency, a new parallel computational mechanism is established by subdividing and restructuring calculation processes after analyzing the extracted "useful" data. As a result, the algorithm saves about 90% of the CPU processing time and 66% of the memory usage needed in a classical Kalman filter. Meanwhile, the method as a numerical approach needs no precise-loss transformation/approximation of system modules and the accuracy suffers little in comparison with the filter before computational optimization. Furthermore, since no complicated matrix theories are needed, the algorithm can be easily transplanted into other modified filters as a secondary optimization method to achieve further efficiency.

Improvements in sparse matrix operations of NASTRAN

NASA Technical Reports Server (NTRS)

Harano, S.

1980-01-01

A "nontransmit" packing routine was added to NASTRAN to allow matrix data to be refered to directly from the input/output buffer. Use of the packing routine permits various routines for matrix handling to perform a direct reference to the input/output buffer if data addresses have once been received. The packing routine offers a buffer by buffer backspace feature for efficient backspacing in sequential access. Unlike a conventional backspacing that needs twice back record for a single read of one record (one column), this feature omits overlapping of READ operation and back record. It eliminates the necessity of writing, in decomposition of a symmetric matrix, of a portion of the matrix to its upper triangular matrix from the last to the first columns of the symmetric matrix, thus saving time for generating the upper triangular matrix. Only a lower triangular matrix must be written onto the secondary storage device, bringing 10 to 30% reduction in use of the disk space of the storage device.

Infrared and visible image fusion based on robust principal component analysis and compressed sensing

NASA Astrophysics Data System (ADS)

Li, Jun; Song, Minghui; Peng, Yuanxi

2018-03-01

Current infrared and visible image fusion methods do not achieve adequate information extraction, i.e., they cannot extract the target information from infrared images while retaining the background information from visible images. Moreover, most of them have high complexity and are time-consuming. This paper proposes an efficient image fusion framework for infrared and visible images on the basis of robust principal component analysis (RPCA) and compressed sensing (CS). The novel framework consists of three phases. First, RPCA decomposition is applied to the infrared and visible images to obtain their sparse and low-rank components, which represent the salient features and background information of the images, respectively. Second, the sparse and low-rank coefficients are fused by different strategies. On the one hand, the measurements of the sparse coefficients are obtained by the random Gaussian matrix, and they are then fused by the standard deviation (SD) based fusion rule. Next, the fused sparse component is obtained by reconstructing the result of the fused measurement using the fast continuous linearized augmented Lagrangian algorithm (FCLALM). On the other hand, the low-rank coefficients are fused using the max-absolute rule. Subsequently, the fused image is superposed by the fused sparse and low-rank components. For comparison, several popular fusion algorithms are tested experimentally. By comparing the fused results subjectively and objectively, we find that the proposed framework can extract the infrared targets while retaining the background information in the visible images. Thus, it exhibits state-of-the-art performance in terms of both fusion effects and timeliness.

Matched field localization based on CS-MUSIC algorithm

NASA Astrophysics Data System (ADS)

Guo, Shuangle; Tang, Ruichun; Peng, Linhui; Ji, Xiaopeng

2016-04-01

The problem caused by shortness or excessiveness of snapshots and by coherent sources in underwater acoustic positioning is considered. A matched field localization algorithm based on CS-MUSIC (Compressive Sensing Multiple Signal Classification) is proposed based on the sparse mathematical model of the underwater positioning. The signal matrix is calculated through the SVD (Singular Value Decomposition) of the observation matrix. The observation matrix in the sparse mathematical model is replaced by the signal matrix, and a new concise sparse mathematical model is obtained, which means not only the scale of the localization problem but also the noise level is reduced; then the new sparse mathematical model is solved by the CS-MUSIC algorithm which is a combination of CS (Compressive Sensing) method and MUSIC (Multiple Signal Classification) method. The algorithm proposed in this paper can overcome effectively the difficulties caused by correlated sources and shortness of snapshots, and it can also reduce the time complexity and noise level of the localization problem by using the SVD of the observation matrix when the number of snapshots is large, which will be proved in this paper.

A Shifted Block Lanczos Algorithm 1: The Block Recurrence

NASA Technical Reports Server (NTRS)

Grimes, Roger G.; Lewis, John G.; Simon, Horst D.

1990-01-01

In this paper we describe a block Lanczos algorithm that is used as the key building block of a software package for the extraction of eigenvalues and eigenvectors of large sparse symmetric generalized eigenproblems. The software package comprises: a version of the block Lanczos algorithm specialized for spectrally transformed eigenproblems; an adaptive strategy for choosing shifts, and efficient codes for factoring large sparse symmetric indefinite matrices. This paper describes the algorithmic details of our block Lanczos recurrence. This uses a novel combination of block generalizations of several features that have only been investigated independently in the past. In particular new forms of partial reorthogonalization, selective reorthogonalization and local reorthogonalization are used, as is a new algorithm for obtaining the M-orthogonal factorization of a matrix. The heuristic shifting strategy, the integration with sparse linear equation solvers and numerical experience with the code are described in a companion paper.

Color Sparse Representations for Image Processing: Review, Models, and Prospects.

PubMed

Barthélemy, Quentin; Larue, Anthony; Mars, Jérôme I

2015-11-01

Sparse representations have been extended to deal with color images composed of three channels. A review of dictionary-learning-based sparse representations for color images is made here, detailing the differences between the models, and comparing their results on the real and simulated data. These models are considered in a unifying framework that is based on the degrees of freedom of the linear filtering/transformation of the color channels. Moreover, this allows it to be shown that the scalar quaternionic linear model is equivalent to constrained matrix-based color filtering, which highlights the filtering implicitly applied through this model. Based on this reformulation, the new color filtering model is introduced, using unconstrained filters. In this model, spatial morphologies of color images are encoded by atoms, and colors are encoded by color filters. Color variability is no longer captured in increasing the dictionary size, but with color filters, this gives an efficient color representation.

A path-oriented matrix-based knowledge representation system

NASA Technical Reports Server (NTRS)

Feyock, Stefan; Karamouzis, Stamos T.

1993-01-01

Experience has shown that designing a good representation is often the key to turning hard problems into simple ones. Most AI (Artificial Intelligence) search/representation techniques are oriented toward an infinite domain of objects and arbitrary relations among them. In reality much of what needs to be represented in AI can be expressed using a finite domain and unary or binary predicates. Well-known vector- and matrix-based representations can efficiently represent finite domains and unary/binary predicates, and allow effective extraction of path information by generalized transitive closure/path matrix computations. In order to avoid space limitations a set of abstract sparse matrix data types was developed along with a set of operations on them. This representation forms the basis of an intelligent information system for representing and manipulating relational data.

1-norm support vector novelty detection and its sparseness.

PubMed

Zhang, Li; Zhou, WeiDa

2013-12-01

This paper proposes a 1-norm support vector novelty detection (SVND) method and discusses its sparseness. 1-norm SVND is formulated as a linear programming problem and uses two techniques for inducing sparseness, or the 1-norm regularization and the hinge loss function. We also find two upper bounds on the sparseness of 1-norm SVND, or exact support vector (ESV) and kernel Gram matrix rank bounds. The ESV bound indicates that 1-norm SVND has a sparser representation model than SVND. The kernel Gram matrix rank bound can loosely estimate the sparseness of 1-norm SVND. Experimental results show that 1-norm SVND is feasible and effective. Copyright © 2013 Elsevier Ltd. All rights reserved.

Multitasking the Davidson algorithm for the large, sparse eigenvalue problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Umar, V.M.; Fischer, C.F.

1989-01-01

The authors report how the Davidson algorithm, developed for handling the eigenvalue problem for large and sparse matrices arising in quantum chemistry, was modified for use in atomic structure calculations. To date these calculations have used traditional eigenvalue methods, which limit the range of feasible calculations because of their excessive memory requirements and unsatisfactory performance attributed to time-consuming and costly processing of zero valued elements. The replacement of a traditional matrix eigenvalue method by the Davidson algorithm reduced these limitations. Significant speedup was found, which varied with the size of the underlying problem and its sparsity. Furthermore, the range ofmore » matrix sizes that can be manipulated efficiently was expended by more than one order or magnitude. On the CRAY X-MP the code was vectorized and the importance of gather/scatter analyzed. A parallelized version of the algorithm obtained an additional 35% reduction in execution time. Speedup due to vectorization and concurrency was also measured on the Alliant FX/8.« less

Holographic implementation of a binary associative memory for improved recognition

NASA Astrophysics Data System (ADS)

Bandyopadhyay, Somnath; Ghosh, Ajay; Datta, Asit K.

1998-03-01

Neural network associate memory has found wide application sin pattern recognition techniques. We propose an associative memory model for binary character recognition. The interconnection strengths of the memory are binary valued. The concept of sparse coding is sued to enhance the storage efficiency of the model. The question of imposed preconditioning of pattern vectors, which is inherent in a sparsely coded conventional memory, is eliminated by using a multistep correlation technique an the ability of correct association is enhanced in a real-time application. A potential optoelectronic implementation of the proposed associative memory is also described. The learning and recall is possible by using digital optical matrix-vector multiplication, where full use of parallelism and connectivity of optics is made. A hologram is used in the experiment as a longer memory (LTM) for storing all input information. The short-term memory or the interconnection weight matrix required during the recall process is configured by retrieving the necessary information from the holographic LTM.

Exploring Deep Learning and Sparse Matrix Format Selection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, Y.; Liao, C.; Shen, X.

We proposed to explore the use of Deep Neural Networks (DNN) for addressing the longstanding barriers. The recent rapid progress of DNN technology has created a large impact in many fields, which has significantly improved the prediction accuracy over traditional machine learning techniques in image classifications, speech recognitions, machine translations, and so on. To some degree, these tasks resemble the decision makings in many HPC tasks, including the aforementioned format selection for SpMV and linear solver selection. For instance, sparse matrix format selection is akin to image classification—such as, to tell whether an image contains a dog or a cat;more » in both problems, the right decisions are primarily determined by the spatial patterns of the elements in an input. For image classification, the patterns are of pixels, and for sparse matrix format selection, they are of non-zero elements. DNN could be naturally applied if we regard a sparse matrix as an image and the format selection or solver selection as classification problems.« less

Reconstruction of Complex Network based on the Noise via QR Decomposition and Compressed Sensing.

PubMed

Li, Lixiang; Xu, Dafei; Peng, Haipeng; Kurths, Jürgen; Yang, Yixian

2017-11-08

It is generally known that the states of network nodes are stable and have strong correlations in a linear network system. We find that without the control input, the method of compressed sensing can not succeed in reconstructing complex networks in which the states of nodes are generated through the linear network system. However, noise can drive the dynamics between nodes to break the stability of the system state. Therefore, a new method integrating QR decomposition and compressed sensing is proposed to solve the reconstruction problem of complex networks under the assistance of the input noise. The state matrix of the system is decomposed by QR decomposition. We construct the measurement matrix with the aid of Gaussian noise so that the sparse input matrix can be reconstructed by compressed sensing. We also discover that noise can build a bridge between the dynamics and the topological structure. Experiments are presented to show that the proposed method is more accurate and more efficient to reconstruct four model networks and six real networks by the comparisons between the proposed method and only compressed sensing. In addition, the proposed method can reconstruct not only the sparse complex networks, but also the dense complex networks.

Discovering mutated driver genes through a robust and sparse co-regularized matrix factorization framework with prior information from mRNA expression patterns and interaction network.

PubMed

Xi, Jianing; Wang, Minghui; Li, Ao

2018-06-05

Discovery of mutated driver genes is one of the primary objective for studying tumorigenesis. To discover some relatively low frequently mutated driver genes from somatic mutation data, many existing methods incorporate interaction network as prior information. However, the prior information of mRNA expression patterns are not exploited by these existing network-based methods, which is also proven to be highly informative of cancer progressions. To incorporate prior information from both interaction network and mRNA expressions, we propose a robust and sparse co-regularized nonnegative matrix factorization to discover driver genes from mutation data. Furthermore, our framework also conducts Frobenius norm regularization to overcome overfitting issue. Sparsity-inducing penalty is employed to obtain sparse scores in gene representations, of which the top scored genes are selected as driver candidates. Evaluation experiments by known benchmarking genes indicate that the performance of our method benefits from the two type of prior information. Our method also outperforms the existing network-based methods, and detect some driver genes that are not predicted by the competing methods. In summary, our proposed method can improve the performance of driver gene discovery by effectively incorporating prior information from interaction network and mRNA expression patterns into a robust and sparse co-regularized matrix factorization framework.

Elongation cutoff technique armed with quantum fast multipole method for linear scaling.

PubMed

Korchowiec, Jacek; Lewandowski, Jakub; Makowski, Marcin; Gu, Feng Long; Aoki, Yuriko

2009-11-30

A linear-scaling implementation of the elongation cutoff technique (ELG/C) that speeds up Hartree-Fock (HF) self-consistent field calculations is presented. The cutoff method avoids the known bottleneck of the conventional HF scheme, that is, diagonalization, because it operates within the low dimension subspace of the whole atomic orbital space. The efficiency of ELG/C is illustrated for two model systems. The obtained results indicate that the ELG/C is a very efficient sparse matrix algebra scheme. Copyright 2009 Wiley Periodicals, Inc.

Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. I. An efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pinski, Peter; Riplinger, Christoph; Neese, Frank, E-mail: evaleev@vt.edu, E-mail: frank.neese@cec.mpg.de

2015-07-21

In this work, a systematic infrastructure is described that formalizes concepts implicit in previous work and greatly simplifies computer implementation of reduced-scaling electronic structure methods. The key concept is sparse representation of tensors using chains of sparse maps between two index sets. Sparse map representation can be viewed as a generalization of compressed sparse row, a common representation of a sparse matrix, to tensor data. By combining few elementary operations on sparse maps (inversion, chaining, intersection, etc.), complex algorithms can be developed, illustrated here by a linear-scaling transformation of three-center Coulomb integrals based on our compact code library that implementsmore » sparse maps and operations on them. The sparsity of the three-center integrals arises from spatial locality of the basis functions and domain density fitting approximation. A novel feature of our approach is the use of differential overlap integrals computed in linear-scaling fashion for screening products of basis functions. Finally, a robust linear scaling domain based local pair natural orbital second-order Möller-Plesset (DLPNO-MP2) method is described based on the sparse map infrastructure that only depends on a minimal number of cutoff parameters that can be systematically tightened to approach 100% of the canonical MP2 correlation energy. With default truncation thresholds, DLPNO-MP2 recovers more than 99.9% of the canonical resolution of the identity MP2 (RI-MP2) energy while still showing a very early crossover with respect to the computational effort. Based on extensive benchmark calculations, relative energies are reproduced with an error of typically <0.2 kcal/mol. The efficiency of the local MP2 (LMP2) method can be drastically improved by carrying out the LMP2 iterations in a basis of pair natural orbitals. While the present work focuses on local electron correlation, it is of much broader applicability to computation with sparse tensors in quantum chemistry and beyond.« less

Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. I. An efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals.

PubMed

Pinski, Peter; Riplinger, Christoph; Valeev, Edward F; Neese, Frank

2015-07-21

In this work, a systematic infrastructure is described that formalizes concepts implicit in previous work and greatly simplifies computer implementation of reduced-scaling electronic structure methods. The key concept is sparse representation of tensors using chains of sparse maps between two index sets. Sparse map representation can be viewed as a generalization of compressed sparse row, a common representation of a sparse matrix, to tensor data. By combining few elementary operations on sparse maps (inversion, chaining, intersection, etc.), complex algorithms can be developed, illustrated here by a linear-scaling transformation of three-center Coulomb integrals based on our compact code library that implements sparse maps and operations on them. The sparsity of the three-center integrals arises from spatial locality of the basis functions and domain density fitting approximation. A novel feature of our approach is the use of differential overlap integrals computed in linear-scaling fashion for screening products of basis functions. Finally, a robust linear scaling domain based local pair natural orbital second-order Möller-Plesset (DLPNO-MP2) method is described based on the sparse map infrastructure that only depends on a minimal number of cutoff parameters that can be systematically tightened to approach 100% of the canonical MP2 correlation energy. With default truncation thresholds, DLPNO-MP2 recovers more than 99.9% of the canonical resolution of the identity MP2 (RI-MP2) energy while still showing a very early crossover with respect to the computational effort. Based on extensive benchmark calculations, relative energies are reproduced with an error of typically <0.2 kcal/mol. The efficiency of the local MP2 (LMP2) method can be drastically improved by carrying out the LMP2 iterations in a basis of pair natural orbitals. While the present work focuses on local electron correlation, it is of much broader applicability to computation with sparse tensors in quantum chemistry and beyond.

3D Reconstruction of human bones based on dictionary learning.

PubMed

Zhang, Binkai; Wang, Xiang; Liang, Xiao; Zheng, Jinjin

2017-11-01

An effective method for reconstructing a 3D model of human bones from computed tomography (CT) image data based on dictionary learning is proposed. In this study, the dictionary comprises the vertices of triangular meshes, and the sparse coefficient matrix indicates the connectivity information. For better reconstruction performance, we proposed a balance coefficient between the approximation and regularisation terms and a method for optimisation. Moreover, we applied a local updating strategy and a mesh-optimisation method to update the dictionary and the sparse matrix, respectively. The two updating steps are iterated alternately until the objective function converges. Thus, a reconstructed mesh could be obtained with high accuracy and regularisation. The experimental results show that the proposed method has the potential to obtain high precision and high-quality triangular meshes for rapid prototyping, medical diagnosis, and tissue engineering. Copyright © 2017 IPEM. Published by Elsevier Ltd. All rights reserved.

Communication Optimal Parallel Multiplication of Sparse Random Matrices

DTIC Science & Technology

2013-02-21

Definition 2.1), and (2) the algorithm is sparsity- independent, where the computation is statically partitioned to processors independent of the sparsity...struc- ture of the input matrices (see Definition 2.5). The second assumption applies to nearly all existing al- gorithms for general sparse matrix-matrix...where A and B are n× n ER(d) matrices: Definition 2.1 An ER(d) matrix is an adjacency matrix of an Erdős-Rényi graph with parameters n and d/n. That

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chow, Edmond

Solving sparse problems is at the core of many DOE computational science applications. We focus on the challenge of developing sparse algorithms that can fully exploit the parallelism in extreme-scale computing systems, in particular systems with massive numbers of cores per node. Our approach is to express a sparse matrix factorization as a large number of bilinear constraint equations, and then solving these equations via an asynchronous iterative method. The unknowns in these equations are the matrix entries of the factorization that is desired.

Yielding physically-interpretable emulators - A Sparse PCA approach

NASA Astrophysics Data System (ADS)

Galelli, S.; Alsahaf, A.; Giuliani, M.; Castelletti, A.

2015-12-01

Projection-based techniques, such as Principal Orthogonal Decomposition (POD), are a common approach to surrogate high-fidelity process-based models by lower order dynamic emulators. With POD, the dimensionality reduction is achieved by using observations, or 'snapshots' - generated with the high-fidelity model -, to project the entire set of input and state variables of this model onto a smaller set of basis functions that account for most of the variability in the data. While reduction efficiency and variance control of POD techniques are usually very high, the resulting emulators are structurally highly complex and can hardly be given a physically meaningful interpretation as each basis is a projection of the entire set of inputs and states. In this work, we propose a novel approach based on Sparse Principal Component Analysis (SPCA) that combines the several assets of POD methods with the potential for ex-post interpretation of the emulator structure. SPCA reduces the number of non-zero coefficients in the basis functions by identifying a sparse matrix of coefficients. While the resulting set of basis functions may retain less variance of the snapshots, the presence of a few non-zero coefficients assists in the interpretation of the underlying physical processes. The SPCA approach is tested on the reduction of a 1D hydro-ecological model (DYRESM-CAEDYM) used to describe the main ecological and hydrodynamic processes in Tono Dam, Japan. An experimental comparison against a standard POD approach shows that SPCA achieves the same accuracy in emulating a given output variable - for the same level of dimensionality reduction - while yielding better insights of the main process dynamics.

Reprint of "Two-stage sparse coding of region covariance via Log-Euclidean kernels to detect saliency".

PubMed

Zhang, Ying-Ying; Yang, Cai; Zhang, Ping

2017-08-01

In this paper, we present a novel bottom-up saliency detection algorithm from the perspective of covariance matrices on a Riemannian manifold. Each superpixel is described by a region covariance matrix on Riemannian Manifolds. We carry out a two-stage sparse coding scheme via Log-Euclidean kernels to extract salient objects efficiently. In the first stage, given background dictionary on image borders, sparse coding of each region covariance via Log-Euclidean kernels is performed. The reconstruction error on the background dictionary is regarded as the initial saliency of each superpixel. In the second stage, an improvement of the initial result is achieved by calculating reconstruction errors of the superpixels on foreground dictionary, which is extracted from the first stage saliency map. The sparse coding in the second stage is similar to the first stage, but is able to effectively highlight the salient objects uniformly from the background. Finally, three post-processing methods-highlight-inhibition function, context-based saliency weighting, and the graph cut-are adopted to further refine the saliency map. Experiments on four public benchmark datasets show that the proposed algorithm outperforms the state-of-the-art methods in terms of precision, recall and mean absolute error, and demonstrate the robustness and efficiency of the proposed method. Copyright © 2017 Elsevier Ltd. All rights reserved.

Computational efficiency improvements for image colorization

NASA Astrophysics Data System (ADS)

Yu, Chao; Sharma, Gaurav; Aly, Hussein

2013-03-01

We propose an efficient algorithm for colorization of greyscale images. As in prior work, colorization is posed as an optimization problem: a user specifies the color for a few scribbles drawn on the greyscale image and the color image is obtained by propagating color information from the scribbles to surrounding regions, while maximizing the local smoothness of colors. In this formulation, colorization is obtained by solving a large sparse linear system, which normally requires substantial computation and memory resources. Our algorithm improves the computational performance through three innovations over prior colorization implementations. First, the linear system is solved iteratively without explicitly constructing the sparse matrix, which significantly reduces the required memory. Second, we formulate each iteration in terms of integral images obtained by dynamic programming, reducing repetitive computation. Third, we use a coarseto- fine framework, where a lower resolution subsampled image is first colorized and this low resolution color image is upsampled to initialize the colorization process for the fine level. The improvements we develop provide significant speedup and memory savings compared to the conventional approach of solving the linear system directly using off-the-shelf sparse solvers, and allow us to colorize images with typical sizes encountered in realistic applications on typical commodity computing platforms.

Decentralized state estimation for a large-scale spatially interconnected system.

PubMed

Liu, Huabo; Yu, Haisheng

2018-03-01

A decentralized state estimator is derived for the spatially interconnected systems composed of many subsystems with arbitrary connection relations. An optimization problem on the basis of linear matrix inequality (LMI) is constructed for the computations of improved subsystem parameter matrices. Several computationally effective approaches are derived which efficiently utilize the block-diagonal characteristic of system parameter matrices and the sparseness of subsystem connection matrix. Moreover, this decentralized state estimator is proved to converge to a stable system and obtain a bounded covariance matrix of estimation errors under certain conditions. Numerical simulations show that the obtained decentralized state estimator is attractive in the synthesis of a large-scale networked system. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

A new global approach to obtain three-dimensional displacement maps by integrating GPS and DInSAR data

NASA Astrophysics Data System (ADS)

Guglielmino, F.; Nunnari, G.; Puglisi, G.; Spata, A.

2009-04-01

We propose a new technique, based on the elastic theory, to efficiently produce an estimate of three-dimensional surface displacement maps by integrating sparse Global Position System (GPS) measurements of deformations and Differential Interferometric Synthetic Aperture Radar (DInSAR) maps of movements of the Earth's surface. The previous methodologies known in literature, for combining data from GPS and DInSAR surveys, require two steps: the first, in which sparse GPS measurements are interpolated in order to fill in GPS displacements at the DInSAR grid, and the second, to estimate the three-dimensional surface displacement maps by using a suitable optimization technique. One of the advantages of the proposed approach is that both these steps are unified. We propose a linear matrix equation which accounts for both GPS and DInSAR data whose solution provide simultaneously the strain tensor, the displacement field and the rigid body rotation tensor throughout the entire investigated area. The mentioned linear matrix equation is solved by using the Weighted Least Square (WLS) thus assuring both numerical robustness and high computation efficiency. The proposed methodology was tested on both synthetic and experimental data, these last from GPS and DInSAR measurements carried out on Mt. Etna. The goodness of the results has been evaluated by using standard errors. These tests also allow optimising the choice of specific parameters of this algorithm. This "open" structure of the method will allow in the near future to take account of other available data sets, such as additional interferograms, or other geodetic data (e.g. levelling, tilt, etc.), in order to achieve even higher accuracy.

Acceleration of Linear Finite-Difference Poisson-Boltzmann Methods on Graphics Processing Units.

PubMed

Qi, Ruxi; Botello-Smith, Wesley M; Luo, Ray

2017-07-11

Electrostatic interactions play crucial roles in biophysical processes such as protein folding and molecular recognition. Poisson-Boltzmann equation (PBE)-based models have emerged as widely used in modeling these important processes. Though great efforts have been put into developing efficient PBE numerical models, challenges still remain due to the high dimensionality of typical biomolecular systems. In this study, we implemented and analyzed commonly used linear PBE solvers for the ever-improving graphics processing units (GPU) for biomolecular simulations, including both standard and preconditioned conjugate gradient (CG) solvers with several alternative preconditioners. Our implementation utilizes the standard Nvidia CUDA libraries cuSPARSE, cuBLAS, and CUSP. Extensive tests show that good numerical accuracy can be achieved given that the single precision is often used for numerical applications on GPU platforms. The optimal GPU performance was observed with the Jacobi-preconditioned CG solver, with a significant speedup over standard CG solver on CPU in our diversified test cases. Our analysis further shows that different matrix storage formats also considerably affect the efficiency of different linear PBE solvers on GPU, with the diagonal format best suited for our standard finite-difference linear systems. Further efficiency may be possible with matrix-free operations and integrated grid stencil setup specifically tailored for the banded matrices in PBE-specific linear systems.

Fast space-varying convolution using matrix source coding with applications to camera stray light reduction.

PubMed

Wei, Jianing; Bouman, Charles A; Allebach, Jan P

2014-05-01

Many imaging applications require the implementation of space-varying convolution for accurate restoration and reconstruction of images. Here, we use the term space-varying convolution to refer to linear operators whose impulse response has slow spatial variation. In addition, these space-varying convolution operators are often dense, so direct implementation of the convolution operator is typically computationally impractical. One such example is the problem of stray light reduction in digital cameras, which requires the implementation of a dense space-varying deconvolution operator. However, other inverse problems, such as iterative tomographic reconstruction, can also depend on the implementation of dense space-varying convolution. While space-invariant convolution can be efficiently implemented with the fast Fourier transform, this approach does not work for space-varying operators. So direct convolution is often the only option for implementing space-varying convolution. In this paper, we develop a general approach to the efficient implementation of space-varying convolution, and demonstrate its use in the application of stray light reduction. Our approach, which we call matrix source coding, is based on lossy source coding of the dense space-varying convolution matrix. Importantly, by coding the transformation matrix, we not only reduce the memory required to store it; we also dramatically reduce the computation required to implement matrix-vector products. Our algorithm is able to reduce computation by approximately factoring the dense space-varying convolution operator into a product of sparse transforms. Experimental results show that our method can dramatically reduce the computation required for stray light reduction while maintaining high accuracy.

A Chess-Like Game for Teaching Engineering Students to Solve Large System of Simultaneous Linear Equations

NASA Technical Reports Server (NTRS)

Nguyen, Duc T.; Mohammed, Ahmed Ali; Kadiam, Subhash

2010-01-01

Solving large (and sparse) system of simultaneous linear equations has been (and continues to be) a major challenging problem for many real-world engineering/science applications [1-2]. For many practical/large-scale problems, the sparse, Symmetrical and Positive Definite (SPD) system of linear equations can be conveniently represented in matrix notation as [A] {x} = {b} , where the square coefficient matrix [A] and the Right-Hand-Side (RHS) vector {b} are known. The unknown solution vector {x} can be efficiently solved by the following step-by-step procedures [1-2]: Reordering phase, Matrix Factorization phase, Forward solution phase, and Backward solution phase. In this research work, a Game-Based Learning (GBL) approach has been developed to help engineering students to understand crucial details about matrix reordering and factorization phases. A "chess-like" game has been developed and can be played by either a single player, or two players. Through this "chess-like" open-ended game, the players/learners will not only understand the key concepts involved in reordering algorithms (based on existing algorithms), but also have the opportunities to "discover new algorithms" which are better than existing algorithms. Implementing the proposed "chess-like" game for matrix reordering and factorization phases can be enhanced by FLASH [3] computer environments, where computer simulation with animated human voice, sound effects, visual/graphical/colorful displays of matrix tables, score (or monetary) awards for the best game players, etc. can all be exploited. Preliminary demonstrations of the developed GBL approach can be viewed by anyone who has access to the internet web-site [4]!

Wavelet-like bases for thin-wire integral equations in electromagnetics

NASA Astrophysics Data System (ADS)

Francomano, E.; Tortorici, A.; Toscano, E.; Ala, G.; Viola, F.

2005-03-01

In this paper, wavelets are used in solving, by the method of moments, a modified version of the thin-wire electric field integral equation, in frequency domain. The time domain electromagnetic quantities, are obtained by using the inverse discrete fast Fourier transform. The retarded scalar electric and vector magnetic potentials are employed in order to obtain the integral formulation. The discretized model generated by applying the direct method of moments via point-matching procedure, results in a linear system with a dense matrix which have to be solved for each frequency of the Fourier spectrum of the time domain impressed source. Therefore, orthogonal wavelet-like basis transform is used to sparsify the moment matrix. In particular, dyadic and M-band wavelet transforms have been adopted, so generating different sparse matrix structures. This leads to an efficient solution in solving the resulting sparse matrix equation. Moreover, a wavelet preconditioner is used to accelerate the convergence rate of the iterative solver employed. These numerical features are used in analyzing the transient behavior of a lightning protection system. In particular, the transient performance of the earth termination system of a lightning protection system or of the earth electrode of an electric power substation, during its operation is focused. The numerical results, obtained by running a complex structure, are discussed and the features of the used method are underlined.

Multiple Kernel Sparse Representation based Orthogonal Discriminative Projection and Its Cost-Sensitive Extension.

PubMed

Zhang, Guoqing; Sun, Huaijiang; Xia, Guiyu; Sun, Quansen

2016-07-07

Sparse representation based classification (SRC) has been developed and shown great potential for real-world application. Based on SRC, Yang et al. [10] devised a SRC steered discriminative projection (SRC-DP) method. However, as a linear algorithm, SRC-DP cannot handle the data with highly nonlinear distribution. Kernel sparse representation-based classifier (KSRC) is a non-linear extension of SRC and can remedy the drawback of SRC. KSRC requires the use of a predetermined kernel function and selection of the kernel function and its parameters is difficult. Recently, multiple kernel learning for SRC (MKL-SRC) [22] has been proposed to learn a kernel from a set of base kernels. However, MKL-SRC only considers the within-class reconstruction residual while ignoring the between-class relationship, when learning the kernel weights. In this paper, we propose a novel multiple kernel sparse representation-based classifier (MKSRC), and then we use it as a criterion to design a multiple kernel sparse representation based orthogonal discriminative projection method (MK-SR-ODP). The proposed algorithm aims at learning a projection matrix and a corresponding kernel from the given base kernels such that in the low dimension subspace the between-class reconstruction residual is maximized and the within-class reconstruction residual is minimized. Furthermore, to achieve a minimum overall loss by performing recognition in the learned low-dimensional subspace, we introduce cost information into the dimensionality reduction method. The solutions for the proposed method can be efficiently found based on trace ratio optimization method [33]. Extensive experimental results demonstrate the superiority of the proposed algorithm when compared with the state-of-the-art methods.

Semi-implicit integration factor methods on sparse grids for high-dimensional systems

NASA Astrophysics Data System (ADS)

Wang, Dongyong; Chen, Weitao; Nie, Qing

2015-07-01

Numerical methods for partial differential equations in high-dimensional spaces are often limited by the curse of dimensionality. Though the sparse grid technique, based on a one-dimensional hierarchical basis through tensor products, is popular for handling challenges such as those associated with spatial discretization, the stability conditions on time step size due to temporal discretization, such as those associated with high-order derivatives in space and stiff reactions, remain. Here, we incorporate the sparse grids with the implicit integration factor method (IIF) that is advantageous in terms of stability conditions for systems containing stiff reactions and diffusions. We combine IIF, in which the reaction is treated implicitly and the diffusion is treated explicitly and exactly, with various sparse grid techniques based on the finite element and finite difference methods and a multi-level combination approach. The overall method is found to be efficient in terms of both storage and computational time for solving a wide range of PDEs in high dimensions. In particular, the IIF with the sparse grid combination technique is flexible and effective in solving systems that may include cross-derivatives and non-constant diffusion coefficients. Extensive numerical simulations in both linear and nonlinear systems in high dimensions, along with applications of diffusive logistic equations and Fokker-Planck equations, demonstrate the accuracy, efficiency, and robustness of the new methods, indicating potential broad applications of the sparse grid-based integration factor method.

Blind compressed sensing image reconstruction based on alternating direction method

NASA Astrophysics Data System (ADS)

Liu, Qinan; Guo, Shuxu

2018-04-01

In order to solve the problem of how to reconstruct the original image under the condition of unknown sparse basis, this paper proposes an image reconstruction method based on blind compressed sensing model. In this model, the image signal is regarded as the product of a sparse coefficient matrix and a dictionary matrix. Based on the existing blind compressed sensing theory, the optimal solution is solved by the alternative minimization method. The proposed method solves the problem that the sparse basis in compressed sensing is difficult to represent, which restrains the noise and improves the quality of reconstructed image. This method ensures that the blind compressed sensing theory has a unique solution and can recover the reconstructed original image signal from a complex environment with a stronger self-adaptability. The experimental results show that the image reconstruction algorithm based on blind compressed sensing proposed in this paper can recover high quality image signals under the condition of under-sampling.

Stability and stabilisation of a class of networked dynamic systems

NASA Astrophysics Data System (ADS)

Liu, H. B.; Wang, D. Q.

2018-04-01

We investigate the stability and stabilisation of a linear time invariant networked heterogeneous system with arbitrarily connected subsystems. A new linear matrix inequality based sufficient and necessary condition for the stability is derived, based on which the stabilisation is provided. The obtained conditions efficiently utilise the block-diagonal characteristic of system parameter matrices and the sparseness of subsystem connection matrix. Moreover, a sufficient condition only dependent on each individual subsystem is also presented for the stabilisation of the networked systems with a large scale. Numerical simulations show that these conditions are computationally valid in the analysis and synthesis of a large-scale networked system.

Improved Success of Sparse Matrix Protein Crystallization Screening with Heterogeneous Nucleating Agents

PubMed Central

Thakur, Anil S.; Robin, Gautier; Guncar, Gregor; Saunders, Neil F. W.; Newman, Janet; Martin, Jennifer L.; Kobe, Bostjan

2007-01-01

Background Crystallization is a major bottleneck in the process of macromolecular structure determination by X-ray crystallography. Successful crystallization requires the formation of nuclei and their subsequent growth to crystals of suitable size. Crystal growth generally occurs spontaneously in a supersaturated solution as a result of homogenous nucleation. However, in a typical sparse matrix screening experiment, precipitant and protein concentration are not sampled extensively, and supersaturation conditions suitable for nucleation are often missed. Methodology/Principal Findings We tested the effect of nine potential heterogenous nucleating agents on crystallization of ten test proteins in a sparse matrix screen. Several nucleating agents induced crystal formation under conditions where no crystallization occurred in the absence of the nucleating agent. Four nucleating agents: dried seaweed; horse hair; cellulose and hydroxyapatite, had a considerable overall positive effect on crystallization success. This effect was further enhanced when these nucleating agents were used in combination with each other. Conclusions/Significance Our results suggest that the addition of heterogeneous nucleating agents increases the chances of crystal formation when using sparse matrix screens. PMID:17971854

Compressed sensing for high-resolution nonlipid suppressed 1 H FID MRSI of the human brain at 9.4T.

PubMed

Nassirpour, Sahar; Chang, Paul; Avdievitch, Nikolai; Henning, Anke

2018-04-29

The aim of this study was to apply compressed sensing to accelerate the acquisition of high resolution metabolite maps of the human brain using a nonlipid suppressed ultra-short TR and TE 1 H FID MRSI sequence at 9.4T. X-t sparse compressed sensing reconstruction was optimized for nonlipid suppressed 1 H FID MRSI data. Coil-by-coil x-t sparse reconstruction was compared with SENSE x-t sparse and low rank reconstruction. The effect of matrix size and spatial resolution on the achievable acceleration factor was studied. Finally, in vivo metabolite maps with different acceleration factors of 2, 4, 5, and 10 were acquired and compared. Coil-by-coil x-t sparse compressed sensing reconstruction was not able to reliably recover the nonlipid suppressed data, rather a combination of parallel and sparse reconstruction was necessary (SENSE x-t sparse). For acceleration factors of up to 5, both the low-rank and the compressed sensing methods were able to reconstruct the data comparably well (root mean squared errors [RMSEs] ≤ 10.5% for Cre). However, the reconstruction time of the low rank algorithm was drastically longer than compressed sensing. Using the optimized compressed sensing reconstruction, acceleration factors of 4 or 5 could be reached for the MRSI data with a matrix size of 64 × 64. For lower spatial resolutions, an acceleration factor of up to R∼4 was successfully achieved. By tailoring the reconstruction scheme to the nonlipid suppressed data through parameter optimization and performance evaluation, we present high resolution (97 µL voxel size) accelerated in vivo metabolite maps of the human brain acquired at 9.4T within scan times of 3 to 3.75 min. © 2018 International Society for Magnetic Resonance in Medicine.

Multi-GPU implementation of a VMAT treatment plan optimization algorithm.

PubMed

Tian, Zhen; Peng, Fei; Folkerts, Michael; Tan, Jun; Jia, Xun; Jiang, Steve B

2015-06-01

Volumetric modulated arc therapy (VMAT) optimization is a computationally challenging problem due to its large data size, high degrees of freedom, and many hardware constraints. High-performance graphics processing units (GPUs) have been used to speed up the computations. However, GPU's relatively small memory size cannot handle cases with a large dose-deposition coefficient (DDC) matrix in cases of, e.g., those with a large target size, multiple targets, multiple arcs, and/or small beamlet size. The main purpose of this paper is to report an implementation of a column-generation-based VMAT algorithm, previously developed in the authors' group, on a multi-GPU platform to solve the memory limitation problem. While the column-generation-based VMAT algorithm has been previously developed, the GPU implementation details have not been reported. Hence, another purpose is to present detailed techniques employed for GPU implementation. The authors also would like to utilize this particular problem as an example problem to study the feasibility of using a multi-GPU platform to solve large-scale problems in medical physics. The column-generation approach generates VMAT apertures sequentially by solving a pricing problem (PP) and a master problem (MP) iteratively. In the authors' method, the sparse DDC matrix is first stored on a CPU in coordinate list format (COO). On the GPU side, this matrix is split into four submatrices according to beam angles, which are stored on four GPUs in compressed sparse row format. Computation of beamlet price, the first step in PP, is accomplished using multi-GPUs. A fast inter-GPU data transfer scheme is accomplished using peer-to-peer access. The remaining steps of PP and MP problems are implemented on CPU or a single GPU due to their modest problem scale and computational loads. Barzilai and Borwein algorithm with a subspace step scheme is adopted here to solve the MP problem. A head and neck (H&N) cancer case is then used to validate the authors' method. The authors also compare their multi-GPU implementation with three different single GPU implementation strategies, i.e., truncating DDC matrix (S1), repeatedly transferring DDC matrix between CPU and GPU (S2), and porting computations involving DDC matrix to CPU (S3), in terms of both plan quality and computational efficiency. Two more H&N patient cases and three prostate cases are used to demonstrate the advantages of the authors' method. The authors' multi-GPU implementation can finish the optimization process within ∼ 1 min for the H&N patient case. S1 leads to an inferior plan quality although its total time was 10 s shorter than the multi-GPU implementation due to the reduced matrix size. S2 and S3 yield the same plan quality as the multi-GPU implementation but take ∼4 and ∼6 min, respectively. High computational efficiency was consistently achieved for the other five patient cases tested, with VMAT plans of clinically acceptable quality obtained within 23-46 s. Conversely, to obtain clinically comparable or acceptable plans for all six of these VMAT cases that the authors have tested in this paper, the optimization time needed in a commercial TPS system on CPU was found to be in an order of several minutes. The results demonstrate that the multi-GPU implementation of the authors' column-generation-based VMAT optimization can handle the large-scale VMAT optimization problem efficiently without sacrificing plan quality. The authors' study may serve as an example to shed some light on other large-scale medical physics problems that require multi-GPU techniques.

Sparse coded image super-resolution using K-SVD trained dictionary based on regularized orthogonal matching pursuit.

PubMed

Sajjad, Muhammad; Mehmood, Irfan; Baik, Sung Wook

2015-01-01

Image super-resolution (SR) plays a vital role in medical imaging that allows a more efficient and effective diagnosis process. Usually, diagnosing is difficult and inaccurate from low-resolution (LR) and noisy images. Resolution enhancement through conventional interpolation methods strongly affects the precision of consequent processing steps, such as segmentation and registration. Therefore, we propose an efficient sparse coded image SR reconstruction technique using a trained dictionary. We apply a simple and efficient regularized version of orthogonal matching pursuit (ROMP) to seek the coefficients of sparse representation. ROMP has the transparency and greediness of OMP and the robustness of the L1-minization that enhance the dictionary learning process to capture feature descriptors such as oriented edges and contours from complex images like brain MRIs. The sparse coding part of the K-SVD dictionary training procedure is modified by substituting OMP with ROMP. The dictionary update stage allows simultaneously updating an arbitrary number of atoms and vectors of sparse coefficients. In SR reconstruction, ROMP is used to determine the vector of sparse coefficients for the underlying patch. The recovered representations are then applied to the trained dictionary, and finally, an optimization leads to high-resolution output of high-quality. Experimental results demonstrate that the super-resolution reconstruction quality of the proposed scheme is comparatively better than other state-of-the-art schemes.

Effects of Ordering Strategies and Programming Paradigms on Sparse Matrix Computations

NASA Technical Reports Server (NTRS)

Oliker, Leonid; Li, Xiaoye; Husbands, Parry; Biswas, Rupak; Biegel, Bryan (Technical Monitor)

2002-01-01

The Conjugate Gradient (CG) algorithm is perhaps the best-known iterative technique to solve sparse linear systems that are symmetric and positive definite. For systems that are ill-conditioned, it is often necessary to use a preconditioning technique. In this paper, we investigate the effects of various ordering and partitioning strategies on the performance of parallel CG and ILU(O) preconditioned CG (PCG) using different programming paradigms and architectures. Results show that for this class of applications: ordering significantly improves overall performance on both distributed and distributed shared-memory systems, that cache reuse may be more important than reducing communication, that it is possible to achieve message-passing performance using shared-memory constructs through careful data ordering and distribution, and that a hybrid MPI+OpenMP paradigm increases programming complexity with little performance gains. A implementation of CG on the Cray MTA does not require special ordering or partitioning to obtain high efficiency and scalability, giving it a distinct advantage for adaptive applications; however, it shows limited scalability for PCG due to a lack of thread level parallelism.

An Efficient Multicore Implementation of a Novel HSS-Structured Multifrontal Solver Using Randomized Sampling

DOE PAGES

Ghysels, Pieter; Li, Xiaoye S.; Rouet, Francois -Henry; ...

2016-10-27

Here, we present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which have low-rank off-diagonal blocks, to approximate the frontal matrices. For HSS matrix construction, a randomized sampling algorithm is used together with interpolative decompositions. The combination of the randomized compression with a fast ULV HSS factoriz ation leads to a solver with lower computational complexity than the standard multifrontal method for many applications, resulting in speedups up to 7 fold for problems in our test suite.more » The implementation targets many-core systems by using task parallelism with dynamic runtime scheduling. Numerical experiments show performance improvements over state-of-the-art sparse direct solvers. The implementation achieves high performance and good scalability on a range of modern shared memory parallel systems, including the Intel Xeon Phi (MIC). The code is part of a software package called STRUMPACK - STRUctured Matrices PACKage, which also has a distributed memory component for dense rank-structured matrices.« less

Efficient Implementations of the Quadrature-Free Discontinuous Galerkin Method

NASA Technical Reports Server (NTRS)

Lockard, David P.; Atkins, Harold L.

1999-01-01

The efficiency of the quadrature-free form of the dis- continuous Galerkin method in two dimensions, and briefly in three dimensions, is examined. Most of the work for constant-coefficient, linear problems involves the volume and edge integrations, and the transformation of information from the volume to the edges. These operations can be viewed as matrix-vector multiplications. Many of the matrices are sparse as a result of symmetry, and blocking and specialized multiplication routines are used to account for the sparsity. By optimizing these operations, a 35% reduction in total CPU time is achieved. For nonlinear problems, the calculation of the flux becomes dominant because of the cost associated with polynomial products and inversion. This component of the work can be reduced by up to 75% when the products are approximated by truncating terms. Because the cost is high for nonlinear problems on general elements, it is suggested that simplified physics and the most efficient element types be used over most of the domain.

Dense and Sparse Matrix Operations on the Cell Processor

DOE Office of Scientific and Technical Information (OSTI.GOV)

Williams, Samuel W.; Shalf, John; Oliker, Leonid

2005-05-01

The slowing pace of commodity microprocessor performance improvements combined with ever-increasing chip power demands has become of utmost concern to computational scientists. Therefore, the high performance computing community is examining alternative architectures that address the limitations of modern superscalar designs. In this work, we examine STI's forthcoming Cell processor: a novel, low-power architecture that combines a PowerPC core with eight independent SIMD processing units coupled with a software-controlled memory to offer high FLOP/s/Watt. Since neither Cell hardware nor cycle-accurate simulators are currently publicly available, we develop an analytic framework to predict Cell performance on dense and sparse matrix operations, usingmore » a variety of algorithmic approaches. Results demonstrate Cell's potential to deliver more than an order of magnitude better GFLOP/s per watt performance, when compared with the Intel Itanium2 and Cray X1 processors.« less

SparRec: An effective matrix completion framework of missing data imputation for GWAS

NASA Astrophysics Data System (ADS)

Jiang, Bo; Ma, Shiqian; Causey, Jason; Qiao, Linbo; Hardin, Matthew Price; Bitts, Ian; Johnson, Daniel; Zhang, Shuzhong; Huang, Xiuzhen

2016-10-01

Genome-wide association studies present computational challenges for missing data imputation, while the advances of genotype technologies are generating datasets of large sample sizes with sample sets genotyped on multiple SNP chips. We present a new framework SparRec (Sparse Recovery) for imputation, with the following properties: (1) The optimization models of SparRec, based on low-rank and low number of co-clusters of matrices, are different from current statistics methods. While our low-rank matrix completion (LRMC) model is similar to Mendel-Impute, our matrix co-clustering factorization (MCCF) model is completely new. (2) SparRec, as other matrix completion methods, is flexible to be applied to missing data imputation for large meta-analysis with different cohorts genotyped on different sets of SNPs, even when there is no reference panel. This kind of meta-analysis is very challenging for current statistics based methods. (3) SparRec has consistent performance and achieves high recovery accuracy even when the missing data rate is as high as 90%. Compared with Mendel-Impute, our low-rank based method achieves similar accuracy and efficiency, while the co-clustering based method has advantages in running time. The testing results show that SparRec has significant advantages and competitive performance over other state-of-the-art existing statistics methods including Beagle and fastPhase.

A general parallel sparse-blocked matrix multiply for linear scaling SCF theory

NASA Astrophysics Data System (ADS)

Challacombe, Matt

2000-06-01

A general approach to the parallel sparse-blocked matrix-matrix multiply is developed in the context of linear scaling self-consistent-field (SCF) theory. The data-parallel message passing method uses non-blocking communication to overlap computation and communication. The space filling curve heuristic is used to achieve data locality for sparse matrix elements that decay with “separation”. Load balance is achieved by solving the bin packing problem for blocks with variable size.With this new method as the kernel, parallel performance of the simplified density matrix minimization (SDMM) for solution of the SCF equations is investigated for RHF/6-31G ∗∗ water clusters and RHF/3-21G estane globules. Sustained rates above 5.7 GFLOPS for the SDMM have been achieved for (H 2 O) 200 with 95 Origin 2000 processors. Scalability is found to be limited by load imbalance, which increases with decreasing granularity, due primarily to the inhomogeneous distribution of variable block sizes.

Data traffic reduction schemes for sparse Cholesky factorizations

NASA Technical Reports Server (NTRS)

Naik, Vijay K.; Patrick, Merrell L.

1988-01-01

Load distribution schemes are presented which minimize the total data traffic in the Cholesky factorization of dense and sparse, symmetric, positive definite matrices on multiprocessor systems with local and shared memory. The total data traffic in factoring an n x n sparse, symmetric, positive definite matrix representing an n-vertex regular 2-D grid graph using n (sup alpha), alpha is equal to or less than 1, processors are shown to be O(n(sup 1 + alpha/2)). It is O(n(sup 3/2)), when n (sup alpha), alpha is equal to or greater than 1, processors are used. Under the conditions of uniform load distribution, these results are shown to be asymptotically optimal. The schemes allow efficient use of up to O(n) processors before the total data traffic reaches the maximum value of O(n(sup 3/2)). The partitioning employed within the scheme, allows a better utilization of the data accessed from shared memory than those of previously published methods.

Sparse matrix-vector multiplication on network-on-chip

NASA Astrophysics Data System (ADS)

Sun, C.-C.; Götze, J.; Jheng, H.-Y.; Ruan, S.-J.

2010-12-01

In this paper, we present an idea for performing matrix-vector multiplication by using Network-on-Chip (NoC) architecture. In traditional IC design on-chip communications have been designed with dedicated point-to-point interconnections. Therefore, regular local data transfer is the major concept of many parallel implementations. However, when dealing with the parallel implementation of sparse matrix-vector multiplication (SMVM), which is the main step of all iterative algorithms for solving systems of linear equation, the required data transfers depend on the sparsity structure of the matrix and can be extremely irregular. Using the NoC architecture makes it possible to deal with arbitrary structure of the data transfers; i.e. with the irregular structure of the sparse matrices. So far, we have already implemented the proposed SMVM-NoC architecture with the size 4×4 and 5×5 in IEEE 754 single float point precision using FPGA.

Structure-preserving and rank-revealing QR-factorizations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bischof, C.H.; Hansen, P.C.

1991-11-01

The rank-revealing QR-factorization (RRQR-factorization) is a special QR-factorization that is guaranteed to reveal the numerical rank of the matrix under consideration. This makes the RRQR-factorization a useful tool in the numerical treatment of many rank-deficient problems in numerical linear algebra. In this paper, a framework is presented for the efficient implementation of RRQR algorithms, in particular, for sparse matrices. A sparse RRQR-algorithm should seek to preserve the structure and sparsity of the matrix as much as possible while retaining the ability to capture safely the numerical rank. To this end, the paper proposes to compute an initial QR-factorization using amore » restricted pivoting strategy guarded by incremental condition estimation (ICE), and then applies the algorithm suggested by Chan and Foster to this QR-factorization. The column exchange strategy used in the initial QR factorization will exploit the fact that certain column exchanges do not change the sparsity structure, and compute a sparse QR-factorization that is a good approximation of the sought-after RRQR-factorization. Due to quantities produced by ICE, the Chan/Foster RRQR algorithm can be implemented very cheaply, thus verifying that the sought-after RRQR-factorization has indeed been computed. Experimental results on a model problem show that the initial QR-factorization is indeed very likely to produce RRQR-factorization.« less

Joint analysis of multiple high-dimensional data types using sparse matrix approximations of rank-1 with applications to ovarian and liver cancer.

PubMed

Okimoto, Gordon; Zeinalzadeh, Ashkan; Wenska, Tom; Loomis, Michael; Nation, James B; Fabre, Tiphaine; Tiirikainen, Maarit; Hernandez, Brenda; Chan, Owen; Wong, Linda; Kwee, Sandi

2016-01-01

Technological advances enable the cost-effective acquisition of Multi-Modal Data Sets (MMDS) composed of measurements for multiple, high-dimensional data types obtained from a common set of bio-samples. The joint analysis of the data matrices associated with the different data types of a MMDS should provide a more focused view of the biology underlying complex diseases such as cancer that would not be apparent from the analysis of a single data type alone. As multi-modal data rapidly accumulate in research laboratories and public databases such as The Cancer Genome Atlas (TCGA), the translation of such data into clinically actionable knowledge has been slowed by the lack of computational tools capable of analyzing MMDSs. Here, we describe the Joint Analysis of Many Matrices by ITeration (JAMMIT) algorithm that jointly analyzes the data matrices of a MMDS using sparse matrix approximations of rank-1. The JAMMIT algorithm jointly approximates an arbitrary number of data matrices by rank-1 outer-products composed of "sparse" left-singular vectors (eigen-arrays) that are unique to each matrix and a right-singular vector (eigen-signal) that is common to all the matrices. The non-zero coefficients of the eigen-arrays identify small subsets of variables for each data type (i.e., signatures) that in aggregate, or individually, best explain a dominant eigen-signal defined on the columns of the data matrices. The approximation is specified by a single "sparsity" parameter that is selected based on false discovery rate estimated by permutation testing. Multiple signals of interest in a given MDDS are sequentially detected and modeled by iterating JAMMIT on "residual" data matrices that result from a given sparse approximation. We show that JAMMIT outperforms other joint analysis algorithms in the detection of multiple signatures embedded in simulated MDDS. On real multimodal data for ovarian and liver cancer we show that JAMMIT identified multi-modal signatures that were clinically informative and enriched for cancer-related biology. Sparse matrix approximations of rank-1 provide a simple yet effective means of jointly reducing multiple, big data types to a small subset of variables that characterize important clinical and/or biological attributes of the bio-samples from which the data were acquired.

lme4qtl: linear mixed models with flexible covariance structure for genetic studies of related individuals.

PubMed

Ziyatdinov, Andrey; Vázquez-Santiago, Miquel; Brunel, Helena; Martinez-Perez, Angel; Aschard, Hugues; Soria, Jose Manuel

2018-02-27

Quantitative trait locus (QTL) mapping in genetic data often involves analysis of correlated observations, which need to be accounted for to avoid false association signals. This is commonly performed by modeling such correlations as random effects in linear mixed models (LMMs). The R package lme4 is a well-established tool that implements major LMM features using sparse matrix methods; however, it is not fully adapted for QTL mapping association and linkage studies. In particular, two LMM features are lacking in the base version of lme4: the definition of random effects by custom covariance matrices; and parameter constraints, which are essential in advanced QTL models. Apart from applications in linkage studies of related individuals, such functionalities are of high interest for association studies in situations where multiple covariance matrices need to be modeled, a scenario not covered by many genome-wide association study (GWAS) software. To address the aforementioned limitations, we developed a new R package lme4qtl as an extension of lme4. First, lme4qtl contributes new models for genetic studies within a single tool integrated with lme4 and its companion packages. Second, lme4qtl offers a flexible framework for scenarios with multiple levels of relatedness and becomes efficient when covariance matrices are sparse. We showed the value of our package using real family-based data in the Genetic Analysis of Idiopathic Thrombophilia 2 (GAIT2) project. Our software lme4qtl enables QTL mapping models with a versatile structure of random effects and efficient computation for sparse covariances. lme4qtl is available at https://github.com/variani/lme4qtl .

A Sparse Bayesian Approach for Forward-Looking Superresolution Radar Imaging

PubMed Central

Zhang, Yin; Zhang, Yongchao; Huang, Yulin; Yang, Jianyu

2017-01-01

This paper presents a sparse superresolution approach for high cross-range resolution imaging of forward-looking scanning radar based on the Bayesian criterion. First, a novel forward-looking signal model is established as the product of the measurement matrix and the cross-range target distribution, which is more accurate than the conventional convolution model. Then, based on the Bayesian criterion, the widely-used sparse regularization is considered as the penalty term to recover the target distribution. The derivation of the cost function is described, and finally, an iterative expression for minimizing this function is presented. Alternatively, this paper discusses how to estimate the single parameter of Gaussian noise. With the advantage of a more accurate model, the proposed sparse Bayesian approach enjoys a lower model error. Meanwhile, when compared with the conventional superresolution methods, the proposed approach shows high cross-range resolution and small location error. The superresolution results for the simulated point target, scene data, and real measured data are presented to demonstrate the superior performance of the proposed approach. PMID:28604583

Robust extraction of basis functions for simultaneous and proportional myoelectric control via sparse non-negative matrix factorization

NASA Astrophysics Data System (ADS)

Lin, Chuang; Wang, Binghui; Jiang, Ning; Farina, Dario

2018-04-01

Objective. This paper proposes a novel simultaneous and proportional multiple degree of freedom (DOF) myoelectric control method for active prostheses. Approach. The approach is based on non-negative matrix factorization (NMF) of surface EMG signals with the inclusion of sparseness constraints. By applying a sparseness constraint to the control signal matrix, it is possible to extract the basis information from arbitrary movements (quasi-unsupervised approach) for multiple DOFs concurrently. Main Results. In online testing based on target hitting, able-bodied subjects reached a greater throughput (TP) when using sparse NMF (SNMF) than with classic NMF or with linear regression (LR). Accordingly, the completion time (CT) was shorter for SNMF than NMF or LR. The same observations were made in two patients with unilateral limb deficiencies. Significance. The addition of sparseness constraints to NMF allows for a quasi-unsupervised approach to myoelectric control with superior results with respect to previous methods for the simultaneous and proportional control of multi-DOF. The proposed factorization algorithm allows robust simultaneous and proportional control, is superior to previous supervised algorithms, and, because of minimal supervision, paves the way to online adaptation in myoelectric control.

FPGA architecture and implementation of sparse matrix vector multiplication for the finite element method

NASA Astrophysics Data System (ADS)

Elkurdi, Yousef; Fernández, David; Souleimanov, Evgueni; Giannacopoulos, Dennis; Gross, Warren J.

2008-04-01

The Finite Element Method (FEM) is a computationally intensive scientific and engineering analysis tool that has diverse applications ranging from structural engineering to electromagnetic simulation. The trends in floating-point performance are moving in favor of Field-Programmable Gate Arrays (FPGAs), hence increasing interest has grown in the scientific community to exploit this technology. We present an architecture and implementation of an FPGA-based sparse matrix-vector multiplier (SMVM) for use in the iterative solution of large, sparse systems of equations arising from FEM applications. FEM matrices display specific sparsity patterns that can be exploited to improve the efficiency of hardware designs. Our architecture exploits FEM matrix sparsity structure to achieve a balance between performance and hardware resource requirements by relying on external SDRAM for data storage while utilizing the FPGAs computational resources in a stream-through systolic approach. The architecture is based on a pipelined linear array of processing elements (PEs) coupled with a hardware-oriented matrix striping algorithm and a partitioning scheme which enables it to process arbitrarily big matrices without changing the number of PEs in the architecture. Therefore, this architecture is only limited by the amount of external RAM available to the FPGA. The implemented SMVM-pipeline prototype contains 8 PEs and is clocked at 110 MHz obtaining a peak performance of 1.76 GFLOPS. For 8 GB/s of memory bandwidth typical of recent FPGA systems, this architecture can achieve 1.5 GFLOPS sustained performance. Using multiple instances of the pipeline, linear scaling of the peak and sustained performance can be achieved. Our stream-through architecture provides the added advantage of enabling an iterative implementation of the SMVM computation required by iterative solution techniques such as the conjugate gradient method, avoiding initialization time due to data loading and setup inside the FPGA internal memory.

Bit error rate tester using fast parallel generation of linear recurring sequences

DOEpatents

Pierson, Lyndon G.; Witzke, Edward L.; Maestas, Joseph H.

2003-05-06

A fast method for generating linear recurring sequences by parallel linear recurring sequence generators (LRSGs) with a feedback circuit optimized to balance minimum propagation delay against maximal sequence period. Parallel generation of linear recurring sequences requires decimating the sequence (creating small contiguous sections of the sequence in each LRSG). A companion matrix form is selected depending on whether the LFSR is right-shifting or left-shifting. The companion matrix is completed by selecting a primitive irreducible polynomial with 1's most closely grouped in a corner of the companion matrix. A decimation matrix is created by raising the companion matrix to the (n*k).sup.th power, where k is the number of parallel LRSGs and n is the number of bits to be generated at a time by each LRSG. Companion matrices with 1's closely grouped in a corner will yield sparse decimation matrices. A feedback circuit comprised of XOR logic gates implements the decimation matrix in hardware. Sparse decimation matrices can be implemented with minimum number of XOR gates, and therefore a minimum propagation delay through the feedback circuit. The LRSG of the invention is particularly well suited to use as a bit error rate tester on high speed communication lines because it permits the receiver to synchronize to the transmitted pattern within 2n bits.

Energy Efficient Sparse Connectivity from Imbalanced Synaptic Plasticity Rules

PubMed Central

Sacramento, João; Wichert, Andreas; van Rossum, Mark C. W.

2015-01-01

It is believed that energy efficiency is an important constraint in brain evolution. As synaptic transmission dominates energy consumption, energy can be saved by ensuring that only a few synapses are active. It is therefore likely that the formation of sparse codes and sparse connectivity are fundamental objectives of synaptic plasticity. In this work we study how sparse connectivity can result from a synaptic learning rule of excitatory synapses. Information is maximised when potentiation and depression are balanced according to the mean presynaptic activity level and the resulting fraction of zero-weight synapses is around 50%. However, an imbalance towards depression increases the fraction of zero-weight synapses without significantly affecting performance. We show that imbalanced plasticity corresponds to imposing a regularising constraint on the L 1-norm of the synaptic weight vector, a procedure that is well-known to induce sparseness. Imbalanced plasticity is biophysically plausible and leads to more efficient synaptic configurations than a previously suggested approach that prunes synapses after learning. Our framework gives a novel interpretation to the high fraction of silent synapses found in brain regions like the cerebellum. PMID:26046817

Effects of partitioning and scheduling sparse matrix factorization on communication and load balance

NASA Technical Reports Server (NTRS)

Venugopal, Sesh; Naik, Vijay K.

1991-01-01

A block based, automatic partitioning and scheduling methodology is presented for sparse matrix factorization on distributed memory systems. Using experimental results, this technique is analyzed for communication and load imbalance overhead. To study the performance effects, these overheads were compared with those obtained from a straightforward 'wrap mapped' column assignment scheme. All experimental results were obtained using test sparse matrices from the Harwell-Boeing data set. The results show that there is a communication and load balance tradeoff. The block based method results in lower communication cost whereas the wrap mapped scheme gives better load balance.

Scalability improvements to NRLMOL for DFT calculations of large molecules

NASA Astrophysics Data System (ADS)

Diaz, Carlos Manuel

Advances in high performance computing (HPC) have provided a way to treat large, computationally demanding tasks using thousands of processors. With the development of more powerful HPC architectures, the need to create efficient and scalable code has grown more important. Electronic structure calculations are valuable in understanding experimental observations and are routinely used for new materials predictions. For the electronic structure calculations, the memory and computation time are proportional to the number of atoms. Memory requirements for these calculations scale as N2, where N is the number of atoms. While the recent advances in HPC offer platforms with large numbers of cores, the limited amount of memory available on a given node and poor scalability of the electronic structure code hinder their efficient usage of these platforms. This thesis will present some developments to overcome these bottlenecks in order to study large systems. These developments, which are implemented in the NRLMOL electronic structure code, involve the use of sparse matrix storage formats and the use of linear algebra using sparse and distributed matrices. These developments along with other related development now allow ground state density functional calculations using up to 25,000 basis functions and the excited state calculations using up to 17,000 basis functions while utilizing all cores on a node. An example on a light-harvesting triad molecule is described. Finally, future plans to further improve the scalability will be presented.

Response of selected binomial coefficients to varying degrees of matrix sparseness and to matrices with known data interrelationships

USGS Publications Warehouse

Archer, A.W.; Maples, C.G.

1989-01-01

Numerous departures from ideal relationships are revealed by Monte Carlo simulations of widely accepted binomial coefficients. For example, simulations incorporating varying levels of matrix sparseness (presence of zeros indicating lack of data) and computation of expected values reveal that not only are all common coefficients influenced by zero data, but also that some coefficients do not discriminate between sparse or dense matrices (few zero data). Such coefficients computationally merge mutually shared and mutually absent information and do not exploit all the information incorporated within the standard 2 ?? 2 contingency table; therefore, the commonly used formulae for such coefficients are more complicated than the actual range of values produced. Other coefficients do differentiate between mutual presences and absences; however, a number of these coefficients do not demonstrate a linear relationship to matrix sparseness. Finally, simulations using nonrandom matrices with known degrees of row-by-row similarities signify that several coefficients either do not display a reasonable range of values or are nonlinear with respect to known relationships within the data. Analyses with nonrandom matrices yield clues as to the utility of certain coefficients for specific applications. For example, coefficients such as Jaccard, Dice, and Baroni-Urbani and Buser are useful if correction of sparseness is desired, whereas the Russell-Rao coefficient is useful when sparseness correction is not desired. ?? 1989 International Association for Mathematical Geology.

Sparse representation of whole-brain fMRI signals for identification of functional networks.

PubMed

Lv, Jinglei; Jiang, Xi; Li, Xiang; Zhu, Dajiang; Chen, Hanbo; Zhang, Tuo; Zhang, Shu; Hu, Xintao; Han, Junwei; Huang, Heng; Zhang, Jing; Guo, Lei; Liu, Tianming

2015-02-01

There have been several recent studies that used sparse representation for fMRI signal analysis and activation detection based on the assumption that each voxel's fMRI signal is linearly composed of sparse components. Previous studies have employed sparse coding to model functional networks in various modalities and scales. These prior contributions inspired the exploration of whether/how sparse representation can be used to identify functional networks in a voxel-wise way and on the whole brain scale. This paper presents a novel, alternative methodology of identifying multiple functional networks via sparse representation of whole-brain task-based fMRI signals. Our basic idea is that all fMRI signals within the whole brain of one subject are aggregated into a big data matrix, which is then factorized into an over-complete dictionary basis matrix and a reference weight matrix via an effective online dictionary learning algorithm. Our extensive experimental results have shown that this novel methodology can uncover multiple functional networks that can be well characterized and interpreted in spatial, temporal and frequency domains based on current brain science knowledge. Importantly, these well-characterized functional network components are quite reproducible in different brains. In general, our methods offer a novel, effective and unified solution to multiple fMRI data analysis tasks including activation detection, de-activation detection, and functional network identification. Copyright © 2014 Elsevier B.V. All rights reserved.

STRONG ORACLE OPTIMALITY OF FOLDED CONCAVE PENALIZED ESTIMATION.

PubMed

Fan, Jianqing; Xue, Lingzhou; Zou, Hui

2014-06-01

Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To close this important theoretical gap in over a decade, we provide a unified theory to show explicitly how to obtain the oracle solution via the local linear approximation algorithm. For a folded concave penalized estimation problem, we show that as long as the problem is localizable and the oracle estimator is well behaved, we can obtain the oracle estimator by using the one-step local linear approximation. In addition, once the oracle estimator is obtained, the local linear approximation algorithm converges, namely it produces the same estimator in the next iteration. The general theory is demonstrated by using four classical sparse estimation problems, i.e., sparse linear regression, sparse logistic regression, sparse precision matrix estimation and sparse quantile regression.

STRONG ORACLE OPTIMALITY OF FOLDED CONCAVE PENALIZED ESTIMATION

PubMed Central

Fan, Jianqing; Xue, Lingzhou; Zou, Hui

2014-01-01

Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To close this important theoretical gap in over a decade, we provide a unified theory to show explicitly how to obtain the oracle solution via the local linear approximation algorithm. For a folded concave penalized estimation problem, we show that as long as the problem is localizable and the oracle estimator is well behaved, we can obtain the oracle estimator by using the one-step local linear approximation. In addition, once the oracle estimator is obtained, the local linear approximation algorithm converges, namely it produces the same estimator in the next iteration. The general theory is demonstrated by using four classical sparse estimation problems, i.e., sparse linear regression, sparse logistic regression, sparse precision matrix estimation and sparse quantile regression. PMID:25598560

An overview of NSPCG: A nonsymmetric preconditioned conjugate gradient package

NASA Astrophysics Data System (ADS)

Oppe, Thomas C.; Joubert, Wayne D.; Kincaid, David R.

1989-05-01

The most recent research-oriented software package developed as part of the ITPACK Project is called "NSPCG" since it contains many nonsymmetric preconditioned conjugate gradient procedures. It is designed to solve large sparse systems of linear algebraic equations by a variety of different iterative methods. One of the main purposes for the development of the package is to provide a common modular structure for research on iterative methods for nonsymmetric matrices. Another purpose for the development of the package is to investigate the suitability of several iterative methods for vector computers. Since the vectorizability of an iterative method depends greatly on the matrix structure, NSPCG allows great flexibility in the operator representation. The coefficient matrix can be passed in one of several different matrix data storage schemes. These sparse data formats allow matrices with a wide range of structures from highly structured ones such as those with all nonzeros along a relatively small number of diagonals to completely unstructured sparse matrices. Alternatively, the package allows the user to call the accelerators directly with user-supplied routines for performing certain matrix operations. In this case, one can use the data format from an application program and not be required to copy the matrix into one of the package formats. This is particularly advantageous when memory space is limited. Some of the basic preconditioners that are available are point methods such as Jacobi, Incomplete LU Decomposition and Symmetric Successive Overrelaxation as well as block and multicolor preconditioners. The user can select from a large collection of accelerators such as Conjugate Gradient (CG), Chebyshev (SI, for semi-iterative), Generalized Minimal Residual (GMRES), Biconjugate Gradient Squared (BCGS) and many others. The package is modular so that almost any accelerator can be used with almost any preconditioner.

A Digital Compressed Sensing-Based Energy-Efficient Single-Spot Bluetooth ECG Node

PubMed Central

Cai, Zhipeng; Zou, Fumin; Zhang, Xiangyu

2018-01-01

Energy efficiency is still the obstacle for long-term real-time wireless ECG monitoring. In this paper, a digital compressed sensing- (CS-) based single-spot Bluetooth ECG node is proposed to deal with the challenge in wireless ECG application. A periodic sleep/wake-up scheme and a CS-based compression algorithm are implemented in a node, which consists of ultra-low-power analog front-end, microcontroller, Bluetooth 4.0 communication module, and so forth. The efficiency improvement and the node's specifics are evidenced by the experiments using the ECG signals sampled by the proposed node under daily activities of lay, sit, stand, walk, and run. Under using sparse binary matrix (SBM), block sparse Bayesian learning (BSBL) method, and discrete cosine transform (DCT) basis, all ECG signals were essentially undistorted recovered with root-mean-square differences (PRDs) which are less than 6%. The proposed sleep/wake-up scheme and data compression can reduce the airtime over energy-hungry wireless links, the energy consumption of proposed node is 6.53 mJ, and the energy consumption of radio decreases 77.37%. Moreover, the energy consumption increase caused by CS code execution is negligible, which is 1.3% of the total energy consumption. PMID:29599945

A Digital Compressed Sensing-Based Energy-Efficient Single-Spot Bluetooth ECG Node.

PubMed

Luo, Kan; Cai, Zhipeng; Du, Keqin; Zou, Fumin; Zhang, Xiangyu; Li, Jianqing

2018-01-01

Energy efficiency is still the obstacle for long-term real-time wireless ECG monitoring. In this paper, a digital compressed sensing- (CS-) based single-spot Bluetooth ECG node is proposed to deal with the challenge in wireless ECG application. A periodic sleep/wake-up scheme and a CS-based compression algorithm are implemented in a node, which consists of ultra-low-power analog front-end, microcontroller, Bluetooth 4.0 communication module, and so forth. The efficiency improvement and the node's specifics are evidenced by the experiments using the ECG signals sampled by the proposed node under daily activities of lay, sit, stand, walk, and run. Under using sparse binary matrix (SBM), block sparse Bayesian learning (BSBL) method, and discrete cosine transform (DCT) basis, all ECG signals were essentially undistorted recovered with root-mean-square differences (PRDs) which are less than 6%. The proposed sleep/wake-up scheme and data compression can reduce the airtime over energy-hungry wireless links, the energy consumption of proposed node is 6.53 mJ, and the energy consumption of radio decreases 77.37%. Moreover, the energy consumption increase caused by CS code execution is negligible, which is 1.3% of the total energy consumption.

Automatic segmentation of right ventricle on ultrasound images using sparse matrix transform and level set

NASA Astrophysics Data System (ADS)

Qin, Xulei; Cong, Zhibin; Halig, Luma V.; Fei, Baowei

2013-03-01

An automatic framework is proposed to segment right ventricle on ultrasound images. This method can automatically segment both epicardial and endocardial boundaries from a continuous echocardiography series by combining sparse matrix transform (SMT), a training model, and a localized region based level set. First, the sparse matrix transform extracts main motion regions of myocardium as eigenimages by analyzing statistical information of these images. Second, a training model of right ventricle is registered to the extracted eigenimages in order to automatically detect the main location of the right ventricle and the corresponding transform relationship between the training model and the SMT-extracted results in the series. Third, the training model is then adjusted as an adapted initialization for the segmentation of each image in the series. Finally, based on the adapted initializations, a localized region based level set algorithm is applied to segment both epicardial and endocardial boundaries of the right ventricle from the whole series. Experimental results from real subject data validated the performance of the proposed framework in segmenting right ventricle from echocardiography. The mean Dice scores for both epicardial and endocardial boundaries are 89.1%+/-2.3% and 83.6+/-7.3%, respectively. The automatic segmentation method based on sparse matrix transform and level set can provide a useful tool for quantitative cardiac imaging.

Adaptive regulation of sparseness by feedforward inhibition

PubMed Central

Assisi, Collins; Stopfer, Mark; Laurent, Gilles; Bazhenov, Maxim

2014-01-01

In the mushroom body of insects, odors are represented by very few spikes in a small number of neurons, a highly efficient strategy known as sparse coding. Physiological studies of these neurons have shown that sparseness is maintained across thousand-fold changes in odor concentration. Using a realistic computational model, we propose that sparseness in the olfactory system is regulated by adaptive feedforward inhibition. When odor concentration changes, feedforward inhibition modulates the duration of the temporal window over which the mushroom body neurons may integrate excitatory presynaptic input. This simple adaptive mechanism could maintain the sparseness of sensory representations across wide ranges of stimulus conditions. PMID:17660812

Aztec user`s guide. Version 1

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hutchinson, S.A.; Shadid, J.N.; Tuminaro, R.S.

1995-10-01

Aztec is an iterative library that greatly simplifies the parallelization process when solving the linear systems of equations Ax = b where A is a user supplied n x n sparse matrix, b is a user supplied vector of length n and x is a vector of length n to be computed. Aztec is intended as a software tool for users who want to avoid cumbersome parallel programming details but who have large sparse linear systems which require an efficiently utilized parallel processing system. A collection of data transformation tools are provided that allow for easy creation of distributed sparsemore » unstructured matrices for parallel solution. Once the distributed matrix is created, computation can be performed on any of the parallel machines running Aztec: nCUBE 2, IBM SP2 and Intel Paragon, MPI platforms as well as standard serial and vector platforms. Aztec includes a number of Krylov iterative methods such as conjugate gradient (CG), generalized minimum residual (GMRES) and stabilized biconjugate gradient (BICGSTAB) to solve systems of equations. These Krylov methods are used in conjunction with various preconditioners such as polynomial or domain decomposition methods using LU or incomplete LU factorizations within subdomains. Although the matrix A can be general, the package has been designed for matrices arising from the approximation of partial differential equations (PDEs). In particular, the Aztec package is oriented toward systems arising from PDE applications.« less

Symmetrized density matrix renormalization group algorithm for low-lying excited states of conjugated carbon systems: Application to 1,12-benzoperylene and polychrysene

NASA Astrophysics Data System (ADS)

Prodhan, Suryoday; Ramasesha, S.

2018-05-01

The symmetry adapted density matrix renormalization group (SDMRG) technique has been an efficient method for studying low-lying eigenstates in one- and quasi-one-dimensional electronic systems. However, the SDMRG method had bottlenecks involving the construction of linearly independent symmetry adapted basis states as the symmetry matrices in the DMRG basis were not sparse. We have developed a modified algorithm to overcome this bottleneck. The new method incorporates end-to-end interchange symmetry (C2) , electron-hole symmetry (J ) , and parity or spin-flip symmetry (P ) in these calculations. The one-to-one correspondence between direct-product basis states in the DMRG Hilbert space for these symmetry operations renders the symmetry matrices in the new basis with maximum sparseness, just one nonzero matrix element per row. Using methods similar to those employed in the exact diagonalization technique for Pariser-Parr-Pople (PPP) models, developed in the 1980s, it is possible to construct orthogonal SDMRG basis states while bypassing the slow step of the Gram-Schmidt orthonormalization procedure. The method together with the PPP model which incorporates long-range electronic correlations is employed to study the correlated excited-state spectra of 1,12-benzoperylene and a narrow mixed graphene nanoribbon with a chrysene molecule as the building unit, comprising both zigzag and cove-edge structures.

Fast super-resolution estimation of DOA and DOD in bistatic MIMO Radar with off-grid targets

NASA Astrophysics Data System (ADS)

Zhang, Dong; Zhang, Yongshun; Zheng, Guimei; Feng, Cunqian; Tang, Jun

2018-05-01

In this paper, we focus on the problem of joint DOA and DOD estimation in Bistatic MIMO Radar using sparse reconstruction method. In traditional ways, we usually convert the 2D parameter estimation problem into 1D parameter estimation problem by Kronecker product which will enlarge the scale of the parameter estimation problem and bring more computational burden. Furthermore, it requires that the targets must fall on the predefined grids. In this paper, a 2D-off-grid model is built which can solve the grid mismatch problem of 2D parameters estimation. Then in order to solve the joint 2D sparse reconstruction problem directly and efficiently, three kinds of fast joint sparse matrix reconstruction methods are proposed which are Joint-2D-OMP algorithm, Joint-2D-SL0 algorithm and Joint-2D-SOONE algorithm. Simulation results demonstrate that our methods not only can improve the 2D parameter estimation accuracy but also reduce the computational complexity compared with the traditional Kronecker Compressed Sensing method.

Linear-scaling density-functional simulations of charged point defects in Al2O3 using hierarchical sparse matrix algebra.

PubMed

Hine, N D M; Haynes, P D; Mostofi, A A; Payne, M C

2010-09-21

We present calculations of formation energies of defects in an ionic solid (Al(2)O(3)) extrapolated to the dilute limit, corresponding to a simulation cell of infinite size. The large-scale calculations required for this extrapolation are enabled by developments in the approach to parallel sparse matrix algebra operations, which are central to linear-scaling density-functional theory calculations. The computational cost of manipulating sparse matrices, whose sizes are determined by the large number of basis functions present, is greatly improved with this new approach. We present details of the sparse algebra scheme implemented in the ONETEP code using hierarchical sparsity patterns, and demonstrate its use in calculations on a wide range of systems, involving thousands of atoms on hundreds to thousands of parallel processes.

Characterizing and differentiating task-based and resting state fMRI signals via two-stage sparse representations.

PubMed

Zhang, Shu; Li, Xiang; Lv, Jinglei; Jiang, Xi; Guo, Lei; Liu, Tianming

2016-03-01

A relatively underexplored question in fMRI is whether there are intrinsic differences in terms of signal composition patterns that can effectively characterize and differentiate task-based or resting state fMRI (tfMRI or rsfMRI) signals. In this paper, we propose a novel two-stage sparse representation framework to examine the fundamental difference between tfMRI and rsfMRI signals. Specifically, in the first stage, the whole-brain tfMRI or rsfMRI signals of each subject were composed into a big data matrix, which was then factorized into a subject-specific dictionary matrix and a weight coefficient matrix for sparse representation. In the second stage, all of the dictionary matrices from both tfMRI/rsfMRI data across multiple subjects were composed into another big data-matrix, which was further sparsely represented by a cross-subjects common dictionary and a weight matrix. This framework has been applied on the recently publicly released Human Connectome Project (HCP) fMRI data and experimental results revealed that there are distinctive and descriptive atoms in the cross-subjects common dictionary that can effectively characterize and differentiate tfMRI and rsfMRI signals, achieving 100% classification accuracy. Moreover, our methods and results can be meaningfully interpreted, e.g., the well-known default mode network (DMN) activities can be recovered from the very noisy and heterogeneous aggregated big-data of tfMRI and rsfMRI signals across all subjects in HCP Q1 release.

A General Sparse Tensor Framework for Electronic Structure Theory

DOE PAGES

Manzer, Samuel; Epifanovsky, Evgeny; Krylov, Anna I.; ...

2017-01-24

Linear-scaling algorithms must be developed in order to extend the domain of applicability of electronic structure theory to molecules of any desired size. But, the increasing complexity of modern linear-scaling methods makes code development and maintenance a significant challenge. A major contributor to this difficulty is the lack of robust software abstractions for handling block-sparse tensor operations. We therefore report the development of a highly efficient symbolic block-sparse tensor library in order to provide access to high-level software constructs to treat such problems. Our implementation supports arbitrary multi-dimensional sparsity in all input and output tensors. We then avoid cumbersome machine-generatedmore » code by implementing all functionality as a high-level symbolic C++ language library and demonstrate that our implementation attains very high performance for linear-scaling sparse tensor contractions.« less

Task-driven dictionary learning.

PubMed

Mairal, Julien; Bach, Francis; Ponce, Jean

2012-04-01

Modeling data with linear combinations of a few elements from a learned dictionary has been the focus of much recent research in machine learning, neuroscience, and signal processing. For signals such as natural images that admit such sparse representations, it is now well established that these models are well suited to restoration tasks. In this context, learning the dictionary amounts to solving a large-scale matrix factorization problem, which can be done efficiently with classical optimization tools. The same approach has also been used for learning features from data for other purposes, e.g., image classification, but tuning the dictionary in a supervised way for these tasks has proven to be more difficult. In this paper, we present a general formulation for supervised dictionary learning adapted to a wide variety of tasks, and present an efficient algorithm for solving the corresponding optimization problem. Experiments on handwritten digit classification, digital art identification, nonlinear inverse image problems, and compressed sensing demonstrate that our approach is effective in large-scale settings, and is well suited to supervised and semi-supervised classification, as well as regression tasks for data that admit sparse representations.

Sparse matrix methods research using the CSM testbed software system

NASA Technical Reports Server (NTRS)

Chu, Eleanor; George, J. Alan

1989-01-01

Research is described on sparse matrix techniques for the Computational Structural Mechanics (CSM) Testbed. The primary objective was to compare the performance of state-of-the-art techniques for solving sparse systems with those that are currently available in the CSM Testbed. Thus, one of the first tasks was to become familiar with the structure of the testbed, and to install some or all of the SPARSPAK package in the testbed. A suite of subroutines to extract from the data base the relevant structural and numerical information about the matrix equations was written, and all the demonstration problems distributed with the testbed were successfully solved. These codes were documented, and performance studies comparing the SPARSPAK technology to the methods currently in the testbed were completed. In addition, some preliminary studies were done comparing some recently developed out-of-core techniques with the performance of the testbed processor INV.

A tight and explicit representation of Q in sparse QR factorization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ng, E.G.; Peyton, B.W.

1992-05-01

In QR factorization of a sparse m{times}n matrix A (m {ge} n) the orthogonal factor Q is often stored implicitly as a lower trapezoidal matrix H known as the Householder matrix. This paper presents a simple characterization of the row structure of Q, which could be used as the basis for a sparse data structure that can store Q explicitly. The new characterization is a simple extension of a well known row-oriented characterization of the structure of H. Hare, Johnson, Olesky, and van den Driessche have recently provided a complete sparsity analysis of the QR factorization. Let U be themore » matrix consisting of the first n columns of Q. Using results from, we show that the data structures for H and U resulting from our characterizations are tight when A is a strong Hall matrix. We also show that H and the lower trapezoidal part of U have the same sparsity characterization when A is strong Hall. We then show that this characterization can be extended to any weak Hall matrix that has been permuted into block upper triangular form. Finally, we show that permuting to block triangular form never increases the fill incurred during the factorization.« less

DNA melting profiles from a matrix method.

PubMed

Poland, Douglas

2004-02-05

In this article we give a new method for the calculation of DNA melting profiles. Based on the matrix formulation of the DNA partition function, the method relies for its efficiency on the fact that the required matrices are very sparse, essentially reducing matrix multiplication to vector multiplication and thus making the computer time required to treat a DNA molecule containing N base pairs proportional to N(2). A key ingredient in the method is the result that multiplication by the inverse matrix can also be reduced to vector multiplication. The task of calculating the melting profile for the entire genome is further reduced by treating regions of the molecule between helix-plateaus, thus breaking the molecule up into independent parts that can each be treated individually. The method is easily modified to incorporate changes in the assignment of statistical weights to the different structural features of DNA. We illustrate the method using the genome of Haemophilus influenzae. Copyright 2003 Wiley Periodicals, Inc.

Preconditioned conjugate gradient wave-front reconstructors for multiconjugate adaptive optics

NASA Astrophysics Data System (ADS)

Gilles, Luc; Ellerbroek, Brent L.; Vogel, Curtis R.

2003-09-01

Multiconjugate adaptive optics (MCAO) systems with 104-105 degrees of freedom have been proposed for future giant telescopes. Using standard matrix methods to compute, optimize, and implement wave-front control algorithms for these systems is impractical, since the number of calculations required to compute and apply the reconstruction matrix scales respectively with the cube and the square of the number of adaptive optics degrees of freedom. We develop scalable open-loop iterative sparse matrix implementations of minimum variance wave-front reconstruction for telescope diameters up to 32 m with more than 104 actuators. The basic approach is the preconditioned conjugate gradient method with an efficient preconditioner, whose block structure is defined by the atmospheric turbulent layers very much like the layer-oriented MCAO algorithms of current interest. Two cost-effective preconditioners are investigated: a multigrid solver and a simpler block symmetric Gauss-Seidel (BSGS) sweep. Both options require off-line sparse Cholesky factorizations of the diagonal blocks of the matrix system. The cost to precompute these factors scales approximately as the three-halves power of the number of estimated phase grid points per atmospheric layer, and their average update rate is typically of the order of 10-2 Hz, i.e., 4-5 orders of magnitude lower than the typical 103 Hz temporal sampling rate. All other computations scale almost linearly with the total number of estimated phase grid points. We present numerical simulation results to illustrate algorithm convergence. Convergence rates of both preconditioners are similar, regardless of measurement noise level, indicating that the layer-oriented BSGS sweep is as effective as the more elaborated multiresolution preconditioner.

An efficient dictionary learning algorithm and its application to 3-D medical image denoising.

PubMed

Li, Shutao; Fang, Leyuan; Yin, Haitao

2012-02-01

In this paper, we propose an efficient dictionary learning algorithm for sparse representation of given data and suggest a way to apply this algorithm to 3-D medical image denoising. Our learning approach is composed of two main parts: sparse coding and dictionary updating. On the sparse coding stage, an efficient algorithm named multiple clusters pursuit (MCP) is proposed. The MCP first applies a dictionary structuring strategy to cluster the atoms with high coherence together, and then employs a multiple-selection strategy to select several competitive atoms at each iteration. These two strategies can greatly reduce the computation complexity of the MCP and assist it to obtain better sparse solution. On the dictionary updating stage, the alternating optimization that efficiently approximates the singular value decomposition is introduced. Furthermore, in the 3-D medical image denoising application, a joint 3-D operation is proposed for taking the learning capabilities of the presented algorithm to simultaneously capture the correlations within each slice and correlations across the nearby slices, thereby obtaining better denoising results. The experiments on both synthetically generated data and real 3-D medical images demonstrate that the proposed approach has superior performance compared to some well-known methods. © 2011 IEEE

Finite difference method accelerated with sparse solvers for structural analysis of the metal-organic complexes

NASA Astrophysics Data System (ADS)

Guda, A. A.; Guda, S. A.; Soldatov, M. A.; Lomachenko, K. A.; Bugaev, A. L.; Lamberti, C.; Gawelda, W.; Bressler, C.; Smolentsev, G.; Soldatov, A. V.; Joly, Y.

2016-05-01

Finite difference method (FDM) implemented in the FDMNES software [Phys. Rev. B, 2001, 63, 125120] was revised. Thorough analysis shows, that the calculated diagonal in the FDM matrix consists of about 96% zero elements. Thus a sparse solver would be more suitable for the problem instead of traditional Gaussian elimination for the diagonal neighbourhood. We have tried several iterative sparse solvers and the direct one MUMPS solver with METIS ordering turned out to be the best. Compared to the Gaussian solver present method is up to 40 times faster and allows XANES simulations for complex systems already on personal computers. We show applicability of the software for metal-organic [Fe(bpy)3]2+ complex both for low spin and high spin states populated after laser excitation.

GPU-accelerated Modeling and Element-free Reverse-time Migration with Gauss Points Partition

NASA Astrophysics Data System (ADS)

Zhen, Z.; Jia, X.

2014-12-01

Element-free method (EFM) has been applied to seismic modeling and migration. Compared with finite element method (FEM) and finite difference method (FDM), it is much cheaper and more flexible because only the information of the nodes and the boundary of the study area are required in computation. In the EFM, the number of Gauss points should be consistent with the number of model nodes; otherwise the accuracy of the intermediate coefficient matrices would be harmed. Thus when we increase the nodes of velocity model in order to obtain higher resolution, we find that the size of the computer's memory will be a bottleneck. The original EFM can deal with at most 81×81 nodes in the case of 2G memory, as tested by Jia and Hu (2006). In order to solve the problem of storage and computation efficiency, we propose a concept of Gauss points partition (GPP), and utilize the GPUs to improve the computation efficiency. Considering the characteristics of the Gaussian points, the GPP method doesn't influence the propagation of seismic wave in the velocity model. To overcome the time-consuming computation of the stiffness matrix (K) and the mass matrix (M), we also use the GPUs in our computation program. We employ the compressed sparse row (CSR) format to compress the intermediate sparse matrices and try to simplify the operations by solving the linear equations with the CULA Sparse's Conjugate Gradient (CG) solver instead of the linear sparse solver 'PARDISO'. It is observed that our strategy can significantly reduce the computational time of K and Mcompared with the algorithm based on CPU. The model tested is Marmousi model. The length of the model is 7425m and the depth is 2990m. We discretize the model with 595x298 nodes, 300x300 Gauss cells and 3x3 Gauss points in each cell. In contrast to the computational time of the conventional EFM, the GPUs-GPP approach can substantially improve the efficiency. The speedup ratio of time consumption of computing K, M is 120 and the speedup ratio time consumption of RTM is 11.5. At the same time, the accuracy of imaging is not harmed. Another advantage of the GPUs-GPP method is its easy applications in other numerical methods such as the FEM. Finally, in the GPUs-GPP method, the arrays require quite limited memory storage, which makes the method promising in dealing with large-scale 3D problems.

Fast Solution in Sparse LDA for Binary Classification

NASA Technical Reports Server (NTRS)

Moghaddam, Baback

2010-01-01

An algorithm that performs sparse linear discriminant analysis (Sparse-LDA) finds near-optimal solutions in far less time than the prior art when specialized to binary classification (of 2 classes). Sparse-LDA is a type of feature- or variable- selection problem with numerous applications in statistics, machine learning, computer vision, computational finance, operations research, and bio-informatics. Because of its combinatorial nature, feature- or variable-selection problems are NP-hard or computationally intractable in cases involving more than 30 variables or features. Therefore, one typically seeks approximate solutions by means of greedy search algorithms. The prior Sparse-LDA algorithm was a greedy algorithm that considered the best variable or feature to add/ delete to/ from its subsets in order to maximally discriminate between multiple classes of data. The present algorithm is designed for the special but prevalent case of 2-class or binary classification (e.g. 1 vs. 0, functioning vs. malfunctioning, or change versus no change). The present algorithm provides near-optimal solutions on large real-world datasets having hundreds or even thousands of variables or features (e.g. selecting the fewest wavelength bands in a hyperspectral sensor to do terrain classification) and does so in typical computation times of minutes as compared to days or weeks as taken by the prior art. Sparse LDA requires solving generalized eigenvalue problems for a large number of variable subsets (represented by the submatrices of the input within-class and between-class covariance matrices). In the general (fullrank) case, the amount of computation scales at least cubically with the number of variables and thus the size of the problems that can be solved is limited accordingly. However, in binary classification, the principal eigenvalues can be found using a special analytic formula, without resorting to costly iterative techniques. The present algorithm exploits this analytic form along with the inherent sequential nature of greedy search itself. Together this enables the use of highly-efficient partitioned-matrix-inverse techniques that result in large speedups of computation in both the forward-selection and backward-elimination stages of greedy algorithms in general.

Efficient Storage Scheme of Covariance Matrix during Inverse Modeling

NASA Astrophysics Data System (ADS)

Mao, D.; Yeh, T. J.

2013-12-01

During stochastic inverse modeling, the covariance matrix of geostatistical based methods carries the information about the geologic structure. Its update during iterations reflects the decrease of uncertainty with the incorporation of observed data. For large scale problem, its storage and update cost too much memory and computational resources. In this study, we propose a new efficient storage scheme for storage and update. Compressed Sparse Column (CSC) format is utilized to storage the covariance matrix, and users can assign how many data they prefer to store based on correlation scales since the data beyond several correlation scales are usually not very informative for inverse modeling. After every iteration, only the diagonal terms of the covariance matrix are updated. The off diagonal terms are calculated and updated based on shortened correlation scales with a pre-assigned exponential model. The correlation scales are shortened by a coefficient, i.e. 0.95, every iteration to show the decrease of uncertainty. There is no universal coefficient for all the problems and users are encouraged to try several times. This new scheme is tested with 1D examples first. The estimated results and uncertainty are compared with the traditional full storage method. In the end, a large scale numerical model is utilized to validate this new scheme.

Discrete Kalman filtering equations of second-order form for control-structure interaction simulations

NASA Technical Reports Server (NTRS)

Park, K. C.; Alvin, K. F.; Belvin, W. Keith

1991-01-01

A second-order form of discrete Kalman filtering equations is proposed as a candidate state estimator for efficient simulations of control-structure interactions in coupled physical coordinate configurations as opposed to decoupled modal coordinates. The resulting matrix equation of the present state estimator consists of the same symmetric, sparse N x N coupled matrices of the governing structural dynamics equations as opposed to unsymmetric 2N x 2N state space-based estimators. Thus, in addition to substantial computational efficiency improvement, the present estimator can be applied to control-structure design optimization for which the physical coordinates associated with the mass, damping and stiffness matrices of the structure are needed instead of modal coordinates.

Collaborative sparse priors for multi-view ATR

NASA Astrophysics Data System (ADS)

Li, Xuelu; Monga, Vishal

2018-04-01

Recent work has seen a surge of sparse representation based classification (SRC) methods applied to automatic target recognition problems. While traditional SRC approaches used l0 or l1 norm to quantify sparsity, spike and slab priors have established themselves as the gold standard for providing general tunable sparse structures on vectors. In this work, we employ collaborative spike and slab priors that can be applied to matrices to encourage sparsity for the problem of multi-view ATR. That is, target images captured from multiple views are expanded in terms of a training dictionary multiplied with a coefficient matrix. Ideally, for a test image set comprising of multiple views of a target, coefficients corresponding to its identifying class are expected to be active, while others should be zero, i.e. the coefficient matrix is naturally sparse. We develop a new approach to solve the optimization problem that estimates the sparse coefficient matrix jointly with the sparsity inducing parameters in the collaborative prior. ATR problems are investigated on the mid-wave infrared (MWIR) database made available by the US Army Night Vision and Electronic Sensors Directorate, which has a rich collection of views. Experimental results show that the proposed joint prior and coefficient estimation method (JPCEM) can: 1.) enable improved accuracy when multiple views vs. a single one are invoked, and 2.) outperform state of the art alternatives particularly when training imagery is limited.

Sparse Bayesian learning for DOA estimation with mutual coupling.

PubMed

Dai, Jisheng; Hu, Nan; Xu, Weichao; Chang, Chunqi

2015-10-16

Sparse Bayesian learning (SBL) has given renewed interest to the problem of direction-of-arrival (DOA) estimation. It is generally assumed that the measurement matrix in SBL is precisely known. Unfortunately, this assumption may be invalid in practice due to the imperfect manifold caused by unknown or misspecified mutual coupling. This paper describes a modified SBL method for joint estimation of DOAs and mutual coupling coefficients with uniform linear arrays (ULAs). Unlike the existing method that only uses stationary priors, our new approach utilizes a hierarchical form of the Student t prior to enforce the sparsity of the unknown signal more heavily. We also provide a distinct Bayesian inference for the expectation-maximization (EM) algorithm, which can update the mutual coupling coefficients more efficiently. Another difference is that our method uses an additional singular value decomposition (SVD) to reduce the computational complexity of the signal reconstruction process and the sensitivity to the measurement noise.

Efficient Transition Probability Computation for Continuous-Time Branching Processes via Compressed Sensing.

PubMed

Xu, Jason; Minin, Vladimir N

2015-07-01

Branching processes are a class of continuous-time Markov chains (CTMCs) with ubiquitous applications. A general difficulty in statistical inference under partially observed CTMC models arises in computing transition probabilities when the discrete state space is large or uncountable. Classical methods such as matrix exponentiation are infeasible for large or countably infinite state spaces, and sampling-based alternatives are computationally intensive, requiring integration over all possible hidden events. Recent work has successfully applied generating function techniques to computing transition probabilities for linear multi-type branching processes. While these techniques often require significantly fewer computations than matrix exponentiation, they also become prohibitive in applications with large populations. We propose a compressed sensing framework that significantly accelerates the generating function method, decreasing computational cost up to a logarithmic factor by only assuming the probability mass of transitions is sparse. We demonstrate accurate and efficient transition probability computations in branching process models for blood cell formation and evolution of self-replicating transposable elements in bacterial genomes.

Efficient Transition Probability Computation for Continuous-Time Branching Processes via Compressed Sensing

PubMed Central

Xu, Jason; Minin, Vladimir N.

2016-01-01

Branching processes are a class of continuous-time Markov chains (CTMCs) with ubiquitous applications. A general difficulty in statistical inference under partially observed CTMC models arises in computing transition probabilities when the discrete state space is large or uncountable. Classical methods such as matrix exponentiation are infeasible for large or countably infinite state spaces, and sampling-based alternatives are computationally intensive, requiring integration over all possible hidden events. Recent work has successfully applied generating function techniques to computing transition probabilities for linear multi-type branching processes. While these techniques often require significantly fewer computations than matrix exponentiation, they also become prohibitive in applications with large populations. We propose a compressed sensing framework that significantly accelerates the generating function method, decreasing computational cost up to a logarithmic factor by only assuming the probability mass of transitions is sparse. We demonstrate accurate and efficient transition probability computations in branching process models for blood cell formation and evolution of self-replicating transposable elements in bacterial genomes. PMID:26949377

Multi-GPU implementation of a VMAT treatment plan optimization algorithm

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tian, Zhen, E-mail: Zhen.Tian@UTSouthwestern.edu, E-mail: Xun.Jia@UTSouthwestern.edu, E-mail: Steve.Jiang@UTSouthwestern.edu; Folkerts, Michael; Tan, Jun

Purpose: Volumetric modulated arc therapy (VMAT) optimization is a computationally challenging problem due to its large data size, high degrees of freedom, and many hardware constraints. High-performance graphics processing units (GPUs) have been used to speed up the computations. However, GPU’s relatively small memory size cannot handle cases with a large dose-deposition coefficient (DDC) matrix in cases of, e.g., those with a large target size, multiple targets, multiple arcs, and/or small beamlet size. The main purpose of this paper is to report an implementation of a column-generation-based VMAT algorithm, previously developed in the authors’ group, on a multi-GPU platform tomore » solve the memory limitation problem. While the column-generation-based VMAT algorithm has been previously developed, the GPU implementation details have not been reported. Hence, another purpose is to present detailed techniques employed for GPU implementation. The authors also would like to utilize this particular problem as an example problem to study the feasibility of using a multi-GPU platform to solve large-scale problems in medical physics. Methods: The column-generation approach generates VMAT apertures sequentially by solving a pricing problem (PP) and a master problem (MP) iteratively. In the authors’ method, the sparse DDC matrix is first stored on a CPU in coordinate list format (COO). On the GPU side, this matrix is split into four submatrices according to beam angles, which are stored on four GPUs in compressed sparse row format. Computation of beamlet price, the first step in PP, is accomplished using multi-GPUs. A fast inter-GPU data transfer scheme is accomplished using peer-to-peer access. The remaining steps of PP and MP problems are implemented on CPU or a single GPU due to their modest problem scale and computational loads. Barzilai and Borwein algorithm with a subspace step scheme is adopted here to solve the MP problem. A head and neck (H and N) cancer case is then used to validate the authors’ method. The authors also compare their multi-GPU implementation with three different single GPU implementation strategies, i.e., truncating DDC matrix (S1), repeatedly transferring DDC matrix between CPU and GPU (S2), and porting computations involving DDC matrix to CPU (S3), in terms of both plan quality and computational efficiency. Two more H and N patient cases and three prostate cases are used to demonstrate the advantages of the authors’ method. Results: The authors’ multi-GPU implementation can finish the optimization process within ∼1 min for the H and N patient case. S1 leads to an inferior plan quality although its total time was 10 s shorter than the multi-GPU implementation due to the reduced matrix size. S2 and S3 yield the same plan quality as the multi-GPU implementation but take ∼4 and ∼6 min, respectively. High computational efficiency was consistently achieved for the other five patient cases tested, with VMAT plans of clinically acceptable quality obtained within 23–46 s. Conversely, to obtain clinically comparable or acceptable plans for all six of these VMAT cases that the authors have tested in this paper, the optimization time needed in a commercial TPS system on CPU was found to be in an order of several minutes. Conclusions: The results demonstrate that the multi-GPU implementation of the authors’ column-generation-based VMAT optimization can handle the large-scale VMAT optimization problem efficiently without sacrificing plan quality. The authors’ study may serve as an example to shed some light on other large-scale medical physics problems that require multi-GPU techniques.« less

Solving large tomographic linear systems: size reduction and error estimation

NASA Astrophysics Data System (ADS)

Voronin, Sergey; Mikesell, Dylan; Slezak, Inna; Nolet, Guust

2014-10-01

We present a new approach to reduce a sparse, linear system of equations associated with tomographic inverse problems. We begin by making a modification to the commonly used compressed sparse-row format, whereby our format is tailored to the sparse structure of finite-frequency (volume) sensitivity kernels in seismic tomography. Next, we cluster the sparse matrix rows to divide a large matrix into smaller subsets representing ray paths that are geographically close. Singular value decomposition of each subset allows us to project the data onto a subspace associated with the largest eigenvalues of the subset. After projection we reject those data that have a signal-to-noise ratio (SNR) below a chosen threshold. Clustering in this way assures that the sparse nature of the system is minimally affected by the projection. Moreover, our approach allows for a precise estimation of the noise affecting the data while also giving us the ability to identify outliers. We illustrate the method by reducing large matrices computed for global tomographic systems with cross-correlation body wave delays, as well as with surface wave phase velocity anomalies. For a massive matrix computed for 3.7 million Rayleigh wave phase velocity measurements, imposing a threshold of 1 for the SNR, we condensed the matrix size from 1103 to 63 Gbyte. For a global data set of multiple-frequency P wave delays from 60 well-distributed deep earthquakes we obtain a reduction to 5.9 per cent. This type of reduction allows one to avoid loss of information due to underparametrizing models. Alternatively, if data have to be rejected to fit the system into computer memory, it assures that the most important data are preserved.

Discriminative Transfer Subspace Learning via Low-Rank and Sparse Representation.

PubMed

Xu, Yong; Fang, Xiaozhao; Wu, Jian; Li, Xuelong; Zhang, David

2016-02-01

In this paper, we address the problem of unsupervised domain transfer learning in which no labels are available in the target domain. We use a transformation matrix to transfer both the source and target data to a common subspace, where each target sample can be represented by a combination of source samples such that the samples from different domains can be well interlaced. In this way, the discrepancy of the source and target domains is reduced. By imposing joint low-rank and sparse constraints on the reconstruction coefficient matrix, the global and local structures of data can be preserved. To enlarge the margins between different classes as much as possible and provide more freedom to diminish the discrepancy, a flexible linear classifier (projection) is obtained by learning a non-negative label relaxation matrix that allows the strict binary label matrix to relax into a slack variable matrix. Our method can avoid a potentially negative transfer by using a sparse matrix to model the noise and, thus, is more robust to different types of noise. We formulate our problem as a constrained low-rankness and sparsity minimization problem and solve it by the inexact augmented Lagrange multiplier method. Extensive experiments on various visual domain adaptation tasks show the superiority of the proposed method over the state-of-the art methods. The MATLAB code of our method will be publicly available at http://www.yongxu.org/lunwen.html.

Improved analysis of SP and CoSaMP under total perturbations

NASA Astrophysics Data System (ADS)

Li, Haifeng

2016-12-01

Practically, in the underdetermined model y= A x, where x is a K sparse vector (i.e., it has no more than K nonzero entries), both y and A could be totally perturbed. A more relaxed condition means less number of measurements are needed to ensure the sparse recovery from theoretical aspect. In this paper, based on restricted isometry property (RIP), for subspace pursuit (SP) and compressed sampling matching pursuit (CoSaMP), two relaxed sufficient conditions are presented under total perturbations to guarantee that the sparse vector x is recovered. Taking random matrix as measurement matrix, we also discuss the advantage of our condition. Numerical experiments validate that SP and CoSaMP can provide oracle-order recovery performance.

Multi-energy CT based on a prior rank, intensity and sparsity model (PRISM).

PubMed

Gao, Hao; Yu, Hengyong; Osher, Stanley; Wang, Ge

2011-11-01

We propose a compressive sensing approach for multi-energy computed tomography (CT), namely the prior rank, intensity and sparsity model (PRISM). To further compress the multi-energy image for allowing the reconstruction with fewer CT data and less radiation dose, the PRISM models a multi-energy image as the superposition of a low-rank matrix and a sparse matrix (with row dimension in space and column dimension in energy), where the low-rank matrix corresponds to the stationary background over energy that has a low matrix rank, and the sparse matrix represents the rest of distinct spectral features that are often sparse. Distinct from previous methods, the PRISM utilizes the generalized rank, e.g., the matrix rank of tight-frame transform of a multi-energy image, which offers a way to characterize the multi-level and multi-filtered image coherence across the energy spectrum. Besides, the energy-dependent intensity information can be incorporated into the PRISM in terms of the spectral curves for base materials, with which the restoration of the multi-energy image becomes the reconstruction of the energy-independent material composition matrix. In other words, the PRISM utilizes prior knowledge on the generalized rank and sparsity of a multi-energy image, and intensity/spectral characteristics of base materials. Furthermore, we develop an accurate and fast split Bregman method for the PRISM and demonstrate the superior performance of the PRISM relative to several competing methods in simulations.

Exponentially more precise quantum simulation of fermions in the configuration interaction representation

NASA Astrophysics Data System (ADS)

Babbush, Ryan; Berry, Dominic W.; Sanders, Yuval R.; Kivlichan, Ian D.; Scherer, Artur; Wei, Annie Y.; Love, Peter J.; Aspuru-Guzik, Alán

2018-01-01

We present a quantum algorithm for the simulation of molecular systems that is asymptotically more efficient than all previous algorithms in the literature in terms of the main problem parameters. As in Babbush et al (2016 New Journal of Physics 18, 033032), we employ a recently developed technique for simulating Hamiltonian evolution using a truncated Taylor series to obtain logarithmic scaling with the inverse of the desired precision. The algorithm of this paper involves simulation under an oracle for the sparse, first-quantized representation of the molecular Hamiltonian known as the configuration interaction (CI) matrix. We construct and query the CI matrix oracle to allow for on-the-fly computation of molecular integrals in a way that is exponentially more efficient than classical numerical methods. Whereas second-quantized representations of the wavefunction require \\widetilde{{ O }}(N) qubits, where N is the number of single-particle spin-orbitals, the CI matrix representation requires \\widetilde{{ O }}(η ) qubits, where η \\ll N is the number of electrons in the molecule of interest. We show that the gate count of our algorithm scales at most as \\widetilde{{ O }}({η }2{N}3t).

High-performance sparse matrix-matrix products on Intel KNL and multicore architectures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nagasaka, Y; Matsuoka, S; Azad, A

Sparse matrix-matrix multiplication (SpGEMM) is a computational primitive that is widely used in areas ranging from traditional numerical applications to recent big data analysis and machine learning. Although many SpGEMM algorithms have been proposed, hardware specific optimizations for multi- and many-core processors are lacking and a detailed analysis of their performance under various use cases and matrices is not available. We firstly identify and mitigate multiple bottlenecks with memory management and thread scheduling on Intel Xeon Phi (Knights Landing or KNL). Specifically targeting multi- and many-core processors, we develop a hash-table-based algorithm and optimize a heap-based shared-memory SpGEMM algorithm. Wemore » examine their performance together with other publicly available codes. Different from the literature, our evaluation also includes use cases that are representative of real graph algorithms, such as multi-source breadth-first search or triangle counting. Our hash-table and heap-based algorithms are showing significant speedups from libraries in the majority of the cases while different algorithms dominate the other scenarios with different matrix size, sparsity, compression factor and operation type. We wrap up in-depth evaluation results and make a recipe to give the best SpGEMM algorithm for target scenario. A critical finding is that hash-table-based SpGEMM gets a significant performance boost if the nonzeros are not required to be sorted within each row of the output matrix.« less

Target detection in GPR data using joint low-rank and sparsity constraints

NASA Astrophysics Data System (ADS)

Bouzerdoum, Abdesselam; Tivive, Fok Hing Chi; Abeynayake, Canicious

2016-05-01

In ground penetrating radars, background clutter, which comprises the signals backscattered from the rough, uneven ground surface and the background noise, impairs the visualization of buried objects and subsurface inspections. In this paper, a clutter mitigation method is proposed for target detection. The removal of background clutter is formulated as a constrained optimization problem to obtain a low-rank matrix and a sparse matrix. The low-rank matrix captures the ground surface reflections and the background noise, whereas the sparse matrix contains the target reflections. An optimization method based on split-Bregman algorithm is developed to estimate these two matrices from the input GPR data. Evaluated on real radar data, the proposed method achieves promising results in removing the background clutter and enhancing the target signature.

Social Collaborative Filtering by Trust.

PubMed

Yang, Bo; Lei, Yu; Liu, Jiming; Li, Wenjie

2017-08-01

Recommender systems are used to accurately and actively provide users with potentially interesting information or services. Collaborative filtering is a widely adopted approach to recommendation, but sparse data and cold-start users are often barriers to providing high quality recommendations. To address such issues, we propose a novel method that works to improve the performance of collaborative filtering recommendations by integrating sparse rating data given by users and sparse social trust network among these same users. This is a model-based method that adopts matrix factorization technique that maps users into low-dimensional latent feature spaces in terms of their trust relationship, and aims to more accurately reflect the users reciprocal influence on the formation of their own opinions and to learn better preferential patterns of users for high-quality recommendations. We use four large-scale datasets to show that the proposed method performs much better, especially for cold start users, than state-of-the-art recommendation algorithms for social collaborative filtering based on trust.

Inference for High-dimensional Differential Correlation Matrices.

PubMed

Cai, T Tony; Zhang, Anru

2016-01-01

Motivated by differential co-expression analysis in genomics, we consider in this paper estimation and testing of high-dimensional differential correlation matrices. An adaptive thresholding procedure is introduced and theoretical guarantees are given. Minimax rate of convergence is established and the proposed estimator is shown to be adaptively rate-optimal over collections of paired correlation matrices with approximately sparse differences. Simulation results show that the procedure significantly outperforms two other natural methods that are based on separate estimation of the individual correlation matrices. The procedure is also illustrated through an analysis of a breast cancer dataset, which provides evidence at the gene co-expression level that several genes, of which a subset has been previously verified, are associated with the breast cancer. Hypothesis testing on the differential correlation matrices is also considered. A test, which is particularly well suited for testing against sparse alternatives, is introduced. In addition, other related problems, including estimation of a single sparse correlation matrix, estimation of the differential covariance matrices, and estimation of the differential cross-correlation matrices, are also discussed.

Preconditioned conjugate gradient wave-front reconstructors for multiconjugate adaptive optics.

PubMed

Gilles, Luc; Ellerbroek, Brent L; Vogel, Curtis R

2003-09-10

Multiconjugate adaptive optics (MCAO) systems with 10(4)-10(5) degrees of freedom have been proposed for future giant telescopes. Using standard matrix methods to compute, optimize, and implement wavefront control algorithms for these systems is impractical, since the number of calculations required to compute and apply the reconstruction matrix scales respectively with the cube and the square of the number of adaptive optics degrees of freedom. We develop scalable open-loop iterative sparse matrix implementations of minimum variance wave-front reconstruction for telescope diameters up to 32 m with more than 10(4) actuators. The basic approach is the preconditioned conjugate gradient method with an efficient preconditioner, whose block structure is defined by the atmospheric turbulent layers very much like the layer-oriented MCAO algorithms of current interest. Two cost-effective preconditioners are investigated: a multigrid solver and a simpler block symmetric Gauss-Seidel (BSGS) sweep. Both options require off-line sparse Cholesky factorizations of the diagonal blocks of the matrix system. The cost to precompute these factors scales approximately as the three-halves power of the number of estimated phase grid points per atmospheric layer, and their average update rate is typically of the order of 10(-2) Hz, i.e., 4-5 orders of magnitude lower than the typical 10(3) Hz temporal sampling rate. All other computations scale almost linearly with the total number of estimated phase grid points. We present numerical simulation results to illustrate algorithm convergence. Convergence rates of both preconditioners are similar, regardless of measurement noise level, indicating that the layer-oriented BSGS sweep is as effective as the more elaborated multiresolution preconditioner.

Randomized subspace-based robust principal component analysis for hyperspectral anomaly detection

NASA Astrophysics Data System (ADS)

Sun, Weiwei; Yang, Gang; Li, Jialin; Zhang, Dianfa

2018-01-01

A randomized subspace-based robust principal component analysis (RSRPCA) method for anomaly detection in hyperspectral imagery (HSI) is proposed. The RSRPCA combines advantages of randomized column subspace and robust principal component analysis (RPCA). It assumes that the background has low-rank properties, and the anomalies are sparse and do not lie in the column subspace of the background. First, RSRPCA implements random sampling to sketch the original HSI dataset from columns and to construct a randomized column subspace of the background. Structured random projections are also adopted to sketch the HSI dataset from rows. Sketching from columns and rows could greatly reduce the computational requirements of RSRPCA. Second, the RSRPCA adopts the columnwise RPCA (CWRPCA) to eliminate negative effects of sampled anomaly pixels and that purifies the previous randomized column subspace by removing sampled anomaly columns. The CWRPCA decomposes the submatrix of the HSI data into a low-rank matrix (i.e., background component), a noisy matrix (i.e., noise component), and a sparse anomaly matrix (i.e., anomaly component) with only a small proportion of nonzero columns. The algorithm of inexact augmented Lagrange multiplier is utilized to optimize the CWRPCA problem and estimate the sparse matrix. Nonzero columns of the sparse anomaly matrix point to sampled anomaly columns in the submatrix. Third, all the pixels are projected onto the complemental subspace of the purified randomized column subspace of the background and the anomaly pixels in the original HSI data are finally exactly located. Several experiments on three real hyperspectral images are carefully designed to investigate the detection performance of RSRPCA, and the results are compared with four state-of-the-art methods. Experimental results show that the proposed RSRPCA outperforms four comparison methods both in detection performance and in computational time.

Energy Efficient GNSS Signal Acquisition Using Singular Value Decomposition (SVD).

PubMed

Bermúdez Ordoñez, Juan Carlos; Arnaldo Valdés, Rosa María; Gómez Comendador, Fernando

2018-05-16

A significant challenge in global navigation satellite system (GNSS) signal processing is a requirement for a very high sampling rate. The recently-emerging compressed sensing (CS) theory makes processing GNSS signals at a low sampling rate possible if the signal has a sparse representation in a certain space. Based on CS and SVD theories, an algorithm for sampling GNSS signals at a rate much lower than the Nyquist rate and reconstructing the compressed signal is proposed in this research, which is validated after the output from that process still performs signal detection using the standard fast Fourier transform (FFT) parallel frequency space search acquisition. The sparse representation of the GNSS signal is the most important precondition for CS, by constructing a rectangular Toeplitz matrix (TZ) of the transmitted signal, calculating the left singular vectors using SVD from the TZ, to achieve sparse signal representation. Next, obtaining the M-dimensional observation vectors based on the left singular vectors of the SVD, which are equivalent to the sampler operator in standard compressive sensing theory, the signal can be sampled below the Nyquist rate, and can still be reconstructed via ℓ 1 minimization with accuracy using convex optimization. As an added value, there is a GNSS signal acquisition enhancement effect by retaining the useful signal and filtering out noise by projecting the signal into the most significant proper orthogonal modes (PODs) which are the optimal distributions of signal power. The algorithm is validated with real recorded signals, and the results show that the proposed method is effective for sampling, reconstructing intermediate frequency (IF) GNSS signals in the time discrete domain.

Energy Efficient GNSS Signal Acquisition Using Singular Value Decomposition (SVD)

PubMed Central

Arnaldo Valdés, Rosa María; Gómez Comendador, Fernando

2018-01-01

A significant challenge in global navigation satellite system (GNSS) signal processing is a requirement for a very high sampling rate. The recently-emerging compressed sensing (CS) theory makes processing GNSS signals at a low sampling rate possible if the signal has a sparse representation in a certain space. Based on CS and SVD theories, an algorithm for sampling GNSS signals at a rate much lower than the Nyquist rate and reconstructing the compressed signal is proposed in this research, which is validated after the output from that process still performs signal detection using the standard fast Fourier transform (FFT) parallel frequency space search acquisition. The sparse representation of the GNSS signal is the most important precondition for CS, by constructing a rectangular Toeplitz matrix (TZ) of the transmitted signal, calculating the left singular vectors using SVD from the TZ, to achieve sparse signal representation. Next, obtaining the M-dimensional observation vectors based on the left singular vectors of the SVD, which are equivalent to the sampler operator in standard compressive sensing theory, the signal can be sampled below the Nyquist rate, and can still be reconstructed via ℓ1 minimization with accuracy using convex optimization. As an added value, there is a GNSS signal acquisition enhancement effect by retaining the useful signal and filtering out noise by projecting the signal into the most significant proper orthogonal modes (PODs) which are the optimal distributions of signal power. The algorithm is validated with real recorded signals, and the results show that the proposed method is effective for sampling, reconstructing intermediate frequency (IF) GNSS signals in the time discrete domain. PMID:29772731

Framework to trade optimality for local processing in large-scale wavefront reconstruction problems.

PubMed

Haber, Aleksandar; Verhaegen, Michel

2016-11-15

We show that the minimum variance wavefront estimation problems permit localized approximate solutions, in the sense that the wavefront value at a point (excluding unobservable modes, such as the piston mode) can be approximated by a linear combination of the wavefront slope measurements in the point's neighborhood. This enables us to efficiently compute a wavefront estimate by performing a single sparse matrix-vector multiplication. Moreover, our results open the possibility for the development of wavefront estimators that can be easily implemented in a decentralized/distributed manner, and in which the estimate optimality can be easily traded for computational efficiency. We numerically validate our approach on Hudgin wavefront sensor geometries, and the results can be easily generalized to Fried geometries.

Parallel Preconditioning for CFD Problems on the CM-5

NASA Technical Reports Server (NTRS)

Simon, Horst D.; Kremenetsky, Mark D.; Richardson, John; Lasinski, T. A. (Technical Monitor)

1994-01-01

Up to today, preconditioning methods on massively parallel systems have faced a major difficulty. The most successful preconditioning methods in terms of accelerating the convergence of the iterative solver such as incomplete LU factorizations are notoriously difficult to implement on parallel machines for two reasons: (1) the actual computation of the preconditioner is not very floating-point intensive, but requires a large amount of unstructured communication, and (2) the application of the preconditioning matrix in the iteration phase (i.e. triangular solves) are difficult to parallelize because of the recursive nature of the computation. Here we present a new approach to preconditioning for very large, sparse, unsymmetric, linear systems, which avoids both difficulties. We explicitly compute an approximate inverse to our original matrix. This new preconditioning matrix can be applied most efficiently for iterative methods on massively parallel machines, since the preconditioning phase involves only a matrix-vector multiplication, with possibly a dense matrix. Furthermore the actual computation of the preconditioning matrix has natural parallelism. For a problem of size n, the preconditioning matrix can be computed by solving n independent small least squares problems. The algorithm and its implementation on the Connection Machine CM-5 are discussed in detail and supported by extensive timings obtained from real problem data.

Dimension-Factorized Range Migration Algorithm for Regularly Distributed Array Imaging

PubMed Central

Guo, Qijia; Wang, Jie; Chang, Tianying

2017-01-01

The two-dimensional planar MIMO array is a popular approach for millimeter wave imaging applications. As a promising practical alternative, sparse MIMO arrays have been devised to reduce the number of antenna elements and transmitting/receiving channels with predictable and acceptable loss in image quality. In this paper, a high precision three-dimensional imaging algorithm is proposed for MIMO arrays of the regularly distributed type, especially the sparse varieties. Termed the Dimension-Factorized Range Migration Algorithm, the new imaging approach factorizes the conventional MIMO Range Migration Algorithm into multiple operations across the sparse dimensions. The thinner the sparse dimensions of the array, the more efficient the new algorithm will be. Advantages of the proposed approach are demonstrated by comparison with the conventional MIMO Range Migration Algorithm and its non-uniform fast Fourier transform based variant in terms of all the important characteristics of the approaches, especially the anti-noise capability. The computation cost is analyzed as well to evaluate the efficiency quantitatively. PMID:29113083

Overcoming Challenges in Kinetic Modeling of Magnetized Plasmas and Vacuum Electronic Devices

NASA Astrophysics Data System (ADS)

Omelchenko, Yuri; Na, Dong-Yeop; Teixeira, Fernando

2017-10-01

We transform the state-of-the art of plasma modeling by taking advantage of novel computational techniques for fast and robust integration of multiscale hybrid (full particle ions, fluid electrons, no displacement current) and full-PIC models. These models are implemented in 3D HYPERS and axisymmetric full-PIC CONPIC codes. HYPERS is a massively parallel, asynchronous code. The HYPERS solver does not step fields and particles synchronously in time but instead executes local variable updates (events) at their self-adaptive rates while preserving fundamental conservation laws. The charge-conserving CONPIC code has a matrix-free explicit finite-element (FE) solver based on a sparse-approximate inverse (SPAI) algorithm. This explicit solver approximates the inverse FE system matrix (``mass'' matrix) using successive sparsity pattern orders of the original matrix. It does not reduce the set of Maxwell's equations to a vector-wave (curl-curl) equation of second order but instead utilizes the standard coupled first-order Maxwell's system. We discuss the ability of our codes to accurately and efficiently account for multiscale physical phenomena in 3D magnetized space and laboratory plasmas and axisymmetric vacuum electronic devices.

Joint Smoothed l₀-Norm DOA Estimation Algorithm for Multiple Measurement Vectors in MIMO Radar.

PubMed

Liu, Jing; Zhou, Weidong; Juwono, Filbert H

2017-05-08

Direction-of-arrival (DOA) estimation is usually confronted with a multiple measurement vector (MMV) case. In this paper, a novel fast sparse DOA estimation algorithm, named the joint smoothed l 0 -norm algorithm, is proposed for multiple measurement vectors in multiple-input multiple-output (MIMO) radar. To eliminate the white or colored Gaussian noises, the new method first obtains a low-complexity high-order cumulants based data matrix. Then, the proposed algorithm designs a joint smoothed function tailored for the MMV case, based on which joint smoothed l 0 -norm sparse representation framework is constructed. Finally, for the MMV-based joint smoothed function, the corresponding gradient-based sparse signal reconstruction is designed, thus the DOA estimation can be achieved. The proposed method is a fast sparse representation algorithm, which can solve the MMV problem and perform well for both white and colored Gaussian noises. The proposed joint algorithm is about two orders of magnitude faster than the l 1 -norm minimization based methods, such as l 1 -SVD (singular value decomposition), RV (real-valued) l 1 -SVD and RV l 1 -SRACV (sparse representation array covariance vectors), and achieves better DOA estimation performance.

A sparse differential clustering algorithm for tracing cell type changes via single-cell RNA-sequencing data

PubMed Central

Barron, Martin; Zhang, Siyuan

2018-01-01

Abstract Cell types in cell populations change as the condition changes: some cell types die out, new cell types may emerge and surviving cell types evolve to adapt to the new condition. Using single-cell RNA-sequencing data that measure the gene expression of cells before and after the condition change, we propose an algorithm, SparseDC, which identifies cell types, traces their changes across conditions and identifies genes which are marker genes for these changes. By solving a unified optimization problem, SparseDC completes all three tasks simultaneously. SparseDC is highly computationally efficient and demonstrates its accuracy on both simulated and real data. PMID:29140455

Sparse electrocardiogram signals recovery based on solving a row echelon-like form of system.

PubMed

Cai, Pingmei; Wang, Guinan; Yu, Shiwei; Zhang, Hongjuan; Ding, Shuxue; Wu, Zikai

2016-02-01

The study of biology and medicine in a noise environment is an evolving direction in biological data analysis. Among these studies, analysis of electrocardiogram (ECG) signals in a noise environment is a challenging direction in personalized medicine. Due to its periodic characteristic, ECG signal can be roughly regarded as sparse biomedical signals. This study proposes a two-stage recovery algorithm for sparse biomedical signals in time domain. In the first stage, the concentration subspaces are found in advance. Then by exploiting these subspaces, the mixing matrix is estimated accurately. In the second stage, based on the number of active sources at each time point, the time points are divided into different layers. Next, by constructing some transformation matrices, these time points form a row echelon-like system. After that, the sources at each layer can be solved out explicitly by corresponding matrix operations. It is noting that all these operations are conducted under a weak sparse condition that the number of active sources is less than the number of observations. Experimental results show that the proposed method has a better performance for sparse ECG signal recovery problem.

Sparsity of the normal matrix in the refinement of macromolecules at atomic and subatomic resolution.

PubMed

Jelsch, C

2001-09-01

The normal matrix in the least-squares refinement of macromolecules is very sparse when the resolution reaches atomic and subatomic levels. The elements of the normal matrix, related to coordinates, thermal motion and charge-density parameters, have a global tendency to decrease rapidly with the interatomic distance between the atoms concerned. For instance, in the case of the protein crambin at 0.54 A resolution, the elements are reduced by two orders of magnitude for distances above 1.5 A. The neglect a priori of most of the normal-matrix elements according to a distance criterion represents an approximation in the refinement of macromolecules, which is particularly valid at very high resolution. The analytical expressions of the normal-matrix elements, which have been derived for the coordinates and the thermal parameters, show that the degree of matrix sparsity increases with the diffraction resolution and the size of the asymmetric unit.

Optimization of sparse matrix-vector multiplication on emerging multicore platforms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Williams, Samuel; Oliker, Leonid; Vuduc, Richard

2007-01-01

We are witnessing a dramatic change in computer architecture due to the multicore paradigm shift, as every electronic device from cell phones to supercomputers confronts parallelism of unprecedented scale. To fully unleash the potential of these systems, the HPC community must develop multicore specific optimization methodologies for important scientific computations. In this work, we examine sparse matrix-vector multiply (SpMV) - one of the most heavily used kernels in scientific computing - across a broad spectrum of multicore designs. Our experimental platform includes the homogeneous AMD dual-core and Intel quad-core designs, the heterogeneous STI Cell, as well as the first scientificmore » study of the highly multithreaded Sun Niagara2. We present several optimization strategies especially effective for the multicore environment, and demonstrate significant performance improvements compared to existing state-of-the-art serial and parallel SpMV implementations. Additionally, we present key insights into the architectural tradeoffs of leading multicore design strategies, in the context of demanding memory-bound numerical algorithms.« less

Fragmented habitats of traditional fruit orchards are important for dead wood-dependent beetles associated with open canopy deciduous woodlands.

PubMed

Horak, Jakub

2014-06-01

The conservation of traditional fruit orchards might be considered to be a fashion, and many people might find it difficult to accept that these artificial habitats can be significant for overall biodiversity. The main aim of this study was to identify possible roles of traditional fruit orchards for dead wood-dependent (saproxylic) beetles. The study was performed in the Central European landscape in the Czech Republic, which was historically covered by lowland sparse deciduous woodlands. Window traps were used to catch saproxylic beetles in 25 traditional fruit orchards. The species richness, as one of the best indicators of biodiversity, was positively driven by very high canopy openness and the rising proportion of deciduous woodlands in the matrix of the surrounding landscape. Due to the disappearance of natural and semi-natural habitats (i.e., sparse deciduous woodlands) of saproxylic beetles, orchards might complement the functions of suitable habitat fragments as the last biotic islands in the matrix of the cultural Central European landscape.

Fast-SNP: a fast matrix pre-processing algorithm for efficient loopless flux optimization of metabolic models

PubMed Central

Saa, Pedro A.; Nielsen, Lars K.

2016-01-01

Motivation: Computation of steady-state flux solutions in large metabolic models is routinely performed using flux balance analysis based on a simple LP (Linear Programming) formulation. A minimal requirement for thermodynamic feasibility of the flux solution is the absence of internal loops, which are enforced using ‘loopless constraints’. The resulting loopless flux problem is a substantially harder MILP (Mixed Integer Linear Programming) problem, which is computationally expensive for large metabolic models. Results: We developed a pre-processing algorithm that significantly reduces the size of the original loopless problem into an easier and equivalent MILP problem. The pre-processing step employs a fast matrix sparsification algorithm—Fast- sparse null-space pursuit (SNP)—inspired by recent results on SNP. By finding a reduced feasible ‘loop-law’ matrix subject to known directionalities, Fast-SNP considerably improves the computational efficiency in several metabolic models running different loopless optimization problems. Furthermore, analysis of the topology encoded in the reduced loop matrix enabled identification of key directional constraints for the potential permanent elimination of infeasible loops in the underlying model. Overall, Fast-SNP is an effective and simple algorithm for efficient formulation of loop-law constraints, making loopless flux optimization feasible and numerically tractable at large scale. Availability and Implementation: Source code for MATLAB including examples is freely available for download at http://www.aibn.uq.edu.au/cssb-resources under Software. Optimization uses Gurobi, CPLEX or GLPK (the latter is included with the algorithm). Contact: lars.nielsen@uq.edu.au Supplementary information: Supplementary data are available at Bioinformatics online. PMID:27559155

An approach to solving large reliability models

NASA Technical Reports Server (NTRS)

Boyd, Mark A.; Veeraraghavan, Malathi; Dugan, Joanne Bechta; Trivedi, Kishor S.

1988-01-01

This paper describes a unified approach to the problem of solving large realistic reliability models. The methodology integrates behavioral decomposition, state trunction, and efficient sparse matrix-based numerical methods. The use of fault trees, together with ancillary information regarding dependencies to automatically generate the underlying Markov model state space is proposed. The effectiveness of this approach is illustrated by modeling a state-of-the-art flight control system and a multiprocessor system. Nonexponential distributions for times to failure of components are assumed in the latter example. The modeling tool used for most of this analysis is HARP (the Hybrid Automated Reliability Predictor).

A pressure flux-split technique for computation of inlet flow behavior

NASA Technical Reports Server (NTRS)

Pordal, H. S.; Khosla, P. K.; Rubin, S. G.

1991-01-01

A method for calculating the flow field in aircraft engine inlets is presented. The phenomena of inlet unstart and restart are investigated. Solutions of the reduced Navier-Stokes (RNS) equations are obtained with a time consistent direct sparse matrix solver that computes the transient flow field both internal and external to the inlet. Time varying shocks and time varying recirculation regions can be efficiently analyzed. The code is quite general and is suitable for the computation of flow for a wide variety of geometries and over a wide range of Mach and Reynolds numbers.

A sparse equivalent source method for near-field acoustic holography.

PubMed

Fernandez-Grande, Efren; Xenaki, Angeliki; Gerstoft, Peter

2017-01-01

This study examines a near-field acoustic holography method consisting of a sparse formulation of the equivalent source method, based on the compressive sensing (CS) framework. The method, denoted Compressive-Equivalent Source Method (C-ESM), encourages spatially sparse solutions (based on the superposition of few waves) that are accurate when the acoustic sources are spatially localized. The importance of obtaining a non-redundant representation, i.e., a sensing matrix with low column coherence, and the inherent ill-conditioning of near-field reconstruction problems is addressed. Numerical and experimental results on a classical guitar and on a highly reactive dipole-like source are presented. C-ESM is valid beyond the conventional sampling limits, making wide-band reconstruction possible. Spatially extended sources can also be addressed with C-ESM, although in this case the obtained solution does not recover the spatial extent of the source.

HPC-NMF: A High-Performance Parallel Algorithm for Nonnegative Matrix Factorization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kannan, Ramakrishnan; Sukumar, Sreenivas R.; Ballard, Grey M.

NMF is a useful tool for many applications in different domains such as topic modeling in text mining, background separation in video analysis, and community detection in social networks. Despite its popularity in the data mining community, there is a lack of efficient distributed algorithms to solve the problem for big data sets. We propose a high-performance distributed-memory parallel algorithm that computes the factorization by iteratively solving alternating non-negative least squares (NLS) subproblems formore » $$\\WW$$ and $$\\HH$$. It maintains the data and factor matrices in memory (distributed across processors), uses MPI for interprocessor communication, and, in the dense case, provably minimizes communication costs (under mild assumptions). As opposed to previous implementation, our algorithm is also flexible: It performs well for both dense and sparse matrices, and allows the user to choose any one of the multiple algorithms for solving the updates to low rank factors $$\\WW$$ and $$\\HH$$ within the alternating iterations.« less

An hp symplectic pseudospectral method for nonlinear optimal control

NASA Astrophysics Data System (ADS)

Peng, Haijun; Wang, Xinwei; Li, Mingwu; Chen, Biaosong

2017-01-01

An adaptive symplectic pseudospectral method based on the dual variational principle is proposed and is successfully applied to solving nonlinear optimal control problems in this paper. The proposed method satisfies the first order necessary conditions of continuous optimal control problems, also the symplectic property of the original continuous Hamiltonian system is preserved. The original optimal control problem is transferred into a set of nonlinear equations which can be solved easily by Newton-Raphson iterations, and the Jacobian matrix is found to be sparse and symmetric. The proposed method, on one hand, exhibits exponent convergence rates when the number of collocation points are increasing with the fixed number of sub-intervals; on the other hand, exhibits linear convergence rates when the number of sub-intervals is increasing with the fixed number of collocation points. Furthermore, combining with the hp method based on the residual error of dynamic constraints, the proposed method can achieve given precisions in a few iterations. Five examples highlight the high precision and high computational efficiency of the proposed method.

Fast global image smoothing based on weighted least squares.

PubMed

Min, Dongbo; Choi, Sunghwan; Lu, Jiangbo; Ham, Bumsub; Sohn, Kwanghoon; Do, Minh N

2014-12-01

This paper presents an efficient technique for performing a spatially inhomogeneous edge-preserving image smoothing, called fast global smoother. Focusing on sparse Laplacian matrices consisting of a data term and a prior term (typically defined using four or eight neighbors for 2D image), our approach efficiently solves such global objective functions. In particular, we approximate the solution of the memory-and computation-intensive large linear system, defined over a d-dimensional spatial domain, by solving a sequence of 1D subsystems. Our separable implementation enables applying a linear-time tridiagonal matrix algorithm to solve d three-point Laplacian matrices iteratively. Our approach combines the best of two paradigms, i.e., efficient edge-preserving filters and optimization-based smoothing. Our method has a comparable runtime to the fast edge-preserving filters, but its global optimization formulation overcomes many limitations of the local filtering approaches. Our method also achieves high-quality results as the state-of-the-art optimization-based techniques, but runs ∼10-30 times faster. Besides, considering the flexibility in defining an objective function, we further propose generalized fast algorithms that perform Lγ norm smoothing (0 < γ < 2) and support an aggregated (robust) data term for handling imprecise data constraints. We demonstrate the effectiveness and efficiency of our techniques in a range of image processing and computer graphics applications.

High-performance equation solvers and their impact on finite element analysis

NASA Technical Reports Server (NTRS)

Poole, Eugene L.; Knight, Norman F., Jr.; Davis, D. Dale, Jr.

1990-01-01

The role of equation solvers in modern structural analysis software is described. Direct and iterative equation solvers which exploit vectorization on modern high-performance computer systems are described and compared. The direct solvers are two Cholesky factorization methods. The first method utilizes a novel variable-band data storage format to achieve very high computation rates and the second method uses a sparse data storage format designed to reduce the number of operations. The iterative solvers are preconditioned conjugate gradient methods. Two different preconditioners are included; the first uses a diagonal matrix storage scheme to achieve high computation rates and the second requires a sparse data storage scheme and converges to the solution in fewer iterations that the first. The impact of using all of the equation solvers in a common structural analysis software system is demonstrated by solving several representative structural analysis problems.

High-performance equation solvers and their impact on finite element analysis

NASA Technical Reports Server (NTRS)

Poole, Eugene L.; Knight, Norman F., Jr.; Davis, D. D., Jr.

1992-01-01

The role of equation solvers in modern structural analysis software is described. Direct and iterative equation solvers which exploit vectorization on modern high-performance computer systems are described and compared. The direct solvers are two Cholesky factorization methods. The first method utilizes a novel variable-band data storage format to achieve very high computation rates and the second method uses a sparse data storage format designed to reduce the number od operations. The iterative solvers are preconditioned conjugate gradient methods. Two different preconditioners are included; the first uses a diagonal matrix storage scheme to achieve high computation rates and the second requires a sparse data storage scheme and converges to the solution in fewer iterations that the first. The impact of using all of the equation solvers in a common structural analysis software system is demonstrated by solving several representative structural analysis problems.

A physiologically motivated sparse, compact, and smooth (SCS) approach to EEG source localization.

PubMed

Cao, Cheng; Akalin Acar, Zeynep; Kreutz-Delgado, Kenneth; Makeig, Scott

2012-01-01

Here, we introduce a novel approach to the EEG inverse problem based on the assumption that principal cortical sources of multi-channel EEG recordings may be assumed to be spatially sparse, compact, and smooth (SCS). To enforce these characteristics of solutions to the EEG inverse problem, we propose a correlation-variance model which factors a cortical source space covariance matrix into the multiplication of a pre-given correlation coefficient matrix and the square root of the diagonal variance matrix learned from the data under a Bayesian learning framework. We tested the SCS method using simulated EEG data with various SNR and applied it to a real ECOG data set. We compare the results of SCS to those of an established SBL algorithm.

Robust and sparse correlation matrix estimation for the analysis of high-dimensional genomics data.

PubMed

Serra, Angela; Coretto, Pietro; Fratello, Michele; Tagliaferri, Roberto; Stegle, Oliver

2018-02-15

Microarray technology can be used to study the expression of thousands of genes across a number of different experimental conditions, usually hundreds. The underlying principle is that genes sharing similar expression patterns, across different samples, can be part of the same co-expression system, or they may share the same biological functions. Groups of genes are usually identified based on cluster analysis. Clustering methods rely on the similarity matrix between genes. A common choice to measure similarity is to compute the sample correlation matrix. Dimensionality reduction is another popular data analysis task which is also based on covariance/correlation matrix estimates. Unfortunately, covariance/correlation matrix estimation suffers from the intrinsic noise present in high-dimensional data. Sources of noise are: sampling variations, presents of outlying sample units, and the fact that in most cases the number of units is much larger than the number of genes. In this paper, we propose a robust correlation matrix estimator that is regularized based on adaptive thresholding. The resulting method jointly tames the effects of the high-dimensionality, and data contamination. Computations are easy to implement and do not require hand tunings. Both simulated and real data are analyzed. A Monte Carlo experiment shows that the proposed method is capable of remarkable performances. Our correlation metric is more robust to outliers compared with the existing alternatives in two gene expression datasets. It is also shown how the regularization allows to automatically detect and filter spurious correlations. The same regularization is also extended to other less robust correlation measures. Finally, we apply the ARACNE algorithm on the SyNTreN gene expression data. Sensitivity and specificity of the reconstructed network is compared with the gold standard. We show that ARACNE performs better when it takes the proposed correlation matrix estimator as input. The R software is available at https://github.com/angy89/RobustSparseCorrelation. aserra@unisa.it or robtag@unisa.it. Supplementary data are available at Bioinformatics online. © The Author (2017). Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com

Matrix Algebra for GPU and Multicore Architectures (MAGMA) for Large Petascale Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dongarra, Jack J.; Tomov, Stanimire

2014-03-24

The goal of the MAGMA project is to create a new generation of linear algebra libraries that achieve the fastest possible time to an accurate solution on hybrid Multicore+GPU-based systems, using all the processing power that future high-end systems can make available within given energy constraints. Our efforts at the University of Tennessee achieved the goals set in all of the five areas identified in the proposal: 1. Communication optimal algorithms; 2. Autotuning for GPU and hybrid processors; 3. Scheduling and memory management techniques for heterogeneity and scale; 4. Fault tolerance and robustness for large scale systems; 5. Building energymore » efficiency into software foundations. The University of Tennessee’s main contributions, as proposed, were the research and software development of new algorithms for hybrid multi/many-core CPUs and GPUs, as related to two-sided factorizations and complete eigenproblem solvers, hybrid BLAS, and energy efficiency for dense, as well as sparse, operations. Furthermore, as proposed, we investigated and experimented with various techniques targeting the five main areas outlined.« less

Sparse Gaussian elimination with controlled fill-in on a shared memory multiprocessor

NASA Technical Reports Server (NTRS)

Alaghband, Gita; Jordan, Harry F.

1989-01-01

It is shown that in sparse matrices arising from electronic circuits, it is possible to do computations on many diagonal elements simultaneously. A technique for obtaining an ordered compatible set directly from the ordered incompatible table is given. The ordering is based on the Markowitz number of the pivot candidates. This technique generates a set of compatible pivots with the property of generating few fills. A novel heuristic algorithm is presented that combines the idea of an order-compatible set with a limited binary tree search to generate several sets of compatible pivots in linear time. An elimination set for reducing the matrix is generated and selected on the basis of a minimum Markowitz sum number. The parallel pivoting technique presented is a stepwise algorithm and can be applied to any submatrix of the original matrix. Thus, it is not a preordering of the sparse matrix and is applied dynamically as the decomposition proceeds. Parameters are suggested to obtain a balance between parallelism and fill-ins. Results of applying the proposed algorithms on several large application matrices using the HEP multiprocessor (Kowalik, 1985) are presented and analyzed.

A deconvolution extraction method for 2D multi-object fibre spectroscopy based on the regularized least-squares QR-factorization algorithm

NASA Astrophysics Data System (ADS)

Yu, Jian; Yin, Qian; Guo, Ping; Luo, A.-li

2014-09-01

This paper presents an efficient method for the extraction of astronomical spectra from two-dimensional (2D) multifibre spectrographs based on the regularized least-squares QR-factorization (LSQR) algorithm. We address two issues: we propose a modified Gaussian point spread function (PSF) for modelling the 2D PSF from multi-emission-line gas-discharge lamp images (arc images), and we develop an efficient deconvolution method to extract spectra in real circumstances. The proposed modified 2D Gaussian PSF model can fit various types of 2D PSFs, including different radial distortion angles and ellipticities. We adopt the regularized LSQR algorithm to solve the sparse linear equations constructed from the sparse convolution matrix, which we designate the deconvolution spectrum extraction method. Furthermore, we implement a parallelized LSQR algorithm based on graphics processing unit programming in the Compute Unified Device Architecture to accelerate the computational processing. Experimental results illustrate that the proposed extraction method can greatly reduce the computational cost and memory use of the deconvolution method and, consequently, increase its efficiency and practicability. In addition, the proposed extraction method has a stronger noise tolerance than other methods, such as the boxcar (aperture) extraction and profile extraction methods. Finally, we present an analysis of the sensitivity of the extraction results to the radius and full width at half-maximum of the 2D PSF.

Fast Component Pursuit for Large-Scale Inverse Covariance Estimation.

PubMed

Han, Lei; Zhang, Yu; Zhang, Tong

2016-08-01

The maximum likelihood estimation (MLE) for the Gaussian graphical model, which is also known as the inverse covariance estimation problem, has gained increasing interest recently. Most existing works assume that inverse covariance estimators contain sparse structure and then construct models with the ℓ 1 regularization. In this paper, different from existing works, we study the inverse covariance estimation problem from another perspective by efficiently modeling the low-rank structure in the inverse covariance, which is assumed to be a combination of a low-rank part and a diagonal matrix. One motivation for this assumption is that the low-rank structure is common in many applications including the climate and financial analysis, and another one is that such assumption can reduce the computational complexity when computing its inverse. Specifically, we propose an efficient COmponent Pursuit (COP) method to obtain the low-rank part, where each component can be sparse. For optimization, the COP method greedily learns a rank-one component in each iteration by maximizing the log-likelihood. Moreover, the COP algorithm enjoys several appealing properties including the existence of an efficient solution in each iteration and the theoretical guarantee on the convergence of this greedy approach. Experiments on large-scale synthetic and real-world datasets including thousands of millions variables show that the COP method is faster than the state-of-the-art techniques for the inverse covariance estimation problem when achieving comparable log-likelihood on test data.

Action Recognition Using Nonnegative Action Component Representation and Sparse Basis Selection.

PubMed

Wang, Haoran; Yuan, Chunfeng; Hu, Weiming; Ling, Haibin; Yang, Wankou; Sun, Changyin

2014-02-01

In this paper, we propose using high-level action units to represent human actions in videos and, based on such units, a novel sparse model is developed for human action recognition. There are three interconnected components in our approach. First, we propose a new context-aware spatial-temporal descriptor, named locally weighted word context, to improve the discriminability of the traditionally used local spatial-temporal descriptors. Second, from the statistics of the context-aware descriptors, we learn action units using the graph regularized nonnegative matrix factorization, which leads to a part-based representation and encodes the geometrical information. These units effectively bridge the semantic gap in action recognition. Third, we propose a sparse model based on a joint l2,1-norm to preserve the representative items and suppress noise in the action units. Intuitively, when learning the dictionary for action representation, the sparse model captures the fact that actions from the same class share similar units. The proposed approach is evaluated on several publicly available data sets. The experimental results and analysis clearly demonstrate the effectiveness of the proposed approach.

A fast indirect method to compute functions of genomic relationships concerning genotyped and ungenotyped individuals, for diversity management.

PubMed

Colleau, Jean-Jacques; Palhière, Isabelle; Rodríguez-Ramilo, Silvia T; Legarra, Andres

2017-12-01

Pedigree-based management of genetic diversity in populations, e.g., using optimal contributions, involves computation of the [Formula: see text] type yielding elements (relationships) or functions (usually averages) of relationship matrices. For pedigree-based relationships [Formula: see text], a very efficient method exists. When all the individuals of interest are genotyped, genomic management can be addressed using the genomic relationship matrix [Formula: see text]; however, to date, the computational problem of efficiently computing [Formula: see text] has not been well studied. When some individuals of interest are not genotyped, genomic management should consider the relationship matrix [Formula: see text] that combines genotyped and ungenotyped individuals; however, direct computation of [Formula: see text] is computationally very demanding, because construction of a possibly huge matrix is required. Our work presents efficient ways of computing [Formula: see text] and [Formula: see text], with applications on real data from dairy sheep and dairy goat breeding schemes. For genomic relationships, an efficient indirect computation with quadratic instead of cubic cost is [Formula: see text], where Z is a matrix relating animals to genotypes. For the relationship matrix [Formula: see text], we propose an indirect method based on the difference between vectors [Formula: see text], which involves computation of [Formula: see text] and of products such as [Formula: see text] and [Formula: see text], where [Formula: see text] is a working vector derived from [Formula: see text]. The latter computation is the most demanding but can be done using sparse Cholesky decompositions of matrix [Formula: see text], which allows handling very large genomic and pedigree data files. Studies based on simulations reported in the literature show that the trends of average relationships in [Formula: see text] and [Formula: see text] differ as genomic selection proceeds. When selection is based on genomic relationships but management is based on pedigree data, the true genetic diversity is overestimated. However, our tests on real data from sheep and goat obtained before genomic selection started do not show this. We present efficient methods to compute elements and statistics of the genomic relationships [Formula: see text] and of matrix [Formula: see text] that combines ungenotyped and genotyped individuals. These methods should be useful to monitor and handle genomic diversity.

Group sparse multiview patch alignment framework with view consistency for image classification.

PubMed

Gui, Jie; Tao, Dacheng; Sun, Zhenan; Luo, Yong; You, Xinge; Tang, Yuan Yan

2014-07-01

No single feature can satisfactorily characterize the semantic concepts of an image. Multiview learning aims to unify different kinds of features to produce a consensual and efficient representation. This paper redefines part optimization in the patch alignment framework (PAF) and develops a group sparse multiview patch alignment framework (GSM-PAF). The new part optimization considers not only the complementary properties of different views, but also view consistency. In particular, view consistency models the correlations between all possible combinations of any two kinds of view. In contrast to conventional dimensionality reduction algorithms that perform feature extraction and feature selection independently, GSM-PAF enjoys joint feature extraction and feature selection by exploiting l(2,1)-norm on the projection matrix to achieve row sparsity, which leads to the simultaneous selection of relevant features and learning transformation, and thus makes the algorithm more discriminative. Experiments on two real-world image data sets demonstrate the effectiveness of GSM-PAF for image classification.

Efficiency analysis of numerical integrations for finite element substructure in real-time hybrid simulation

NASA Astrophysics Data System (ADS)

Wang, Jinting; Lu, Liqiao; Zhu, Fei

2018-01-01

Finite element (FE) is a powerful tool and has been applied by investigators to real-time hybrid simulations (RTHSs). This study focuses on the computational efficiency, including the computational time and accuracy, of numerical integrations in solving FE numerical substructure in RTHSs. First, sparse matrix storage schemes are adopted to decrease the computational time of FE numerical substructure. In this way, the task execution time (TET) decreases such that the scale of the numerical substructure model increases. Subsequently, several commonly used explicit numerical integration algorithms, including the central difference method (CDM), the Newmark explicit method, the Chang method and the Gui-λ method, are comprehensively compared to evaluate their computational time in solving FE numerical substructure. CDM is better than the other explicit integration algorithms when the damping matrix is diagonal, while the Gui-λ (λ = 4) method is advantageous when the damping matrix is non-diagonal. Finally, the effect of time delay on the computational accuracy of RTHSs is investigated by simulating structure-foundation systems. Simulation results show that the influences of time delay on the displacement response become obvious with the mass ratio increasing, and delay compensation methods may reduce the relative error of the displacement peak value to less than 5% even under the large time-step and large time delay.

MPI-FAUN: An MPI-Based Framework for Alternating-Updating Nonnegative Matrix Factorization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kannan, Ramakrishnan; Ballard, Grey; Park, Haesun

Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors W and H, for the given input matrix A, such that A≈WH. NMF is a useful tool for many applications in different domains such as topic modeling in text mining, background separation in video analysis, and community detection in social networks. Despite its popularity in the data mining community, there is a lack of efficient parallel algorithms to solve the problem for big data sets. The main contribution of this work is a new, high-performance parallel computational framework for a broad class of NMF algorithms thatmore » iteratively solves alternating non-negative least squares (NLS) subproblems for W and H. It maintains the data and factor matrices in memory (distributed across processors), uses MPI for interprocessor communication, and, in the dense case, provably minimizes communication costs (under mild assumptions). The framework is flexible and able to leverage a variety of NMF and NLS algorithms, including Multiplicative Update, Hierarchical Alternating Least Squares, and Block Principal Pivoting. Our implementation allows us to benchmark and compare different algorithms on massive dense and sparse data matrices of size that spans from few hundreds of millions to billions. We demonstrate the scalability of our algorithm and compare it with baseline implementations, showing significant performance improvements. The code and the datasets used for conducting the experiments are available online.« less

MPI-FAUN: An MPI-Based Framework for Alternating-Updating Nonnegative Matrix Factorization

DOE PAGES

Kannan, Ramakrishnan; Ballard, Grey; Park, Haesun

2017-10-30

Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors W and H, for the given input matrix A, such that A≈WH. NMF is a useful tool for many applications in different domains such as topic modeling in text mining, background separation in video analysis, and community detection in social networks. Despite its popularity in the data mining community, there is a lack of efficient parallel algorithms to solve the problem for big data sets. The main contribution of this work is a new, high-performance parallel computational framework for a broad class of NMF algorithms thatmore » iteratively solves alternating non-negative least squares (NLS) subproblems for W and H. It maintains the data and factor matrices in memory (distributed across processors), uses MPI for interprocessor communication, and, in the dense case, provably minimizes communication costs (under mild assumptions). The framework is flexible and able to leverage a variety of NMF and NLS algorithms, including Multiplicative Update, Hierarchical Alternating Least Squares, and Block Principal Pivoting. Our implementation allows us to benchmark and compare different algorithms on massive dense and sparse data matrices of size that spans from few hundreds of millions to billions. We demonstrate the scalability of our algorithm and compare it with baseline implementations, showing significant performance improvements. The code and the datasets used for conducting the experiments are available online.« less

Large-region acoustic source mapping using a movable array and sparse covariance fitting.

PubMed

Zhao, Shengkui; Tuna, Cagdas; Nguyen, Thi Ngoc Tho; Jones, Douglas L

2017-01-01

Large-region acoustic source mapping is important for city-scale noise monitoring. Approaches using a single-position measurement scheme to scan large regions using small arrays cannot provide clean acoustic source maps, while deploying large arrays spanning the entire region of interest is prohibitively expensive. A multiple-position measurement scheme is applied to scan large regions at multiple spatial positions using a movable array of small size. Based on the multiple-position measurement scheme, a sparse-constrained multiple-position vectorized covariance matrix fitting approach is presented. In the proposed approach, the overall sample covariance matrix of the incoherent virtual array is first estimated using the multiple-position array data and then vectorized using the Khatri-Rao (KR) product. A linear model is then constructed for fitting the vectorized covariance matrix and a sparse-constrained reconstruction algorithm is proposed for recovering source powers from the model. The user parameter settings are discussed. The proposed approach is tested on a 30 m × 40 m region and a 60 m × 40 m region using simulated and measured data. Much cleaner acoustic source maps and lower sound pressure level errors are obtained compared to the beamforming approaches and the previous sparse approach [Zhao, Tuna, Nguyen, and Jones, Proc. IEEE Intl. Conf. on Acoustics, Speech and Signal Processing (ICASSP) (2016)].

Incomplete Sparse Approximate Inverses for Parallel Preconditioning

DOE PAGES

Anzt, Hartwig; Huckle, Thomas K.; Bräckle, Jürgen; ...

2017-10-28

In this study, we propose a new preconditioning method that can be seen as a generalization of block-Jacobi methods, or as a simplification of the sparse approximate inverse (SAI) preconditioners. The “Incomplete Sparse Approximate Inverses” (ISAI) is in particular efficient in the solution of sparse triangular linear systems of equations. Those arise, for example, in the context of incomplete factorization preconditioning. ISAI preconditioners can be generated via an algorithm providing fine-grained parallelism, which makes them attractive for hardware with a high concurrency level. Finally, in a study covering a large number of matrices, we identify the ISAI preconditioner as anmore » attractive alternative to exact triangular solves in the context of incomplete factorization preconditioning.« less

A Sparse Matrix Approach for Simultaneous Quantification of Nystagmus and Saccade

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.; Stone, Lee; Boyle, Richard D.

2012-01-01

The vestibulo-ocular reflex (VOR) consists of two intermingled non-linear subsystems; namely, nystagmus and saccade. Typically, nystagmus is analysed using a single sufficiently long signal or a concatenation of them. Saccade information is not analysed and discarded due to insufficient data length to provide consistent and minimum variance estimates. This paper presents a novel sparse matrix approach to system identification of the VOR. It allows for the simultaneous estimation of both nystagmus and saccade signals. We show via simulation of the VOR that our technique provides consistent and unbiased estimates in the presence of output additive noise.

Low-count PET image restoration using sparse representation

NASA Astrophysics Data System (ADS)

Li, Tao; Jiang, Changhui; Gao, Juan; Yang, Yongfeng; Liang, Dong; Liu, Xin; Zheng, Hairong; Hu, Zhanli

2018-04-01

In the field of positron emission tomography (PET), reconstructed images are often blurry and contain noise. These problems are primarily caused by the low resolution of projection data. Solving this problem by improving hardware is an expensive solution, and therefore, we attempted to develop a solution based on optimizing several related algorithms in both the reconstruction and image post-processing domains. As sparse technology is widely used, sparse prediction is increasingly applied to solve this problem. In this paper, we propose a new sparse method to process low-resolution PET images. Two dictionaries (D1 for low-resolution PET images and D2 for high-resolution PET images) are learned from a group real PET image data sets. Among these two dictionaries, D1 is used to obtain a sparse representation for each patch of the input PET image. Then, a high-resolution PET image is generated from this sparse representation using D2. Experimental results indicate that the proposed method exhibits a stable and superior ability to enhance image resolution and recover image details. Quantitatively, this method achieves better performance than traditional methods. This proposed strategy is a new and efficient approach for improving the quality of PET images.

Sparsity-promoting orthogonal dictionary updating for image reconstruction from highly undersampled magnetic resonance data.

PubMed

Huang, Jinhong; Guo, Li; Feng, Qianjin; Chen, Wufan; Feng, Yanqiu

2015-07-21

Image reconstruction from undersampled k-space data accelerates magnetic resonance imaging (MRI) by exploiting image sparseness in certain transform domains. Employing image patch representation over a learned dictionary has the advantage of being adaptive to local image structures and thus can better sparsify images than using fixed transforms (e.g. wavelets and total variations). Dictionary learning methods have recently been introduced to MRI reconstruction, and these methods demonstrate significantly reduced reconstruction errors compared to sparse MRI reconstruction using fixed transforms. However, the synthesis sparse coding problem in dictionary learning is NP-hard and computationally expensive. In this paper, we present a novel sparsity-promoting orthogonal dictionary updating method for efficient image reconstruction from highly undersampled MRI data. The orthogonality imposed on the learned dictionary enables the minimization problem in the reconstruction to be solved by an efficient optimization algorithm which alternately updates representation coefficients, orthogonal dictionary, and missing k-space data. Moreover, both sparsity level and sparse representation contribution using updated dictionaries gradually increase during iterations to recover more details, assuming the progressively improved quality of the dictionary. Simulation and real data experimental results both demonstrate that the proposed method is approximately 10 to 100 times faster than the K-SVD-based dictionary learning MRI method and simultaneously improves reconstruction accuracy.

Inference for High-dimensional Differential Correlation Matrices *

PubMed Central

Cai, T. Tony; Zhang, Anru

2015-01-01

Motivated by differential co-expression analysis in genomics, we consider in this paper estimation and testing of high-dimensional differential correlation matrices. An adaptive thresholding procedure is introduced and theoretical guarantees are given. Minimax rate of convergence is established and the proposed estimator is shown to be adaptively rate-optimal over collections of paired correlation matrices with approximately sparse differences. Simulation results show that the procedure significantly outperforms two other natural methods that are based on separate estimation of the individual correlation matrices. The procedure is also illustrated through an analysis of a breast cancer dataset, which provides evidence at the gene co-expression level that several genes, of which a subset has been previously verified, are associated with the breast cancer. Hypothesis testing on the differential correlation matrices is also considered. A test, which is particularly well suited for testing against sparse alternatives, is introduced. In addition, other related problems, including estimation of a single sparse correlation matrix, estimation of the differential covariance matrices, and estimation of the differential cross-correlation matrices, are also discussed. PMID:26500380

Disrupted Small-World Networks in Schizophrenia

ERIC Educational Resources Information Center

Liu, Yong; Liang, Meng; Zhou, Yuan; He, Yong; Hao, Yihui; Song, Ming; Yu, Chunshui; Liu, Haihong; Liu, Zhening; Jiang, Tianzi

2008-01-01

The human brain has been described as a large, sparse, complex network characterized by efficient small-world properties, which assure that the brain generates and integrates information with high efficiency. Many previous neuroimaging studies have provided consistent evidence of "dysfunctional connectivity" among the brain regions in…

BinTree Seeking: A Novel Approach to Mine Both Bi-Sparse and Cohesive Modules in Protein Interaction Networks

PubMed Central

Shen, Hong-Bin

2011-01-01

Modern science of networks has brought significant advances to our understanding of complex systems biology. As a representative model of systems biology, Protein Interaction Networks (PINs) are characterized by a remarkable modular structures, reflecting functional associations between their components. Many methods were proposed to capture cohesive modules so that there is a higher density of edges within modules than those across them. Recent studies reveal that cohesively interacting modules of proteins is not a universal organizing principle in PINs, which has opened up new avenues for revisiting functional modules in PINs. In this paper, functional clusters in PINs are found to be able to form unorthodox structures defined as bi-sparse module. In contrast to the traditional cohesive module, the nodes in the bi-sparse module are sparsely connected internally and densely connected with other bi-sparse or cohesive modules. We present a novel protocol called the BinTree Seeking (BTS) for mining both bi-sparse and cohesive modules in PINs based on Edge Density of Module (EDM) and matrix theory. BTS detects modules by depicting links and nodes rather than nodes alone and its derivation procedure is totally performed on adjacency matrix of networks. The number of modules in a PIN can be automatically determined in the proposed BTS approach. BTS is tested on three real PINs and the results demonstrate that functional modules in PINs are not dominantly cohesive but can be sparse. BTS software and the supporting information are available at: www.csbio.sjtu.edu.cn/bioinf/BTS/. PMID:22140454

A Spectral Algorithm for Envelope Reduction of Sparse Matrices

NASA Technical Reports Server (NTRS)

Barnard, Stephen T.; Pothen, Alex; Simon, Horst D.

1993-01-01

The problem of reordering a sparse symmetric matrix to reduce its envelope size is considered. A new spectral algorithm for computing an envelope-reducing reordering is obtained by associating a Laplacian matrix with the given matrix and then sorting the components of a specified eigenvector of the Laplacian. This Laplacian eigenvector solves a continuous relaxation of a discrete problem related to envelope minimization called the minimum 2-sum problem. The permutation vector computed by the spectral algorithm is a closest permutation vector to the specified Laplacian eigenvector. Numerical results show that the new reordering algorithm usually computes smaller envelope sizes than those obtained from the current standard algorithms such as Gibbs-Poole-Stockmeyer (GPS) or SPARSPAK reverse Cuthill-McKee (RCM), in some cases reducing the envelope by more than a factor of two.

Unsupervised Learning for Monaural Source Separation Using Maximization–Minimization Algorithm with Time–Frequency Deconvolution †

PubMed Central

Bouridane, Ahmed; Ling, Bingo Wing-Kuen

2018-01-01

This paper presents an unsupervised learning algorithm for sparse nonnegative matrix factor time–frequency deconvolution with optimized fractional β-divergence. The β-divergence is a group of cost functions parametrized by a single parameter β. The Itakura–Saito divergence, Kullback–Leibler divergence and Least Square distance are special cases that correspond to β=0, 1, 2, respectively. This paper presents a generalized algorithm that uses a flexible range of β that includes fractional values. It describes a maximization–minimization (MM) algorithm leading to the development of a fast convergence multiplicative update algorithm with guaranteed convergence. The proposed model operates in the time–frequency domain and decomposes an information-bearing matrix into two-dimensional deconvolution of factor matrices that represent the spectral dictionary and temporal codes. The deconvolution process has been optimized to yield sparse temporal codes through maximizing the likelihood of the observations. The paper also presents a method to estimate the fractional β value. The method is demonstrated on separating audio mixtures recorded from a single channel. The paper shows that the extraction of the spectral dictionary and temporal codes is significantly more efficient by using the proposed algorithm and subsequently leads to better source separation performance. Experimental tests and comparisons with other factorization methods have been conducted to verify its efficacy. PMID:29702629

Automatic segmentation of right ventricular ultrasound images using sparse matrix transform and a level set

NASA Astrophysics Data System (ADS)

Qin, Xulei; Cong, Zhibin; Fei, Baowei

2013-11-01

An automatic segmentation framework is proposed to segment the right ventricle (RV) in echocardiographic images. The method can automatically segment both epicardial and endocardial boundaries from a continuous echocardiography series by combining sparse matrix transform, a training model, and a localized region-based level set. First, the sparse matrix transform extracts main motion regions of the myocardium as eigen-images by analyzing the statistical information of the images. Second, an RV training model is registered to the eigen-images in order to locate the position of the RV. Third, the training model is adjusted and then serves as an optimized initialization for the segmentation of each image. Finally, based on the initializations, a localized, region-based level set algorithm is applied to segment both epicardial and endocardial boundaries in each echocardiograph. Three evaluation methods were used to validate the performance of the segmentation framework. The Dice coefficient measures the overall agreement between the manual and automatic segmentation. The absolute distance and the Hausdorff distance between the boundaries from manual and automatic segmentation were used to measure the accuracy of the segmentation. Ultrasound images of human subjects were used for validation. For the epicardial and endocardial boundaries, the Dice coefficients were 90.8 ± 1.7% and 87.3 ± 1.9%, the absolute distances were 2.0 ± 0.42 mm and 1.79 ± 0.45 mm, and the Hausdorff distances were 6.86 ± 1.71 mm and 7.02 ± 1.17 mm, respectively. The automatic segmentation method based on a sparse matrix transform and level set can provide a useful tool for quantitative cardiac imaging.

Classification of multispectral or hyperspectral satellite imagery using clustering of sparse approximations on sparse representations in learned dictionaries obtained using efficient convolutional sparse coding

DOEpatents

Moody, Daniela; Wohlberg, Brendt

2018-01-02

An approach for land cover classification, seasonal and yearly change detection and monitoring, and identification of changes in man-made features may use a clustering of sparse approximations (CoSA) on sparse representations in learned dictionaries. The learned dictionaries may be derived using efficient convolutional sparse coding to build multispectral or hyperspectral, multiresolution dictionaries that are adapted to regional satellite image data. Sparse image representations of images over the learned dictionaries may be used to perform unsupervised k-means clustering into land cover categories. The clustering process behaves as a classifier in detecting real variability. This approach may combine spectral and spatial textural characteristics to detect geologic, vegetative, hydrologic, and man-made features, as well as changes in these features over time.

Compressive sensing using optimized sensing matrix for face verification

NASA Astrophysics Data System (ADS)

Oey, Endra; Jeffry; Wongso, Kelvin; Tommy

2017-12-01

Biometric appears as one of the solutions which is capable in solving problems that occurred in the usage of password in terms of data access, for example there is possibility in forgetting password and hard to recall various different passwords. With biometrics, physical characteristics of a person can be captured and used in the identification process. In this research, facial biometric is used in the verification process to determine whether the user has the authority to access the data or not. Facial biometric is chosen as its low cost implementation and generate quite accurate result for user identification. Face verification system which is adopted in this research is Compressive Sensing (CS) technique, in which aims to reduce dimension size as well as encrypt data in form of facial test image where the image is represented in sparse signals. Encrypted data can be reconstructed using Sparse Coding algorithm. Two types of Sparse Coding namely Orthogonal Matching Pursuit (OMP) and Iteratively Reweighted Least Squares -ℓp (IRLS-ℓp) will be used for comparison face verification system research. Reconstruction results of sparse signals are then used to find Euclidean norm with the sparse signal of user that has been previously saved in system to determine the validity of the facial test image. Results of system accuracy obtained in this research are 99% in IRLS with time response of face verification for 4.917 seconds and 96.33% in OMP with time response of face verification for 0.4046 seconds with non-optimized sensing matrix, while 99% in IRLS with time response of face verification for 13.4791 seconds and 98.33% for OMP with time response of face verification for 3.1571 seconds with optimized sensing matrix.

Preconditioner-free Wiener filtering with a dense noise matrix

NASA Astrophysics Data System (ADS)

Huffenberger, Kevin M.

2018-05-01

This work extends the Elsner & Wandelt (2013) iterative method for efficient, preconditioner-free Wiener filtering to cases in which the noise covariance matrix is dense, but can be decomposed into a sum whose parts are sparse in convenient bases. The new method, which uses multiple messenger fields, reproduces Wiener-filter solutions for test problems, and we apply it to a case beyond the reach of the Elsner & Wandelt (2013) method. We compute the Wiener-filter solution for a simulated Cosmic Microwave Background (CMB) map that contains spatially varying, uncorrelated noise, isotropic 1/f noise, and large-scale horizontal stripes (like those caused by atmospheric noise). We discuss simple extensions that can filter contaminated modes or inverse-noise-filter the data. These techniques help to address complications in the noise properties of maps from current and future generations of ground-based Microwave Background experiments, like Advanced ACTPol, Simons Observatory, and CMB-S4.

Interpretation of the Precision Matrix and Its Application in Estimating Sparse Brain Connectivity during Sleep Spindles from Human Electrocorticography Recordings

PubMed Central

Das, Anup; Sampson, Aaron L.; Lainscsek, Claudia; Muller, Lyle; Lin, Wutu; Doyle, John C.; Cash, Sydney S.; Halgren, Eric; Sejnowski, Terrence J.

2017-01-01

The correlation method from brain imaging has been used to estimate functional connectivity in the human brain. However, brain regions might show very high correlation even when the two regions are not directly connected due to the strong interaction of the two regions with common input from a third region. One previously proposed solution to this problem is to use a sparse regularized inverse covariance matrix or precision matrix (SRPM) assuming that the connectivity structure is sparse. This method yields partial correlations to measure strong direct interactions between pairs of regions while simultaneously removing the influence of the rest of the regions, thus identifying regions that are conditionally independent. To test our methods, we first demonstrated conditions under which the SRPM method could indeed find the true physical connection between a pair of nodes for a spring-mass example and an RC circuit example. The recovery of the connectivity structure using the SRPM method can be explained by energy models using the Boltzmann distribution. We then demonstrated the application of the SRPM method for estimating brain connectivity during stage 2 sleep spindles from human electrocorticography (ECoG) recordings using an 8 × 8 electrode array. The ECoG recordings that we analyzed were from a 32-year-old male patient with long-standing pharmaco-resistant left temporal lobe complex partial epilepsy. Sleep spindles were automatically detected using delay differential analysis and then analyzed with SRPM and the Louvain method for community detection. We found spatially localized brain networks within and between neighboring cortical areas during spindles, in contrast to the case when sleep spindles were not present. PMID:28095202

Sparse deconvolution for the large-scale ill-posed inverse problem of impact force reconstruction

NASA Astrophysics Data System (ADS)

Qiao, Baijie; Zhang, Xingwu; Gao, Jiawei; Liu, Ruonan; Chen, Xuefeng

2017-01-01

Most previous regularization methods for solving the inverse problem of force reconstruction are to minimize the l2-norm of the desired force. However, these traditional regularization methods such as Tikhonov regularization and truncated singular value decomposition, commonly fail to solve the large-scale ill-posed inverse problem in moderate computational cost. In this paper, taking into account the sparse characteristic of impact force, the idea of sparse deconvolution is first introduced to the field of impact force reconstruction and a general sparse deconvolution model of impact force is constructed. Second, a novel impact force reconstruction method based on the primal-dual interior point method (PDIPM) is proposed to solve such a large-scale sparse deconvolution model, where minimizing the l2-norm is replaced by minimizing the l1-norm. Meanwhile, the preconditioned conjugate gradient algorithm is used to compute the search direction of PDIPM with high computational efficiency. Finally, two experiments including the small-scale or medium-scale single impact force reconstruction and the relatively large-scale consecutive impact force reconstruction are conducted on a composite wind turbine blade and a shell structure to illustrate the advantage of PDIPM. Compared with Tikhonov regularization, PDIPM is more efficient, accurate and robust whether in the single impact force reconstruction or in the consecutive impact force reconstruction.

A high-order spatial filter for a cubed-sphere spectral element model

NASA Astrophysics Data System (ADS)

Kang, Hyun-Gyu; Cheong, Hyeong-Bin

2017-04-01

A high-order spatial filter is developed for the spectral-element-method dynamical core on the cubed-sphere grid which employs the Gauss-Lobatto Lagrange interpolating polynomials (GLLIP) as orthogonal basis functions. The filter equation is the high-order Helmholtz equation which corresponds to the implicit time-differencing of a diffusion equation employing the high-order Laplacian. The Laplacian operator is discretized within a cell which is a building block of the cubed sphere grid and consists of the Gauss-Lobatto grid. When discretizing a high-order Laplacian, due to the requirement of C0 continuity along the cell boundaries the grid-points in neighboring cells should be used for the target cell: The number of neighboring cells is nearly quadratically proportional to the filter order. Discrete Helmholtz equation yields a huge-sized and highly sparse matrix equation whose size is N*N with N the number of total grid points on the globe. The number of nonzero entries is also almost in quadratic proportion to the filter order. Filtering is accomplished by solving the huge-matrix equation. While requiring a significant computing time, the solution of global matrix provides the filtered field free of discontinuity along the cell boundaries. To achieve the computational efficiency and the accuracy at the same time, the solution of the matrix equation was obtained by only accounting for the finite number of adjacent cells. This is called as a local-domain filter. It was shown that to remove the numerical noise near the grid-scale, inclusion of 5*5 cells for the local-domain filter was found sufficient, giving the same accuracy as that obtained by global domain solution while reducing the computing time to a considerably lower level. The high-order filter was evaluated using the standard test cases including the baroclinic instability of the zonal flow. Results indicated that the filter performs better on the removal of grid-scale numerical noises than the explicit high-order viscosity. It was also presented that the filter can be easily implemented on the distributed-memory parallel computers with a desirable scalability.

Nonnegative matrix factorization and sparse representation for the automated detection of periodic limb movements in sleep.

PubMed

Shokrollahi, Mehrnaz; Krishnan, Sridhar; Dopsa, Dustin D; Muir, Ryan T; Black, Sandra E; Swartz, Richard H; Murray, Brian J; Boulos, Mark I

2016-11-01

Stroke is a leading cause of death and disability in adults, and incurs a significant economic burden to society. Periodic limb movements (PLMs) in sleep are repetitive movements involving the great toe, ankle, and hip. Evolving evidence suggests that PLMs may be associated with high blood pressure and stroke, but this relationship remains underexplored. Several issues limit the study of PLMs including the need to manually score them, which is time-consuming and costly. For this reason, we developed a novel automated method for nocturnal PLM detection, which was shown to be correlated with (a) the manually scored PLM index on polysomnography, and (b) white matter hyperintensities on brain imaging, which have been demonstrated to be associated with PLMs. Our proposed algorithm consists of three main stages: (1) representing the signal in the time-frequency plane using time-frequency matrices (TFM), (2) applying K-nonnegative matrix factorization technique to decompose the TFM matrix into its significant components, and (3) applying kernel sparse representation for classification (KSRC) to the decomposed signal. Our approach was applied to a dataset that consisted of 65 subjects who underwent polysomnography. An overall classification of 97 % was achieved for discrimination of the aforementioned signals, demonstrating the potential of the presented method.

An adaptive sparse-grid high-order stochastic collocation method for Bayesian inference in groundwater reactive transport modeling

NASA Astrophysics Data System (ADS)

Zhang, Guannan; Lu, Dan; Ye, Ming; Gunzburger, Max; Webster, Clayton

2013-10-01

Bayesian analysis has become vital to uncertainty quantification in groundwater modeling, but its application has been hindered by the computational cost associated with numerous model executions required by exploring the posterior probability density function (PPDF) of model parameters. This is particularly the case when the PPDF is estimated using Markov Chain Monte Carlo (MCMC) sampling. In this study, a new approach is developed to improve the computational efficiency of Bayesian inference by constructing a surrogate of the PPDF, using an adaptive sparse-grid high-order stochastic collocation (aSG-hSC) method. Unlike previous works using first-order hierarchical basis, this paper utilizes a compactly supported higher-order hierarchical basis to construct the surrogate system, resulting in a significant reduction in the number of required model executions. In addition, using the hierarchical surplus as an error indicator allows locally adaptive refinement of sparse grids in the parameter space, which further improves computational efficiency. To efficiently build the surrogate system for the PPDF with multiple significant modes, optimization techniques are used to identify the modes, for which high-probability regions are defined and components of the aSG-hSC approximation are constructed. After the surrogate is determined, the PPDF can be evaluated by sampling the surrogate system directly without model execution, resulting in improved efficiency of the surrogate-based MCMC compared with conventional MCMC. The developed method is evaluated using two synthetic groundwater reactive transport models. The first example involves coupled linear reactions and demonstrates the accuracy of our high-order hierarchical basis approach in approximating high-dimensional posteriori distribution. The second example is highly nonlinear because of the reactions of uranium surface complexation, and demonstrates how the iterative aSG-hSC method is able to capture multimodal and non-Gaussian features of PPDF caused by model nonlinearity. Both experiments show that aSG-hSC is an effective and efficient tool for Bayesian inference.

Harnessing data structure for recovery of randomly missing structural vibration responses time history: Sparse representation versus low-rank structure

NASA Astrophysics Data System (ADS)

Yang, Yongchao; Nagarajaiah, Satish

2016-06-01

Randomly missing data of structural vibration responses time history often occurs in structural dynamics and health monitoring. For example, structural vibration responses are often corrupted by outliers or erroneous measurements due to sensor malfunction; in wireless sensing platforms, data loss during wireless communication is a common issue. Besides, to alleviate the wireless data sampling or communication burden, certain accounts of data are often discarded during sampling or before transmission. In these and other applications, recovery of the randomly missing structural vibration responses from the available, incomplete data, is essential for system identification and structural health monitoring; it is an ill-posed inverse problem, however. This paper explicitly harnesses the data structure itself-of the structural vibration responses-to address this (inverse) problem. What is relevant is an empirical, but often practically true, observation, that is, typically there are only few modes active in the structural vibration responses; hence a sparse representation (in frequency domain) of the single-channel data vector, or, a low-rank structure (by singular value decomposition) of the multi-channel data matrix. Exploiting such prior knowledge of data structure (intra-channel sparse or inter-channel low-rank), the new theories of ℓ1-minimization sparse recovery and nuclear-norm-minimization low-rank matrix completion enable recovery of the randomly missing or corrupted structural vibration response data. The performance of these two alternatives, in terms of recovery accuracy and computational time under different data missing rates, is investigated on a few structural vibration response data sets-the seismic responses of the super high-rise Canton Tower and the structural health monitoring accelerations of a real large-scale cable-stayed bridge. Encouraging results are obtained and the applicability and limitation of the presented methods are discussed.

Efficient convolutional sparse coding

DOEpatents

Wohlberg, Brendt

2017-06-20

Computationally efficient algorithms may be applied for fast dictionary learning solving the convolutional sparse coding problem in the Fourier domain. More specifically, efficient convolutional sparse coding may be derived within an alternating direction method of multipliers (ADMM) framework that utilizes fast Fourier transforms (FFT) to solve the main linear system in the frequency domain. Such algorithms may enable a significant reduction in computational cost over conventional approaches by implementing a linear solver for the most critical and computationally expensive component of the conventional iterative algorithm. The theoretical computational cost of the algorithm may be reduced from O(M.sup.3N) to O(MN log N), where N is the dimensionality of the data and M is the number of elements in the dictionary. This significant improvement in efficiency may greatly increase the range of problems that can practically be addressed via convolutional sparse representations.

Direction of Arrival Estimation for MIMO Radar via Unitary Nuclear Norm Minimization

PubMed Central

Wang, Xianpeng; Huang, Mengxing; Wu, Xiaoqin; Bi, Guoan

2017-01-01

In this paper, we consider the direction of arrival (DOA) estimation issue of noncircular (NC) source in multiple-input multiple-output (MIMO) radar and propose a novel unitary nuclear norm minimization (UNNM) algorithm. In the proposed method, the noncircular properties of signals are used to double the virtual array aperture, and the real-valued data are obtained by utilizing unitary transformation. Then a real-valued block sparse model is established based on a novel over-complete dictionary, and a UNNM algorithm is formulated for recovering the block-sparse matrix. In addition, the real-valued NC-MUSIC spectrum is used to design a weight matrix for reweighting the nuclear norm minimization to achieve the enhanced sparsity of solutions. Finally, the DOA is estimated by searching the non-zero blocks of the recovered matrix. Because of using the noncircular properties of signals to extend the virtual array aperture and an additional real structure to suppress the noise, the proposed method provides better performance compared with the conventional sparse recovery based algorithms. Furthermore, the proposed method can handle the case of underdetermined DOA estimation. Simulation results show the effectiveness and advantages of the proposed method. PMID:28441770

Optimization of Sparse Matrix-Vector Multiplication on Emerging Multicore Platforms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Williams, Samuel; Oliker, Leonid; Vuduc, Richard

2008-10-16

We are witnessing a dramatic change in computer architecture due to the multicore paradigm shift, as every electronic device from cell phones to supercomputers confronts parallelism of unprecedented scale. To fully unleash the potential of these systems, the HPC community must develop multicore specific-optimization methodologies for important scientific computations. In this work, we examine sparse matrix-vector multiply (SpMV) - one of the most heavily used kernels in scientific computing - across a broad spectrum of multicore designs. Our experimental platform includes the homogeneous AMD quad-core, AMD dual-core, and Intel quad-core designs, the heterogeneous STI Cell, as well as one ofmore » the first scientific studies of the highly multithreaded Sun Victoria Falls (a Niagara2 SMP). We present several optimization strategies especially effective for the multicore environment, and demonstrate significant performance improvements compared to existing state-of-the-art serial and parallel SpMV implementations. Additionally, we present key insights into the architectural trade-offs of leading multicore design strategies, in the context of demanding memory-bound numerical algorithms.« less

Sparse RNA folding revisited: space-efficient minimum free energy structure prediction.

PubMed

Will, Sebastian; Jabbari, Hosna

2016-01-01

RNA secondary structure prediction by energy minimization is the central computational tool for the analysis of structural non-coding RNAs and their interactions. Sparsification has been successfully applied to improve the time efficiency of various structure prediction algorithms while guaranteeing the same result; however, for many such folding problems, space efficiency is of even greater concern, particularly for long RNA sequences. So far, space-efficient sparsified RNA folding with fold reconstruction was solved only for simple base-pair-based pseudo-energy models. Here, we revisit the problem of space-efficient free energy minimization. Whereas the space-efficient minimization of the free energy has been sketched before, the reconstruction of the optimum structure has not even been discussed. We show that this reconstruction is not possible in trivial extension of the method for simple energy models. Then, we present the time- and space-efficient sparsified free energy minimization algorithm SparseMFEFold that guarantees MFE structure prediction. In particular, this novel algorithm provides efficient fold reconstruction based on dynamically garbage-collected trace arrows. The complexity of our algorithm depends on two parameters, the number of candidates Z and the number of trace arrows T; both are bounded by [Formula: see text], but are typically much smaller. The time complexity of RNA folding is reduced from [Formula: see text] to [Formula: see text]; the space complexity, from [Formula: see text] to [Formula: see text]. Our empirical results show more than 80 % space savings over RNAfold [Vienna RNA package] on the long RNAs from the RNA STRAND database (≥2500 bases). The presented technique is intentionally generalizable to complex prediction algorithms; due to their high space demands, algorithms like pseudoknot prediction and RNA-RNA-interaction prediction are expected to profit even stronger than "standard" MFE folding. SparseMFEFold is free software, available at http://www.bioinf.uni-leipzig.de/~will/Software/SparseMFEFold.

A Generalized Sampling and Preconditioning Scheme for Sparse Approximation of Polynomial Chaos Expansions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jakeman, John D.; Narayan, Akil; Zhou, Tao

We propose an algorithm for recovering sparse orthogonal polynomial expansions via collocation. A standard sampling approach for recovering sparse polynomials uses Monte Carlo sampling, from the density of orthogonality, which results in poor function recovery when the polynomial degree is high. Our proposed approach aims to mitigate this limitation by sampling with respect to the weighted equilibrium measure of the parametric domain and subsequently solves a preconditionedmore » $$\\ell^1$$-minimization problem, where the weights of the diagonal preconditioning matrix are given by evaluations of the Christoffel function. Our algorithm can be applied to a wide class of orthogonal polynomial families on bounded and unbounded domains, including all classical families. We present theoretical analysis to motivate the algorithm and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest. In conclusion, numerical examples are also provided to demonstrate that our proposed algorithm leads to comparable or improved accuracy even when compared with Legendre- and Hermite-specific algorithms.« less

A Generalized Sampling and Preconditioning Scheme for Sparse Approximation of Polynomial Chaos Expansions

DOE PAGES

Jakeman, John D.; Narayan, Akil; Zhou, Tao

2017-06-22

We propose an algorithm for recovering sparse orthogonal polynomial expansions via collocation. A standard sampling approach for recovering sparse polynomials uses Monte Carlo sampling, from the density of orthogonality, which results in poor function recovery when the polynomial degree is high. Our proposed approach aims to mitigate this limitation by sampling with respect to the weighted equilibrium measure of the parametric domain and subsequently solves a preconditionedmore » $$\\ell^1$$-minimization problem, where the weights of the diagonal preconditioning matrix are given by evaluations of the Christoffel function. Our algorithm can be applied to a wide class of orthogonal polynomial families on bounded and unbounded domains, including all classical families. We present theoretical analysis to motivate the algorithm and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest. In conclusion, numerical examples are also provided to demonstrate that our proposed algorithm leads to comparable or improved accuracy even when compared with Legendre- and Hermite-specific algorithms.« less

Detecting double compressed MPEG videos with the same quantization matrix and synchronized group of pictures structure

NASA Astrophysics Data System (ADS)

Aghamaleki, Javad Abbasi; Behrad, Alireza

2018-01-01

Double compression detection is a crucial stage in digital image and video forensics. However, the detection of double compressed videos is challenging when the video forger uses the same quantization matrix and synchronized group of pictures (GOP) structure during the recompression history to conceal tampering effects. A passive approach is proposed for detecting double compressed MPEG videos with the same quantization matrix and synchronized GOP structure. To devise the proposed algorithm, the effects of recompression on P frames are mathematically studied. Then, based on the obtained guidelines, a feature vector is proposed to detect double compressed frames on the GOP level. Subsequently, sparse representations of the feature vectors are used for dimensionality reduction and enrich the traces of recompression. Finally, a support vector machine classifier is employed to detect and localize double compression in temporal domain. The experimental results show that the proposed algorithm achieves the accuracy of more than 95%. In addition, the comparisons of the results of the proposed method with those of other methods reveal the efficiency of the proposed algorithm.

A density matrix-based method for the linear-scaling calculation of dynamic second- and third-order properties at the Hartree-Fock and Kohn-Sham density functional theory levels.

PubMed

Kussmann, Jörg; Ochsenfeld, Christian

2007-11-28

A density matrix-based time-dependent self-consistent field (D-TDSCF) method for the calculation of dynamic polarizabilities and first hyperpolarizabilities using the Hartree-Fock and Kohn-Sham density functional theory approaches is presented. The D-TDSCF method allows us to reduce the asymptotic scaling behavior of the computational effort from cubic to linear for systems with a nonvanishing band gap. The linear scaling is achieved by combining a density matrix-based reformulation of the TDSCF equations with linear-scaling schemes for the formation of Fock- or Kohn-Sham-type matrices. In our reformulation only potentially linear-scaling matrices enter the formulation and efficient sparse algebra routines can be employed. Furthermore, the corresponding formulas for the first hyperpolarizabilities are given in terms of zeroth- and first-order one-particle reduced density matrices according to Wigner's (2n+1) rule. The scaling behavior of our method is illustrated for first exemplary calculations with systems of up to 1011 atoms and 8899 basis functions.

Analysis of Monte Carlo accelerated iterative methods for sparse linear systems: Analysis of Monte Carlo accelerated iterative methods for sparse linear systems

DOE PAGES

Benzi, Michele; Evans, Thomas M.; Hamilton, Steven P.; ...

2017-03-05

Here, we consider hybrid deterministic-stochastic iterative algorithms for the solution of large, sparse linear systems. Starting from a convergent splitting of the coefficient matrix, we analyze various types of Monte Carlo acceleration schemes applied to the original preconditioned Richardson (stationary) iteration. We expect that these methods will have considerable potential for resiliency to faults when implemented on massively parallel machines. We also establish sufficient conditions for the convergence of the hybrid schemes, and we investigate different types of preconditioners including sparse approximate inverses. Numerical experiments on linear systems arising from the discretization of partial differential equations are presented.

Clutter Mitigation in Echocardiography Using Sparse Signal Separation

PubMed Central

Yavneh, Irad

2015-01-01

In ultrasound imaging, clutter artifacts degrade images and may cause inaccurate diagnosis. In this paper, we apply a method called Morphological Component Analysis (MCA) for sparse signal separation with the objective of reducing such clutter artifacts. The MCA approach assumes that the two signals in the additive mix have each a sparse representation under some dictionary of atoms (a matrix), and separation is achieved by finding these sparse representations. In our work, an adaptive approach is used for learning the dictionary from the echo data. MCA is compared to Singular Value Filtering (SVF), a Principal Component Analysis- (PCA-) based filtering technique, and to a high-pass Finite Impulse Response (FIR) filter. Each filter is applied to a simulated hypoechoic lesion sequence, as well as experimental cardiac ultrasound data. MCA is demonstrated in both cases to outperform the FIR filter and obtain results comparable to the SVF method in terms of contrast-to-noise ratio (CNR). Furthermore, MCA shows a lower impact on tissue sections while removing the clutter artifacts. In experimental heart data, MCA obtains in our experiments clutter mitigation with an average CNR improvement of 1.33 dB. PMID:26199622

Parallel Domain Decomposition Formulation and Software for Large-Scale Sparse Symmetrical/Unsymmetrical Aeroacoustic Applications

NASA Technical Reports Server (NTRS)

Nguyen, D. T.; Watson, Willie R. (Technical Monitor)

2005-01-01

The overall objectives of this research work are to formulate and validate efficient parallel algorithms, and to efficiently design/implement computer software for solving large-scale acoustic problems, arised from the unified frameworks of the finite element procedures. The adopted parallel Finite Element (FE) Domain Decomposition (DD) procedures should fully take advantages of multiple processing capabilities offered by most modern high performance computing platforms for efficient parallel computation. To achieve this objective. the formulation needs to integrate efficient sparse (and dense) assembly techniques, hybrid (or mixed) direct and iterative equation solvers, proper pre-conditioned strategies, unrolling strategies, and effective processors' communicating schemes. Finally, the numerical performance of the developed parallel finite element procedures will be evaluated by solving series of structural, and acoustic (symmetrical and un-symmetrical) problems (in different computing platforms). Comparisons with existing "commercialized" and/or "public domain" software are also included, whenever possible.

Sparse Matrix Motivated Reconstruction of Far-Field Radiation Patterns

DTIC Science & Technology

2015-03-01

method for base - station antenna radiation patterns. IEEE Antennas Propagation Magazine. 2001;43(2):132. 4. Vasiliadis TG, Dimitriou D, Sergiadis JD...algorithm based on sparse representations of radiation patterns using the inverse Discrete Fourier Transform (DFT) and the inverse Discrete Cosine...patterns using a Model- Based Parameter Estimation (MBPE) technique that reduces the computational time required to model radiation patterns. Another

Task Parallel Incomplete Cholesky Factorization using 2D Partitioned-Block Layout

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Kyungjoo; Rajamanickam, Sivasankaran; Stelle, George Widgery

We introduce a task-parallel algorithm for sparse incomplete Cholesky factorization that utilizes a 2D sparse partitioned-block layout of a matrix. Our factorization algorithm follows the idea of algorithms-by-blocks by using the block layout. The algorithm-byblocks approach induces a task graph for the factorization. These tasks are inter-related to each other through their data dependences in the factorization algorithm. To process the tasks on various manycore architectures in a portable manner, we also present a portable tasking API that incorporates different tasking backends and device-specific features using an open-source framework for manycore platforms i.e., Kokkos. A performance evaluation is presented onmore » both Intel Sandybridge and Xeon Phi platforms for matrices from the University of Florida sparse matrix collection to illustrate merits of the proposed task-based factorization. Experimental results demonstrate that our task-parallel implementation delivers about 26.6x speedup (geometric mean) over single-threaded incomplete Choleskyby- blocks and 19.2x speedup over serial Cholesky performance which does not carry tasking overhead using 56 threads on the Intel Xeon Phi processor for sparse matrices arising from various application problems.« less

Discriminative Dictionary Learning With Two-Level Low Rank and Group Sparse Decomposition for Image Classification.

PubMed

Wen, Zaidao; Hou, Zaidao; Jiao, Licheng

2017-11-01

Discriminative dictionary learning (DDL) framework has been widely used in image classification which aims to learn some class-specific feature vectors as well as a representative dictionary according to a set of labeled training samples. However, interclass similarities and intraclass variances among input samples and learned features will generally weaken the representability of dictionary and the discrimination of feature vectors so as to degrade the classification performance. Therefore, how to explicitly represent them becomes an important issue. In this paper, we present a novel DDL framework with two-level low rank and group sparse decomposition model. In the first level, we learn a class-shared and several class-specific dictionaries, where a low rank and a group sparse regularization are, respectively, imposed on the corresponding feature matrices. In the second level, the class-specific feature matrix will be further decomposed into a low rank and a sparse matrix so that intraclass variances can be separated to concentrate the corresponding feature vectors. Extensive experimental results demonstrate the effectiveness of our model. Compared with the other state-of-the-arts on several popular image databases, our model can achieve a competitive or better performance in terms of the classification accuracy.

Nonlocal low-rank and sparse matrix decomposition for spectral CT reconstruction

NASA Astrophysics Data System (ADS)

Niu, Shanzhou; Yu, Gaohang; Ma, Jianhua; Wang, Jing

2018-02-01

Spectral computed tomography (CT) has been a promising technique in research and clinics because of its ability to produce improved energy resolution images with narrow energy bins. However, the narrow energy bin image is often affected by serious quantum noise because of the limited number of photons used in the corresponding energy bin. To address this problem, we present an iterative reconstruction method for spectral CT using nonlocal low-rank and sparse matrix decomposition (NLSMD), which exploits the self-similarity of patches that are collected in multi-energy images. Specifically, each set of patches can be decomposed into a low-rank component and a sparse component, and the low-rank component represents the stationary background over different energy bins, while the sparse component represents the rest of the different spectral features in individual energy bins. Subsequently, an effective alternating optimization algorithm was developed to minimize the associated objective function. To validate and evaluate the NLSMD method, qualitative and quantitative studies were conducted by using simulated and real spectral CT data. Experimental results show that the NLSMD method improves spectral CT images in terms of noise reduction, artifact suppression and resolution preservation.

Parallel heterogeneous architectures for efficient OMP compressive sensing reconstruction

NASA Astrophysics Data System (ADS)

Kulkarni, Amey; Stanislaus, Jerome L.; Mohsenin, Tinoosh

2014-05-01

Compressive Sensing (CS) is a novel scheme, in which a signal that is sparse in a known transform domain can be reconstructed using fewer samples. The signal reconstruction techniques are computationally intensive and have sluggish performance, which make them impractical for real-time processing applications . The paper presents novel architectures for Orthogonal Matching Pursuit algorithm, one of the popular CS reconstruction algorithms. We show the implementation results of proposed architectures on FPGA, ASIC and on a custom many-core platform. For FPGA and ASIC implementation, a novel thresholding method is used to reduce the processing time for the optimization problem by at least 25%. Whereas, for the custom many-core platform, efficient parallelization techniques are applied, to reconstruct signals with variant signal lengths of N and sparsity of m. The algorithm is divided into three kernels. Each kernel is parallelized to reduce execution time, whereas efficient reuse of the matrix operators allows us to reduce area. Matrix operations are efficiently paralellized by taking advantage of blocked algorithms. For demonstration purpose, all architectures reconstruct a 256-length signal with maximum sparsity of 8 using 64 measurements. Implementation on Xilinx Virtex-5 FPGA, requires 27.14 μs to reconstruct the signal using basic OMP. Whereas, with thresholding method it requires 18 μs. ASIC implementation reconstructs the signal in 13 μs. However, our custom many-core, operating at 1.18 GHz, takes 18.28 μs to complete. Our results show that compared to the previous published work of the same algorithm and matrix size, proposed architectures for FPGA and ASIC implementations perform 1.3x and 1.8x respectively faster. Also, the proposed many-core implementation performs 3000x faster than the CPU and 2000x faster than the GPU.

Modal analysis of circular Bragg fibers with arbitrary index profiles

NASA Astrophysics Data System (ADS)

Horikis, Theodoros P.; Kath, William L.

2006-12-01

A finite-difference approach based upon the immersed interface method is used to analyze the mode structure of Bragg fibers with arbitrary index profiles. The method allows general propagation constants and eigenmodes to be calculated to a high degree of accuracy, while computation times are kept to a minimum by exploiting sparse matrix algebra. The method is well suited to handle complicated structures comprised of a large number of thin layers with high-index contrast and simultaneously determines multiple eigenmodes without modification.

Hyperspectral imagery super-resolution by compressive sensing inspired dictionary learning and spatial-spectral regularization.

PubMed

Huang, Wei; Xiao, Liang; Liu, Hongyi; Wei, Zhihui

2015-01-19

Due to the instrumental and imaging optics limitations, it is difficult to acquire high spatial resolution hyperspectral imagery (HSI). Super-resolution (SR) imagery aims at inferring high quality images of a given scene from degraded versions of the same scene. This paper proposes a novel hyperspectral imagery super-resolution (HSI-SR) method via dictionary learning and spatial-spectral regularization. The main contributions of this paper are twofold. First, inspired by the compressive sensing (CS) framework, for learning the high resolution dictionary, we encourage stronger sparsity on image patches and promote smaller coherence between the learned dictionary and sensing matrix. Thus, a sparsity and incoherence restricted dictionary learning method is proposed to achieve higher efficiency sparse representation. Second, a variational regularization model combing a spatial sparsity regularization term and a new local spectral similarity preserving term is proposed to integrate the spectral and spatial-contextual information of the HSI. Experimental results show that the proposed method can effectively recover spatial information and better preserve spectral information. The high spatial resolution HSI reconstructed by the proposed method outperforms reconstructed results by other well-known methods in terms of both objective measurements and visual evaluation.

Multi-scale Material Appearance

NASA Astrophysics Data System (ADS)

Wu, Hongzhi

Modeling and rendering the appearance of materials is important for a diverse range of applications of computer graphics - from automobile design to movies and cultural heritage. The appearance of materials varies considerably at different scales, posing significant challenges due to the sheer complexity of the data, as well the need to maintain inter-scale consistency constraints. This thesis presents a series of studies around the modeling, rendering and editing of multi-scale material appearance. To efficiently render material appearance at multiple scales, we develop an object-space precomputed adaptive sampling method, which precomputes a hierarchy of view-independent points that preserve multi-level appearance. To support bi-scale material appearance design, we propose a novel reflectance filtering algorithm, which rapidly computes the large-scale appearance from small-scale details, by exploiting the low-rank structures of Bidirectional Visible Normal Distribution Functions and pre-rotated Bidirectional Reflectance Distribution Functions in the matrix formulation of the rendering algorithm. This approach can guide the physical realization of appearance, as well as the modeling of real-world materials using very sparse measurements. Finally, we present a bi-scale-inspired high-quality general representation for material appearance described by Bidirectional Texture Functions. Our representation is at once compact, easily editable, and amenable to efficient rendering.

The Development of a Finite Volume Method for Modeling Sound in Coastal Ocean Environment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Long, Wen; Yang, Zhaoqing; Copping, Andrea E.

: As the rapid growth of marine renewable energy and off-shore wind energy, there have been concerns that the noises generated from construction and operation of the devices may interfere marine animals’ communication. In this research, a underwater sound model is developed to simulate sound prorogation generated by marine-hydrokinetic energy (MHK) devices or offshore wind (OSW) energy platforms. Finite volume and finite difference methods are developed to solve the 3D Helmholtz equation of sound propagation in the coastal environment. For finite volume method, the grid system consists of triangular grids in horizontal plane and sigma-layers in vertical dimension. A 3Dmore » sparse matrix solver with complex coefficients is formed for solving the resulting acoustic pressure field. The Complex Shifted Laplacian Preconditioner (CSLP) method is applied to efficiently solve the matrix system iteratively with MPI parallelization using a high performance cluster. The sound model is then coupled with the Finite Volume Community Ocean Model (FVCOM) for simulating sound propagation generated by human activities in a range-dependent setting, such as offshore wind energy platform constructions and tidal stream turbines. As a proof of concept, initial validation of the finite difference solver is presented for two coastal wedge problems. Validation of finite volume method will be reported separately.« less

Sparse partial least squares regression for simultaneous dimension reduction and variable selection

PubMed Central

Chun, Hyonho; Keleş, Sündüz

2010-01-01

Partial least squares regression has been an alternative to ordinary least squares for handling multicollinearity in several areas of scientific research since the 1960s. It has recently gained much attention in the analysis of high dimensional genomic data. We show that known asymptotic consistency of the partial least squares estimator for a univariate response does not hold with the very large p and small n paradigm. We derive a similar result for a multivariate response regression with partial least squares. We then propose a sparse partial least squares formulation which aims simultaneously to achieve good predictive performance and variable selection by producing sparse linear combinations of the original predictors. We provide an efficient implementation of sparse partial least squares regression and compare it with well-known variable selection and dimension reduction approaches via simulation experiments. We illustrate the practical utility of sparse partial least squares regression in a joint analysis of gene expression and genomewide binding data. PMID:20107611

Segmentation of High Angular Resolution Diffusion MRI using Sparse Riemannian Manifold Clustering

PubMed Central

Wright, Margaret J.; Thompson, Paul M.; Vidal, René

2015-01-01

We address the problem of segmenting high angular resolution diffusion imaging (HARDI) data into multiple regions (or fiber tracts) with distinct diffusion properties. We use the orientation distribution function (ODF) to represent HARDI data and cast the problem as a clustering problem in the space of ODFs. Our approach integrates tools from sparse representation theory and Riemannian geometry into a graph theoretic segmentation framework. By exploiting the Riemannian properties of the space of ODFs, we learn a sparse representation for each ODF and infer the segmentation by applying spectral clustering to a similarity matrix built from these representations. In cases where regions with similar (resp. distinct) diffusion properties belong to different (resp. same) fiber tracts, we obtain the segmentation by incorporating spatial and user-specified pairwise relationships into the formulation. Experiments on synthetic data evaluate the sensitivity of our method to image noise and the presence of complex fiber configurations, and show its superior performance compared to alternative segmentation methods. Experiments on phantom and real data demonstrate the accuracy of the proposed method in segmenting simulated fibers, as well as white matter fiber tracts of clinical importance in the human brain. PMID:24108748

Eigensolver for a Sparse, Large Hermitian Matrix

NASA Technical Reports Server (NTRS)

Tisdale, E. Robert; Oyafuso, Fabiano; Klimeck, Gerhard; Brown, R. Chris

2003-01-01

A parallel-processing computer program finds a few eigenvalues in a sparse Hermitian matrix that contains as many as 100 million diagonal elements. This program finds the eigenvalues faster, using less memory, than do other, comparable eigensolver programs. This program implements a Lanczos algorithm in the American National Standards Institute/ International Organization for Standardization (ANSI/ISO) C computing language, using the Message Passing Interface (MPI) standard to complement an eigensolver in PARPACK. [PARPACK (Parallel Arnoldi Package) is an extension, to parallel-processing computer architectures, of ARPACK (Arnoldi Package), which is a collection of Fortran 77 subroutines that solve large-scale eigenvalue problems.] The eigensolver runs on Beowulf clusters of computers at the Jet Propulsion Laboratory (JPL).

An Optimal Bahadur-Efficient Method in Detection of Sparse Signals with Applications to Pathway Analysis in Sequencing Association Studies.

PubMed

Dai, Hongying; Wu, Guodong; Wu, Michael; Zhi, Degui

2016-01-01

Next-generation sequencing data pose a severe curse of dimensionality, complicating traditional "single marker-single trait" analysis. We propose a two-stage combined p-value method for pathway analysis. The first stage is at the gene level, where we integrate effects within a gene using the Sequence Kernel Association Test (SKAT). The second stage is at the pathway level, where we perform a correlated Lancaster procedure to detect joint effects from multiple genes within a pathway. We show that the Lancaster procedure is optimal in Bahadur efficiency among all combined p-value methods. The Bahadur efficiency,[Formula: see text], compares sample sizes among different statistical tests when signals become sparse in sequencing data, i.e. ε →0. The optimal Bahadur efficiency ensures that the Lancaster procedure asymptotically requires a minimal sample size to detect sparse signals ([Formula: see text]). The Lancaster procedure can also be applied to meta-analysis. Extensive empirical assessments of exome sequencing data show that the proposed method outperforms Gene Set Enrichment Analysis (GSEA). We applied the competitive Lancaster procedure to meta-analysis data generated by the Global Lipids Genetics Consortium to identify pathways significantly associated with high-density lipoprotein cholesterol, low-density lipoprotein cholesterol, triglycerides, and total cholesterol.

A study of the parallel algorithm for large-scale DC simulation of nonlinear systems

NASA Astrophysics Data System (ADS)

Cortés Udave, Diego Ernesto; Ogrodzki, Jan; Gutiérrez de Anda, Miguel Angel

Newton-Raphson DC analysis of large-scale nonlinear circuits may be an extremely time consuming process even if sparse matrix techniques and bypassing of nonlinear models calculation are used. A slight decrease in the time required for this task may be enabled on multi-core, multithread computers if the calculation of the mathematical models for the nonlinear elements as well as the stamp management of the sparse matrix entries are managed through concurrent processes. This numerical complexity can be further reduced via the circuit decomposition and parallel solution of blocks taking as a departure point the BBD matrix structure. This block-parallel approach may give a considerable profit though it is strongly dependent on the system topology and, of course, on the processor type. This contribution presents the easy-parallelizable decomposition-based algorithm for DC simulation and provides a detailed study of its effectiveness.

Sparse distributed memory and related models

NASA Technical Reports Server (NTRS)

Kanerva, Pentti

1992-01-01

Described here is sparse distributed memory (SDM) as a neural-net associative memory. It is characterized by two weight matrices and by a large internal dimension - the number of hidden units is much larger than the number of input or output units. The first matrix, A, is fixed and possibly random, and the second matrix, C, is modifiable. The SDM is compared and contrasted to (1) computer memory, (2) correlation-matrix memory, (3) feet-forward artificial neural network, (4) cortex of the cerebellum, (5) Marr and Albus models of the cerebellum, and (6) Albus' cerebellar model arithmetic computer (CMAC). Several variations of the basic SDM design are discussed: the selected-coordinate and hyperplane designs of Jaeckel, the pseudorandom associative neural memory of Hassoun, and SDM with real-valued input variables by Prager and Fallside. SDM research conducted mainly at the Research Institute for Advanced Computer Science (RIACS) in 1986-1991 is highlighted.

TESTING HIGH-DIMENSIONAL COVARIANCE MATRICES, WITH APPLICATION TO DETECTING SCHIZOPHRENIA RISK GENES

PubMed Central

Zhu, Lingxue; Lei, Jing; Devlin, Bernie; Roeder, Kathryn

2017-01-01

Scientists routinely compare gene expression levels in cases versus controls in part to determine genes associated with a disease. Similarly, detecting case-control differences in co-expression among genes can be critical to understanding complex human diseases; however statistical methods have been limited by the high dimensional nature of this problem. In this paper, we construct a sparse-Leading-Eigenvalue-Driven (sLED) test for comparing two high-dimensional covariance matrices. By focusing on the spectrum of the differential matrix, sLED provides a novel perspective that accommodates what we assume to be common, namely sparse and weak signals in gene expression data, and it is closely related with Sparse Principal Component Analysis. We prove that sLED achieves full power asymptotically under mild assumptions, and simulation studies verify that it outperforms other existing procedures under many biologically plausible scenarios. Applying sLED to the largest gene-expression dataset obtained from post-mortem brain tissue from Schizophrenia patients and controls, we provide a novel list of genes implicated in Schizophrenia and reveal intriguing patterns in gene co-expression change for Schizophrenia subjects. We also illustrate that sLED can be generalized to compare other gene-gene “relationship” matrices that are of practical interest, such as the weighted adjacency matrices. PMID:29081874

TESTING HIGH-DIMENSIONAL COVARIANCE MATRICES, WITH APPLICATION TO DETECTING SCHIZOPHRENIA RISK GENES.

PubMed

Zhu, Lingxue; Lei, Jing; Devlin, Bernie; Roeder, Kathryn

2017-09-01

Scientists routinely compare gene expression levels in cases versus controls in part to determine genes associated with a disease. Similarly, detecting case-control differences in co-expression among genes can be critical to understanding complex human diseases; however statistical methods have been limited by the high dimensional nature of this problem. In this paper, we construct a sparse-Leading-Eigenvalue-Driven (sLED) test for comparing two high-dimensional covariance matrices. By focusing on the spectrum of the differential matrix, sLED provides a novel perspective that accommodates what we assume to be common, namely sparse and weak signals in gene expression data, and it is closely related with Sparse Principal Component Analysis. We prove that sLED achieves full power asymptotically under mild assumptions, and simulation studies verify that it outperforms other existing procedures under many biologically plausible scenarios. Applying sLED to the largest gene-expression dataset obtained from post-mortem brain tissue from Schizophrenia patients and controls, we provide a novel list of genes implicated in Schizophrenia and reveal intriguing patterns in gene co-expression change for Schizophrenia subjects. We also illustrate that sLED can be generalized to compare other gene-gene "relationship" matrices that are of practical interest, such as the weighted adjacency matrices.

Visual recognition and inference using dynamic overcomplete sparse learning.

PubMed

Murray, Joseph F; Kreutz-Delgado, Kenneth

2007-09-01

We present a hierarchical architecture and learning algorithm for visual recognition and other visual inference tasks such as imagination, reconstruction of occluded images, and expectation-driven segmentation. Using properties of biological vision for guidance, we posit a stochastic generative world model and from it develop a simplified world model (SWM) based on a tractable variational approximation that is designed to enforce sparse coding. Recent developments in computational methods for learning overcomplete representations (Lewicki & Sejnowski, 2000; Teh, Welling, Osindero, & Hinton, 2003) suggest that overcompleteness can be useful for visual tasks, and we use an overcomplete dictionary learning algorithm (Kreutz-Delgado, et al., 2003) as a preprocessing stage to produce accurate, sparse codings of images. Inference is performed by constructing a dynamic multilayer network with feedforward, feedback, and lateral connections, which is trained to approximate the SWM. Learning is done with a variant of the back-propagation-through-time algorithm, which encourages convergence to desired states within a fixed number of iterations. Vision tasks require large networks, and to make learning efficient, we take advantage of the sparsity of each layer to update only a small subset of elements in a large weight matrix at each iteration. Experiments on a set of rotated objects demonstrate various types of visual inference and show that increasing the degree of overcompleteness improves recognition performance in difficult scenes with occluded objects in clutter.

Fast Sparse Coding for Range Data Denoising with Sparse Ridges Constraint.

PubMed

Gao, Zhi; Lao, Mingjie; Sang, Yongsheng; Wen, Fei; Ramesh, Bharath; Zhai, Ruifang

2018-05-06

Light detection and ranging (LiDAR) sensors have been widely deployed on intelligent systems such as unmanned ground vehicles (UGVs) and unmanned aerial vehicles (UAVs) to perform localization, obstacle detection, and navigation tasks. Thus, research into range data processing with competitive performance in terms of both accuracy and efficiency has attracted increasing attention. Sparse coding has revolutionized signal processing and led to state-of-the-art performance in a variety of applications. However, dictionary learning, which plays the central role in sparse coding techniques, is computationally demanding, resulting in its limited applicability in real-time systems. In this study, we propose sparse coding algorithms with a fixed pre-learned ridge dictionary to realize range data denoising via leveraging the regularity of laser range measurements in man-made environments. Experiments on both synthesized data and real data demonstrate that our method obtains accuracy comparable to that of sophisticated sparse coding methods, but with much higher computational efficiency.

Scalable Coding of Plenoptic Images by Using a Sparse Set and Disparities.

PubMed

Li, Yun; Sjostrom, Marten; Olsson, Roger; Jennehag, Ulf

2016-01-01

One of the light field capturing techniques is the focused plenoptic capturing. By placing a microlens array in front of the photosensor, the focused plenoptic cameras capture both spatial and angular information of a scene in each microlens image and across microlens images. The capturing results in a significant amount of redundant information, and the captured image is usually of a large resolution. A coding scheme that removes the redundancy before coding can be of advantage for efficient compression, transmission, and rendering. In this paper, we propose a lossy coding scheme to efficiently represent plenoptic images. The format contains a sparse image set and its associated disparities. The reconstruction is performed by disparity-based interpolation and inpainting, and the reconstructed image is later employed as a prediction reference for the coding of the full plenoptic image. As an outcome of the representation, the proposed scheme inherits a scalable structure with three layers. The results show that plenoptic images are compressed efficiently with over 60 percent bit rate reduction compared with High Efficiency Video Coding intra coding, and with over 20 percent compared with an High Efficiency Video Coding block copying mode.

Solving lattice QCD systems of equations using mixed precision solvers on GPUs

NASA Astrophysics Data System (ADS)

Clark, M. A.; Babich, R.; Barros, K.; Brower, R. C.; Rebbi, C.

2010-09-01

Modern graphics hardware is designed for highly parallel numerical tasks and promises significant cost and performance benefits for many scientific applications. One such application is lattice quantum chromodynamics (lattice QCD), where the main computational challenge is to efficiently solve the discretized Dirac equation in the presence of an SU(3) gauge field. Using NVIDIA's CUDA platform we have implemented a Wilson-Dirac sparse matrix-vector product that performs at up to 40, 135 and 212 Gflops for double, single and half precision respectively on NVIDIA's GeForce GTX 280 GPU. We have developed a new mixed precision approach for Krylov solvers using reliable updates which allows for full double precision accuracy while using only single or half precision arithmetic for the bulk of the computation. The resulting BiCGstab and CG solvers run in excess of 100 Gflops and, in terms of iterations until convergence, perform better than the usual defect-correction approach for mixed precision.

Communication requirements of sparse Cholesky factorization with nested dissection ordering

NASA Technical Reports Server (NTRS)

Naik, Vijay K.; Patrick, Merrell L.

1989-01-01

Load distribution schemes for minimizing the communication requirements of the Cholesky factorization of dense and sparse, symmetric, positive definite matrices on multiprocessor systems are presented. The total data traffic in factoring an n x n sparse symmetric positive definite matrix representing an n-vertex regular two-dimensional grid graph using n exp alpha, alpha not greater than 1, processors are shown to be O(n exp 1 + alpha/2). It is O(n), when n exp alpha, alpha not smaller than 1, processors are used. Under the conditions of uniform load distribution, these results are shown to be asymptotically optimal.

An Energy-Efficient Compressive Image Coding for Green Internet of Things (IoT).

PubMed

Li, Ran; Duan, Xiaomeng; Li, Xu; He, Wei; Li, Yanling

2018-04-17

Aimed at a low-energy consumption of Green Internet of Things (IoT), this paper presents an energy-efficient compressive image coding scheme, which provides compressive encoder and real-time decoder according to Compressive Sensing (CS) theory. The compressive encoder adaptively measures each image block based on the block-based gradient field, which models the distribution of block sparse degree, and the real-time decoder linearly reconstructs each image block through a projection matrix, which is learned by Minimum Mean Square Error (MMSE) criterion. Both the encoder and decoder have a low computational complexity, so that they only consume a small amount of energy. Experimental results show that the proposed scheme not only has a low encoding and decoding complexity when compared with traditional methods, but it also provides good objective and subjective reconstruction qualities. In particular, it presents better time-distortion performance than JPEG. Therefore, the proposed compressive image coding is a potential energy-efficient scheme for Green IoT.

A revised MRCI-algorithm. I. Efficient combination of spin adaptation with individual configuration selection coupled to an effective valence-shell Hamiltonian

NASA Astrophysics Data System (ADS)

Strodel, Paul; Tavan, Paul

2002-09-01

We present a revised multi-reference configuration interaction (MRCI) algorithm for balanced and efficient calculation of electronic excitations in molecules. The revision takes up an earlier method, which had been designed for flexible, state-specific, and individual selection (IS) of MRCI expansions, included perturbational corrections (PERT), and used the spin-coupled hole-particle formalism of Tavan and Schulten (1980) for matrix-element evaluation. It removes the deficiencies of this method by introducing tree structures, which code the CI bases and allow us to efficiently exploit the sparseness of the Hamiltonian matrices. The algorithmic complexity is shown to be optimal for IS/MRCI applications. The revised IS/MRCI/PERT module is combined with the effective valence shell Hamiltonian OM2 suggested by Weber and Thiel (2000). This coupling serves the purpose of making excited state surfaces of organic dye molecules accessible to relatively cheap and sufficiently precise descriptions.

SIMD Optimization of Linear Expressions for Programmable Graphics Hardware

PubMed Central

Bajaj, Chandrajit; Ihm, Insung; Min, Jungki; Oh, Jinsang

2009-01-01

The increased programmability of graphics hardware allows efficient graphical processing unit (GPU) implementations of a wide range of general computations on commodity PCs. An important factor in such implementations is how to fully exploit the SIMD computing capacities offered by modern graphics processors. Linear expressions in the form of ȳ = Ax̄ + b̄, where A is a matrix, and x̄, ȳ and b̄ are vectors, constitute one of the most basic operations in many scientific computations. In this paper, we propose a SIMD code optimization technique that enables efficient shader codes to be generated for evaluating linear expressions. It is shown that performance can be improved considerably by efficiently packing arithmetic operations into four-wide SIMD instructions through reordering of the operations in linear expressions. We demonstrate that the presented technique can be used effectively for programming both vertex and pixel shaders for a variety of mathematical applications, including integrating differential equations and solving a sparse linear system of equations using iterative methods. PMID:19946569

Sparse matrix beamforming and image reconstruction for real-time 2D HIFU monitoring using Harmonic Motion Imaging for Focused Ultrasound (HMIFU) with in vitro validation

PubMed Central

Hou, Gary Y.; Provost, Jean; Grondin, Julien; Wang, Shutao; Marquet, Fabrice; Bunting, Ethan; Konofagou, Elisa E.

2015-01-01

Harmonic Motion Imaging for Focused Ultrasound (HMIFU) is a recently developed High-Intensity Focused Ultrasound (HIFU) treatment monitoring method. HMIFU utilizes an Amplitude-Modulated (fAM = 25 Hz) HIFU beam to induce a localized focal oscillatory motion, which is simultaneously estimated and imaged by confocally-aligned imaging transducer. HMIFU feasibilities have been previously shown in silico, in vitro, and in vivo in 1-D or 2-D monitoring of HIFU treatment. The objective of this study is to develop and show the feasibility of a novel fast beamforming algorithm for image reconstruction using GPU-based sparse-matrix operation with real-time feedback. In this study, the algorithm was implemented onto a fully integrated, clinically relevant HMIFU system composed of a 93-element HIFU transducer (fcenter = 4.5MHz) and coaxially-aligned 64-element phased array (fcenter = 2.5MHz) for displacement excitation and motion estimation, respectively. A single transmit beam with divergent beam transmit was used while fast beamforming was implemented using a GPU-based delay-and-sum method and a sparse-matrix operation. Axial HMI displacements were then estimated from the RF signals using a 1-D normalized cross-correlation method and streamed to a graphic user interface. The present work developed and implemented a sparse matrix beamforming onto a fully-integrated, clinically relevant system, which can stream displacement images up to 15 Hz using a GPU-based processing, an increase of 100 fold in rate of streaming displacement images compared to conventional CPU-based conventional beamforming and reconstruction processing. The achieved feedback rate is also currently the fastest and only approach that does not require interrupting the HIFU treatment amongst the acoustic radiation force based HIFU imaging techniques. Results in phantom experiments showed reproducible displacement imaging, and monitoring of twenty two in vitro HIFU treatments using the new 2D system showed a consistent average focal displacement decrease of 46.7±14.6% during lesion formation. Complementary focal temperature monitoring also indicated an average rate of displacement increase and decrease with focal temperature at 0.84±1.15 %/ °C, and 2.03± 0.93%/ °C, respectively. These results reinforce the HMIFU capability of estimating and monitoring stiffness related changes in real time. Current ongoing studies include clinical translation of the presented system for monitoring of HIFU treatment for breast and pancreatic tumor applications. PMID:24960528

spammpack, Version 2013-06-18

DOE Office of Scientific and Technical Information (OSTI.GOV)

2014-01-17

This library is an implementation of the Sparse Approximate Matrix Multiplication (SpAMM) algorithm introduced. It provides a matrix data type, and an approximate matrix product, which exhibits linear scaling computational complexity for matrices with decay. The product error and the performance of the multiply can be tuned by choosing an appropriate tolerance. The library can be compiled for serial execution or parallel execution on shared memory systems with an OpenMP capable compiler

Tensor Sparse Coding for Positive Definite Matrices.

PubMed

Sivalingam, Ravishankar; Boley, Daniel; Morellas, Vassilios; Papanikolopoulos, Nikos

2013-08-02

In recent years, there has been extensive research on sparse representation of vector-valued signals. In the matrix case, the data points are merely vectorized and treated as vectors thereafter (for e.g., image patches). However, this approach cannot be used for all matrices, as it may destroy the inherent structure of the data. Symmetric positive definite (SPD) matrices constitute one such class of signals, where their implicit structure of positive eigenvalues is lost upon vectorization. This paper proposes a novel sparse coding technique for positive definite matrices, which respects the structure of the Riemannian manifold and preserves the positivity of their eigenvalues, without resorting to vectorization. Synthetic and real-world computer vision experiments with region covariance descriptors demonstrate the need for and the applicability of the new sparse coding model. This work serves to bridge the gap between the sparse modeling paradigm and the space of positive definite matrices.

Tensor sparse coding for positive definite matrices.

PubMed

Sivalingam, Ravishankar; Boley, Daniel; Morellas, Vassilios; Papanikolopoulos, Nikolaos

2014-03-01

In recent years, there has been extensive research on sparse representation of vector-valued signals. In the matrix case, the data points are merely vectorized and treated as vectors thereafter (for example, image patches). However, this approach cannot be used for all matrices, as it may destroy the inherent structure of the data. Symmetric positive definite (SPD) matrices constitute one such class of signals, where their implicit structure of positive eigenvalues is lost upon vectorization. This paper proposes a novel sparse coding technique for positive definite matrices, which respects the structure of the Riemannian manifold and preserves the positivity of their eigenvalues, without resorting to vectorization. Synthetic and real-world computer vision experiments with region covariance descriptors demonstrate the need for and the applicability of the new sparse coding model. This work serves to bridge the gap between the sparse modeling paradigm and the space of positive definite matrices.

Efficient Sparse Signal Transmission over a Lossy Link Using Compressive Sensing

PubMed Central

Wu, Liantao; Yu, Kai; Cao, Dongyu; Hu, Yuhen; Wang, Zhi

2015-01-01

Reliable data transmission over lossy communication link is expensive due to overheads for error protection. For signals that have inherent sparse structures, compressive sensing (CS) is applied to facilitate efficient sparse signal transmissions over lossy communication links without data compression or error protection. The natural packet loss in the lossy link is modeled as a random sampling process of the transmitted data, and the original signal will be reconstructed from the lossy transmission results using the CS-based reconstruction method at the receiving end. The impacts of packet lengths on transmission efficiency under different channel conditions have been discussed, and interleaving is incorporated to mitigate the impact of burst data loss. Extensive simulations and experiments have been conducted and compared to the traditional automatic repeat request (ARQ) interpolation technique, and very favorable results have been observed in terms of both accuracy of the reconstructed signals and the transmission energy consumption. Furthermore, the packet length effect provides useful insights for using compressed sensing for efficient sparse signal transmission via lossy links. PMID:26287195

Towards Protein Crystallization as a Process Step in Downstream Processing of Therapeutic Antibodies: Screening and Optimization at Microbatch Scale

PubMed Central

Zang, Yuguo; Kammerer, Bernd; Eisenkolb, Maike; Lohr, Katrin; Kiefer, Hans

2011-01-01

Crystallization conditions of an intact monoclonal IgG4 (immunoglobulin G, subclass 4) antibody were established in vapor diffusion mode by sparse matrix screening and subsequent optimization. The procedure was transferred to microbatch conditions and a phase diagram was built showing surprisingly low solubility of the antibody at equilibrium. With up-scaling to process scale in mind, purification efficiency of the crystallization step was investigated. Added model protein contaminants were excluded from the crystals to more than 95%. No measurable loss of Fc-binding activity was observed in the crystallized and redissolved antibody. Conditions could be adapted to crystallize the antibody directly from concentrated and diafiltrated cell culture supernatant, showing purification efficiency similar to that of Protein A chromatography. We conclude that crystallization has the potential to be included in downstream processing as a low-cost purification or formulation step. PMID:21966480

LiDAR point classification based on sparse representation

NASA Astrophysics Data System (ADS)

Li, Nan; Pfeifer, Norbert; Liu, Chun

2017-04-01

In order to combine the initial spatial structure and features of LiDAR data for accurate classification. The LiDAR data is represented as a 4-order tensor. Sparse representation for classification(SRC) method is used for LiDAR tensor classification. It turns out SRC need only a few of training samples from each class, meanwhile can achieve good classification result. Multiple features are extracted from raw LiDAR points to generate a high-dimensional vector at each point. Then the LiDAR tensor is built by the spatial distribution and feature vectors of the point neighborhood. The entries of LiDAR tensor are accessed via four indexes. Each index is called mode: three spatial modes in direction X ,Y ,Z and one feature mode. Sparse representation for classification(SRC) method is proposed in this paper. The sparsity algorithm is to find the best represent the test sample by sparse linear combination of training samples from a dictionary. To explore the sparsity of LiDAR tensor, the tucker decomposition is used. It decomposes a tensor into a core tensor multiplied by a matrix along each mode. Those matrices could be considered as the principal components in each mode. The entries of core tensor show the level of interaction between the different components. Therefore, the LiDAR tensor can be approximately represented by a sparse tensor multiplied by a matrix selected from a dictionary along each mode. The matrices decomposed from training samples are arranged as initial elements in the dictionary. By dictionary learning, a reconstructive and discriminative structure dictionary along each mode is built. The overall structure dictionary composes of class-specified sub-dictionaries. Then the sparse core tensor is calculated by tensor OMP(Orthogonal Matching Pursuit) method based on dictionaries along each mode. It is expected that original tensor should be well recovered by sub-dictionary associated with relevant class, while entries in the sparse tensor associated with other classed should be nearly zero. Therefore, SRC use the reconstruction error associated with each class to do data classification. A section of airborne LiDAR points of Vienna city is used and classified into 6classes: ground, roofs, vegetation, covered ground, walls and other points. Only 6 training samples from each class are taken. For the final classification result, ground and covered ground are merged into one same class(ground). The classification accuracy for ground is 94.60%, roof is 95.47%, vegetation is 85.55%, wall is 76.17%, other object is 20.39%.

SPAR reference manual

NASA Technical Reports Server (NTRS)

Whetstone, W. D.

1976-01-01

The functions and operating rules of the SPAR system, which is a group of computer programs used primarily to perform stress, buckling, and vibrational analyses of linear finite element systems, were given. The following subject areas were discussed: basic information, structure definition, format system matrix processors, utility programs, static solutions, stresses, sparse matrix eigensolver, dynamic response, graphics, and substructure processors.

Matrix Recipes for Hard Thresholding Methods

DTIC Science & Technology

2012-11-07

have been proposed to approximate the solution. In [11], Donoho et al . demonstrate that, in the sparse approximation problem, under basic incoherence...inducing convex surrogate ‖ · ‖1 with provable guarantees for unique signal recovery. In the ARM problem, Fazel et al . [12] identified the nuclear norm...sparse recovery for all. Technical report, EPFL, 2011 . [25] N. Halko , P. G. Martinsson, and J. A. Tropp. Finding structure with randomness: Probabilistic

Extending R packages to support 64-bit compiled code: An illustration with spam64 and GIMMS NDVI3g data

NASA Astrophysics Data System (ADS)

Gerber, Florian; Mösinger, Kaspar; Furrer, Reinhard

2017-07-01

Software packages for spatial data often implement a hybrid approach of interpreted and compiled programming languages. The compiled parts are usually written in C, C++, or Fortran, and are efficient in terms of computational speed and memory usage. Conversely, the interpreted part serves as a convenient user-interface and calls the compiled code for computationally demanding operations. The price paid for the user friendliness of the interpreted component is-besides performance-the limited access to low level and optimized code. An example of such a restriction is the 64-bit vector support of the widely used statistical language R. On the R side, users do not need to change existing code and may not even notice the extension. On the other hand, interfacing 64-bit compiled code efficiently is challenging. Since many R packages for spatial data could benefit from 64-bit vectors, we investigate strategies to efficiently pass 64-bit vectors to compiled languages. More precisely, we show how to simply extend existing R packages using the foreign function interface to seamlessly support 64-bit vectors. This extension is shown with the sparse matrix algebra R package spam. The new capabilities are illustrated with an example of GIMMS NDVI3g data featuring a parametric modeling approach for a non-stationary covariance matrix.

Correlated activity supports efficient cortical processing

PubMed Central

Hung, Chou P.; Cui, Ding; Chen, Yueh-peng; Lin, Chia-pei; Levine, Matthew R.

2015-01-01

Visual recognition is a computational challenge that is thought to occur via efficient coding. An important concept is sparseness, a measure of coding efficiency. The prevailing view is that sparseness supports efficiency by minimizing redundancy and correlations in spiking populations. Yet, we recently reported that “choristers”, neurons that behave more similarly (have correlated stimulus preferences and spontaneous coincident spiking), carry more generalizable object information than uncorrelated neurons (“soloists”) in macaque inferior temporal (IT) cortex. The rarity of choristers (as low as 6% of IT neurons) indicates that they were likely missed in previous studies. Here, we report that correlation strength is distinct from sparseness (choristers are not simply broadly tuned neurons), that choristers are located in non-granular output layers, and that correlated activity predicts human visual search efficiency. These counterintuitive results suggest that a redundant correlational structure supports efficient processing and behavior. PMID:25610392

A path-oriented knowledge representation system: Defusing the combinatorial system

NASA Technical Reports Server (NTRS)

Karamouzis, Stamos T.; Barry, John S.; Smith, Steven L.; Feyock, Stefan

1995-01-01

LIMAP is a programming system oriented toward efficient information manipulation over fixed finite domains, and quantification over paths and predicates. A generalization of Warshall's Algorithm to precompute paths in a sparse matrix representation of semantic nets is employed to allow questions involving paths between components to be posed and answered easily. LIMAP's ability to cache all paths between two components in a matrix cell proved to be a computational obstacle, however, when the semantic net grew to realistic size. The present paper describes a means of mitigating this combinatorial explosion to an extent that makes the use of the LIMAP representation feasible for problems of significant size. The technique we describe radically reduces the size of the search space in which LIMAP must operate; semantic nets of more than 500 nodes have been attacked successfully. Furthermore, it appears that the procedure described is applicable not only to LIMAP, but to a number of other combinatorially explosive search space problems found in AI as well.

HO2 rovibrational eigenvalue studies for nonzero angular momentum

NASA Astrophysics Data System (ADS)

Wu, Xudong T.; Hayes, Edward F.

1997-08-01

An efficient parallel algorithm is reported for determining all bound rovibrational energy levels for the HO2 molecule for nonzero angular momentum values, J=1, 2, and 3. Performance tests on the CRAY T3D indicate that the algorithm scales almost linearly when up to 128 processors are used. Sustained performance levels of up to 3.8 Gflops have been achieved using 128 processors for J=3. The algorithm uses a direct product discrete variable representation (DVR) basis and the implicitly restarted Lanczos method (IRLM) of Sorensen to compute the eigenvalues of the polyatomic Hamiltonian. Since the IRLM is an iterative method, it does not require storage of the full Hamiltonian matrix—it only requires the multiplication of the Hamiltonian matrix by a vector. When the IRLM is combined with a formulation such as DVR, which produces a very sparse matrix, both memory and computation times can be reduced dramatically. This algorithm has the potential to achieve even higher performance levels for larger values of the total angular momentum.

Reconstructing cortical current density by exploring sparseness in the transform domain

NASA Astrophysics Data System (ADS)

Ding, Lei

2009-05-01

In the present study, we have developed a novel electromagnetic source imaging approach to reconstruct extended cortical sources by means of cortical current density (CCD) modeling and a novel EEG imaging algorithm which explores sparseness in cortical source representations through the use of L1-norm in objective functions. The new sparse cortical current density (SCCD) imaging algorithm is unique since it reconstructs cortical sources by attaining sparseness in a transform domain (the variation map of cortical source distributions). While large variations are expected to occur along boundaries (sparseness) between active and inactive cortical regions, cortical sources can be reconstructed and their spatial extents can be estimated by locating these boundaries. We studied the SCCD algorithm using numerous simulations to investigate its capability in reconstructing cortical sources with different extents and in reconstructing multiple cortical sources with different extent contrasts. The SCCD algorithm was compared with two L2-norm solutions, i.e. weighted minimum norm estimate (wMNE) and cortical LORETA. Our simulation data from the comparison study show that the proposed sparse source imaging algorithm is able to accurately and efficiently recover extended cortical sources and is promising to provide high-accuracy estimation of cortical source extents.

Sparse gammatone signal model optimized for English speech does not match the human auditory filters.

PubMed

Strahl, Stefan; Mertins, Alfred

2008-07-18

Evidence that neurosensory systems use sparse signal representations as well as improved performance of signal processing algorithms using sparse signal models raised interest in sparse signal coding in the last years. For natural audio signals like speech and environmental sounds, gammatone atoms have been derived as expansion functions that generate a nearly optimal sparse signal model (Smith, E., Lewicki, M., 2006. Efficient auditory coding. Nature 439, 978-982). Furthermore, gammatone functions are established models for the human auditory filters. Thus far, a practical application of a sparse gammatone signal model has been prevented by the fact that deriving the sparsest representation is, in general, computationally intractable. In this paper, we applied an accelerated version of the matching pursuit algorithm for gammatone dictionaries allowing real-time and large data set applications. We show that a sparse signal model in general has advantages in audio coding and that a sparse gammatone signal model encodes speech more efficiently in terms of sparseness than a sparse modified discrete cosine transform (MDCT) signal model. We also show that the optimal gammatone parameters derived for English speech do not match the human auditory filters, suggesting for signal processing applications to derive the parameters individually for each applied signal class instead of using psychometrically derived parameters. For brain research, it means that care should be taken with directly transferring findings of optimality for technical to biological systems.

A critical analysis of computational protein design with sparse residue interaction graphs

PubMed Central

Georgiev, Ivelin S.

2017-01-01

Protein design algorithms enumerate a combinatorial number of candidate structures to compute the Global Minimum Energy Conformation (GMEC). To efficiently find the GMEC, protein design algorithms must methodically reduce the conformational search space. By applying distance and energy cutoffs, the protein system to be designed can thus be represented using a sparse residue interaction graph, where the number of interacting residue pairs is less than all pairs of mutable residues, and the corresponding GMEC is called the sparse GMEC. However, ignoring some pairwise residue interactions can lead to a change in the energy, conformation, or sequence of the sparse GMEC vs. the original or the full GMEC. Despite the widespread use of sparse residue interaction graphs in protein design, the above mentioned effects of their use have not been previously analyzed. To analyze the costs and benefits of designing with sparse residue interaction graphs, we computed the GMECs for 136 different protein design problems both with and without distance and energy cutoffs, and compared their energies, conformations, and sequences. Our analysis shows that the differences between the GMECs depend critically on whether or not the design includes core, boundary, or surface residues. Moreover, neglecting long-range interactions can alter local interactions and introduce large sequence differences, both of which can result in significant structural and functional changes. Designs on proteins with experimentally measured thermostability show it is beneficial to compute both the full and the sparse GMEC accurately and efficiently. To this end, we show that a provable, ensemble-based algorithm can efficiently compute both GMECs by enumerating a small number of conformations, usually fewer than 1000. This provides a novel way to combine sparse residue interaction graphs with provable, ensemble-based algorithms to reap the benefits of sparse residue interaction graphs while avoiding their potential inaccuracies. PMID:28358804

Remote sensing image segmentation using local sparse structure constrained latent low rank representation

NASA Astrophysics Data System (ADS)

Tian, Shu; Zhang, Ye; Yan, Yimin; Su, Nan; Zhang, Junping

2016-09-01

Latent low-rank representation (LatLRR) has been attached considerable attention in the field of remote sensing image segmentation, due to its effectiveness in exploring the multiple subspace structures of data. However, the increasingly heterogeneous texture information in the high spatial resolution remote sensing images, leads to more severe interference of pixels in local neighborhood, and the LatLRR fails to capture the local complex structure information. Therefore, we present a local sparse structure constrainted latent low-rank representation (LSSLatLRR) segmentation method, which explicitly imposes the local sparse structure constraint on LatLRR to capture the intrinsic local structure in manifold structure feature subspaces. The whole segmentation framework can be viewed as two stages in cascade. In the first stage, we use the local histogram transform to extract the texture local histogram features (LHOG) at each pixel, which can efficiently capture the complex and micro-texture pattern. In the second stage, a local sparse structure (LSS) formulation is established on LHOG, which aims to preserve the local intrinsic structure and enhance the relationship between pixels having similar local characteristics. Meanwhile, by integrating the LSS and the LatLRR, we can efficiently capture the local sparse and low-rank structure in the mixture of feature subspace, and we adopt the subspace segmentation method to improve the segmentation accuracy. Experimental results on the remote sensing images with different spatial resolution show that, compared with three state-of-the-art image segmentation methods, the proposed method achieves more accurate segmentation results.

[Formula: see text]-regularized recursive total least squares based sparse system identification for the error-in-variables.

PubMed

Lim, Jun-Seok; Pang, Hee-Suk

2016-01-01

In this paper an [Formula: see text]-regularized recursive total least squares (RTLS) algorithm is considered for the sparse system identification. Although recursive least squares (RLS) has been successfully applied in sparse system identification, the estimation performance in RLS based algorithms becomes worse, when both input and output are contaminated by noise (the error-in-variables problem). We proposed an algorithm to handle the error-in-variables problem. The proposed [Formula: see text]-RTLS algorithm is an RLS like iteration using the [Formula: see text] regularization. The proposed algorithm not only gives excellent performance but also reduces the required complexity through the effective inversion matrix handling. Simulations demonstrate the superiority of the proposed [Formula: see text]-regularized RTLS for the sparse system identification setting.

A modified dual-level algorithm for large-scale three-dimensional Laplace and Helmholtz equation

NASA Astrophysics Data System (ADS)

Li, Junpu; Chen, Wen; Fu, Zhuojia

2018-01-01

A modified dual-level algorithm is proposed in the article. By the help of the dual level structure, the fully-populated interpolation matrix on the fine level is transformed to a local supported sparse matrix to solve the highly ill-conditioning and excessive storage requirement resulting from fully-populated interpolation matrix. The kernel-independent fast multipole method is adopted to expediting the solving process of the linear equations on the coarse level. Numerical experiments up to 2-million fine-level nodes have successfully been achieved. It is noted that the proposed algorithm merely needs to place 2-3 coarse-level nodes in each wavelength per direction to obtain the reasonable solution, which almost down to the minimum requirement allowed by the Shannon's sampling theorem. In the real human head model example, it is observed that the proposed algorithm can simulate well computationally very challenging exterior high-frequency harmonic acoustic wave propagation up to 20,000 Hz.

A new approach for solving seismic tomography problems and assessing the uncertainty through the use of graph theory and direct methods

NASA Astrophysics Data System (ADS)

Bogiatzis, P.; Ishii, M.; Davis, T. A.

2016-12-01

Seismic tomography inverse problems are among the largest high-dimensional parameter estimation tasks in Earth science. We show how combinatorics and graph theory can be used to analyze the structure of such problems, and to effectively decompose them into smaller ones that can be solved efficiently by means of the least squares method. In combination with recent high performance direct sparse algorithms, this reduction in dimensionality allows for an efficient computation of the model resolution and covariance matrices using limited resources. Furthermore, we show that a new sparse singular value decomposition method can be used to obtain the complete spectrum of the singular values. This procedure provides the means for more objective regularization and further dimensionality reduction of the problem. We apply this methodology to a moderate size, non-linear seismic tomography problem to image the structure of the crust and the upper mantle beneath Japan using local deep earthquakes recorded by the High Sensitivity Seismograph Network stations.

Fast Sparse Coding for Range Data Denoising with Sparse Ridges Constraint

PubMed Central

Lao, Mingjie; Sang, Yongsheng; Wen, Fei; Zhai, Ruifang

2018-01-01

Light detection and ranging (LiDAR) sensors have been widely deployed on intelligent systems such as unmanned ground vehicles (UGVs) and unmanned aerial vehicles (UAVs) to perform localization, obstacle detection, and navigation tasks. Thus, research into range data processing with competitive performance in terms of both accuracy and efficiency has attracted increasing attention. Sparse coding has revolutionized signal processing and led to state-of-the-art performance in a variety of applications. However, dictionary learning, which plays the central role in sparse coding techniques, is computationally demanding, resulting in its limited applicability in real-time systems. In this study, we propose sparse coding algorithms with a fixed pre-learned ridge dictionary to realize range data denoising via leveraging the regularity of laser range measurements in man-made environments. Experiments on both synthesized data and real data demonstrate that our method obtains accuracy comparable to that of sophisticated sparse coding methods, but with much higher computational efficiency. PMID:29734793

NoGOA: predicting noisy GO annotations using evidences and sparse representation.

PubMed

Yu, Guoxian; Lu, Chang; Wang, Jun

2017-07-21

Gene Ontology (GO) is a community effort to represent functional features of gene products. GO annotations (GOA) provide functional associations between GO terms and gene products. Due to resources limitation, only a small portion of annotations are manually checked by curators, and the others are electronically inferred. Although quality control techniques have been applied to ensure the quality of annotations, the community consistently report that there are still considerable noisy (or incorrect) annotations. Given the wide application of annotations, however, how to identify noisy annotations is an important but yet seldom studied open problem. We introduce a novel approach called NoGOA to predict noisy annotations. NoGOA applies sparse representation on the gene-term association matrix to reduce the impact of noisy annotations, and takes advantage of sparse representation coefficients to measure the semantic similarity between genes. Secondly, it preliminarily predicts noisy annotations of a gene based on aggregated votes from semantic neighborhood genes of that gene. Next, NoGOA estimates the ratio of noisy annotations for each evidence code based on direct annotations in GOA files archived on different periods, and then weights entries of the association matrix via estimated ratios and propagates weights to ancestors of direct annotations using GO hierarchy. Finally, it integrates evidence-weighted association matrix and aggregated votes to predict noisy annotations. Experiments on archived GOA files of six model species (H. sapiens, A. thaliana, S. cerevisiae, G. gallus, B. Taurus and M. musculus) demonstrate that NoGOA achieves significantly better results than other related methods and removing noisy annotations improves the performance of gene function prediction. The comparative study justifies the effectiveness of integrating evidence codes with sparse representation for predicting noisy GO annotations. Codes and datasets are available at http://mlda.swu.edu.cn/codes.php?name=NoGOA .

Project APhiD: A Lorenz-gauged A-Φ decomposition for parallelized computation of ultra-broadband electromagnetic induction in a fully heterogeneous Earth

NASA Astrophysics Data System (ADS)

Weiss, Chester J.

2013-08-01

An essential element for computational hypothesis testing, data inversion and experiment design for electromagnetic geophysics is a robust forward solver, capable of easily and quickly evaluating the electromagnetic response of arbitrary geologic structure. The usefulness of such a solver hinges on the balance among competing desires like ease of use, speed of forward calculation, scalability to large problems or compute clusters, parsimonious use of memory access, accuracy and by necessity, the ability to faithfully accommodate a broad range of geologic scenarios over extremes in length scale and frequency content. This is indeed a tall order. The present study addresses recent progress toward the development of a forward solver with these properties. Based on the Lorenz-gauged Helmholtz decomposition, a new finite volume solution over Cartesian model domains endowed with complex-valued electrical properties is shown to be stable over the frequency range 10-2-1010 Hz and range 10-3-105 m in length scale. Benchmark examples are drawn from magnetotellurics, exploration geophysics, geotechnical mapping and laboratory-scale analysis, showing excellent agreement with reference analytic solutions. Computational efficiency is achieved through use of a matrix-free implementation of the quasi-minimum-residual (QMR) iterative solver, which eliminates explicit storage of finite volume matrix elements in favor of "on the fly" computation as needed by the iterative Krylov sequence. Further efficiency is achieved through sparse coupling matrices between the vector and scalar potentials whose non-zero elements arise only in those parts of the model domain where the conductivity gradient is non-zero. Multi-thread parallelization in the QMR solver through OpenMP pragmas is used to reduce the computational cost of its most expensive step: the single matrix-vector product at each iteration. High-level MPI communicators farm independent processes to available compute nodes for simultaneous computation of multi-frequency or multi-transmitter responses.

Hybrid reconstruction of quantum density matrix: when low-rank meets sparsity

NASA Astrophysics Data System (ADS)

Li, Kezhi; Zheng, Kai; Yang, Jingbei; Cong, Shuang; Liu, Xiaomei; Li, Zhaokai

2017-12-01

Both the mathematical theory and experiments have verified that the quantum state tomography based on compressive sensing is an efficient framework for the reconstruction of quantum density states. In recent physical experiments, we found that many unknown density matrices in which people are interested in are low-rank as well as sparse. Bearing this information in mind, in this paper we propose a reconstruction algorithm that combines the low-rank and the sparsity property of density matrices and further theoretically prove that the solution of the optimization function can be, and only be, the true density matrix satisfying the model with overwhelming probability, as long as a necessary number of measurements are allowed. The solver leverages the fixed-point equation technique in which a step-by-step strategy is developed by utilizing an extended soft threshold operator that copes with complex values. Numerical experiments of the density matrix estimation for real nuclear magnetic resonance devices reveal that the proposed method achieves a better accuracy compared to some existing methods. We believe that the proposed method could be leveraged as a generalized approach and widely implemented in the quantum state estimation.

Improving temporal resolution in fMRI using a 3D spiral acquisition and low rank plus sparse (L+S) reconstruction.

PubMed

Petrov, Andrii Y; Herbst, Michael; Andrew Stenger, V

2017-08-15

Rapid whole-brain dynamic Magnetic Resonance Imaging (MRI) is of particular interest in Blood Oxygen Level Dependent (BOLD) functional MRI (fMRI). Faster acquisitions with higher temporal sampling of the BOLD time-course provide several advantages including increased sensitivity in detecting functional activation, the possibility of filtering out physiological noise for improving temporal SNR, and freezing out head motion. Generally, faster acquisitions require undersampling of the data which results in aliasing artifacts in the object domain. A recently developed low-rank (L) plus sparse (S) matrix decomposition model (L+S) is one of the methods that has been introduced to reconstruct images from undersampled dynamic MRI data. The L+S approach assumes that the dynamic MRI data, represented as a space-time matrix M, is a linear superposition of L and S components, where L represents highly spatially and temporally correlated elements, such as the image background, while S captures dynamic information that is sparse in an appropriate transform domain. This suggests that L+S might be suited for undersampled task or slow event-related fMRI acquisitions because the periodic nature of the BOLD signal is sparse in the temporal Fourier transform domain and slowly varying low-rank brain background signals, such as physiological noise and drift, will be predominantly low-rank. In this work, as a proof of concept, we exploit the L+S method for accelerating block-design fMRI using a 3D stack of spirals (SoS) acquisition where undersampling is performed in the k z -t domain. We examined the feasibility of the L+S method to accurately separate temporally correlated brain background information in the L component while capturing periodic BOLD signals in the S component. We present results acquired in control human volunteers at 3T for both retrospective and prospectively acquired fMRI data for a visual activation block-design task. We show that a SoS fMRI acquisition with an acceleration of four and L+S reconstruction can achieve a brain coverage of 40 slices at 2mm isotropic resolution and 64 x 64 matrix size every 500ms. Copyright © 2017 Elsevier Inc. All rights reserved.

Rectified factor networks for biclustering of omics data.

PubMed

Clevert, Djork-Arné; Unterthiner, Thomas; Povysil, Gundula; Hochreiter, Sepp

2017-07-15

Biclustering has become a major tool for analyzing large datasets given as matrix of samples times features and has been successfully applied in life sciences and e-commerce for drug design and recommender systems, respectively. actor nalysis for cluster cquisition (FABIA), one of the most successful biclustering methods, is a generative model that represents each bicluster by two sparse membership vectors: one for the samples and one for the features. However, FABIA is restricted to about 20 code units because of the high computational complexity of computing the posterior. Furthermore, code units are sometimes insufficiently decorrelated and sample membership is difficult to determine. We propose to use the recently introduced unsupervised Deep Learning approach Rectified Factor Networks (RFNs) to overcome the drawbacks of existing biclustering methods. RFNs efficiently construct very sparse, non-linear, high-dimensional representations of the input via their posterior means. RFN learning is a generalized alternating minimization algorithm based on the posterior regularization method which enforces non-negative and normalized posterior means. Each code unit represents a bicluster, where samples for which the code unit is active belong to the bicluster and features that have activating weights to the code unit belong to the bicluster. On 400 benchmark datasets and on three gene expression datasets with known clusters, RFN outperformed 13 other biclustering methods including FABIA. On data of the 1000 Genomes Project, RFN could identify DNA segments which indicate, that interbreeding with other hominins starting already before ancestors of modern humans left Africa. https://github.com/bioinf-jku/librfn. djork-arne.clevert@bayer.com or hochreit@bioinf.jku.at. © The Author 2017. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com

Development of a Real Time Sparse Non-Negative Matrix Factorization Module for Cochlear Implants by Using xPC Target

PubMed Central

Hu, Hongmei; Krasoulis, Agamemnon; Lutman, Mark; Bleeck, Stefan

2013-01-01

Cochlear implants (CIS) require efficient speech processing to maximize information transmission to the brain, especially in noise. A novel CI processing strategy was proposed in our previous studies, in which sparsity-constrained non-negative matrix factorization (NMF) was applied to the envelope matrix in order to improve the CI performance in noisy environments. It showed that the algorithm needs to be adaptive, rather than fixed, in order to adjust to acoustical conditions and individual characteristics. Here, we explore the benefit of a system that allows the user to adjust the signal processing in real time according to their individual listening needs and their individual hearing capabilities. In this system, which is based on MATLAB®, SIMULINK® and the xPC Target™ environment, the input/outupt (I/O) boards are interfaced between the SIMULINK blocks and the CI stimulation system, such that the output can be controlled successfully in the manner of a hardware-in-the-loop (HIL) simulation, hence offering a convenient way to implement a real time signal processing module that does not require any low level language. The sparsity constrained parameter of the algorithm was adapted online subjectively during an experiment with normal-hearing subjects and noise vocoded speech simulation. Results show that subjects chose different parameter values according to their own intelligibility preferences, indicating that adaptive real time algorithms are beneficial to fully explore subjective preferences. We conclude that the adaptive real time systems are beneficial for the experimental design, and such systems allow one to conduct psychophysical experiments with high ecological validity. PMID:24129021

Development of a real time sparse non-negative matrix factorization module for cochlear implants by using xPC target.

PubMed

Hu, Hongmei; Krasoulis, Agamemnon; Lutman, Mark; Bleeck, Stefan

2013-10-14

Cochlear implants (CIs) require efficient speech processing to maximize information transmission to the brain, especially in noise. A novel CI processing strategy was proposed in our previous studies, in which sparsity-constrained non-negative matrix factorization (NMF) was applied to the envelope matrix in order to improve the CI performance in noisy environments. It showed that the algorithm needs to be adaptive, rather than fixed, in order to adjust to acoustical conditions and individual characteristics. Here, we explore the benefit of a system that allows the user to adjust the signal processing in real time according to their individual listening needs and their individual hearing capabilities. In this system, which is based on MATLAB®, SIMULINK® and the xPC Target™ environment, the input/outupt (I/O) boards are interfaced between the SIMULINK blocks and the CI stimulation system, such that the output can be controlled successfully in the manner of a hardware-in-the-loop (HIL) simulation, hence offering a convenient way to implement a real time signal processing module that does not require any low level language. The sparsity constrained parameter of the algorithm was adapted online subjectively during an experiment with normal-hearing subjects and noise vocoded speech simulation. Results show that subjects chose different parameter values according to their own intelligibility preferences, indicating that adaptive real time algorithms are beneficial to fully explore subjective preferences. We conclude that the adaptive real time systems are beneficial for the experimental design, and such systems allow one to conduct psychophysical experiments with high ecological validity.

Efficient Computation of Anharmonic Force Constants via q-space, with Application to Graphene

NASA Astrophysics Data System (ADS)

Kornbluth, Mordechai; Marianetti, Chris

We present a new approach for extracting anharmonic force constants from a sparse sampling of the anharmonic dynamical tensor. We calculate the derivative of the energy with respect to q-space displacements (phonons) and strain, which guarantees the absence of supercell image errors. Central finite differences provide a well-converged quadratic error tail for each derivative, separating the contribution of each anharmonic order. These derivatives populate the anharmonic dynamical tensor in a sparse mesh that bounds the Brillouin Zone, which ensures comprehensive sampling of q-space while exploiting small-cell calculations for efficient, high-throughput computation. This produces a well-converged and precisely-defined dataset, suitable for big-data approaches. We transform this sparsely-sampled anharmonic dynamical tensor to real-space anharmonic force constants that obey full space-group symmetries by construction. Machine-learning techniques identify the range of real-space interactions. We show the entire process executed for graphene, up to and including the fifth-order anharmonic force constants. This method successfully calculates strain-based phonon renormalization in graphene, even under large strains, which solves a major shortcoming of previous potentials.

Amesos2 and Belos: Direct and Iterative Solvers for Large Sparse Linear Systems

DOE PAGES

Bavier, Eric; Hoemmen, Mark; Rajamanickam, Sivasankaran; ...

2012-01-01

Solvers for large sparse linear systems come in two categories: direct and iterative. Amesos2, a package in the Trilinos software project, provides direct methods, and Belos, another Trilinos package, provides iterative methods. Amesos2 offers a common interface to many different sparse matrix factorization codes, and can handle any implementation of sparse matrices and vectors, via an easy-to-extend C++ traits interface. It can also factor matrices whose entries have arbitrary “Scalar” type, enabling extended-precision and mixed-precision algorithms. Belos includes many different iterative methods for solving large sparse linear systems and least-squares problems. Unlike competing iterative solver libraries, Belos completely decouples themore » algorithms from the implementations of the underlying linear algebra objects. This lets Belos exploit the latest hardware without changes to the code. Belos favors algorithms that solve higher-level problems, such as multiple simultaneous linear systems and sequences of related linear systems, faster than standard algorithms. The package also supports extended-precision and mixed-precision algorithms. Together, Amesos2 and Belos form a complete suite of sparse linear solvers.« less

Towards a Highly Efficient Meshfree Simulation of Non-Newtonian Free Surface Ice Flow: Application to the Haut Glacier d'Arolla

NASA Astrophysics Data System (ADS)

Shcherbakov, V.; Ahlkrona, J.

2016-12-01

In this work we develop a highly efficient meshfree approach to ice sheet modeling. Traditionally mesh based methods such as finite element methods are employed to simulate glacier and ice sheet dynamics. These methods are mature and well developed. However, despite of numerous advantages these methods suffer from some drawbacks such as necessity to remesh the computational domain every time it changes its shape, which significantly complicates the implementation on moving domains, or a costly assembly procedure for nonlinear problems. We introduce a novel meshfree approach that frees us from all these issues. The approach is built upon a radial basis function (RBF) method that, thanks to its meshfree nature, allows for an efficient handling of moving margins and free ice surface. RBF methods are also accurate and easy to implement. Since the formulation is stated in strong form it allows for a substantial reduction of the computational cost associated with the linear system assembly inside the nonlinear solver. We implement a global RBF method that defines an approximation on the entire computational domain. This method exhibits high accuracy properties. However, it suffers from a disadvantage that the coefficient matrix is dense, and therefore the computational efficiency decreases. In order to overcome this issue we also implement a localized RBF method that rests upon a partition of unity approach to subdivide the domain into several smaller subdomains. The radial basis function partition of unity method (RBF-PUM) inherits high approximation characteristics form the global RBF method while resulting in a sparse system of equations, which essentially increases the computational efficiency. To demonstrate the usefulness of the RBF methods we model the velocity field of ice flow in the Haut Glacier d'Arolla. We assume that the flow is governed by the nonlinear Blatter-Pattyn equations. We test the methods for different basal conditions and for a free moving surface. Both RBF methods are compared with a classical finite element method in terms of accuracy and efficiency. We find that the RBF methods are more efficient than the finite element method and well suited for ice dynamics modeling, especially the partition of unity approach.

Matrix computations in MACSYMA

NASA Technical Reports Server (NTRS)

Wang, P. S.

1977-01-01

Facilities built into MACSYMA for manipulating matrices with numeric or symbolic entries are described. Computations will be done exactly, keeping symbols as symbols. Topics discussed include how to form a matrix and create other matrices by transforming existing matrices within MACSYMA; arithmetic and other computation with matrices; and user control of computational processes through the use of optional variables. Two algorithms designed for sparse matrices are given. The computing times of several different ways to compute the determinant of a matrix are compared.

Fabric defect detection based on visual saliency using deep feature and low-rank recovery

NASA Astrophysics Data System (ADS)

Liu, Zhoufeng; Wang, Baorui; Li, Chunlei; Li, Bicao; Dong, Yan

2018-04-01

Fabric defect detection plays an important role in improving the quality of fabric product. In this paper, a novel fabric defect detection method based on visual saliency using deep feature and low-rank recovery was proposed. First, unsupervised training is carried out by the initial network parameters based on MNIST large datasets. The supervised fine-tuning of fabric image library based on Convolutional Neural Networks (CNNs) is implemented, and then more accurate deep neural network model is generated. Second, the fabric images are uniformly divided into the image block with the same size, then we extract their multi-layer deep features using the trained deep network. Thereafter, all the extracted features are concentrated into a feature matrix. Third, low-rank matrix recovery is adopted to divide the feature matrix into the low-rank matrix which indicates the background and the sparse matrix which indicates the salient defect. In the end, the iterative optimal threshold segmentation algorithm is utilized to segment the saliency maps generated by the sparse matrix to locate the fabric defect area. Experimental results demonstrate that the feature extracted by CNN is more suitable for characterizing the fabric texture than the traditional LBP, HOG and other hand-crafted features extraction method, and the proposed method can accurately detect the defect regions of various fabric defects, even for the image with complex texture.

On efficient randomized algorithms for finding the PageRank vector

NASA Astrophysics Data System (ADS)

Gasnikov, A. V.; Dmitriev, D. Yu.

2015-03-01

Two randomized methods are considered for finding the PageRank vector; in other words, the solution of the system p T = p T P with a stochastic n × n matrix P, where n ˜ 107-109, is sought (in the class of probability distributions) with accuracy ɛ: ɛ ≫ n -1. Thus, the possibility of brute-force multiplication of P by the column is ruled out in the case of dense objects. The first method is based on the idea of Markov chain Monte Carlo algorithms. This approach is efficient when the iterative process p {/t+1 T} = p {/t T} P quickly reaches a steady state. Additionally, it takes into account another specific feature of P, namely, the nonzero off-diagonal elements of P are equal in rows (this property is used to organize a random walk over the graph with the matrix P). Based on modern concentration-of-measure inequalities, new bounds for the running time of this method are presented that take into account the specific features of P. In the second method, the search for a ranking vector is reduced to finding the equilibrium in the antagonistic matrix game where S n (1) is a unit simplex in ℝ n and I is the identity matrix. The arising problem is solved by applying a slightly modified Grigoriadis-Khachiyan algorithm (1995). This technique, like the Nazin-Polyak method (2009), is a randomized version of Nemirovski's mirror descent method. The difference is that randomization in the Grigoriadis-Khachiyan algorithm is used when the gradient is projected onto the simplex rather than when the stochastic gradient is computed. For sparse matrices P, the method proposed yields noticeably better results.

Recursive Factorization of the Inverse Overlap Matrix in Linear Scaling Quantum Molecular Dynamics Simulations

DOE PAGES

Negre, Christian F. A; Mniszewski, Susan M.; Cawkwell, Marc Jon; ...

2016-06-06

We present a reduced complexity algorithm to compute the inverse overlap factors required to solve the generalized eigenvalue problem in a quantum-based molecular dynamics (MD) simulation. Our method is based on the recursive iterative re nement of an initial guess Z of the inverse overlap matrix S. The initial guess of Z is obtained beforehand either by using an approximate divide and conquer technique or dynamically, propagated within an extended Lagrangian dynamics from previous MD time steps. With this formulation, we achieve long-term stability and energy conservation even under incomplete approximate iterative re nement of Z. Linear scaling performance ismore » obtained using numerically thresholded sparse matrix algebra based on the ELLPACK-R sparse matrix data format, which also enables e cient shared memory parallelization. As we show in this article using selfconsistent density functional based tight-binding MD, our approach is faster than conventional methods based on the direct diagonalization of the overlap matrix S for systems as small as a few hundred atoms, substantially accelerating quantum-based simulations even for molecular structures of intermediate size. For a 4,158 atom water-solvated polyalanine system we nd an average speedup factor of 122 for the computation of Z in each MD step.« less

A two-stage adaptive stochastic collocation method on nested sparse grids for multiphase flow in randomly heterogeneous porous media

NASA Astrophysics Data System (ADS)

Liao, Qinzhuo; Zhang, Dongxiao; Tchelepi, Hamdi

2017-02-01

A new computational method is proposed for efficient uncertainty quantification of multiphase flow in porous media with stochastic permeability. For pressure estimation, it combines the dimension-adaptive stochastic collocation method on Smolyak sparse grids and the Kronrod-Patterson-Hermite nested quadrature formulas. For saturation estimation, an additional stage is developed, in which the pressure and velocity samples are first generated by the sparse grid interpolation and then substituted into the transport equation to solve for the saturation samples, to address the low regularity problem of the saturation. Numerical examples are presented for multiphase flow with stochastic permeability fields to demonstrate accuracy and efficiency of the proposed two-stage adaptive stochastic collocation method on nested sparse grids.

Data traffic reduction schemes for Cholesky factorization on asynchronous multiprocessor systems

NASA Technical Reports Server (NTRS)

Naik, Vijay K.; Patrick, Merrell L.

1989-01-01

Communication requirements of Cholesky factorization of dense and sparse symmetric, positive definite matrices are analyzed. The communication requirement is characterized by the data traffic generated on multiprocessor systems with local and shared memory. Lower bound proofs are given to show that when the load is uniformly distributed the data traffic associated with factoring an n x n dense matrix using n to the alpha power (alpha less than or equal 2) processors is omega(n to the 2 + alpha/2 power). For n x n sparse matrices representing a square root of n x square root of n regular grid graph the data traffic is shown to be omega(n to the 1 + alpha/2 power), alpha less than or equal 1. Partitioning schemes that are variations of block assignment scheme are described and it is shown that the data traffic generated by these schemes are asymptotically optimal. The schemes allow efficient use of up to O(n to the 2nd power) processors in the dense case and up to O(n) processors in the sparse case before the total data traffic reaches the maximum value of O(n to the 3rd power) and O(n to the 3/2 power), respectively. It is shown that the block based partitioning schemes allow a better utilization of the data accessed from shared memory and thus reduce the data traffic than those based on column-wise wrap around assignment schemes.

Newton-based optimization for Kullback-Leibler nonnegative tensor factorizations

DOE PAGES

Plantenga, Todd; Kolda, Tamara G.; Hansen, Samantha

2015-04-30

Tensor factorizations with nonnegativity constraints have found application in analysing data from cyber traffic, social networks, and other areas. We consider application data best described as being generated by a Poisson process (e.g. count data), which leads to sparse tensors that can be modelled by sparse factor matrices. In this paper, we investigate efficient techniques for computing an appropriate canonical polyadic tensor factorization based on the Kullback–Leibler divergence function. We propose novel subproblem solvers within the standard alternating block variable approach. Our new methods exploit structure and reformulate the optimization problem as small independent subproblems. We employ bound-constrained Newton andmore » quasi-Newton methods. Finally, we compare our algorithms against other codes, demonstrating superior speed for high accuracy results and the ability to quickly find sparse solutions.« less

Computing the full spectrum of large sparse palindromic quadratic eigenvalue problems arising from surface Green's function calculations

NASA Astrophysics Data System (ADS)

Huang, Tsung-Ming; Lin, Wen-Wei; Tian, Heng; Chen, Guan-Hua

2018-03-01

Full spectrum of a large sparse ⊤-palindromic quadratic eigenvalue problem (⊤-PQEP) is considered arguably for the first time in this article. Such a problem is posed by calculation of surface Green's functions (SGFs) of mesoscopic transistors with a tremendous non-periodic cross-section. For this problem, general purpose eigensolvers are not efficient, nor is advisable to resort to the decimation method etc. to obtain the Wiener-Hopf factorization. After reviewing some rigorous understanding of SGF calculation from the perspective of ⊤-PQEP and nonlinear matrix equation, we present our new approach to this problem. In a nutshell, the unit disk where the spectrum of interest lies is broken down adaptively into pieces small enough that they each can be locally tackled by the generalized ⊤-skew-Hamiltonian implicitly restarted shift-and-invert Arnoldi (G⊤SHIRA) algorithm with suitable shifts and other parameters, and the eigenvalues missed by this divide-and-conquer strategy can be recovered thanks to the accurate estimation provided by our newly developed scheme. Notably the novel non-equivalence deflation is proposed to avoid as much as possible duplication of nearby known eigenvalues when a new shift of G⊤SHIRA is determined. We demonstrate our new approach by calculating the SGF of a realistic nanowire whose unit cell is described by a matrix of size 4000 × 4000 at the density functional tight binding level, corresponding to a 8 × 8nm2 cross-section. We believe that quantum transport simulation of realistic nano-devices in the mesoscopic regime will greatly benefit from this work.

A Space-Time-Frequency Dictionary for Sparse Cortical Source Localization.

PubMed

Korats, Gundars; Le Cam, Steven; Ranta, Radu; Louis-Dorr, Valerie

2016-09-01

Cortical source imaging aims at identifying activated cortical areas on the surface of the cortex from the raw electroencephalogram (EEG) data. This problem is ill posed, the number of channels being very low compared to the number of possible source positions. In some realistic physiological situations, the active areas are sparse in space and of short time durations, and the amount of spatio-temporal data to carry the inversion is then limited. In this study, we propose an original data driven space-time-frequency (STF) dictionary which takes into account simultaneously both spatial and time-frequency sparseness while preserving smoothness in the time frequency (i.e., nonstationary smooth time courses in sparse locations). Based on these assumptions, we take benefit of the matching pursuit (MP) framework for selecting the most relevant atoms in this highly redundant dictionary. We apply two recent MP algorithms, single best replacement (SBR) and source deflated matching pursuit, and we compare the results using a spatial dictionary and the proposed STF dictionary to demonstrate the improvements of our multidimensional approach. We also provide comparison using well-established inversion methods, FOCUSS and RAP-MUSIC, analyzing performances under different degrees of nonstationarity and signal to noise ratio. Our STF dictionary combined with the SBR approach provides robust performances on realistic simulations. From a computational point of view, the algorithm is embedded in the wavelet domain, ensuring high efficiency in term of computation time. The proposed approach ensures fast and accurate sparse cortical localizations on highly nonstationary and noisy data.

Implicit Kalman filtering

NASA Technical Reports Server (NTRS)

Skliar, M.; Ramirez, W. F.

1997-01-01

For an implicitly defined discrete system, a new algorithm for Kalman filtering is developed and an efficient numerical implementation scheme is proposed. Unlike the traditional explicit approach, the implicit filter can be readily applied to ill-conditioned systems and allows for generalization to descriptor systems. The implementation of the implicit filter depends on the solution of the congruence matrix equation (A1)(Px)(AT1) = Py. We develop a general iterative method for the solution of this equation, and prove necessary and sufficient conditions for convergence. It is shown that when the system matrices of an implicit system are sparse, the implicit Kalman filter requires significantly less computer time and storage to implement as compared to the traditional explicit Kalman filter. Simulation results are presented to illustrate and substantiate the theoretical developments.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Spotz, William F.

PyTrilinos is a set of Python interfaces to compiled Trilinos packages. This collection supports serial and parallel dense linear algebra, serial and parallel sparse linear algebra, direct and iterative linear solution techniques, algebraic and multilevel preconditioners, nonlinear solvers and continuation algorithms, eigensolvers and partitioning algorithms. Also included are a variety of related utility functions and classes, including distributed I/O, coloring algorithms and matrix generation. PyTrilinos vector objects are compatible with the popular NumPy Python package. As a Python front end to compiled libraries, PyTrilinos takes advantage of the flexibility and ease of use of Python, and the efficiency of themore » underlying C++, C and Fortran numerical kernels. This paper covers recent, previously unpublished advances in the PyTrilinos package.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Clark, Darin P.; Badea, Cristian T., E-mail: cristian.badea@duke.edu; Lee, Chang-Lung

Purpose: X-ray computed tomography (CT) is widely used, both clinically and preclinically, for fast, high-resolution anatomic imaging; however, compelling opportunities exist to expand its use in functional imaging applications. For instance, spectral information combined with nanoparticle contrast agents enables quantification of tissue perfusion levels, while temporal information details cardiac and respiratory dynamics. The authors propose and demonstrate a projection acquisition and reconstruction strategy for 5D CT (3D + dual energy + time) which recovers spectral and temporal information without substantially increasing radiation dose or sampling time relative to anatomic imaging protocols. Methods: The authors approach the 5D reconstruction problem withinmore » the framework of low-rank and sparse matrix decomposition. Unlike previous work on rank-sparsity constrained CT reconstruction, the authors establish an explicit rank-sparse signal model to describe the spectral and temporal dimensions. The spectral dimension is represented as a well-sampled time and energy averaged image plus regularly undersampled principal components describing the spectral contrast. The temporal dimension is represented as the same time and energy averaged reconstruction plus contiguous, spatially sparse, and irregularly sampled temporal contrast images. Using a nonlinear, image domain filtration approach, the authors refer to as rank-sparse kernel regression, the authors transfer image structure from the well-sampled time and energy averaged reconstruction to the spectral and temporal contrast images. This regularization strategy strictly constrains the reconstruction problem while approximately separating the temporal and spectral dimensions. Separability results in a highly compressed representation for the 5D data in which projections are shared between the temporal and spectral reconstruction subproblems, enabling substantial undersampling. The authors solved the 5D reconstruction problem using the split Bregman method and GPU-based implementations of backprojection, reprojection, and kernel regression. Using a preclinical mouse model, the authors apply the proposed algorithm to study myocardial injury following radiation treatment of breast cancer. Results: Quantitative 5D simulations are performed using the MOBY mouse phantom. Twenty data sets (ten cardiac phases, two energies) are reconstructed with 88 μm, isotropic voxels from 450 total projections acquired over a single 360° rotation. In vivo 5D myocardial injury data sets acquired in two mice injected with gold and iodine nanoparticles are also reconstructed with 20 data sets per mouse using the same acquisition parameters (dose: ∼60 mGy). For both the simulations and the in vivo data, the reconstruction quality is sufficient to perform material decomposition into gold and iodine maps to localize the extent of myocardial injury (gold accumulation) and to measure cardiac functional metrics (vascular iodine). Their 5D CT imaging protocol represents a 95% reduction in radiation dose per cardiac phase and energy and a 40-fold decrease in projection sampling time relative to their standard imaging protocol. Conclusions: Their 5D CT data acquisition and reconstruction protocol efficiently exploits the rank-sparse nature of spectral and temporal CT data to provide high-fidelity reconstruction results without increased radiation dose or sampling time.« less

Spectrotemporal CT data acquisition and reconstruction at low dose

PubMed Central

Clark, Darin P.; Lee, Chang-Lung; Kirsch, David G.; Badea, Cristian T.

2015-01-01

Purpose: X-ray computed tomography (CT) is widely used, both clinically and preclinically, for fast, high-resolution anatomic imaging; however, compelling opportunities exist to expand its use in functional imaging applications. For instance, spectral information combined with nanoparticle contrast agents enables quantification of tissue perfusion levels, while temporal information details cardiac and respiratory dynamics. The authors propose and demonstrate a projection acquisition and reconstruction strategy for 5D CT (3D + dual energy + time) which recovers spectral and temporal information without substantially increasing radiation dose or sampling time relative to anatomic imaging protocols. Methods: The authors approach the 5D reconstruction problem within the framework of low-rank and sparse matrix decomposition. Unlike previous work on rank-sparsity constrained CT reconstruction, the authors establish an explicit rank-sparse signal model to describe the spectral and temporal dimensions. The spectral dimension is represented as a well-sampled time and energy averaged image plus regularly undersampled principal components describing the spectral contrast. The temporal dimension is represented as the same time and energy averaged reconstruction plus contiguous, spatially sparse, and irregularly sampled temporal contrast images. Using a nonlinear, image domain filtration approach, the authors refer to as rank-sparse kernel regression, the authors transfer image structure from the well-sampled time and energy averaged reconstruction to the spectral and temporal contrast images. This regularization strategy strictly constrains the reconstruction problem while approximately separating the temporal and spectral dimensions. Separability results in a highly compressed representation for the 5D data in which projections are shared between the temporal and spectral reconstruction subproblems, enabling substantial undersampling. The authors solved the 5D reconstruction problem using the split Bregman method and GPU-based implementations of backprojection, reprojection, and kernel regression. Using a preclinical mouse model, the authors apply the proposed algorithm to study myocardial injury following radiation treatment of breast cancer. Results: Quantitative 5D simulations are performed using the MOBY mouse phantom. Twenty data sets (ten cardiac phases, two energies) are reconstructed with 88 μm, isotropic voxels from 450 total projections acquired over a single 360° rotation. In vivo 5D myocardial injury data sets acquired in two mice injected with gold and iodine nanoparticles are also reconstructed with 20 data sets per mouse using the same acquisition parameters (dose: ∼60 mGy). For both the simulations and the in vivo data, the reconstruction quality is sufficient to perform material decomposition into gold and iodine maps to localize the extent of myocardial injury (gold accumulation) and to measure cardiac functional metrics (vascular iodine). Their 5D CT imaging protocol represents a 95% reduction in radiation dose per cardiac phase and energy and a 40-fold decrease in projection sampling time relative to their standard imaging protocol. Conclusions: Their 5D CT data acquisition and reconstruction protocol efficiently exploits the rank-sparse nature of spectral and temporal CT data to provide high-fidelity reconstruction results without increased radiation dose or sampling time. PMID:26520724

An Efficient Local Correlation Matrix Decomposition Approach for the Localization Implementation of Ensemble-Based Assimilation Methods

NASA Astrophysics Data System (ADS)

Zhang, Hongqin; Tian, Xiangjun

2018-04-01

Ensemble-based data assimilation methods often use the so-called localization scheme to improve the representation of the ensemble background error covariance (Be). Extensive research has been undertaken to reduce the computational cost of these methods by using the localized ensemble samples to localize Be by means of a direct decomposition of the local correlation matrix C. However, the computational costs of the direct decomposition of the local correlation matrix C are still extremely high due to its high dimension. In this paper, we propose an efficient local correlation matrix decomposition approach based on the concept of alternating directions. This approach is intended to avoid direct decomposition of the correlation matrix. Instead, we first decompose the correlation matrix into 1-D correlation matrices in the three coordinate directions, then construct their empirical orthogonal function decomposition at low resolution. This procedure is followed by the 1-D spline interpolation process to transform the above decompositions to the high-resolution grid. Finally, an efficient correlation matrix decomposition is achieved by computing the very similar Kronecker product. We conducted a series of comparison experiments to illustrate the validity and accuracy of the proposed local correlation matrix decomposition approach. The effectiveness of the proposed correlation matrix decomposition approach and its efficient localization implementation of the nonlinear least-squares four-dimensional variational assimilation are further demonstrated by several groups of numerical experiments based on the Advanced Research Weather Research and Forecasting model.

Pure endmember extraction using robust kernel archetypoid analysis for hyperspectral imagery

NASA Astrophysics Data System (ADS)

Sun, Weiwei; Yang, Gang; Wu, Ke; Li, Weiyue; Zhang, Dianfa

2017-09-01

A robust kernel archetypoid analysis (RKADA) method is proposed to extract pure endmembers from hyperspectral imagery (HSI). The RKADA assumes that each pixel is a sparse linear mixture of all endmembers and each endmember corresponds to a real pixel in the image scene. First, it improves the re8gular archetypal analysis with a new binary sparse constraint, and the adoption of the kernel function constructs the principal convex hull in an infinite Hilbert space and enlarges the divergences between pairwise pixels. Second, the RKADA transfers the pure endmember extraction problem into an optimization problem by minimizing residual errors with the Huber loss function. The Huber loss function reduces the effects from big noises and outliers in the convergence procedure of RKADA and enhances the robustness of the optimization function. Third, the random kernel sinks for fast kernel matrix approximation and the two-stage algorithm for optimizing initial pure endmembers are utilized to improve its computational efficiency in realistic implementations of RKADA, respectively. The optimization equation of RKADA is solved by using the block coordinate descend scheme and the desired pure endmembers are finally obtained. Six state-of-the-art pure endmember extraction methods are employed to make comparisons with the RKADA on both synthetic and real Cuprite HSI datasets, including three geometrical algorithms vertex component analysis (VCA), alternative volume maximization (AVMAX) and orthogonal subspace projection (OSP), and three matrix factorization algorithms the preconditioning for successive projection algorithm (PreSPA), hierarchical clustering based on rank-two nonnegative matrix factorization (H2NMF) and self-dictionary multiple measurement vector (SDMMV). Experimental results show that the RKADA outperforms all the six methods in terms of spectral angle distance (SAD) and root-mean-square-error (RMSE). Moreover, the RKADA has short computational times in offline operations and shows significant improvement in identifying pure endmembers for ground objects with smaller spectrum differences. Therefore, the RKADA could be an alternative for pure endmember extraction from hyperspectral images.

Subspace aware recovery of low rank and jointly sparse signals

PubMed Central

Biswas, Sampurna; Dasgupta, Soura; Mudumbai, Raghuraman; Jacob, Mathews

2017-01-01

We consider the recovery of a matrix X, which is simultaneously low rank and joint sparse, from few measurements of its columns using a two-step algorithm. Each column of X is measured using a combination of two measurement matrices; one which is the same for every column, while the the second measurement matrix varies from column to column. The recovery proceeds by first estimating the row subspace vectors from the measurements corresponding to the common matrix. The estimated row subspace vectors are then used to recover X from all the measurements using a convex program of joint sparsity minimization. Our main contribution is to provide sufficient conditions on the measurement matrices that guarantee the recovery of such a matrix using the above two-step algorithm. The results demonstrate quite significant savings in number of measurements when compared to the standard multiple measurement vector (MMV) scheme, which assumes same time invariant measurement pattern for all the time frames. We illustrate the impact of the sampling pattern on reconstruction quality using breath held cardiac cine MRI and cardiac perfusion MRI data, while the utility of the algorithm to accelerate the acquisition is demonstrated on MR parameter mapping. PMID:28630889

Beyond Low Rank + Sparse: Multi-scale Low Rank Matrix Decomposition

PubMed Central

Ong, Frank; Lustig, Michael

2016-01-01

We present a natural generalization of the recent low rank + sparse matrix decomposition and consider the decomposition of matrices into components of multiple scales. Such decomposition is well motivated in practice as data matrices often exhibit local correlations in multiple scales. Concretely, we propose a multi-scale low rank modeling that represents a data matrix as a sum of block-wise low rank matrices with increasing scales of block sizes. We then consider the inverse problem of decomposing the data matrix into its multi-scale low rank components and approach the problem via a convex formulation. Theoretically, we show that under various incoherence conditions, the convex program recovers the multi-scale low rank components either exactly or approximately. Practically, we provide guidance on selecting the regularization parameters and incorporate cycle spinning to reduce blocking artifacts. Experimentally, we show that the multi-scale low rank decomposition provides a more intuitive decomposition than conventional low rank methods and demonstrate its effectiveness in four applications, including illumination normalization for face images, motion separation for surveillance videos, multi-scale modeling of the dynamic contrast enhanced magnetic resonance imaging and collaborative filtering exploiting age information. PMID:28450978

SU-G-TeP1-15: Toward a Novel GPU Accelerated Deterministic Solution to the Linear Boltzmann Transport Equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, R; Fallone, B; Cross Cancer Institute, Edmonton, AB

Purpose: To develop a Graphic Processor Unit (GPU) accelerated deterministic solution to the Linear Boltzmann Transport Equation (LBTE) for accurate dose calculations in radiotherapy (RT). A deterministic solution yields the potential for major speed improvements due to the sparse matrix-vector and vector-vector multiplications and would thus be of benefit to RT. Methods: In order to leverage the massively parallel architecture of GPUs, the first order LBTE was reformulated as a second order self-adjoint equation using the Least Squares Finite Element Method (LSFEM). This produces a symmetric positive-definite matrix which is efficiently solved using a parallelized conjugate gradient (CG) solver. Themore » LSFEM formalism is applied in space, discrete ordinates is applied in angle, and the Multigroup method is applied in energy. The final linear system of equations produced is tightly coupled in space and angle. Our code written in CUDA-C was benchmarked on an Nvidia GeForce TITAN-X GPU against an Intel i7-6700K CPU. A spatial mesh of 30,950 tetrahedral elements was used with an S4 angular approximation. Results: To avoid repeating a full computationally intensive finite element matrix assembly at each Multigroup energy, a novel mapping algorithm was developed which minimized the operations required at each energy. Additionally, a parallelized memory mapping for the kronecker product between the sparse spatial and angular matrices, including Dirichlet boundary conditions, was created. Atomicity is preserved by graph-coloring overlapping nodes into separate kernel launches. The one-time mapping calculations for matrix assembly, kronecker product, and boundary condition application took 452±1ms on GPU. Matrix assembly for 16 energy groups took 556±3s on CPU, and 358±2ms on GPU using the mappings developed. The CG solver took 93±1s on CPU, and 468±2ms on GPU. Conclusion: Three computationally intensive subroutines in deterministically solving the LBTE have been formulated on GPU, resulting in two orders of magnitude speedup. Funding support from Natural Sciences and Engineering Research Council and Alberta Innovates Health Solutions. Dr. Fallone is a co-founder and CEO of MagnetTx Oncology Solutions (under discussions to license Alberta bi-planar linac MR for commercialization).« less

Sparsity-weighted outlier FLOODing (OFLOOD) method: Efficient rare event sampling method using sparsity of distribution.

PubMed

Harada, Ryuhei; Nakamura, Tomotake; Shigeta, Yasuteru

2016-03-30

As an extension of the Outlier FLOODing (OFLOOD) method [Harada et al., J. Comput. Chem. 2015, 36, 763], the sparsity of the outliers defined by a hierarchical clustering algorithm, FlexDice, was considered to achieve an efficient conformational search as sparsity-weighted "OFLOOD." In OFLOOD, FlexDice detects areas of sparse distribution as outliers. The outliers are regarded as candidates that have high potential to promote conformational transitions and are employed as initial structures for conformational resampling by restarting molecular dynamics simulations. When detecting outliers, FlexDice defines a rank in the hierarchy for each outlier, which relates to sparsity in the distribution. In this study, we define a lower rank (first ranked), a medium rank (second ranked), and the highest rank (third ranked) outliers, respectively. For instance, the first-ranked outliers are located in a given conformational space away from the clusters (highly sparse distribution), whereas those with the third-ranked outliers are nearby the clusters (a moderately sparse distribution). To achieve the conformational search efficiently, resampling from the outliers with a given rank is performed. As demonstrations, this method was applied to several model systems: Alanine dipeptide, Met-enkephalin, Trp-cage, T4 lysozyme, and glutamine binding protein. In each demonstration, the present method successfully reproduced transitions among metastable states. In particular, the first-ranked OFLOOD highly accelerated the exploration of conformational space by expanding the edges. In contrast, the third-ranked OFLOOD reproduced local transitions among neighboring metastable states intensively. For quantitatively evaluations of sampled snapshots, free energy calculations were performed with a combination of umbrella samplings, providing rigorous landscapes of the biomolecules. © 2015 Wiley Periodicals, Inc.

MUTILS - a set of efficient modeling tools for multi-core CPUs implemented in MEX

NASA Astrophysics Data System (ADS)

Krotkiewski, Marcin; Dabrowski, Marcin

2013-04-01

The need for computational performance is common in scientific applications, and in particular in numerical simulations, where high resolution models require efficient processing of large amounts of data. Especially in the context of geological problems the need to increase the model resolution to resolve physical and geometrical complexities seems to have no limits. Alas, the performance of new generations of CPUs does not improve any longer by simply increasing clock speeds. Current industrial trends are to increase the number of computational cores. As a result, parallel implementations are required in order to fully utilize the potential of new processors, and to study more complex models. We target simulations on small to medium scale shared memory computers: laptops and desktop PCs with ~8 CPU cores and up to tens of GB of memory to high-end servers with ~50 CPU cores and hundereds of GB of memory. In this setting MATLAB is often the environment of choice for scientists that want to implement their own models with little effort. It is a useful general purpose mathematical software package, but due to its versatility some of its functionality is not as efficient as it could be. In particular, the challanges of modern multi-core architectures are not fully addressed. We have developed MILAMIN 2 - an efficient FEM modeling environment written in native MATLAB. Amongst others, MILAMIN provides functions to define model geometry, generate and convert structured and unstructured meshes (also through interfaces to external mesh generators), compute element and system matrices, apply boundary conditions, solve the system of linear equations, address non-linear and transient problems, and perform post-processing. MILAMIN strives to combine the ease of code development and the computational efficiency. Where possible, the code is optimized and/or parallelized within the MATLAB framework. Native MATLAB is augmented with the MUTILS library - a set of MEX functions that implement the computationally intensive, performance critical parts of the code, which we have identified to be bottlenecks. Here, we discuss the functionality and performance of the MUTILS library. Currently, it includes: 1. time and memory efficient assembly of sparse matrices for FEM simulations 2. parallel sparse matrix - vector product with optimizations speficic to symmetric matrices and multiple degrees of freedom per node 3. parallel point in triangle location and point in tetrahedron location for unstructured, adaptive 2D and 3D meshes (useful for 'marker in cell' type of methods) 4. parallel FEM interpolation for 2D and 3D meshes of elements of different types and orders, and for different number of degrees of freedom per node 5. a stand-alone, MEX implementation of the Conjugate Gradients iterative solver 6. interface to METIS graph partitioning and a fast implementation of RCM reordering

Spectrum recovery method based on sparse representation for segmented multi-Gaussian model

NASA Astrophysics Data System (ADS)

Teng, Yidan; Zhang, Ye; Ti, Chunli; Su, Nan

2016-09-01

Hyperspectral images can realize crackajack features discriminability for supplying diagnostic characteristics with high spectral resolution. However, various degradations may generate negative influence on the spectral information, including water absorption, bands-continuous noise. On the other hand, the huge data volume and strong redundancy among spectrums produced intense demand on compressing HSIs in spectral dimension, which also leads to the loss of spectral information. The reconstruction of spectral diagnostic characteristics has irreplaceable significance for the subsequent application of HSIs. This paper introduces a spectrum restoration method for HSIs making use of segmented multi-Gaussian model (SMGM) and sparse representation. A SMGM is established to indicating the unsymmetrical spectral absorption and reflection characteristics, meanwhile, its rationality and sparse property are discussed. With the application of compressed sensing (CS) theory, we implement sparse representation to the SMGM. Then, the degraded and compressed HSIs can be reconstructed utilizing the uninjured or key bands. Finally, we take low rank matrix recovery (LRMR) algorithm for post processing to restore the spatial details. The proposed method was tested on the spectral data captured on the ground with artificial water absorption condition and an AVIRIS-HSI data set. The experimental results in terms of qualitative and quantitative assessments demonstrate that the effectiveness on recovering the spectral information from both degradations and loss compression. The spectral diagnostic characteristics and the spatial geometry feature are well preserved.

Lanczos eigensolution method for high-performance computers

NASA Technical Reports Server (NTRS)

Bostic, Susan W.

1991-01-01

The theory, computational analysis, and applications are presented of a Lanczos algorithm on high performance computers. The computationally intensive steps of the algorithm are identified as: the matrix factorization, the forward/backward equation solution, and the matrix vector multiples. These computational steps are optimized to exploit the vector and parallel capabilities of high performance computers. The savings in computational time from applying optimization techniques such as: variable band and sparse data storage and access, loop unrolling, use of local memory, and compiler directives are presented. Two large scale structural analysis applications are described: the buckling of a composite blade stiffened panel with a cutout, and the vibration analysis of a high speed civil transport. The sequential computational time for the panel problem executed on a CONVEX computer of 181.6 seconds was decreased to 14.1 seconds with the optimized vector algorithm. The best computational time of 23 seconds for the transport problem with 17,000 degs of freedom was on the the Cray-YMP using an average of 3.63 processors.

An Online Dictionary Learning-Based Compressive Data Gathering Algorithm in Wireless Sensor Networks

PubMed Central

Wang, Donghao; Wan, Jiangwen; Chen, Junying; Zhang, Qiang

2016-01-01

To adapt to sense signals of enormous diversities and dynamics, and to decrease the reconstruction errors caused by ambient noise, a novel online dictionary learning method-based compressive data gathering (ODL-CDG) algorithm is proposed. The proposed dictionary is learned from a two-stage iterative procedure, alternately changing between a sparse coding step and a dictionary update step. The self-coherence of the learned dictionary is introduced as a penalty term during the dictionary update procedure. The dictionary is also constrained with sparse structure. It’s theoretically demonstrated that the sensing matrix satisfies the restricted isometry property (RIP) with high probability. In addition, the lower bound of necessary number of measurements for compressive sensing (CS) reconstruction is given. Simulation results show that the proposed ODL-CDG algorithm can enhance the recovery accuracy in the presence of noise, and reduce the energy consumption in comparison with other dictionary based data gathering methods. PMID:27669250

An Online Dictionary Learning-Based Compressive Data Gathering Algorithm in Wireless Sensor Networks.

PubMed

Wang, Donghao; Wan, Jiangwen; Chen, Junying; Zhang, Qiang

2016-09-22

To adapt to sense signals of enormous diversities and dynamics, and to decrease the reconstruction errors caused by ambient noise, a novel online dictionary learning method-based compressive data gathering (ODL-CDG) algorithm is proposed. The proposed dictionary is learned from a two-stage iterative procedure, alternately changing between a sparse coding step and a dictionary update step. The self-coherence of the learned dictionary is introduced as a penalty term during the dictionary update procedure. The dictionary is also constrained with sparse structure. It's theoretically demonstrated that the sensing matrix satisfies the restricted isometry property (RIP) with high probability. In addition, the lower bound of necessary number of measurements for compressive sensing (CS) reconstruction is given. Simulation results show that the proposed ODL-CDG algorithm can enhance the recovery accuracy in the presence of noise, and reduce the energy consumption in comparison with other dictionary based data gathering methods.

A sparse structure learning algorithm for Gaussian Bayesian Network identification from high-dimensional data.

PubMed

Huang, Shuai; Li, Jing; Ye, Jieping; Fleisher, Adam; Chen, Kewei; Wu, Teresa; Reiman, Eric

2013-06-01

Structure learning of Bayesian Networks (BNs) is an important topic in machine learning. Driven by modern applications in genetics and brain sciences, accurate and efficient learning of large-scale BN structures from high-dimensional data becomes a challenging problem. To tackle this challenge, we propose a Sparse Bayesian Network (SBN) structure learning algorithm that employs a novel formulation involving one L1-norm penalty term to impose sparsity and another penalty term to ensure that the learned BN is a Directed Acyclic Graph--a required property of BNs. Through both theoretical analysis and extensive experiments on 11 moderate and large benchmark networks with various sample sizes, we show that SBN leads to improved learning accuracy, scalability, and efficiency as compared with 10 existing popular BN learning algorithms. We apply SBN to a real-world application of brain connectivity modeling for Alzheimer's disease (AD) and reveal findings that could lead to advancements in AD research.

A Sparse Structure Learning Algorithm for Gaussian Bayesian Network Identification from High-Dimensional Data

PubMed Central

Huang, Shuai; Li, Jing; Ye, Jieping; Fleisher, Adam; Chen, Kewei; Wu, Teresa; Reiman, Eric

2014-01-01

Structure learning of Bayesian Networks (BNs) is an important topic in machine learning. Driven by modern applications in genetics and brain sciences, accurate and efficient learning of large-scale BN structures from high-dimensional data becomes a challenging problem. To tackle this challenge, we propose a Sparse Bayesian Network (SBN) structure learning algorithm that employs a novel formulation involving one L1-norm penalty term to impose sparsity and another penalty term to ensure that the learned BN is a Directed Acyclic Graph (DAG)—a required property of BNs. Through both theoretical analysis and extensive experiments on 11 moderate and large benchmark networks with various sample sizes, we show that SBN leads to improved learning accuracy, scalability, and efficiency as compared with 10 existing popular BN learning algorithms. We apply SBN to a real-world application of brain connectivity modeling for Alzheimer’s disease (AD) and reveal findings that could lead to advancements in AD research. PMID:22665720

Comparison of l₁-Norm SVR and Sparse Coding Algorithms for Linear Regression.

PubMed

Zhang, Qingtian; Hu, Xiaolin; Zhang, Bo

2015-08-01

Support vector regression (SVR) is a popular function estimation technique based on Vapnik's concept of support vector machine. Among many variants, the l1-norm SVR is known to be good at selecting useful features when the features are redundant. Sparse coding (SC) is a technique widely used in many areas and a number of efficient algorithms are available. Both l1-norm SVR and SC can be used for linear regression. In this brief, the close connection between the l1-norm SVR and SC is revealed and some typical algorithms are compared for linear regression. The results show that the SC algorithms outperform the Newton linear programming algorithm, an efficient l1-norm SVR algorithm, in efficiency. The algorithms are then used to design the radial basis function (RBF) neural networks. Experiments on some benchmark data sets demonstrate the high efficiency of the SC algorithms. In particular, one of the SC algorithms, the orthogonal matching pursuit is two orders of magnitude faster than a well-known RBF network designing algorithm, the orthogonal least squares algorithm.

Structured sparse linear graph embedding.

PubMed

Wang, Haixian

2012-03-01

Subspace learning is a core issue in pattern recognition and machine learning. Linear graph embedding (LGE) is a general framework for subspace learning. In this paper, we propose a structured sparse extension to LGE (SSLGE) by introducing a structured sparsity-inducing norm into LGE. Specifically, SSLGE casts the projection bases learning into a regression-type optimization problem, and then the structured sparsity regularization is applied to the regression coefficients. The regularization selects a subset of features and meanwhile encodes high-order information reflecting a priori structure information of the data. The SSLGE technique provides a unified framework for discovering structured sparse subspace. Computationally, by using a variational equality and the Procrustes transformation, SSLGE is efficiently solved with closed-form updates. Experimental results on face image show the effectiveness of the proposed method. Copyright © 2011 Elsevier Ltd. All rights reserved.

Simultaneous analysis of large INTEGRAL/SPI1 datasets: Optimizing the computation of the solution and its variance using sparse matrix algorithms

NASA Astrophysics Data System (ADS)

Bouchet, L.; Amestoy, P.; Buttari, A.; Rouet, F.-H.; Chauvin, M.

2013-02-01

Nowadays, analyzing and reducing the ever larger astronomical datasets is becoming a crucial challenge, especially for long cumulated observation times. The INTEGRAL/SPI X/γ-ray spectrometer is an instrument for which it is essential to process many exposures at the same time in order to increase the low signal-to-noise ratio of the weakest sources. In this context, the conventional methods for data reduction are inefficient and sometimes not feasible at all. Processing several years of data simultaneously requires computing not only the solution of a large system of equations, but also the associated uncertainties. We aim at reducing the computation time and the memory usage. Since the SPI transfer function is sparse, we have used some popular methods for the solution of large sparse linear systems; we briefly review these methods. We use the Multifrontal Massively Parallel Solver (MUMPS) to compute the solution of the system of equations. We also need to compute the variance of the solution, which amounts to computing selected entries of the inverse of the sparse matrix corresponding to our linear system. This can be achieved through one of the latest features of the MUMPS software that has been partly motivated by this work. In this paper we provide a brief presentation of this feature and evaluate its effectiveness on astrophysical problems requiring the processing of large datasets simultaneously, such as the study of the entire emission of the Galaxy. We used these algorithms to solve the large sparse systems arising from SPI data processing and to obtain both their solutions and the associated variances. In conclusion, thanks to these newly developed tools, processing large datasets arising from SPI is now feasible with both a reasonable execution time and a low memory usage.

Development of a steady potential solver for use with linearized, unsteady aerodynamic analyses

NASA Technical Reports Server (NTRS)

Hoyniak, Daniel; Verdon, Joseph M.

1991-01-01

A full potential steady flow solver (SFLOW) developed explicitly for use with an inviscid unsteady aerodynamic analysis (LINFLO) is described. The steady solver uses the nonconservative form of the nonlinear potential flow equations together with an implicit, least squares, finite difference approximation to solve for the steady flow field. The difference equations were developed on a composite mesh which consists of a C grid embedded in a rectilinear (H grid) cascade mesh. The composite mesh is capable of resolving blade to blade and far field phenomena on the H grid, while accurately resolving local phenomena on the C grid. The resulting system of algebraic equations is arranged in matrix form using a sparse matrix package and solved by Newton's method. Steady and unsteady results are presented for two cascade configurations: a high speed compressor and a turbine with high exit Mach number.

Algorithms and software for solving finite element equations on serial and parallel architectures

NASA Technical Reports Server (NTRS)

Chu, Eleanor; George, Alan

1988-01-01

The primary objective was to compare the performance of state-of-the-art techniques for solving sparse systems with those that are currently available in the Computational Structural Mechanics (MSC) testbed. One of the first tasks was to become familiar with the structure of the testbed, and to install some or all of the SPARSPAK package in the testbed. A brief overview of the CSM Testbed software and its usage is presented. An overview of the sparse matrix research for the Testbed currently employed in the CSM Testbed is given. An interface which was designed and implemented as a research tool for installing and appraising new matrix processors in the CSM Testbed is described. The results of numerical experiments performed in solving a set of testbed demonstration problems using the processor SPK and other experimental processors are contained.

Improved parallel data partitioning by nested dissection with applications to information retrieval.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wolf, Michael M.; Chevalier, Cedric; Boman, Erik Gunnar

The computational work in many information retrieval and analysis algorithms is based on sparse linear algebra. Sparse matrix-vector multiplication is a common kernel in many of these computations. Thus, an important related combinatorial problem in parallel computing is how to distribute the matrix and the vectors among processors so as to minimize the communication cost. We focus on minimizing the total communication volume while keeping the computation balanced across processes. In [1], the first two authors presented a new 2D partitioning method, the nested dissection partitioning algorithm. In this paper, we improve on that algorithm and show that it ismore » a good option for data partitioning in information retrieval. We also show partitioning time can be substantially reduced by using the SCOTCH software, and quality improves in some cases, too.« less

High efficiency solar panel /HESP/

NASA Technical Reports Server (NTRS)

Stella, P. M.; Gay, C.; Uno, F.; Scott-Monck, J.

1978-01-01

A family of high efficiency, weldable silicon solar cells, incorporating nearly every feature of advanced cell technology developed in the past four years, was produced and subjected to space qualification testing. This matrix contained both field and non-field cells ranging in thickness from 0.10 mm to 0.30 mm, and in base resistivity from nominal two to one hundred ohm-cm. Initial power outputs as high as 20 mW/sq cm (14.8% AM0 efficiency) were produced by certain cell types within the matrix.

An embedded system for face classification in infrared video using sparse representation

NASA Astrophysics Data System (ADS)

Saavedra M., Antonio; Pezoa, Jorge E.; Zarkesh-Ha, Payman; Figueroa, Miguel

2017-09-01

We propose a platform for robust face recognition in Infrared (IR) images using Compressive Sensing (CS). In line with CS theory, the classification problem is solved using a sparse representation framework, where test images are modeled by means of a linear combination of the training set. Because the training set constitutes an over-complete dictionary, we identify new images by finding their sparsest representation based on the training set, using standard l1-minimization algorithms. Unlike conventional face-recognition algorithms, we feature extraction is performed using random projections with a precomputed binary matrix, as proposed in the CS literature. This random sampling reduces the effects of noise and occlusions such as facial hair, eyeglasses, and disguises, which are notoriously challenging in IR images. Thus, the performance of our framework is robust to these noise and occlusion factors, achieving an average accuracy of approximately 90% when the UCHThermalFace database is used for training and testing purposes. We implemented our framework on a high-performance embedded digital system, where the computation of the sparse representation of IR images was performed by a dedicated hardware using a deeply pipelined architecture on an Field-Programmable Gate Array (FPGA).

PLATSIM: An efficient linear simulation and analysis package for large-order flexible systems

NASA Technical Reports Server (NTRS)

Maghami, Periman; Kenny, Sean P.; Giesy, Daniel P.

1995-01-01

PLATSIM is a software package designed to provide efficient time and frequency domain analysis of large-order generic space platforms implemented with any linear time-invariant control system. Time domain analysis provides simulations of the overall spacecraft response levels due to either onboard or external disturbances. The time domain results can then be processed by the jitter analysis module to assess the spacecraft's pointing performance in a computationally efficient manner. The resulting jitter analysis algorithms have produced an increase in speed of several orders of magnitude over the brute force approach of sweeping minima and maxima. Frequency domain analysis produces frequency response functions for uncontrolled and controlled platform configurations. The latter represents an enabling technology for large-order flexible systems. PLATSIM uses a sparse matrix formulation for the spacecraft dynamics model which makes both the time and frequency domain operations quite efficient, particularly when a large number of modes are required to capture the true dynamics of the spacecraft. The package is written in MATLAB script language. A graphical user interface (GUI) is included in the PLATSIM software package. This GUI uses MATLAB's Handle graphics to provide a convenient way for setting simulation and analysis parameters.

Improving the energy efficiency of sparse linear system solvers on multicore and manycore systems.

PubMed

Anzt, H; Quintana-Ortí, E S

2014-06-28

While most recent breakthroughs in scientific research rely on complex simulations carried out in large-scale supercomputers, the power draft and energy spent for this purpose is increasingly becoming a limiting factor to this trend. In this paper, we provide an overview of the current status in energy-efficient scientific computing by reviewing different technologies used to monitor power draft as well as power- and energy-saving mechanisms available in commodity hardware. For the particular domain of sparse linear algebra, we analyse the energy efficiency of a broad collection of hardware architectures and investigate how algorithmic and implementation modifications can improve the energy performance of sparse linear system solvers, without negatively impacting their performance. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

An Efficient Image Compressor for Charge Coupled Devices Camera

PubMed Central

Li, Jin; Xing, Fei; You, Zheng

2014-01-01

Recently, the discrete wavelet transforms- (DWT-) based compressor, such as JPEG2000 and CCSDS-IDC, is widely seen as the state of the art compression scheme for charge coupled devices (CCD) camera. However, CCD images project on the DWT basis to produce a large number of large amplitude high-frequency coefficients because these images have a large number of complex texture and contour information, which are disadvantage for the later coding. In this paper, we proposed a low-complexity posttransform coupled with compressing sensing (PT-CS) compression approach for remote sensing image. First, the DWT is applied to the remote sensing image. Then, a pair base posttransform is applied to the DWT coefficients. The pair base are DCT base and Hadamard base, which can be used on the high and low bit-rate, respectively. The best posttransform is selected by the l p-norm-based approach. The posttransform is considered as the sparse representation stage of CS. The posttransform coefficients are resampled by sensing measurement matrix. Experimental results on on-board CCD camera images show that the proposed approach significantly outperforms the CCSDS-IDC-based coder, and its performance is comparable to that of the JPEG2000 at low bit rate and it does not have the high excessive implementation complexity of JPEG2000. PMID:25114977

Covalent organic framework as efficient desorption/ionization matrix for direct detection of small molecules by laser desorption/ionization mass spectrometry.

PubMed

Feng, Dan; Xia, Yan

2018-07-19

Covalent organic framework (COF) was explored as a novel matrix with a high desorption/ionization efficiency for direct detection of small molecules by laser desorption/ionization time-of-flight mass spectrometry (LDI-TOF MS). By using COF as an LDI MS matrix, we could detect not only biological micro molecules such as amino acids and fatty acids, but also emerging environmental pollutants like bisphenol S (BPS) and pyrene. With COF as the matrix, higher desorption/ionization efficiency, and less background interference were achieved than the conventional organic matrices. Good salt tolerance (as high as 500 mM NaCl) and repeatability allowed the detection limit of amino acids was 90 fmol. In addition, COF matrix performed well for amino acids analysis in the honey sample. The ionization mechanism was also discussed. These results demonstrate that COF is a powerful matrix for small molecules analysis in real samples by MS. Copyright © 2018 Elsevier B.V. All rights reserved.

Parallel Computing Strategies for Irregular Algorithms

NASA Technical Reports Server (NTRS)

Biswas, Rupak; Oliker, Leonid; Shan, Hongzhang; Biegel, Bryan (Technical Monitor)

2002-01-01

Parallel computing promises several orders of magnitude increase in our ability to solve realistic computationally-intensive problems, but relies on their efficient mapping and execution on large-scale multiprocessor architectures. Unfortunately, many important applications are irregular and dynamic in nature, making their effective parallel implementation a daunting task. Moreover, with the proliferation of parallel architectures and programming paradigms, the typical scientist is faced with a plethora of questions that must be answered in order to obtain an acceptable parallel implementation of the solution algorithm. In this paper, we consider three representative irregular applications: unstructured remeshing, sparse matrix computations, and N-body problems, and parallelize them using various popular programming paradigms on a wide spectrum of computer platforms ranging from state-of-the-art supercomputers to PC clusters. We present the underlying problems, the solution algorithms, and the parallel implementation strategies. Smart load-balancing, partitioning, and ordering techniques are used to enhance parallel performance. Overall results demonstrate the complexity of efficiently parallelizing irregular algorithms.

Repeated Red-Black ordering

NASA Astrophysics Data System (ADS)

Ciarlet, P.

1994-09-01

Hereafter, we describe and analyze, from both a theoretical and a numerical point of view, an iterative method for efficiently solving symmetric elliptic problems with possibly discontinuous coefficients. In the following, we use the Preconditioned Conjugate Gradient method to solve the symmetric positive definite linear systems which arise from the finite element discretization of the problems. We focus our interest on sparse and efficient preconditioners. In order to define the preconditioners, we perform two steps: first we reorder the unknowns and then we carry out a (modified) incomplete factorization of the original matrix. We study numerically and theoretically two preconditioners, the second preconditioner corresponding to the one investigated by Brand and Heinemann [2]. We prove convergence results about the Poisson equation with either Dirichlet or periodic boundary conditions. For a meshsizeh, Brand proved that the condition number of the preconditioned system is bounded byO(h-1/2) for Dirichlet boundary conditions. By slightly modifying the preconditioning process, we prove that the condition number is bounded byO(h-1/3).

Wavelets in electronic structure calculations

NASA Astrophysics Data System (ADS)

Modisette, Jason Perry

1997-09-01

Ab initio calculations of the electronic structure of bulk materials and large clusters are not possible on today's computers using current techniques. The storage and diagonalization of the Hamiltonian matrix are the limiting factors in both memory and execution time. The scaling of both quantities with problem size can be reduced by using approximate diagonalization or direct minimization of the total energy with respect to the density matrix in conjunction with a localized basis. Wavelet basis members are much more localized than conventional bases such as Gaussians or numerical atomic orbitals. This localization leads to sparse matrices of the operators that arise in SCF multi-electron calculations. We have investigated the construction of the one-electron Hamiltonian, and also the effective one- electron Hamiltonians that appear in density-functional and Hartree-Fock theories. We develop efficient methods for the generation of the kinetic energy and potential matrices, the Hartree and exchange potentials, and the local exchange-correlation potential of the LDA. Test calculations are performed on one-electron problems with a variety of potentials in one and three dimensions.

Subspace Clustering via Learning an Adaptive Low-Rank Graph.

PubMed

Yin, Ming; Xie, Shengli; Wu, Zongze; Zhang, Yun; Gao, Junbin

2018-08-01

By using a sparse representation or low-rank representation of data, the graph-based subspace clustering has recently attracted considerable attention in computer vision, given its capability and efficiency in clustering data. However, the graph weights built using the representation coefficients are not the exact ones as the traditional definition is in a deterministic way. The two steps of representation and clustering are conducted in an independent manner, thus an overall optimal result cannot be guaranteed. Furthermore, it is unclear how the clustering performance will be affected by using this graph. For example, the graph parameters, i.e., the weights on edges, have to be artificially pre-specified while it is very difficult to choose the optimum. To this end, in this paper, a novel subspace clustering via learning an adaptive low-rank graph affinity matrix is proposed, where the affinity matrix and the representation coefficients are learned in a unified framework. As such, the pre-computed graph regularizer is effectively obviated and better performance can be achieved. Experimental results on several famous databases demonstrate that the proposed method performs better against the state-of-the-art approaches, in clustering.

Comparison of two matrix data structures for advanced CSM testbed applications

NASA Technical Reports Server (NTRS)

Regelbrugge, M. E.; Brogan, F. A.; Nour-Omid, B.; Rankin, C. C.; Wright, M. A.

1989-01-01

The first section describes data storage schemes presently used by the Computational Structural Mechanics (CSM) testbed sparse matrix facilities and similar skyline (profile) matrix facilities. The second section contains a discussion of certain features required for the implementation of particular advanced CSM algorithms, and how these features might be incorporated into the data storage schemes described previously. The third section presents recommendations, based on the discussions of the prior sections, for directing future CSM testbed development to provide necessary matrix facilities for advanced algorithm implementation and use. The objective is to lend insight into the matrix structures discussed and to help explain the process of evaluating alternative matrix data structures and utilities for subsequent use in the CSM testbed.

Time-domain analysis of planar microstrip devices using a generalized Yee-algorithm based on unstructured grids

NASA Technical Reports Server (NTRS)

Gedney, Stephen D.; Lansing, Faiza

1993-01-01

The generalized Yee-algorithm is presented for the temporal full-wave analysis of planar microstrip devices. This algorithm has the significant advantage over the traditional Yee-algorithm in that it is based on unstructured and irregular grids. The robustness of the generalized Yee-algorithm is that structures that contain curved conductors or complex three-dimensional geometries can be more accurately, and much more conveniently modeled using standard automatic grid generation techniques. This generalized Yee-algorithm is based on the the time-marching solution of the discrete form of Maxwell's equations in their integral form. To this end, the electric and magnetic fields are discretized over a dual, irregular, and unstructured grid. The primary grid is assumed to be composed of general fitted polyhedra distributed throughout the volume. The secondary grid (or dual grid) is built up of the closed polyhedra whose edges connect the centroid's of adjacent primary cells, penetrating shared faces. Faraday's law and Ampere's law are used to update the fields normal to the primary and secondary grid faces, respectively. Subsequently, a correction scheme is introduced to project the normal fields onto the grid edges. It is shown that this scheme is stable, maintains second-order accuracy, and preserves the divergenceless nature of the flux densities. Finally, for computational efficiency the algorithm is structured as a series of sparse matrix-vector multiplications. Based on this scheme, the generalized Yee-algorithm has been implemented on vector and parallel high performance computers in a highly efficient manner.

Fluid-structure finite-element vibrational analysis

NASA Technical Reports Server (NTRS)

Feng, G. C.; Kiefling, L.

1974-01-01

A fluid finite element has been developed for a quasi-compressible fluid. Both kinetic and potential energy are expressed as functions of nodal displacements. Thus, the formulation is similar to that used for structural elements, with the only differences being that the fluid can possess gravitational potential, and the constitutive equations for fluid contain no shear coefficients. Using this approach, structural and fluid elements can be used interchangeably in existing efficient sparse-matrix structural computer programs such as SPAR. The theoretical development of the element formulations and the relationships of the local and global coordinates are shown. Solutions of fluid slosh, liquid compressibility, and coupled fluid-shell oscillation problems which were completed using a temporary digital computer program are shown. The frequency correlation of the solutions with classical theory is excellent.

Abnormal global and local event detection in compressive sensing domain

NASA Astrophysics Data System (ADS)

Wang, Tian; Qiao, Meina; Chen, Jie; Wang, Chuanyun; Zhang, Wenjia; Snoussi, Hichem

2018-05-01

Abnormal event detection, also known as anomaly detection, is one challenging task in security video surveillance. It is important to develop effective and robust movement representation models for global and local abnormal event detection to fight against factors such as occlusion and illumination change. In this paper, a new algorithm is proposed. It can locate the abnormal events on one frame, and detect the global abnormal frame. The proposed algorithm employs a sparse measurement matrix designed to represent the movement feature based on optical flow efficiently. Then, the abnormal detection mission is constructed as a one-class classification task via merely learning from the training normal samples. Experiments demonstrate that our algorithm performs well on the benchmark abnormal detection datasets against state-of-the-art methods.

Storage of sparse files using parallel log-structured file system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bent, John M.; Faibish, Sorin; Grider, Gary

A sparse file is stored without holes by storing a data portion of the sparse file using a parallel log-structured file system; and generating an index entry for the data portion, the index entry comprising a logical offset, physical offset and length of the data portion. The holes can be restored to the sparse file upon a reading of the sparse file. The data portion can be stored at a logical end of the sparse file. Additional storage efficiency can optionally be achieved by (i) detecting a write pattern for a plurality of the data portions and generating a singlemore » patterned index entry for the plurality of the patterned data portions; and/or (ii) storing the patterned index entries for a plurality of the sparse files in a single directory, wherein each entry in the single directory comprises an identifier of a corresponding sparse file.« less

Low-rank and Adaptive Sparse Signal (LASSI) Models for Highly Accelerated Dynamic Imaging

PubMed Central

Ravishankar, Saiprasad; Moore, Brian E.; Nadakuditi, Raj Rao; Fessler, Jeffrey A.

2017-01-01

Sparsity-based approaches have been popular in many applications in image processing and imaging. Compressed sensing exploits the sparsity of images in a transform domain or dictionary to improve image recovery from undersampled measurements. In the context of inverse problems in dynamic imaging, recent research has demonstrated the promise of sparsity and low-rank techniques. For example, the patches of the underlying data are modeled as sparse in an adaptive dictionary domain, and the resulting image and dictionary estimation from undersampled measurements is called dictionary-blind compressed sensing, or the dynamic image sequence is modeled as a sum of low-rank and sparse (in some transform domain) components (L+S model) that are estimated from limited measurements. In this work, we investigate a data-adaptive extension of the L+S model, dubbed LASSI, where the temporal image sequence is decomposed into a low-rank component and a component whose spatiotemporal (3D) patches are sparse in some adaptive dictionary domain. We investigate various formulations and efficient methods for jointly estimating the underlying dynamic signal components and the spatiotemporal dictionary from limited measurements. We also obtain efficient sparsity penalized dictionary-blind compressed sensing methods as special cases of our LASSI approaches. Our numerical experiments demonstrate the promising performance of LASSI schemes for dynamic magnetic resonance image reconstruction from limited k-t space data compared to recent methods such as k-t SLR and L+S, and compared to the proposed dictionary-blind compressed sensing method. PMID:28092528

Low-Rank and Adaptive Sparse Signal (LASSI) Models for Highly Accelerated Dynamic Imaging.

PubMed

Ravishankar, Saiprasad; Moore, Brian E; Nadakuditi, Raj Rao; Fessler, Jeffrey A

2017-05-01

Sparsity-based approaches have been popular in many applications in image processing and imaging. Compressed sensing exploits the sparsity of images in a transform domain or dictionary to improve image recovery fromundersampledmeasurements. In the context of inverse problems in dynamic imaging, recent research has demonstrated the promise of sparsity and low-rank techniques. For example, the patches of the underlying data are modeled as sparse in an adaptive dictionary domain, and the resulting image and dictionary estimation from undersampled measurements is called dictionary-blind compressed sensing, or the dynamic image sequence is modeled as a sum of low-rank and sparse (in some transform domain) components (L+S model) that are estimated from limited measurements. In this work, we investigate a data-adaptive extension of the L+S model, dubbed LASSI, where the temporal image sequence is decomposed into a low-rank component and a component whose spatiotemporal (3D) patches are sparse in some adaptive dictionary domain. We investigate various formulations and efficient methods for jointly estimating the underlying dynamic signal components and the spatiotemporal dictionary from limited measurements. We also obtain efficient sparsity penalized dictionary-blind compressed sensing methods as special cases of our LASSI approaches. Our numerical experiments demonstrate the promising performance of LASSI schemes for dynamicmagnetic resonance image reconstruction from limited k-t space data compared to recent methods such as k-t SLR and L+S, and compared to the proposed dictionary-blind compressed sensing method.

Sparse polynomial space approach to dissipative quantum systems: application to the sub-ohmic spin-boson model.

PubMed

Alvermann, A; Fehske, H

2009-04-17

We propose a general numerical approach to open quantum systems with a coupling to bath degrees of freedom. The technique combines the methodology of polynomial expansions of spectral functions with the sparse grid concept from interpolation theory. Thereby we construct a Hilbert space of moderate dimension to represent the bath degrees of freedom, which allows us to perform highly accurate and efficient calculations of static, spectral, and dynamic quantities using standard exact diagonalization algorithms. The strength of the approach is demonstrated for the phase transition, critical behavior, and dissipative spin dynamics in the spin-boson model.

A fast time-difference inverse solver for 3D EIT with application to lung imaging.

PubMed

Javaherian, Ashkan; Soleimani, Manuchehr; Moeller, Knut

2016-08-01

A class of sparse optimization techniques that require solely matrix-vector products, rather than an explicit access to the forward matrix and its transpose, has been paid much attention in the recent decade for dealing with large-scale inverse problems. This study tailors application of the so-called Gradient Projection for Sparse Reconstruction (GPSR) to large-scale time-difference three-dimensional electrical impedance tomography (3D EIT). 3D EIT typically suffers from the need for a large number of voxels to cover the whole domain, so its application to real-time imaging, for example monitoring of lung function, remains scarce since the large number of degrees of freedom of the problem extremely increases storage space and reconstruction time. This study shows the great potential of the GPSR for large-size time-difference 3D EIT. Further studies are needed to improve its accuracy for imaging small-size anomalies.

Research on sparse feature matching of improved RANSAC algorithm

NASA Astrophysics Data System (ADS)

Kong, Xiangsi; Zhao, Xian

2018-04-01

In this paper, a sparse feature matching method based on modified RANSAC algorithm is proposed to improve the precision and speed. Firstly, the feature points of the images are extracted using the SIFT algorithm. Then, the image pair is matched roughly by generating SIFT feature descriptor. At last, the precision of image matching is optimized by the modified RANSAC algorithm,. The RANSAC algorithm is improved from three aspects: instead of the homography matrix, this paper uses the fundamental matrix generated by the 8 point algorithm as the model; the sample is selected by a random block selecting method, which ensures the uniform distribution and the accuracy; adds sequential probability ratio test(SPRT) on the basis of standard RANSAC, which cut down the overall running time of the algorithm. The experimental results show that this method can not only get higher matching accuracy, but also greatly reduce the computation and improve the matching speed.

Improved sparse decomposition based on a smoothed L0 norm using a Laplacian kernel to select features from fMRI data.

PubMed

Zhang, Chuncheng; Song, Sutao; Wen, Xiaotong; Yao, Li; Long, Zhiying

2015-04-30

Feature selection plays an important role in improving the classification accuracy of multivariate classification techniques in the context of fMRI-based decoding due to the "few samples and large features" nature of functional magnetic resonance imaging (fMRI) data. Recently, several sparse representation methods have been applied to the voxel selection of fMRI data. Despite the low computational efficiency of the sparse representation methods, they still displayed promise for applications that select features from fMRI data. In this study, we proposed the Laplacian smoothed L0 norm (LSL0) approach for feature selection of fMRI data. Based on the fast sparse decomposition using smoothed L0 norm (SL0) (Mohimani, 2007), the LSL0 method used the Laplacian function to approximate the L0 norm of sources. Results of the simulated and real fMRI data demonstrated the feasibility and robustness of LSL0 for the sparse source estimation and feature selection. Simulated results indicated that LSL0 produced more accurate source estimation than SL0 at high noise levels. The classification accuracy using voxels that were selected by LSL0 was higher than that by SL0 in both simulated and real fMRI experiment. Moreover, both LSL0 and SL0 showed higher classification accuracy and required less time than ICA and t-test for the fMRI decoding. LSL0 outperformed SL0 in sparse source estimation at high noise level and in feature selection. Moreover, LSL0 and SL0 showed better performance than ICA and t-test for feature selection. Copyright © 2015 Elsevier B.V. All rights reserved.

Sparse Partial Equilibrium Tables in Chemically Resolved Reactive Flow

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vitello, P; Fried, L E; Pudliner, B

2003-07-14

The detonation of an energetic material is the result of a complex interaction between kinetic chemical reactions and hydrodynamics. Unfortunately, little is known concerning the detailed chemical kinetics of detonations in energetic materials. CHEETAH uses rate laws to treat species with the slowest chemical reactions, while assuming other chemical species are in equilibrium. CHEETAH supports a wide range of elements and condensed detonation products and can also be applied to gas detonations. A sparse hash table of equation of state values, called the ''cache'' is used in CHEETAH to enhance the efficiency of kinetic reaction calculations. For large-scale parallel hydrodynamicmore » calculations, CHEETAH uses MPI communication to updates to the cache. We present here details of the sparse caching model used in the CHEETAH. To demonstrate the efficiency of modeling using a sparse cache model we consider detonations in energetic materials.« less

Sparse Partial Equilibrium Tables in Chemically Resolved Reactive Flow

NASA Astrophysics Data System (ADS)

Vitello, Peter; Fried, Laurence E.; Pudliner, Brian; McAbee, Tom

2004-07-01

The detonation of an energetic material is the result of a complex interaction between kinetic chemical reactions and hydrodynamics. Unfortunately, little is known concerning the detailed chemical kinetics of detonations in energetic materials. CHEETAH uses rate laws to treat species with the slowest chemical reactions, while assuming other chemical species are in equilibrium. CHEETAH supports a wide range of elements and condensed detonation products and can also be applied to gas detonations. A sparse hash table of equation of state values is used in CHEETAH to enhance the efficiency of kinetic reaction calculations. For large-scale parallel hydrodynamic calculations, CHEETAH uses parallel communication to updates to the cache. We present here details of the sparse caching model used in the CHEETAH coupled to an ALE hydrocode. To demonstrate the efficiency of modeling using a sparse cache model we consider detonations in energetic materials.

JiTTree: A Just-in-Time Compiled Sparse GPU Volume Data Structure.

PubMed

Labschütz, Matthias; Bruckner, Stefan; Gröller, M Eduard; Hadwiger, Markus; Rautek, Peter

2016-01-01

Sparse volume data structures enable the efficient representation of large but sparse volumes in GPU memory for computation and visualization. However, the choice of a specific data structure for a given data set depends on several factors, such as the memory budget, the sparsity of the data, and data access patterns. In general, there is no single optimal sparse data structure, but a set of several candidates with individual strengths and drawbacks. One solution to this problem are hybrid data structures which locally adapt themselves to the sparsity. However, they typically suffer from increased traversal overhead which limits their utility in many applications. This paper presents JiTTree, a novel sparse hybrid volume data structure that uses just-in-time compilation to overcome these problems. By combining multiple sparse data structures and reducing traversal overhead we leverage their individual advantages. We demonstrate that hybrid data structures adapt well to a large range of data sets. They are especially superior to other sparse data structures for data sets that locally vary in sparsity. Possible optimization criteria are memory, performance and a combination thereof. Through just-in-time (JIT) compilation, JiTTree reduces the traversal overhead of the resulting optimal data structure. As a result, our hybrid volume data structure enables efficient computations on the GPU, while being superior in terms of memory usage when compared to non-hybrid data structures.

Adapting iterative algorithms for solving large sparse linear systems for efficient use on the CDC CYBER 205

NASA Technical Reports Server (NTRS)

Kincaid, D. R.; Young, D. M.

1984-01-01

Adapting and designing mathematical software to achieve optimum performance on the CYBER 205 is discussed. Comments and observations are made in light of recent work done on modifying the ITPACK software package and on writing new software for vector supercomputers. The goal was to develop very efficient vector algorithms and software for solving large sparse linear systems using iterative methods.

Parallel pivoting combined with parallel reduction

NASA Technical Reports Server (NTRS)

Alaghband, Gita

1987-01-01

Parallel algorithms for triangularization of large, sparse, and unsymmetric matrices are presented. The method combines the parallel reduction with a new parallel pivoting technique, control over generations of fill-ins and a check for numerical stability, all done in parallel with the work being distributed over the active processes. The parallel technique uses the compatibility relation between pivots to identify parallel pivot candidates and uses the Markowitz number of pivots to minimize fill-in. This technique is not a preordering of the sparse matrix and is applied dynamically as the decomposition proceeds.

Compressive sensing for sparse time-frequency representation of nonstationary signals in the presence of impulsive noise

NASA Astrophysics Data System (ADS)

Orović, Irena; Stanković, Srdjan; Amin, Moeness

2013-05-01

A modified robust two-dimensional compressive sensing algorithm for reconstruction of sparse time-frequency representation (TFR) is proposed. The ambiguity function domain is assumed to be the domain of observations. The two-dimensional Fourier bases are used to linearly relate the observations to the sparse TFR, in lieu of the Wigner distribution. We assume that a set of available samples in the ambiguity domain is heavily corrupted by an impulsive type of noise. Consequently, the problem of sparse TFR reconstruction cannot be tackled using standard compressive sensing optimization algorithms. We introduce a two-dimensional L-statistics based modification into the transform domain representation. It provides suitable initial conditions that will produce efficient convergence of the reconstruction algorithm. This approach applies sorting and weighting operations to discard an expected amount of samples corrupted by noise. The remaining samples serve as observations used in sparse reconstruction of the time-frequency signal representation. The efficiency of the proposed approach is demonstrated on numerical examples that comprise both cases of monocomponent and multicomponent signals.

Accessing sparse arrays in parallel memories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Banerjee, U.; Gajski, D.; Kuck, D.

The concept of dense and sparse execution of arrays is introduced. Arrays themselves can be stored in a dense or sparse manner in a parallel memory with m memory modules. The paper proposes hardware for speeding up the execution of array operations of the form c(c/sub 0/+ci)=a(a/sub 0/+ai) op b(b/sub 0/+bi), where a/sub 0/, a, b/sub 0/, b, c/sub 0/, c are integer constants and i is an index variable. The hardware handles 'sparse execution', in which the operation op is not executed for every value of i. The hardware also makes provision for 'sparse storage', in which memory spacemore » is not provided for every array element. It is shown how to access array elements of the above form without conflict in an efficient way. The efficiency is obtained by using some specialised units which are basically smart memories with priority detection, one's counting or associative searching. Generalisation to multidimensional arrays is shown possible under restrictions defined in the paper. 12 references.« less

Energy-Efficient Wide Datapath Integer Arithmetic Logic Units Using Superconductor Logic

NASA Astrophysics Data System (ADS)

Ayala, Christopher Lawrence

Complementary Metal-Oxide-Semiconductor (CMOS) technology is currently the most widely used integrated circuit technology today. As CMOS approaches the physical limitations of scaling, it is unclear whether or not it can provide long-term support for niche areas such as high-performance computing and telecommunication infrastructure, particularly with the emergence of cloud computing. Alternatively, superconductor technologies based on Josephson junction (JJ) switching elements such as Rapid Single Flux Quantum (RSFQ) logic and especially its new variant, Energy-Efficient Rapid Single Flux Quantum (ERSFQ) logic have the capability to provide an ultra-high-speed, low power platform for digital systems. The objective of this research is to design and evaluate energy-efficient, high-speed 32-bit integer Arithmetic Logic Units (ALUs) implemented using RSFQ and ERSFQ logic as the first steps towards achieving practical Very-Large-Scale-Integration (VLSI) complexity in digital superconductor electronics. First, a tunable VHDL superconductor cell library is created to provide a mechanism to conduct design exploration and evaluation of superconductor digital circuits from the perspectives of functionality, complexity, performance, and energy-efficiency. Second, hybrid wave-pipelining techniques developed earlier for wide datapath RSFQ designs have been used for efficient arithmetic and logic circuit implementations. To develop the core foundation of the ALU, the ripple-carry adder and the Kogge-Stone parallel prefix carry look-ahead adder are studied as representative candidates on opposite ends of the design spectrum. By combining the high-performance features of the Kogge-Stone structure and the low complexity of the ripple-carry adder, a 32-bit asynchronous wave-pipelined hybrid sparse-tree ALU has been designed and evaluated using the VHDL cell library tuned to HYPRES' gate-level characteristics. The designs and techniques from this research have been implemented using RSFQ logic and prototype chips have been fabricated. As a joint work with HYPRES, a 20 GHz 8-bit Kogge-Stone ALU consisting of 7,950 JJs total has been fabricated using a 1.5 μm 4.5 kA/cm2 process and fully demonstrated. An 8-bit sparse-tree ALU (8,832 JJs total) and a 16-bit sparse-tree adder (12,785 JJs total) have also been fabricated using a 1.0 μm 10 kA/cm 2 process and demonstrated under collaboration with Yokohama National University and Nagoya University (Japan).

Matrix decomposition graphics processing unit solver for Poisson image editing

NASA Astrophysics Data System (ADS)

Lei, Zhao; Wei, Li

2012-10-01

In recent years, gradient-domain methods have been widely discussed in the image processing field, including seamless cloning and image stitching. These algorithms are commonly carried out by solving a large sparse linear system: the Poisson equation. However, solving the Poisson equation is a computational and memory intensive task which makes it not suitable for real-time image editing. A new matrix decomposition graphics processing unit (GPU) solver (MDGS) is proposed to settle the problem. A matrix decomposition method is used to distribute the work among GPU threads, so that MDGS will take full advantage of the computing power of current GPUs. Additionally, MDGS is a hybrid solver (combines both the direct and iterative techniques) and has two-level architecture. These enable MDGS to generate identical solutions with those of the common Poisson methods and achieve high convergence rate in most cases. This approach is advantageous in terms of parallelizability, enabling real-time image processing, low memory-taken and extensive applications.

pySAPC, a python package for sparse affinity propagation clustering: Application to odontogenesis whole genome time series gene-expression data.

PubMed

Cao, Huojun; Amendt, Brad A

2016-11-01

Developmental dental anomalies are common forms of congenital defects. The molecular mechanisms of dental anomalies are poorly understood. Systematic approaches such as clustering genes based on similar expression patterns could identify novel genes involved in dental anomalies and provide a framework for understanding molecular regulatory mechanisms of these genes during tooth development (odontogenesis). A python package (pySAPC) of sparse affinity propagation clustering algorithm for large datasets was developed. Whole genome pair-wise similarity was calculated based on expression pattern similarity based on 45 microarrays of several stages during odontogenesis. pySAPC identified 743 gene clusters based on expression pattern similarity during mouse tooth development. Three clusters are significantly enriched for genes associated with dental anomalies (with FDR <0.1). The three clusters of genes have distinct expression patterns during odontogenesis. Clustering genes based on similar expression profiles recovered several known regulatory relationships for genes involved in odontogenesis, as well as many novel genes that may be involved with the same genetic pathways as genes that have already been shown to contribute to dental defects. By using sparse similarity matrix, pySAPC use much less memory and CPU time compared with the original affinity propagation program that uses a full similarity matrix. This python package will be useful for many applications where dataset(s) are too large to use full similarity matrix. This article is part of a Special Issue entitled "System Genetics" Guest Editor: Dr. Yudong Cai and Dr. Tao Huang. Copyright © 2016. Published by Elsevier B.V.

A Performance Comparison of the Parallel Preconditioners for Iterative Methods for Large Sparse Linear Systems Arising from Partial Differential Equations on Structured Grids

NASA Astrophysics Data System (ADS)

Ma, Sangback

In this paper we compare various parallel preconditioners such as Point-SSOR (Symmetric Successive OverRelaxation), ILU(0) (Incomplete LU) in the Wavefront ordering, ILU(0) in the Multi-color ordering, Multi-Color Block SOR (Successive OverRelaxation), SPAI (SParse Approximate Inverse) and pARMS (Parallel Algebraic Recursive Multilevel Solver) for solving large sparse linear systems arising from two-dimensional PDE (Partial Differential Equation)s on structured grids. Point-SSOR is well-known, and ILU(0) is one of the most popular preconditioner, but it is inherently serial. ILU(0) in the Wavefront ordering maximizes the parallelism in the natural order, but the lengths of the wave-fronts are often nonuniform. ILU(0) in the Multi-color ordering is a simple way of achieving a parallelism of the order N, where N is the order of the matrix, but its convergence rate often deteriorates as compared to that of natural ordering. We have chosen the Multi-Color Block SOR preconditioner combined with direct sparse matrix solver, since for the Laplacian matrix the SOR method is known to have a nondeteriorating rate of convergence when used with the Multi-Color ordering. By using block version we expect to minimize the interprocessor communications. SPAI computes the sparse approximate inverse directly by least squares method. Finally, ARMS is a preconditioner recursively exploiting the concept of independent sets and pARMS is the parallel version of ARMS. Experiments were conducted for the Finite Difference and Finite Element discretizations of five two-dimensional PDEs with large meshsizes up to a million on an IBM p595 machine with distributed memory. Our matrices are real positive, i. e., their real parts of the eigenvalues are positive. We have used GMRES(m) as our outer iterative method, so that the convergence of GMRES(m) for our test matrices are mathematically guaranteed. Interprocessor communications were done using MPI (Message Passing Interface) primitives. The results show that in general ILU(0) in the Multi-Color ordering ahd ILU(0) in the Wavefront ordering outperform the other methods but for symmetric and nearly symmetric 5-point matrices Multi-Color Block SOR gives the best performance, except for a few cases with a small number of processors.

Guided-mode resonance nanophotonics in materially sparse architectures

NASA Astrophysics Data System (ADS)

Magnusson, Robert; Niraula, Manoj; Yoon, Jae W.; Ko, Yeong H.; Lee, Kyu J.

2016-03-01

The guided-mode resonance (GMR) concept refers to lateral quasi-guided waveguide modes induced in periodic layers. Whereas these effects have been known for a long time, new attributes and innovations continue to appear. Here, we review some recent progress in this field with emphasis on sparse, or minimal, device embodiments. We discuss properties of wideband resonant reflectors designed with gratings in which the grating ridges are matched to an identical material to eliminate local reflections and phase changes. This critical interface therefore possesses zero refractive-index contrast; hence we call them "zero-contrast gratings." Applying this architecture, we present single-layer, wideband reflectors that are robust under experimentally realistic parametric variations. We introduce a new class of reflectors and polarizers fashioned with dielectric nanowire grids that are mostly empty space. Computed results predict high reflection and attendant polarization extinction for these sparse lattices. Experimental verification with Si nanowire grids yields ~200-nm-wide band of high reflection for one polarization state and free transmission of the orthogonal state. Finally, we present bandpass filters using all-dielectric resonant gratings. We design, fabricate, and test nanostructured single layer filters exhibiting high efficiency and sub-nanometer-wide passbands surrounded by 100-nm-wide stopbands.

Sparse representations via learned dictionaries for x-ray angiogram image denoising

NASA Astrophysics Data System (ADS)

Shang, Jingfan; Huang, Zhenghua; Li, Qian; Zhang, Tianxu

2018-03-01

X-ray angiogram image denoising is always an active research topic in the field of computer vision. In particular, the denoising performance of many existing methods had been greatly improved by the widely use of nonlocal similar patches. However, the only nonlocal self-similar (NSS) patch-based methods can be still be improved and extended. In this paper, we propose an image denoising model based on the sparsity of the NSS patches to obtain high denoising performance and high-quality image. In order to represent the sparsely NSS patches in every location of the image well and solve the image denoising model more efficiently, we obtain dictionaries as a global image prior by the K-SVD algorithm over the processing image; Then the single and effectively alternating directions method of multipliers (ADMM) method is used to solve the image denoising model. The results of widely synthetic experiments demonstrate that, owing to learned dictionaries by K-SVD algorithm, a sparsely augmented lagrangian image denoising (SALID) model, which perform effectively, obtains a state-of-the-art denoising performance and better high-quality images. Moreover, we also give some denoising results of clinical X-ray angiogram images.

Biclustering sparse binary genomic data.

PubMed

van Uitert, Miranda; Meuleman, Wouter; Wessels, Lodewyk

2008-12-01

Genomic datasets often consist of large, binary, sparse data matrices. In such a dataset, one is often interested in finding contiguous blocks that (mostly) contain ones. This is a biclustering problem, and while many algorithms have been proposed to deal with gene expression data, only two algorithms have been proposed that specifically deal with binary matrices. None of the gene expression biclustering algorithms can handle the large number of zeros in sparse binary matrices. The two proposed binary algorithms failed to produce meaningful results. In this article, we present a new algorithm that is able to extract biclusters from sparse, binary datasets. A powerful feature is that biclusters with different numbers of rows and columns can be detected, varying from many rows to few columns and few rows to many columns. It allows the user to guide the search towards biclusters of specific dimensions. When applying our algorithm to an input matrix derived from TRANSFAC, we find transcription factors with distinctly dissimilar binding motifs, but a clear set of common targets that are significantly enriched for GO categories.

Sparse dictionary learning for resting-state fMRI analysis

NASA Astrophysics Data System (ADS)

Lee, Kangjoo; Han, Paul Kyu; Ye, Jong Chul

2011-09-01

Recently, there has been increased interest in the usage of neuroimaging techniques to investigate what happens in the brain at rest. Functional imaging studies have revealed that the default-mode network activity is disrupted in Alzheimer's disease (AD). However, there is no consensus, as yet, on the choice of analysis method for the application of resting-state analysis for disease classification. This paper proposes a novel compressed sensing based resting-state fMRI analysis tool called Sparse-SPM. As the brain's functional systems has shown to have features of complex networks according to graph theoretical analysis, we apply a graph model to represent a sparse combination of information flows in complex network perspectives. In particular, a new concept of spatially adaptive design matrix has been proposed by implementing sparse dictionary learning based on sparsity. The proposed approach shows better performance compared to other conventional methods, such as independent component analysis (ICA) and seed-based approach, in classifying the AD patients from normal using resting-state analysis.

Sparse decomposition of seismic data and migration using Gaussian beams with nonzero initial curvature

NASA Astrophysics Data System (ADS)

Liu, Peng; Wang, Yanfei

2018-04-01

We study problems associated with seismic data decomposition and migration imaging. We first represent the seismic data utilizing Gaussian beam basis functions, which have nonzero curvature, and then consider the sparse decomposition technique. The sparse decomposition problem is an l0-norm constrained minimization problem. In solving the l0-norm minimization, a polynomial Radon transform is performed to achieve sparsity, and a fast gradient descent method is used to calculate the waveform functions. The waveform functions can subsequently be used for sparse Gaussian beam migration. Compared with traditional sparse Gaussian beam methods, the seismic data can be properly reconstructed employing fewer Gaussian beams with nonzero initial curvature. The migration approach described in this paper is more efficient than the traditional sparse Gaussian beam migration.

Unified commutation-pruning technique for efficient computation of composite DFTs

NASA Astrophysics Data System (ADS)

Castro-Palazuelos, David E.; Medina-Melendrez, Modesto Gpe.; Torres-Roman, Deni L.; Shkvarko, Yuriy V.

2015-12-01

An efficient computation of a composite length discrete Fourier transform (DFT), as well as a fast Fourier transform (FFT) of both time and space data sequences in uncertain (non-sparse or sparse) computational scenarios, requires specific processing algorithms. Traditional algorithms typically employ some pruning methods without any commutations, which prevents them from attaining the potential computational efficiency. In this paper, we propose an alternative unified approach with automatic commutations between three computational modalities aimed at efficient computations of the pruned DFTs adapted for variable composite lengths of the non-sparse input-output data. The first modality is an implementation of the direct computation of a composite length DFT, the second one employs the second-order recursive filtering method, and the third one performs the new pruned decomposed transform. The pruned decomposed transform algorithm performs the decimation in time or space (DIT) data acquisition domain and, then, decimation in frequency (DIF). The unified combination of these three algorithms is addressed as the DFTCOMM technique. Based on the treatment of the combinational-type hypotheses testing optimization problem of preferable allocations between all feasible commuting-pruning modalities, we have found the global optimal solution to the pruning problem that always requires a fewer or, at most, the same number of arithmetic operations than other feasible modalities. The DFTCOMM method outperforms the existing competing pruning techniques in the sense of attainable savings in the number of required arithmetic operations. It requires fewer or at most the same number of arithmetic operations for its execution than any other of the competing pruning methods reported in the literature. Finally, we provide the comparison of the DFTCOMM with the recently developed sparse fast Fourier transform (SFFT) algorithmic family. We feature that, in the sensing scenarios with sparse/non-sparse data Fourier spectrum, the DFTCOMM technique manifests robustness against such model uncertainties in the sense of insensitivity for sparsity/non-sparsity restrictions and the variability of the operating parameters.

Scalable domain decomposition solvers for stochastic PDEs in high performance computing

DOE PAGES

Desai, Ajit; Khalil, Mohammad; Pettit, Chris; ...

2017-09-21

Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolutionmore » in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.« less

Scalable domain decomposition solvers for stochastic PDEs in high performance computing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Desai, Ajit; Khalil, Mohammad; Pettit, Chris

Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolutionmore » in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.« less

Predefined Redundant Dictionary for Effective Depth Maps Representation

NASA Astrophysics Data System (ADS)

Sebai, Dorsaf; Chaieb, Faten; Ghorbel, Faouzi

2016-01-01

The multi-view video plus depth (MVD) video format consists of two components: texture and depth map, where a combination of these components enables a receiver to generate arbitrary virtual views. However, MVD presents a very voluminous video format that requires a compression process for storage and especially for transmission. Conventional codecs are perfectly efficient for texture images compression but not for intrinsic depth maps properties. Depth images indeed are characterized by areas of smoothly varying grey levels separated by sharp discontinuities at the position of object boundaries. Preserving these characteristics is important to enable high quality view synthesis at the receiver side. In this paper, sparse representation of depth maps is discussed. It is shown that a significant gain in sparsity is achieved when particular mixed dictionaries are used for approximating these types of images with greedy selection strategies. Experiments are conducted to confirm the effectiveness at producing sparse representations, and competitiveness, with respect to candidate state-of-art dictionaries. Finally, the resulting method is shown to be effective for depth maps compression and represents an advantage over the ongoing 3D high efficiency video coding compression standard, particularly at medium and high bitrates.

Sparse representation based image interpolation with nonlocal autoregressive modeling.

PubMed

Dong, Weisheng; Zhang, Lei; Lukac, Rastislav; Shi, Guangming

2013-04-01

Sparse representation is proven to be a promising approach to image super-resolution, where the low-resolution (LR) image is usually modeled as the down-sampled version of its high-resolution (HR) counterpart after blurring. When the blurring kernel is the Dirac delta function, i.e., the LR image is directly down-sampled from its HR counterpart without blurring, the super-resolution problem becomes an image interpolation problem. In such cases, however, the conventional sparse representation models (SRM) become less effective, because the data fidelity term fails to constrain the image local structures. In natural images, fortunately, many nonlocal similar patches to a given patch could provide nonlocal constraint to the local structure. In this paper, we incorporate the image nonlocal self-similarity into SRM for image interpolation. More specifically, a nonlocal autoregressive model (NARM) is proposed and taken as the data fidelity term in SRM. We show that the NARM-induced sampling matrix is less coherent with the representation dictionary, and consequently makes SRM more effective for image interpolation. Our extensive experimental results demonstrate that the proposed NARM-based image interpolation method can effectively reconstruct the edge structures and suppress the jaggy/ringing artifacts, achieving the best image interpolation results so far in terms of PSNR as well as perceptual quality metrics such as SSIM and FSIM.

Indexing amyloid peptide diffraction from serial femtosecond crystallography: new algorithms for sparse patterns

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brewster, Aaron S.; Sawaya, Michael R.; University of California, Los Angeles, CA 90095-1570

2015-02-01

Special methods are required to interpret sparse diffraction patterns collected from peptide crystals at X-ray free-electron lasers. Bragg spots can be indexed from composite-image powder rings, with crystal orientations then deduced from a very limited number of spot positions. Still diffraction patterns from peptide nanocrystals with small unit cells are challenging to index using conventional methods owing to the limited number of spots and the lack of crystal orientation information for individual images. New indexing algorithms have been developed as part of the Computational Crystallography Toolbox (cctbx) to overcome these challenges. Accurate unit-cell information derived from an aggregate data setmore » from thousands of diffraction patterns can be used to determine a crystal orientation matrix for individual images with as few as five reflections. These algorithms are potentially applicable not only to amyloid peptides but also to any set of diffraction patterns with sparse properties, such as low-resolution virus structures or high-throughput screening of still images captured by raster-scanning at synchrotron sources. As a proof of concept for this technique, successful integration of X-ray free-electron laser (XFEL) data to 2.5 Å resolution for the amyloid segment GNNQQNY from the Sup35 yeast prion is presented.« less

An efficient matrix-matrix multiplication based antisymmetric tensor contraction engine for general order coupled cluster.

PubMed

Hanrath, Michael; Engels-Putzka, Anna

2010-08-14

In this paper, we present an efficient implementation of general tensor contractions, which is part of a new coupled-cluster program. The tensor contractions, used to evaluate the residuals in each coupled-cluster iteration are particularly important for the performance of the program. We developed a generic procedure, which carries out contractions of two tensors irrespective of their explicit structure. It can handle coupled-cluster-type expressions of arbitrary excitation level. To make the contraction efficient without loosing flexibility, we use a three-step procedure. First, the data contained in the tensors are rearranged into matrices, then a matrix-matrix multiplication is performed, and finally the result is backtransformed to a tensor. The current implementation is significantly more efficient than previous ones capable of treating arbitrary high excitations.

The CSM testbed matrix processors internal logic and dataflow descriptions

NASA Technical Reports Server (NTRS)

Regelbrugge, Marc E.; Wright, Mary A.

1988-01-01

This report constitutes the final report for subtask 1 of Task 5 of NASA Contract NAS1-18444, Computational Structural Mechanics (CSM) Research. This report contains a detailed description of the coded workings of selected CSM Testbed matrix processors (i.e., TOPO, K, INV, SSOL) and of the arithmetic utility processor AUS. These processors and the current sparse matrix data structures are studied and documented. Items examined include: details of the data structures, interdependence of data structures, data-blocking logic in the data structures, processor data flow and architecture, and processor algorithmic logic flow.

Energy conserving, linear scaling Born-Oppenheimer molecular dynamics.

PubMed

Cawkwell, M J; Niklasson, Anders M N

2012-10-07

Born-Oppenheimer molecular dynamics simulations with long-term conservation of the total energy and a computational cost that scales linearly with system size have been obtained simultaneously. Linear scaling with a low pre-factor is achieved using density matrix purification with sparse matrix algebra and a numerical threshold on matrix elements. The extended Lagrangian Born-Oppenheimer molecular dynamics formalism [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] yields microcanonical trajectories with the approximate forces obtained from the linear scaling method that exhibit no systematic drift over hundreds of picoseconds and which are indistinguishable from trajectories computed using exact forces.

Data-Driven Sampling Matrix Boolean Optimization for Energy-Efficient Biomedical Signal Acquisition by Compressive Sensing.

PubMed

Wang, Yuhao; Li, Xin; Xu, Kai; Ren, Fengbo; Yu, Hao

2017-04-01

Compressive sensing is widely used in biomedical applications, and the sampling matrix plays a critical role on both quality and power consumption of signal acquisition. It projects a high-dimensional vector of data into a low-dimensional subspace by matrix-vector multiplication. An optimal sampling matrix can ensure accurate data reconstruction and/or high compression ratio. Most existing optimization methods can only produce real-valued embedding matrices that result in large energy consumption during data acquisition. In this paper, we propose an efficient method that finds an optimal Boolean sampling matrix in order to reduce the energy consumption. Compared to random Boolean embedding, our data-driven Boolean sampling matrix can improve the image recovery quality by 9 dB. Moreover, in terms of sampling hardware complexity, it reduces the energy consumption by 4.6× and the silicon area by 1.9× over the data-driven real-valued embedding.

Viewing Angle Classification of Cryo-Electron Microscopy Images Using Eigenvectors

PubMed Central

Singer, A.; Zhao, Z.; Shkolnisky, Y.; Hadani, R.

2012-01-01

The cryo-electron microscopy (cryo-EM) reconstruction problem is to find the three-dimensional structure of a macromolecule given noisy versions of its two-dimensional projection images at unknown random directions. We introduce a new algorithm for identifying noisy cryo-EM images of nearby viewing angles. This identification is an important first step in three-dimensional structure determination of macromolecules from cryo-EM, because once identified, these images can be rotationally aligned and averaged to produce “class averages” of better quality. The main advantage of our algorithm is its extreme robustness to noise. The algorithm is also very efficient in terms of running time and memory requirements, because it is based on the computation of the top few eigenvectors of a specially designed sparse Hermitian matrix. These advantages are demonstrated in numerous numerical experiments. PMID:22506089

Delayed Slater determinant update algorithms for high efficiency quantum Monte Carlo

DOE PAGES

McDaniel, Tyler; D’Azevedo, Ed F.; Li, Ying Wai; ...

2017-11-07

Within ab initio Quantum Monte Carlo simulations, the leading numerical cost for large systems is the computation of the values of the Slater determinants in the trial wavefunction. Each Monte Carlo step requires finding the determinant of a dense matrix. This is most commonly iteratively evaluated using a rank-1 Sherman-Morrison updating scheme to avoid repeated explicit calculation of the inverse. The overall computational cost is therefore formally cubic in the number of electrons or matrix size. To improve the numerical efficiency of this procedure, we propose a novel multiple rank delayed update scheme. This strategy enables probability evaluation with applicationmore » of accepted moves to the matrices delayed until after a predetermined number of moves, K. The accepted events are then applied to the matrices en bloc with enhanced arithmetic intensity and computational efficiency via matrix-matrix operations instead of matrix-vector operations. Here this procedure does not change the underlying Monte Carlo sampling or its statistical efficiency. For calculations on large systems and algorithms such as diffusion Monte Carlo where the acceptance ratio is high, order of magnitude improvements in the update time can be obtained on both multi- core CPUs and GPUs.« less

Delayed Slater determinant update algorithms for high efficiency quantum Monte Carlo

DOE Office of Scientific and Technical Information (OSTI.GOV)

McDaniel, Tyler; D’Azevedo, Ed F.; Li, Ying Wai

Within ab initio Quantum Monte Carlo simulations, the leading numerical cost for large systems is the computation of the values of the Slater determinants in the trial wavefunction. Each Monte Carlo step requires finding the determinant of a dense matrix. This is most commonly iteratively evaluated using a rank-1 Sherman-Morrison updating scheme to avoid repeated explicit calculation of the inverse. The overall computational cost is therefore formally cubic in the number of electrons or matrix size. To improve the numerical efficiency of this procedure, we propose a novel multiple rank delayed update scheme. This strategy enables probability evaluation with applicationmore » of accepted moves to the matrices delayed until after a predetermined number of moves, K. The accepted events are then applied to the matrices en bloc with enhanced arithmetic intensity and computational efficiency via matrix-matrix operations instead of matrix-vector operations. Here this procedure does not change the underlying Monte Carlo sampling or its statistical efficiency. For calculations on large systems and algorithms such as diffusion Monte Carlo where the acceptance ratio is high, order of magnitude improvements in the update time can be obtained on both multi- core CPUs and GPUs.« less

Delayed Slater determinant update algorithms for high efficiency quantum Monte Carlo.

PubMed

McDaniel, T; D'Azevedo, E F; Li, Y W; Wong, K; Kent, P R C

2017-11-07

Within ab initio Quantum Monte Carlo simulations, the leading numerical cost for large systems is the computation of the values of the Slater determinants in the trial wavefunction. Each Monte Carlo step requires finding the determinant of a dense matrix. This is most commonly iteratively evaluated using a rank-1 Sherman-Morrison updating scheme to avoid repeated explicit calculation of the inverse. The overall computational cost is, therefore, formally cubic in the number of electrons or matrix size. To improve the numerical efficiency of this procedure, we propose a novel multiple rank delayed update scheme. This strategy enables probability evaluation with an application of accepted moves to the matrices delayed until after a predetermined number of moves, K. The accepted events are then applied to the matrices en bloc with enhanced arithmetic intensity and computational efficiency via matrix-matrix operations instead of matrix-vector operations. This procedure does not change the underlying Monte Carlo sampling or its statistical efficiency. For calculations on large systems and algorithms such as diffusion Monte Carlo, where the acceptance ratio is high, order of magnitude improvements in the update time can be obtained on both multi-core central processing units and graphical processing units.

Delayed Slater determinant update algorithms for high efficiency quantum Monte Carlo

NASA Astrophysics Data System (ADS)

McDaniel, T.; D'Azevedo, E. F.; Li, Y. W.; Wong, K.; Kent, P. R. C.

2017-11-01

Within ab initio Quantum Monte Carlo simulations, the leading numerical cost for large systems is the computation of the values of the Slater determinants in the trial wavefunction. Each Monte Carlo step requires finding the determinant of a dense matrix. This is most commonly iteratively evaluated using a rank-1 Sherman-Morrison updating scheme to avoid repeated explicit calculation of the inverse. The overall computational cost is, therefore, formally cubic in the number of electrons or matrix size. To improve the numerical efficiency of this procedure, we propose a novel multiple rank delayed update scheme. This strategy enables probability evaluation with an application of accepted moves to the matrices delayed until after a predetermined number of moves, K. The accepted events are then applied to the matrices en bloc with enhanced arithmetic intensity and computational efficiency via matrix-matrix operations instead of matrix-vector operations. This procedure does not change the underlying Monte Carlo sampling or its statistical efficiency. For calculations on large systems and algorithms such as diffusion Monte Carlo, where the acceptance ratio is high, order of magnitude improvements in the update time can be obtained on both multi-core central processing units and graphical processing units.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jakeman, John D.; Narayan, Akil; Zhou, Tao

We propose an algorithm for recovering sparse orthogonal polynomial expansions via collocation. A standard sampling approach for recovering sparse polynomials uses Monte Carlo sampling, from the density of orthogonality, which results in poor function recovery when the polynomial degree is high. Our proposed approach aims to mitigate this limitation by sampling with respect to the weighted equilibrium measure of the parametric domain and subsequently solves a preconditionedmore » $$\\ell^1$$-minimization problem, where the weights of the diagonal preconditioning matrix are given by evaluations of the Christoffel function. Our algorithm can be applied to a wide class of orthogonal polynomial families on bounded and unbounded domains, including all classical families. We present theoretical analysis to motivate the algorithm and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest. In conclusion, numerical examples are also provided to demonstrate that our proposed algorithm leads to comparable or improved accuracy even when compared with Legendre- and Hermite-specific algorithms.« less

A comparison of SuperLU solvers on the intel MIC architecture

NASA Astrophysics Data System (ADS)

Tuncel, Mehmet; Duran, Ahmet; Celebi, M. Serdar; Akaydin, Bora; Topkaya, Figen O.

2016-10-01

In many science and engineering applications, problems may result in solving a sparse linear system AX=B. For example, SuperLU_MCDT, a linear solver, was used for the large penta-diagonal matrices for 2D problems and hepta-diagonal matrices for 3D problems, coming from the incompressible blood flow simulation (see [1]). It is important to test the status and potential improvements of state-of-the-art solvers on new technologies. In this work, sequential, multithreaded and distributed versions of SuperLU solvers (see [2]) are examined on the Intel Xeon Phi coprocessors using offload programming model at the EURORA cluster of CINECA in Italy. We consider a portfolio of test matrices containing patterned matrices from UFMM ([3]) and randomly located matrices. This architecture can benefit from high parallelism and large vectors. We find that the sequential SuperLU benefited up to 45 % performance improvement from the offload programming depending on the sparse matrix type and the size of transferred and processed data.

Indexing amyloid peptide diffraction from serial femtosecond crystallography: New algorithms for sparse patterns

DOE PAGES

Brewster, Aaron S.; Sawaya, Michael R.; Rodriguez, Jose; ...

2015-01-23

Still diffraction patterns from peptide nanocrystals with small unit cells are challenging to index using conventional methods owing to the limited number of spots and the lack of crystal orientation information for individual images. New indexing algorithms have been developed as part of the Computational Crystallography Toolbox( cctbx) to overcome these challenges. Accurate unit-cell information derived from an aggregate data set from thousands of diffraction patterns can be used to determine a crystal orientation matrix for individual images with as few as five reflections. These algorithms are potentially applicable not only to amyloid peptides but also to any set ofmore » diffraction patterns with sparse properties, such as low-resolution virus structures or high-throughput screening of still images captured by raster-scanning at synchrotron sources. As a proof of concept for this technique, successful integration of X-ray free-electron laser (XFEL) data to 2.5 Å resolution for the amyloid segment GNNQQNY from the Sup35 yeast prion is presented.« less

Data-driven cluster reinforcement and visualization in sparsely-matched self-organizing maps.

PubMed

Manukyan, Narine; Eppstein, Margaret J; Rizzo, Donna M

2012-05-01

A self-organizing map (SOM) is a self-organized projection of high-dimensional data onto a typically 2-dimensional (2-D) feature map, wherein vector similarity is implicitly translated into topological closeness in the 2-D projection. However, when there are more neurons than input patterns, it can be challenging to interpret the results, due to diffuse cluster boundaries and limitations of current methods for displaying interneuron distances. In this brief, we introduce a new cluster reinforcement (CR) phase for sparsely-matched SOMs. The CR phase amplifies within-cluster similarity in an unsupervised, data-driven manner. Discontinuities in the resulting map correspond to between-cluster distances and are stored in a boundary (B) matrix. We describe a new hierarchical visualization of cluster boundaries displayed directly on feature maps, which requires no further clustering beyond what was implicitly accomplished during self-organization in SOM training. We use a synthetic benchmark problem and previously published microbial community profile data to demonstrate the benefits of the proposed methods.

Two variants of minimum discarded fill ordering

DOE Office of Scientific and Technical Information (OSTI.GOV)

D'Azevedo, E.F.; Forsyth, P.A.; Tang, Wei-Pai

1991-01-01

It is well known that the ordering of the unknowns can have a significant effect on the convergence of Preconditioned Conjugate Gradient (PCG) methods. There has been considerable experimental work on the effects of ordering for regular finite difference problems. In many cases, good results have been obtained with preconditioners based on diagonal, spiral or natural row orderings. However, for finite element problems having unstructured grids or grids generated by a local refinement approach, it is difficult to define many of the orderings for more regular problems. A recently proposed Minimum Discarded Fill (MDF) ordering technique is effective in findingmore » high quality Incomplete LU (ILU) preconditioners, especially for problems arising from unstructured finite element grids. Testing indicates this algorithm can identify a rather complicated physical structure in an anisotropic problem and orders the unknowns in the preferred'' direction. The MDF technique may be viewed as the numerical analogue of the minimum deficiency algorithm in sparse matrix technology. At any stage of the partial elimination, the MDF technique chooses the next pivot node so as to minimize the amount of discarded fill. In this work, two efficient variants of the MDF technique are explored to produce cost-effective high-order ILU preconditioners. The Threshold MDF orderings combine MDF ideas with drop tolerance techniques to identify the sparsity pattern in the ILU preconditioners. These techniques identify an ordering that encourages fast decay of the entries in the ILU factorization. The Minimum Update Matrix (MUM) ordering technique is a simplification of the MDF ordering and is closely related to the minimum degree algorithm. The MUM ordering is especially for large problems arising from Navier-Stokes problems. Some interesting pictures of the orderings are presented using a visualization tool. 22 refs., 4 figs., 7 tabs.« less

Bilinear Inverse Problems: Theory, Algorithms, and Applications

NASA Astrophysics Data System (ADS)

Ling, Shuyang

We will discuss how several important real-world signal processing problems, such as self-calibration and blind deconvolution, can be modeled as bilinear inverse problems and solved by convex and nonconvex optimization approaches. In Chapter 2, we bring together three seemingly unrelated concepts, self-calibration, compressive sensing and biconvex optimization. We show how several self-calibration problems can be treated efficiently within the framework of biconvex compressive sensing via a new method called SparseLift. More specifically, we consider a linear system of equations y = DAx, where the diagonal matrix D (which models the calibration error) is unknown and x is an unknown sparse signal. By "lifting" this biconvex inverse problem and exploiting sparsity in this model, we derive explicit theoretical guarantees under which both x and D can be recovered exactly, robustly, and numerically efficiently. In Chapter 3, we study the question of the joint blind deconvolution and blind demixing, i.e., extracting a sequence of functions [special characters omitted] from observing only the sum of their convolutions [special characters omitted]. In particular, for the special case s = 1, it becomes the well-known blind deconvolution problem. We present a non-convex algorithm which guarantees exact recovery under conditions that are competitive with convex optimization methods, with the additional advantage of being computationally much more efficient. We discuss several applications of the proposed framework in image processing and wireless communications in connection with the Internet-of-Things. In Chapter 4, we consider three different self-calibration models of practical relevance. We show how their corresponding bilinear inverse problems can be solved by both the simple linear least squares approach and the SVD-based approach. As a consequence, the proposed algorithms are numerically extremely efficient, thus allowing for real-time deployment. Explicit theoretical guarantees and stability theory are derived and the number of sampling complexity is nearly optimal (up to a poly-log factor). Applications in imaging sciences and signal processing are discussed and numerical simulations are presented to demonstrate the effectiveness and efficiency of our approach.

Decoding the encoding of functional brain networks: An fMRI classification comparison of non-negative matrix factorization (NMF), independent component analysis (ICA), and sparse coding algorithms.

PubMed

Xie, Jianwen; Douglas, Pamela K; Wu, Ying Nian; Brody, Arthur L; Anderson, Ariana E

2017-04-15

Brain networks in fMRI are typically identified using spatial independent component analysis (ICA), yet other mathematical constraints provide alternate biologically-plausible frameworks for generating brain networks. Non-negative matrix factorization (NMF) would suppress negative BOLD signal by enforcing positivity. Spatial sparse coding algorithms (L1 Regularized Learning and K-SVD) would impose local specialization and a discouragement of multitasking, where the total observed activity in a single voxel originates from a restricted number of possible brain networks. The assumptions of independence, positivity, and sparsity to encode task-related brain networks are compared; the resulting brain networks within scan for different constraints are used as basis functions to encode observed functional activity. These encodings are then decoded using machine learning, by using the time series weights to predict within scan whether a subject is viewing a video, listening to an audio cue, or at rest, in 304 fMRI scans from 51 subjects. The sparse coding algorithm of L1 Regularized Learning outperformed 4 variations of ICA (p<0.001) for predicting the task being performed within each scan using artifact-cleaned components. The NMF algorithms, which suppressed negative BOLD signal, had the poorest accuracy compared to the ICA and sparse coding algorithms. Holding constant the effect of the extraction algorithm, encodings using sparser spatial networks (containing more zero-valued voxels) had higher classification accuracy (p<0.001). Lower classification accuracy occurred when the extracted spatial maps contained more CSF regions (p<0.001). The success of sparse coding algorithms suggests that algorithms which enforce sparsity, discourage multitasking, and promote local specialization may capture better the underlying source processes than those which allow inexhaustible local processes such as ICA. Negative BOLD signal may capture task-related activations. Copyright © 2017 Elsevier B.V. All rights reserved.

Laplace-domain waveform modeling and inversion for the 3D acoustic-elastic coupled media

NASA Astrophysics Data System (ADS)

Shin, Jungkyun; Shin, Changsoo; Calandra, Henri

2016-06-01

Laplace-domain waveform inversion reconstructs long-wavelength subsurface models by using the zero-frequency component of damped seismic signals. Despite the computational advantages of Laplace-domain waveform inversion over conventional frequency-domain waveform inversion, an acoustic assumption and an iterative matrix solver have been used to invert 3D marine datasets to mitigate the intensive computing cost. In this study, we develop a Laplace-domain waveform modeling and inversion algorithm for 3D acoustic-elastic coupled media by using a parallel sparse direct solver library (MUltifrontal Massively Parallel Solver, MUMPS). We precisely simulate a real marine environment by coupling the 3D acoustic and elastic wave equations with the proper boundary condition at the fluid-solid interface. In addition, we can extract the elastic properties of the Earth below the sea bottom from the recorded acoustic pressure datasets. As a matrix solver, the parallel sparse direct solver is used to factorize the non-symmetric impedance matrix in a distributed memory architecture and rapidly solve the wave field for a number of shots by using the lower and upper matrix factors. Using both synthetic datasets and real datasets obtained by a 3D wide azimuth survey, the long-wavelength component of the P-wave and S-wave velocity models is reconstructed and the proposed modeling and inversion algorithm are verified. A cluster of 80 CPU cores is used for this study.

(EDMUNDS, WA) WILDLAND FIRE EMISSIONS MODELING: INTEGRATING BLUESKY AND SMOKE

EPA Science Inventory

This presentation is a status update of the BlueSky emissions modeling system. BlueSky-EM has been coupled with the Sparse Matrix Operational Kernel Emissions (SMOKE) system, and is now available as a tool for estimating emissions from wildland fires

Automatic Management of Parallel and Distributed System Resources

NASA Technical Reports Server (NTRS)

Yan, Jerry; Ngai, Tin Fook; Lundstrom, Stephen F.

1990-01-01

Viewgraphs on automatic management of parallel and distributed system resources are presented. Topics covered include: parallel applications; intelligent management of multiprocessing systems; performance evaluation of parallel architecture; dynamic concurrent programs; compiler-directed system approach; lattice gaseous cellular automata; and sparse matrix Cholesky factorization.

Sparsely sampling the sky: a Bayesian experimental design approach

NASA Astrophysics Data System (ADS)

Paykari, P.; Jaffe, A. H.

2013-08-01

The next generation of galaxy surveys will observe millions of galaxies over large volumes of the Universe. These surveys are expensive both in time and cost, raising questions regarding the optimal investment of this time and money. In this work, we investigate criteria for selecting amongst observing strategies for constraining the galaxy power spectrum and a set of cosmological parameters. Depending on the parameters of interest, it may be more efficient to observe a larger, but sparsely sampled, area of sky instead of a smaller contiguous area. In this work, by making use of the principles of Bayesian experimental design, we will investigate the advantages and disadvantages of the sparse sampling of the sky and discuss the circumstances in which a sparse survey is indeed the most efficient strategy. For the Dark Energy Survey (DES), we find that by sparsely observing the same area in a smaller amount of time, we only increase the errors on the parameters by a maximum of 0.45 per cent. Conversely, investing the same amount of time as the original DES to observe a sparser but larger area of sky, we can in fact constrain the parameters with errors reduced by 28 per cent.

Classification of Clouds in Satellite Imagery Using Adaptive Fuzzy Sparse Representation.

PubMed

Jin, Wei; Gong, Fei; Zeng, Xingbin; Fu, Randi

2016-12-16

Automatic cloud detection and classification using satellite cloud imagery have various meteorological applications such as weather forecasting and climate monitoring. Cloud pattern analysis is one of the research hotspots recently. Since satellites sense the clouds remotely from space, and different cloud types often overlap and convert into each other, there must be some fuzziness and uncertainty in satellite cloud imagery. Satellite observation is susceptible to noises, while traditional cloud classification methods are sensitive to noises and outliers; it is hard for traditional cloud classification methods to achieve reliable results. To deal with these problems, a satellite cloud classification method using adaptive fuzzy sparse representation-based classification (AFSRC) is proposed. Firstly, by defining adaptive parameters related to attenuation rate and critical membership, an improved fuzzy membership is introduced to accommodate the fuzziness and uncertainty of satellite cloud imagery; secondly, by effective combination of the improved fuzzy membership function and sparse representation-based classification (SRC), atoms in training dictionary are optimized; finally, an adaptive fuzzy sparse representation classifier for cloud classification is proposed. Experiment results on FY-2G satellite cloud image show that, the proposed method not only improves the accuracy of cloud classification, but also has strong stability and adaptability with high computational efficiency.

Interferometric synthetic aperture radar phase unwrapping based on sparse Markov random fields by graph cuts

NASA Astrophysics Data System (ADS)

Zhou, Lifan; Chai, Dengfeng; Xia, Yu; Ma, Peifeng; Lin, Hui

2018-01-01

Phase unwrapping (PU) is one of the key processes in reconstructing the digital elevation model of a scene from its interferometric synthetic aperture radar (InSAR) data. It is known that two-dimensional (2-D) PU problems can be formulated as maximum a posteriori estimation of Markov random fields (MRFs). However, considering that the traditional MRF algorithm is usually defined on a rectangular grid, it fails easily if large parts of the wrapped data are dominated by noise caused by large low-coherence area or rapid-topography variation. A PU solution based on sparse MRF is presented to extend the traditional MRF algorithm to deal with sparse data, which allows the unwrapping of InSAR data dominated by high phase noise. To speed up the graph cuts algorithm for sparse MRF, we designed dual elementary graphs and merged them to obtain the Delaunay triangle graph, which is used to minimize the energy function efficiently. The experiments on simulated and real data, compared with other existing algorithms, both confirm the effectiveness of the proposed MRF approach, which suffers less from decorrelation effects caused by large low-coherence area or rapid-topography variation.

Sparse matrix beamforming and image reconstruction for 2-D HIFU monitoring using harmonic motion imaging for focused ultrasound (HMIFU) with in vitro validation.

PubMed

Hou, Gary Y; Provost, Jean; Grondin, Julien; Wang, Shutao; Marquet, Fabrice; Bunting, Ethan; Konofagou, Elisa E

2014-11-01

Harmonic motion imaging for focused ultrasound (HMIFU) utilizes an amplitude-modulated HIFU beam to induce a localized focal oscillatory motion simultaneously estimated. The objective of this study is to develop and show the feasibility of a novel fast beamforming algorithm for image reconstruction using GPU-based sparse-matrix operation with real-time feedback. In this study, the algorithm was implemented onto a fully integrated, clinically relevant HMIFU system. A single divergent transmit beam was used while fast beamforming was implemented using a GPU-based delay-and-sum method and a sparse-matrix operation. Axial HMI displacements were then estimated from the RF signals using a 1-D normalized cross-correlation method and streamed to a graphic user interface with frame rates up to 15 Hz, a 100-fold increase compared to conventional CPU-based processing. The real-time feedback rate does not require interrupting the HIFU treatment. Results in phantom experiments showed reproducible HMI images and monitoring of 22 in vitro HIFU treatments using the new 2-D system demonstrated reproducible displacement imaging, and monitoring of 22 in vitro HIFU treatments using the new 2-D system showed a consistent average focal displacement decrease of 46.7 ±14.6% during lesion formation. Complementary focal temperature monitoring also indicated an average rate of displacement increase and decrease with focal temperature at 0.84±1.15%/(°)C, and 2.03±0.93%/(°)C , respectively. These results reinforce the HMIFU capability of estimating and monitoring stiffness related changes in real time. Current ongoing studies include clinical translation of the presented system for monitoring of HIFU treatment for breast and pancreatic tumor applications.

Addressing the computational cost of large EIT solutions.

PubMed

Boyle, Alistair; Borsic, Andrea; Adler, Andy

2012-05-01

Electrical impedance tomography (EIT) is a soft field tomography modality based on the application of electric current to a body and measurement of voltages through electrodes at the boundary. The interior conductivity is reconstructed on a discrete representation of the domain using a finite-element method (FEM) mesh and a parametrization of that domain. The reconstruction requires a sequence of numerically intensive calculations. There is strong interest in reducing the cost of these calculations. An improvement in the compute time for current problems would encourage further exploration of computationally challenging problems such as the incorporation of time series data, wide-spread adoption of three-dimensional simulations and correlation of other modalities such as CT and ultrasound. Multicore processors offer an opportunity to reduce EIT computation times but may require some restructuring of the underlying algorithms to maximize the use of available resources. This work profiles two EIT software packages (EIDORS and NDRM) to experimentally determine where the computational costs arise in EIT as problems scale. Sparse matrix solvers, a key component for the FEM forward problem and sensitivity estimates in the inverse problem, are shown to take a considerable portion of the total compute time in these packages. A sparse matrix solver performance measurement tool, Meagre-Crowd, is developed to interface with a variety of solvers and compare their performance over a range of two- and three-dimensional problems of increasing node density. Results show that distributed sparse matrix solvers that operate on multiple cores are advantageous up to a limit that increases as the node density increases. We recommend a selection procedure to find a solver and hardware arrangement matched to the problem and provide guidance and tools to perform that selection.

Performance Analysis of Local Ensemble Kalman Filter

NASA Astrophysics Data System (ADS)

Tong, Xin T.

2018-03-01

Ensemble Kalman filter (EnKF) is an important data assimilation method for high-dimensional geophysical systems. Efficient implementation of EnKF in practice often involves the localization technique, which updates each component using only information within a local radius. This paper rigorously analyzes the local EnKF (LEnKF) for linear systems and shows that the filter error can be dominated by the ensemble covariance, as long as (1) the sample size exceeds the logarithmic of state dimension and a constant that depends only on the local radius; (2) the forecast covariance matrix admits a stable localized structure. In particular, this indicates that with small system and observation noises, the filter error will be accurate in long time even if the initialization is not. The analysis also reveals an intrinsic inconsistency caused by the localization technique, and a stable localized structure is necessary to control this inconsistency. While this structure is usually taken for granted for the operation of LEnKF, it can also be rigorously proved for linear systems with sparse local observations and weak local interactions. These theoretical results are also validated by numerical implementation of LEnKF on a simple stochastic turbulence in two dynamical regimes.

Bayesian statistical ionospheric tomography improved by incorporating ionosonde measurements

NASA Astrophysics Data System (ADS)

Norberg, Johannes; Virtanen, Ilkka I.; Roininen, Lassi; Vierinen, Juha; Orispää, Mikko; Kauristie, Kirsti; Lehtinen, Markku S.

2016-04-01

We validate two-dimensional ionospheric tomography reconstructions against EISCAT incoherent scatter radar measurements. Our tomography method is based on Bayesian statistical inversion with prior distribution given by its mean and covariance. We employ ionosonde measurements for the choice of the prior mean and covariance parameters and use the Gaussian Markov random fields as a sparse matrix approximation for the numerical computations. This results in a computationally efficient tomographic inversion algorithm with clear probabilistic interpretation. We demonstrate how this method works with simultaneous beacon satellite and ionosonde measurements obtained in northern Scandinavia. The performance is compared with results obtained with a zero-mean prior and with the prior mean taken from the International Reference Ionosphere 2007 model. In validating the results, we use EISCAT ultra-high-frequency incoherent scatter radar measurements as the ground truth for the ionization profile shape. We find that in comparison to the alternative prior information sources, ionosonde measurements improve the reconstruction by adding accurate information about the absolute value and the altitude distribution of electron density. With an ionosonde at continuous disposal, the presented method enhances stand-alone near-real-time ionospheric tomography for the given conditions significantly.

Functional brain networks reconstruction using group sparsity-regularized learning.

PubMed

Zhao, Qinghua; Li, Will X Y; Jiang, Xi; Lv, Jinglei; Lu, Jianfeng; Liu, Tianming

2018-06-01

Investigating functional brain networks and patterns using sparse representation of fMRI data has received significant interests in the neuroimaging community. It has been reported that sparse representation is effective in reconstructing concurrent and interactive functional brain networks. To date, most of data-driven network reconstruction approaches rarely take consideration of anatomical structures, which are the substrate of brain function. Furthermore, it has been rarely explored whether structured sparse representation with anatomical guidance could facilitate functional networks reconstruction. To address this problem, in this paper, we propose to reconstruct brain networks utilizing the structure guided group sparse regression (S2GSR) in which 116 anatomical regions from the AAL template, as prior knowledge, are employed to guide the network reconstruction when performing sparse representation of whole-brain fMRI data. Specifically, we extract fMRI signals from standard space aligned with the AAL template. Then by learning a global over-complete dictionary, with the learned dictionary as a set of features (regressors), the group structured regression employs anatomical structures as group information to regress whole brain signals. Finally, the decomposition coefficients matrix is mapped back to the brain volume to represent functional brain networks and patterns. We use the publicly available Human Connectome Project (HCP) Q1 dataset as the test bed, and the experimental results indicate that the proposed anatomically guided structure sparse representation is effective in reconstructing concurrent functional brain networks.

Weighted low-rank sparse model via nuclear norm minimization for bearing fault detection

NASA Astrophysics Data System (ADS)

Du, Zhaohui; Chen, Xuefeng; Zhang, Han; Yang, Boyuan; Zhai, Zhi; Yan, Ruqiang

2017-07-01

It is a fundamental task in the machine fault diagnosis community to detect impulsive signatures generated by the localized faults of bearings. The main goal of this paper is to exploit the low-rank physical structure of periodic impulsive features and further establish a weighted low-rank sparse model for bearing fault detection. The proposed model mainly consists of three basic components: an adaptive partition window, a nuclear norm regularization and a weighted sequence. Firstly, due to the periodic repetition mechanism of impulsive feature, an adaptive partition window could be designed to transform the impulsive feature into a data matrix. The highlight of partition window is to accumulate all local feature information and align them. Then, all columns of the data matrix share similar waveforms and a core physical phenomenon arises, i.e., these singular values of the data matrix demonstrates a sparse distribution pattern. Therefore, a nuclear norm regularization is enforced to capture that sparse prior. However, the nuclear norm regularization treats all singular values equally and thus ignores one basic fact that larger singular values have more information volume of impulsive features and should be preserved as much as possible. Therefore, a weighted sequence with adaptively tuning weights inversely proportional to singular amplitude is adopted to guarantee the distribution consistence of large singular values. On the other hand, the proposed model is difficult to solve due to its non-convexity and thus a new algorithm is developed to search one satisfying stationary solution through alternatively implementing one proximal operator operation and least-square fitting. Moreover, the sensitivity analysis and selection principles of algorithmic parameters are comprehensively investigated through a set of numerical experiments, which shows that the proposed method is robust and only has a few adjustable parameters. Lastly, the proposed model is applied to the wind turbine (WT) bearing fault detection and its effectiveness is sufficiently verified. Compared with the current popular bearing fault diagnosis techniques, wavelet analysis and spectral kurtosis, our model achieves a higher diagnostic accuracy.

An efficient method for model refinement in diffuse optical tomography

NASA Astrophysics Data System (ADS)

Zirak, A. R.; Khademi, M.

2007-11-01

Diffuse optical tomography (DOT) is a non-linear, ill-posed, boundary value and optimization problem which necessitates regularization. Also, Bayesian methods are suitable owing to measurements data are sparse and correlated. In such problems which are solved with iterative methods, for stabilization and better convergence, the solution space must be small. These constraints subject to extensive and overdetermined system of equations which model retrieving criteria specially total least squares (TLS) must to refine model error. Using TLS is limited to linear systems which is not achievable when applying traditional Bayesian methods. This paper presents an efficient method for model refinement using regularized total least squares (RTLS) for treating on linearized DOT problem, having maximum a posteriori (MAP) estimator and Tikhonov regulator. This is done with combination Bayesian and regularization tools as preconditioner matrices, applying them to equations and then using RTLS to the resulting linear equations. The preconditioning matrixes are guided by patient specific information as well as a priori knowledge gained from the training set. Simulation results illustrate that proposed method improves the image reconstruction performance and localize the abnormally well.

A Sparse Self-Consistent Field Algorithm and Its Parallel Implementation: Application to Density-Functional-Based Tight Binding.

PubMed

Scemama, Anthony; Renon, Nicolas; Rapacioli, Mathias

2014-06-10

We present an algorithm and its parallel implementation for solving a self-consistent problem as encountered in Hartree-Fock or density functional theory. The algorithm takes advantage of the sparsity of matrices through the use of local molecular orbitals. The implementation allows one to exploit efficiently modern symmetric multiprocessing (SMP) computer architectures. As a first application, the algorithm is used within the density-functional-based tight binding method, for which most of the computational time is spent in the linear algebra routines (diagonalization of the Fock/Kohn-Sham matrix). We show that with this algorithm (i) single point calculations on very large systems (millions of atoms) can be performed on large SMP machines, (ii) calculations involving intermediate size systems (1000-100 000 atoms) are also strongly accelerated and can run efficiently on standard servers, and (iii) the error on the total energy due to the use of a cutoff in the molecular orbital coefficients can be controlled such that it remains smaller than the SCF convergence criterion.

Sparse approximation of currents for statistics on curves and surfaces.

PubMed

Durrleman, Stanley; Pennec, Xavier; Trouvé, Alain; Ayache, Nicholas

2008-01-01

Computing, processing, visualizing statistics on shapes like curves or surfaces is a real challenge with many applications ranging from medical image analysis to computational geometry. Modelling such geometrical primitives with currents avoids feature-based approach as well as point-correspondence method. This framework has been proved to be powerful to register brain surfaces or to measure geometrical invariants. However, if the state-of-the-art methods perform efficiently pairwise registrations, new numerical schemes are required to process groupwise statistics due to an increasing complexity when the size of the database is growing. Statistics such as mean and principal modes of a set of shapes often have a heavy and highly redundant representation. We propose therefore to find an adapted basis on which mean and principal modes have a sparse decomposition. Besides the computational improvement, this sparse representation offers a way to visualize and interpret statistics on currents. Experiments show the relevance of the approach on 34 sets of 70 sulcal lines and on 50 sets of 10 meshes of deep brain structures.

COMPUTATION OF GLOBAL PHOTOCHEMISTRY WITH SMVGEAR II (R823186)

EPA Science Inventory

A computer model was developed to simulate global gas-phase photochemistry. The model solves chemical equations with SMVGEAR II, a sparse-matrix, vectorized Gear-type code. To obtain SMVGEAR II, the original SMVGEAR code was modified to allow computation of different sets of chem...

Uncertainty Analysis Based on Sparse Grid Collocation and Quasi-Monte Carlo Sampling with Application in Groundwater Modeling

NASA Astrophysics Data System (ADS)

Zhang, G.; Lu, D.; Ye, M.; Gunzburger, M.

2011-12-01

Markov Chain Monte Carlo (MCMC) methods have been widely used in many fields of uncertainty analysis to estimate the posterior distributions of parameters and credible intervals of predictions in the Bayesian framework. However, in practice, MCMC may be computationally unaffordable due to slow convergence and the excessive number of forward model executions required, especially when the forward model is expensive to compute. Both disadvantages arise from the curse of dimensionality, i.e., the posterior distribution is usually a multivariate function of parameters. Recently, sparse grid method has been demonstrated to be an effective technique for coping with high-dimensional interpolation or integration problems. Thus, in order to accelerate the forward model and avoid the slow convergence of MCMC, we propose a new method for uncertainty analysis based on sparse grid interpolation and quasi-Monte Carlo sampling. First, we construct a polynomial approximation of the forward model in the parameter space by using the sparse grid interpolation. This approximation then defines an accurate surrogate posterior distribution that can be evaluated repeatedly at minimal computational cost. Second, instead of using MCMC, a quasi-Monte Carlo method is applied to draw samples in the parameter space. Then, the desired probability density function of each prediction is approximated by accumulating the posterior density values of all the samples according to the prediction values. Our method has the following advantages: (1) the polynomial approximation of the forward model on the sparse grid provides a very efficient evaluation of the surrogate posterior distribution; (2) the quasi-Monte Carlo method retains the same accuracy in approximating the PDF of predictions but avoids all disadvantages of MCMC. The proposed method is applied to a controlled numerical experiment of groundwater flow modeling. The results show that our method attains the same accuracy much more efficiently than traditional MCMC.

Multiprocessor sparse L/U decomposition with controlled fill-in

NASA Technical Reports Server (NTRS)

Alaghband, G.; Jordan, H. F.

1985-01-01

Generation of the maximal compatibles of pivot elements for a class of small sparse matrices is studied. The algorithm involves a binary tree search and has a complexity exponential in the order of the matrix. Different strategies for selection of a set of compatible pivots based on the Markowitz criterion are investigated. The competing issues of parallelism and fill-in generation are studied and results are provided. A technque for obtaining an ordered compatible set directly from the ordered incompatible table is given. This technique generates a set of compatible pivots with the property of generating few fills. A new hueristic algorithm is then proposed that combines the idea of an ordered compatible set with a limited binary tree search to generate several sets of compatible pivots in linear time. Finally, an elimination set to reduce the matrix is selected. Parameters are suggested to obtain a balance between parallelism and fill-ins. Results of applying the proposed algorithms on several large application matrices are presented and analyzed.

Three dimensional iterative beam propagation method for optical waveguide devices

NASA Astrophysics Data System (ADS)

Ma, Changbao; Van Keuren, Edward

2006-10-01

The finite difference beam propagation method (FD-BPM) is an effective model for simulating a wide range of optical waveguide structures. The classical FD-BPMs are based on the Crank-Nicholson scheme, and in tridiagonal form can be solved using the Thomas method. We present a different type of algorithm for 3-D structures. In this algorithm, the wave equation is formulated into a large sparse matrix equation which can be solved using iterative methods. The simulation window shifting scheme and threshold technique introduced in our earlier work are utilized to overcome the convergence problem of iterative methods for large sparse matrix equation and wide-angle simulations. This method enables us to develop higher-order 3-D wide-angle (WA-) BPMs based on Pade approximant operators and the multistep method, which are commonly used in WA-BPMs for 2-D structures. Simulations using the new methods will be compared to the analytical results to assure its effectiveness and applicability.

Observation of infrared absorption of InAs quantum dot structures in AlGaAs matrix toward high-efficiency solar cells

NASA Astrophysics Data System (ADS)

Yoshikawa, Hirofumi; Watanabe, Katsuyuki; Kotani, Teruhisa; Izumi, Makoto; Iwamoto, Satoshi; Arakawa, Yasuhiko

2018-06-01

In accordance with the detailed balance limit model of single-intermediate-band solar cells (IBSCs), the optimum matrix bandgap and IB–conduction band (CB) energy gap are ∼1.9 and 0.7 eV, respectively. We present the room-temperature polarized infrared absorption of 20 stacked InAs quantum dot (QD) structures in the Al0.32Ga0.68As matrix with a bandgap of ∼1.9 eV for the design of high-efficiency IBSCs by using a multipass waveguide geometry. We find that the IB–CB absorption is almost independent of the light polarization, and estimate the magnitude of the absorption per QD layer to be ∼0.01%. We also find that the IB–CB absorption edge of QD structures with a wide-gap matrix is ∼0.41 eV. These results indicate that both the significant increase in the magnitude of IB–CB absorption and the lower energy of the IB state for the higher IB–CB energy gap are necessary toward the realization of high-efficiency IBSCs.

Primum non nocere - The effects of sodium hypochlorite on dentin as used in endodontics.

PubMed

Gu, Li-Sha; Huang, Xue-Qing; Griffin, Brandon; Bergeron, Brian R; Pashley, David H; Niu, Li-Na; Tay, Franklin R

2017-10-01

The medical literature is replete with the maxim 'primum non nocere', cautioning health care providers to avoid doing any harm to human subjects in their delivery of medical care. Sodium hypochlorite (NaOCl) is a well-established irrigant for root canal treatment because of its antimicrobial and organic tissue remnant dissolution capability. However, little is known about the deleterious effect of this strong oxidizing agent on the integrity of human mineralized dentin. Iatrogenically-induced loss of dentin integrity may precipitate post-treatment root fracture and has potential medico-legal complications. In the present work, transmission electron microscopy provided evidence for collagen destruction in the surface/subsurface of dentin treated with high NaOCl concentrations and long contact times. Size exclusion chromatography showed that the hypochlorite anion, because of its small size, penetrated the water compartments of apatite-encapsulated collagen fibrils, degraded the collagen molecules and produced a 25-35µm thick, non-uniform "ghost mineral layer" with enlarged, coalesced dentinal tubules and their lateral branches. Fourier transform-infrared spectroscopy identified increases in apatite/collagen ratio in NaOCl-treated dentin. The apatite-rich, collagen-sparse dentin matrix that remained after NaOCl treatment is more brittle, as shown by the reductions in flexural strength. Understanding the deleterious effects of NaOCl on mineralized dentin enables one to balance the risks and benefits in using high NaOCl concentrations for lengthy periods in root canal debridement. Delineating the mechanism responsible for such a phenomenon enables high molecular weight, polymeric antimicrobial and tissue dissolution irrigants to be designed that abides by the maxim of 'primum non nocere' in contemporary medical practices. The antimicrobial and tissue-dissolution capacities of NaOCl render it a well-accepted agent for root canal debridement. These highly desirable properties, however, appear to be intertwined with the untoward effect of collagen matrix degradation within mineralized dentin. Because of its small size, the hypochlorite anion is capable of infiltrating mineralized collagen and destroying the collagen fibrils, producing a mineral-rich, collagen sparse ghost mineral matrix with reduced flexural strength. Findings from the present work challenge the biosafety of NaOCl when it is used in high concentrations and for lengthy time periods during root canal treatment, and laid the background work for future biomaterials design in debridement of the canal space. Published by Elsevier Ltd.

A Sparse Representation-Based Deployment Method for Optimizing the Observation Quality of Camera Networks

PubMed Central

Wang, Chang; Qi, Fei; Shi, Guangming; Wang, Xiaotian

2013-01-01

Deployment is a critical issue affecting the quality of service of camera networks. The deployment aims at adopting the least number of cameras to cover the whole scene, which may have obstacles to occlude the line of sight, with expected observation quality. This is generally formulated as a non-convex optimization problem, which is hard to solve in polynomial time. In this paper, we propose an efficient convex solution for deployment optimizing the observation quality based on a novel anisotropic sensing model of cameras, which provides a reliable measurement of the observation quality. The deployment is formulated as the selection of a subset of nodes from a redundant initial deployment with numerous cameras, which is an ℓ0 minimization problem. Then, we relax this non-convex optimization to a convex ℓ1 minimization employing the sparse representation. Therefore, the high quality deployment is efficiently obtained via convex optimization. Simulation results confirm the effectiveness of the proposed camera deployment algorithms. PMID:23989826

Compressed sparse tensor based quadrature for vibrational quantum mechanics integrals

DOE PAGES

Rai, Prashant; Sargsyan, Khachik; Najm, Habib N.

2018-03-20

A new method for fast evaluation of high dimensional integrals arising in quantum mechanics is proposed. Here, the method is based on sparse approximation of a high dimensional function followed by a low-rank compression. In the first step, we interpret the high dimensional integrand as a tensor in a suitable tensor product space and determine its entries by a compressed sensing based algorithm using only a few function evaluations. Secondly, we implement a rank reduction strategy to compress this tensor in a suitable low-rank tensor format using standard tensor compression tools. This allows representing a high dimensional integrand function asmore » a small sum of products of low dimensional functions. Finally, a low dimensional Gauss–Hermite quadrature rule is used to integrate this low-rank representation, thus alleviating the curse of dimensionality. Finally, numerical tests on synthetic functions, as well as on energy correction integrals for water and formaldehyde molecules demonstrate the efficiency of this method using very few function evaluations as compared to other integration strategies.« less

Compressed sparse tensor based quadrature for vibrational quantum mechanics integrals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rai, Prashant; Sargsyan, Khachik; Najm, Habib N.

A new method for fast evaluation of high dimensional integrals arising in quantum mechanics is proposed. Here, the method is based on sparse approximation of a high dimensional function followed by a low-rank compression. In the first step, we interpret the high dimensional integrand as a tensor in a suitable tensor product space and determine its entries by a compressed sensing based algorithm using only a few function evaluations. Secondly, we implement a rank reduction strategy to compress this tensor in a suitable low-rank tensor format using standard tensor compression tools. This allows representing a high dimensional integrand function asmore » a small sum of products of low dimensional functions. Finally, a low dimensional Gauss–Hermite quadrature rule is used to integrate this low-rank representation, thus alleviating the curse of dimensionality. Finally, numerical tests on synthetic functions, as well as on energy correction integrals for water and formaldehyde molecules demonstrate the efficiency of this method using very few function evaluations as compared to other integration strategies.« less

Kriging and local polynomial methods for blending satellite-derived and gauge precipitation estimates to support hydrologic early warning systems

USGS Publications Warehouse

Verdin, Andrew; Funk, Christopher C.; Rajagopalan, Balaji; Kleiber, William

2016-01-01

Robust estimates of precipitation in space and time are important for efficient natural resource management and for mitigating natural hazards. This is particularly true in regions with developing infrastructure and regions that are frequently exposed to extreme events. Gauge observations of rainfall are sparse but capture the precipitation process with high fidelity. Due to its high resolution and complete spatial coverage, satellite-derived rainfall data are an attractive alternative in data-sparse regions and are often used to support hydrometeorological early warning systems. Satellite-derived precipitation data, however, tend to underrepresent extreme precipitation events. Thus, it is often desirable to blend spatially extensive satellite-derived rainfall estimates with high-fidelity rain gauge observations to obtain more accurate precipitation estimates. In this research, we use two different methods, namely, ordinary kriging and κ-nearest neighbor local polynomials, to blend rain gauge observations with the Climate Hazards Group Infrared Precipitation satellite-derived precipitation estimates in data-sparse Central America and Colombia. The utility of these methods in producing blended precipitation estimates at pentadal (five-day) and monthly time scales is demonstrated. We find that these blending methods significantly improve the satellite-derived estimates and are competitive in their ability to capture extreme precipitation.

Adaptive sparse grid approach for the efficient simulation of pulsed eddy current testing inspections

NASA Astrophysics Data System (ADS)

Miorelli, Roberto; Reboud, Christophe

2018-04-01

Pulsed Eddy Current Testing (PECT) is a popular NonDestructive Testing (NDT) technique for some applications like corrosion monitoring in the oil and gas industry, or rivet inspection in the aeronautic area. Its particularity is to use a transient excitation, which allows to retrieve more information from the piece than conventional harmonic ECT, in a simpler and cheaper way than multi-frequency ECT setups. Efficient modeling tools prove, as usual, very useful to optimize experimental sensors and devices or evaluate their performance, for instance. This paper proposes an efficient simulation of PECT signals based on standard time harmonic solvers and use of an Adaptive Sparse Grid (ASG) algorithm. An adaptive sampling of the ECT signal spectrum is performed with this algorithm, then the complete spectrum is interpolated from this sparse representation and PECT signals are finally synthesized by means of inverse Fourier transform. Simulation results corresponding to existing industrial configurations are presented and the performance of the strategy is discussed by comparison to reference results.

Assessing the effects of cocaine dependence and pathological gambling using group-wise sparse representation of natural stimulus FMRI data.

PubMed

Ren, Yudan; Fang, Jun; Lv, Jinglei; Hu, Xintao; Guo, Cong Christine; Guo, Lei; Xu, Jiansong; Potenza, Marc N; Liu, Tianming

2017-08-01

Assessing functional brain activation patterns in neuropsychiatric disorders such as cocaine dependence (CD) or pathological gambling (PG) under naturalistic stimuli has received rising interest in recent years. In this paper, we propose and apply a novel group-wise sparse representation framework to assess differences in neural responses to naturalistic stimuli across multiple groups of participants (healthy control, cocaine dependence, pathological gambling). Specifically, natural stimulus fMRI (N-fMRI) signals from all three groups of subjects are aggregated into a big data matrix, which is then decomposed into a common signal basis dictionary and associated weight coefficient matrices via an effective online dictionary learning and sparse coding method. The coefficient matrices associated with each common dictionary atom are statistically assessed for each group separately. With the inter-group comparisons based on the group-wise correspondence established by the common dictionary, our experimental results demonstrated that the group-wise sparse coding and representation strategy can effectively and specifically detect brain networks/regions affected by different pathological conditions of the brain under naturalistic stimuli.

Identification-While-Scanning of a Multi-Aircraft Formation Based on Sparse Recovery for Narrowband Radar.

PubMed

Jiang, Yuan; Xu, Jia; Peng, Shi-Bao; Mao, Er-Ke; Long, Teng; Peng, Ying-Ning

2016-11-23

It is known that the identification performance of a multi-aircraft formation (MAF) of narrowband radar mainly depends on the time on target (TOT). To realize the identification task in one rotated scan with limited TOT, the paper proposes a novel identification-while-scanning (IWS) method based on sparse recovery to maintain high rotating speed and super-resolution for MAF identification, simultaneously. First, a multiple chirp signal model is established for MAF in a single scan, where different aircraft may have different Doppler centers and Doppler rates. Second, based on the sparsity of MAF in the Doppler parameter space, a novel hierarchical basis pursuit (HBP) method is proposed to obtain satisfactory sparse recovery performance as well as high computational efficiency. Furthermore, the parameter estimation performance of the proposed IWS identification method is analyzed with respect to recovery condition, signal-to-noise ratio and TOT. It is shown that an MAF can be effectively identified via HBP with a TOT of only about one hundred microseconds for IWS applications. Finally, some numerical experiment results are provided to demonstrate the effectiveness of the proposed method based on both simulated and real measured data.

Sparse PLS discriminant analysis: biologically relevant feature selection and graphical displays for multiclass problems.

PubMed

Lê Cao, Kim-Anh; Boitard, Simon; Besse, Philippe

2011-06-22

Variable selection on high throughput biological data, such as gene expression or single nucleotide polymorphisms (SNPs), becomes inevitable to select relevant information and, therefore, to better characterize diseases or assess genetic structure. There are different ways to perform variable selection in large data sets. Statistical tests are commonly used to identify differentially expressed features for explanatory purposes, whereas Machine Learning wrapper approaches can be used for predictive purposes. In the case of multiple highly correlated variables, another option is to use multivariate exploratory approaches to give more insight into cell biology, biological pathways or complex traits. A simple extension of a sparse PLS exploratory approach is proposed to perform variable selection in a multiclass classification framework. sPLS-DA has a classification performance similar to other wrapper or sparse discriminant analysis approaches on public microarray and SNP data sets. More importantly, sPLS-DA is clearly competitive in terms of computational efficiency and superior in terms of interpretability of the results via valuable graphical outputs. sPLS-DA is available in the R package mixOmics, which is dedicated to the analysis of large biological data sets.

Efficient Processing of Acoustic Signals for High Rate Information Transmission over Sparse Underwater Channels

DTIC Science & Technology

2016-09-02

the fractionally-spaced channel estimators and the short feedforward equalizer filters . Receiver algorithm is applied to real data transmitted at 10...multichannel decision-feedback equalizer (DFE)[1]. This receiver consists of a bank of adaptive feedforwad filters , one per array element, followed by a...decision-feedback filter . It has been implemented in the prototype high-rate acoustic modem developed at the Woods Hole Oceanographic Institution, and

Compressed normalized block difference for object tracking

NASA Astrophysics Data System (ADS)

Gao, Yun; Zhang, Dengzhuo; Cai, Donglan; Zhou, Hao; Lan, Ge

2018-04-01

Feature extraction is very important for robust and real-time tracking. Compressive sensing provided a technical support for real-time feature extraction. However, all existing compressive tracking were based on compressed Haar-like feature, and how to compress many more excellent high-dimensional features is worth researching. In this paper, a novel compressed normalized block difference feature (CNBD) was proposed. For resisting noise effectively in a highdimensional normalized pixel difference feature (NPD), a normalized block difference feature extends two pixels in the original formula of NPD to two blocks. A CNBD feature can be obtained by compressing a normalized block difference feature based on compressive sensing theory, with the sparse random Gaussian matrix as the measurement matrix. The comparative experiments of 7 trackers on 20 challenging sequences showed that the tracker based on CNBD feature can perform better than other trackers, especially than FCT tracker based on compressed Haar-like feature, in terms of AUC, SR and Precision.

Design and optimization of color lookup tables on a simplex topology.

PubMed

Monga, Vishal; Bala, Raja; Mo, Xuan

2012-04-01

An important computational problem in color imaging is the design of color transforms that map color between devices or from a device-dependent space (e.g., RGB/CMYK) to a device-independent space (e.g., CIELAB) and vice versa. Real-time processing constraints entail that such nonlinear color transforms be implemented using multidimensional lookup tables (LUTs). Furthermore, relatively sparse LUTs (with efficient interpolation) are employed in practice because of storage and memory constraints. This paper presents a principled design methodology rooted in constrained convex optimization to design color LUTs on a simplex topology. The use of n simplexes, i.e., simplexes in n dimensions, as opposed to traditional lattices, recently has been of great interest in color LUT design for simplex topologies that allow both more analytically tractable formulations and greater efficiency in the LUT. In this framework of n-simplex interpolation, our central contribution is to develop an elegant iterative algorithm that jointly optimizes the placement of nodes of the color LUT and the output values at those nodes to minimize interpolation error in an expected sense. This is in contrast to existing work, which exclusively designs either node locations or the output values. We also develop new analytical results for the problem of node location optimization, which reduces to constrained optimization of a large but sparse interpolation matrix in our framework. We evaluate our n -simplex color LUTs against the state-of-the-art lattice (e.g., International Color Consortium profiles) and simplex-based techniques for approximating two representative multidimensional color transforms that characterize a CMYK xerographic printer and an RGB scanner, respectively. The results show that color LUTs designed on simplexes offer very significant benefits over traditional lattice-based alternatives in improving color transform accuracy even with a much smaller number of nodes.