Simultaneous Localization and Mapping with Iterative Sparse Extended Information Filter for Autonomous Vehicles.

PubMed

He, Bo; Liu, Yang; Dong, Diya; Shen, Yue; Yan, Tianhong; Nian, Rui

2015-08-13

In this paper, a novel iterative sparse extended information filter (ISEIF) was proposed to solve the simultaneous localization and mapping problem (SLAM), which is very crucial for autonomous vehicles. The proposed algorithm solves the measurement update equations with iterative methods adaptively to reduce linearization errors. With the scalability advantage being kept, the consistency and accuracy of SEIF is improved. Simulations and practical experiments were carried out with both a land car benchmark and an autonomous underwater vehicle. Comparisons between iterative SEIF (ISEIF), standard EKF and SEIF are presented. All of the results convincingly show that ISEIF yields more consistent and accurate estimates compared to SEIF and preserves the scalability advantage over EKF, as well.

Accelerated Path-following Iterative Shrinkage Thresholding Algorithm with Application to Semiparametric Graph Estimation

PubMed Central

Zhao, Tuo; Liu, Han

2016-01-01

We propose an accelerated path-following iterative shrinkage thresholding algorithm (APISTA) for solving high dimensional sparse nonconvex learning problems. The main difference between APISTA and the path-following iterative shrinkage thresholding algorithm (PISTA) is that APISTA exploits an additional coordinate descent subroutine to boost the computational performance. Such a modification, though simple, has profound impact: APISTA not only enjoys the same theoretical guarantee as that of PISTA, i.e., APISTA attains a linear rate of convergence to a unique sparse local optimum with good statistical properties, but also significantly outperforms PISTA in empirical benchmarks. As an application, we apply APISTA to solve a family of nonconvex optimization problems motivated by estimating sparse semiparametric graphical models. APISTA allows us to obtain new statistical recovery results which do not exist in the existing literature. Thorough numerical results are provided to back up our theory. PMID:28133430

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.

Fast solution of elliptic partial differential equations using linear combinations of plane waves.

PubMed

Pérez-Jordá, José M

2016-02-01

Given an arbitrary elliptic partial differential equation (PDE), a procedure for obtaining its solution is proposed based on the method of Ritz: the solution is written as a linear combination of plane waves and the coefficients are obtained by variational minimization. The PDE to be solved is cast as a system of linear equations Ax=b, where the matrix A is not sparse, which prevents the straightforward application of standard iterative methods in order to solve it. This sparseness problem can be circumvented by means of a recursive bisection approach based on the fast Fourier transform, which makes it possible to implement fast versions of some stationary iterative methods (such as Gauss-Seidel) consuming O(NlogN) memory and executing an iteration in O(Nlog(2)N) time, N being the number of plane waves used. In a similar way, fast versions of Krylov subspace methods and multigrid methods can also be implemented. These procedures are tested on Poisson's equation expressed in adaptive coordinates. It is found that the best results are obtained with the GMRES method using a multigrid preconditioner with Gauss-Seidel relaxation steps.

Realization of preconditioned Lanczos and conjugate gradient algorithms on optical linear algebra processors.

PubMed

Ghosh, A

1988-08-01

Lanczos and conjugate gradient algorithms are important in computational linear algebra. In this paper, a parallel pipelined realization of these algorithms on a ring of optical linear algebra processors is described. The flow of data is designed to minimize the idle times of the optical multiprocessor and the redundancy of computations. The effects of optical round-off errors on the solutions obtained by the optical Lanczos and conjugate gradient algorithms are analyzed, and it is shown that optical preconditioning can improve the accuracy of these algorithms substantially. Algorithms for optical preconditioning and results of numerical experiments on solving linear systems of equations arising from partial differential equations are discussed. Since the Lanczos algorithm is used mostly with sparse matrices, a folded storage scheme to represent sparse matrices on spatial light modulators is also described.

Sparse array angle estimation using reduced-dimension ESPRIT-MUSIC in MIMO radar.

PubMed

Zhang, Chaozhu; Pang, Yucai

2013-01-01

Sparse linear arrays provide better performance than the filled linear arrays in terms of angle estimation and resolution with reduced size and low cost. However, they are subject to manifold ambiguity. In this paper, both the transmit array and receive array are sparse linear arrays in the bistatic MIMO radar. Firstly, we present an ESPRIT-MUSIC method in which ESPRIT algorithm is used to obtain ambiguous angle estimates. The disambiguation algorithm uses MUSIC-based procedure to identify the true direction cosine estimate from a set of ambiguous candidate estimates. The paired transmit angle and receive angle can be estimated and the manifold ambiguity can be solved. However, the proposed algorithm has high computational complexity due to the requirement of two-dimension search. Further, the Reduced-Dimension ESPRIT-MUSIC (RD-ESPRIT-MUSIC) is proposed to reduce the complexity of the algorithm. And the RD-ESPRIT-MUSIC only demands one-dimension search. Simulation results demonstrate the effectiveness of the method.

Graph cuts via l1 norm minimization.

PubMed

Bhusnurmath, Arvind; Taylor, Camillo J

2008-10-01

Graph cuts have become an increasingly important tool for solving a number of energy minimization problems in computer vision and other fields. In this paper, the graph cut problem is reformulated as an unconstrained l1 norm minimization that can be solved effectively using interior point methods. This reformulation exposes connections between the graph cuts and other related continuous optimization problems. Eventually the problem is reduced to solving a sequence of sparse linear systems involving the Laplacian of the underlying graph. The proposed procedure exploits the structure of these linear systems in a manner that is easily amenable to parallel implementations. Experimental results obtained by applying the procedure to graphs derived from image processing problems are provided.

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

Visual Tracking via Sparse and Local Linear Coding.

PubMed

Wang, Guofeng; Qin, Xueying; Zhong, Fan; Liu, Yue; Li, Hongbo; Peng, Qunsheng; Yang, Ming-Hsuan

2015-11-01

The state search is an important component of any object tracking algorithm. Numerous algorithms have been proposed, but stochastic sampling methods (e.g., particle filters) are arguably one of the most effective approaches. However, the discretization of the state space complicates the search for the precise object location. In this paper, we propose a novel tracking algorithm that extends the state space of particle observations from discrete to continuous. The solution is determined accurately via iterative linear coding between two convex hulls. The algorithm is modeled by an optimal function, which can be efficiently solved by either convex sparse coding or locality constrained linear coding. The algorithm is also very flexible and can be combined with many generic object representations. Thus, we first use sparse representation to achieve an efficient searching mechanism of the algorithm and demonstrate its accuracy. Next, two other object representation models, i.e., least soft-threshold squares and adaptive structural local sparse appearance, are implemented with improved accuracy to demonstrate the flexibility of our algorithm. Qualitative and quantitative experimental results demonstrate that the proposed tracking algorithm performs favorably against the state-of-the-art methods in dynamic scenes.

Robust visual tracking via multiscale deep sparse networks

NASA Astrophysics Data System (ADS)

Wang, Xin; Hou, Zhiqiang; Yu, Wangsheng; Xue, Yang; Jin, Zefenfen; Dai, Bo

2017-04-01

In visual tracking, deep learning with offline pretraining can extract more intrinsic and robust features. It has significant success solving the tracking drift in a complicated environment. However, offline pretraining requires numerous auxiliary training datasets and is considerably time-consuming for tracking tasks. To solve these problems, a multiscale sparse networks-based tracker (MSNT) under the particle filter framework is proposed. Based on the stacked sparse autoencoders and rectifier linear unit, the tracker has a flexible and adjustable architecture without the offline pretraining process and exploits the robust and powerful features effectively only through online training of limited labeled data. Meanwhile, the tracker builds four deep sparse networks of different scales, according to the target's profile type. During tracking, the tracker selects the matched tracking network adaptively in accordance with the initial target's profile type. It preserves the inherent structural information more efficiently than the single-scale networks. Additionally, a corresponding update strategy is proposed to improve the robustness of the tracker. Extensive experimental results on a large scale benchmark dataset show that the proposed method performs favorably against state-of-the-art methods in challenging environments.

Simultaneous Localization and Mapping with Iterative Sparse Extended Information Filter for Autonomous Vehicles

PubMed Central

He, Bo; Liu, Yang; Dong, Diya; Shen, Yue; Yan, Tianhong; Nian, Rui

2015-01-01

In this paper, a novel iterative sparse extended information filter (ISEIF) was proposed to solve the simultaneous localization and mapping problem (SLAM), which is very crucial for autonomous vehicles. The proposed algorithm solves the measurement update equations with iterative methods adaptively to reduce linearization errors. With the scalability advantage being kept, the consistency and accuracy of SEIF is improved. Simulations and practical experiments were carried out with both a land car benchmark and an autonomous underwater vehicle. Comparisons between iterative SEIF (ISEIF), standard EKF and SEIF are presented. All of the results convincingly show that ISEIF yields more consistent and accurate estimates compared to SEIF and preserves the scalability advantage over EKF, as well. PMID:26287194

Computational Methods for Sparse Solution of Linear Inverse Problems

DTIC Science & Technology

2009-03-01

this approach is that the algorithms take advantage of fast matrix–vector multiplications. An implementation is available as pdco and SolveBP in the...M. A. Saunders, “ PDCO : primal-dual interior-point method for con- vex objectives,” Systems Optimization Laboratory, Stanford University, Tech. Rep

Numerical methods in Markov chain modeling

NASA Technical Reports Server (NTRS)

Philippe, Bernard; Saad, Youcef; Stewart, William J.

1989-01-01

Several methods for computing stationary probability distributions of Markov chains are described and compared. The main linear algebra problem consists of computing an eigenvector of a sparse, usually nonsymmetric, matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous singular linear system. Several methods based on combinations of Krylov subspace techniques are presented. The performance of these methods on some realistic problems are compared.

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.

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

A Spectral Reconstruction Algorithm of Miniature Spectrometer Based on Sparse Optimization and Dictionary Learning.

PubMed

Zhang, Shang; Dong, Yuhan; Fu, Hongyan; Huang, Shao-Lun; Zhang, Lin

2018-02-22

The miniaturization of spectrometer can broaden the application area of spectrometry, which has huge academic and industrial value. Among various miniaturization approaches, filter-based miniaturization is a promising implementation by utilizing broadband filters with distinct transmission functions. Mathematically, filter-based spectral reconstruction can be modeled as solving a system of linear equations. In this paper, we propose an algorithm of spectral reconstruction based on sparse optimization and dictionary learning. To verify the feasibility of the reconstruction algorithm, we design and implement a simple prototype of a filter-based miniature spectrometer. The experimental results demonstrate that sparse optimization is well applicable to spectral reconstruction whether the spectra are directly sparse or not. As for the non-directly sparse spectra, their sparsity can be enhanced by dictionary learning. In conclusion, the proposed approach has a bright application prospect in fabricating a practical miniature spectrometer.

A Spectral Reconstruction Algorithm of Miniature Spectrometer Based on Sparse Optimization and Dictionary Learning

PubMed Central

Zhang, Shang; Fu, Hongyan; Huang, Shao-Lun; Zhang, Lin

2018-01-01

The miniaturization of spectrometer can broaden the application area of spectrometry, which has huge academic and industrial value. Among various miniaturization approaches, filter-based miniaturization is a promising implementation by utilizing broadband filters with distinct transmission functions. Mathematically, filter-based spectral reconstruction can be modeled as solving a system of linear equations. In this paper, we propose an algorithm of spectral reconstruction based on sparse optimization and dictionary learning. To verify the feasibility of the reconstruction algorithm, we design and implement a simple prototype of a filter-based miniature spectrometer. The experimental results demonstrate that sparse optimization is well applicable to spectral reconstruction whether the spectra are directly sparse or not. As for the non-directly sparse spectra, their sparsity can be enhanced by dictionary learning. In conclusion, the proposed approach has a bright application prospect in fabricating a practical miniature spectrometer. PMID:29470406

Efficient sparse matrix-matrix multiplication for computing periodic responses by shooting method on Intel Xeon Phi

NASA Astrophysics Data System (ADS)

Stoykov, S.; Atanassov, E.; Margenov, S.

2016-10-01

Many of the scientific applications involve sparse or dense matrix operations, such as solving linear systems, matrix-matrix products, eigensolvers, etc. In what concerns structural nonlinear dynamics, the computations of periodic responses and the determination of stability of the solution are of primary interest. Shooting method iswidely used for obtaining periodic responses of nonlinear systems. The method involves simultaneously operations with sparse and dense matrices. One of the computationally expensive operations in the method is multiplication of sparse by dense matrices. In the current work, a new algorithm for sparse matrix by dense matrix products is presented. The algorithm takes into account the structure of the sparse matrix, which is obtained by space discretization of the nonlinear Mindlin's plate equation of motion by the finite element method. The algorithm is developed to use the vector engine of Intel Xeon Phi coprocessors. It is compared with the standard sparse matrix by dense matrix algorithm and the one developed by Intel MKL and it is shown that by considering the properties of the sparse matrix better algorithms can be developed.

Using Chebyshev polynomials and approximate inverse triangular factorizations for preconditioning the conjugate gradient method

NASA Astrophysics Data System (ADS)

Kaporin, I. E.

2012-02-01

In order to precondition a sparse symmetric positive definite matrix, its approximate inverse is examined, which is represented as the product of two sparse mutually adjoint triangular matrices. In this way, the solution of the corresponding system of linear algebraic equations (SLAE) by applying the preconditioned conjugate gradient method (CGM) is reduced to performing only elementary vector operations and calculating sparse matrix-vector products. A method for constructing the above preconditioner is described and analyzed. The triangular factor has a fixed sparsity pattern and is optimal in the sense that the preconditioned matrix has a minimum K-condition number. The use of polynomial preconditioning based on Chebyshev polynomials makes it possible to considerably reduce the amount of scalar product operations (at the cost of an insignificant increase in the total number of arithmetic operations). The possibility of an efficient massively parallel implementation of the resulting method for solving SLAEs is discussed. For a sequential version of this method, the results obtained by solving 56 test problems from the Florida sparse matrix collection (which are large-scale and ill-conditioned) are presented. These results show that the method is highly reliable and has low computational costs.

Krylov Subspace Methods for Complex Non-Hermitian Linear Systems. Thesis

NASA Technical Reports Server (NTRS)

Freund, Roland W.

1991-01-01

We consider Krylov subspace methods for the solution of large sparse linear systems Ax = b with complex non-Hermitian coefficient matrices. Such linear systems arise in important applications, such as inverse scattering, numerical solution of time-dependent Schrodinger equations, underwater acoustics, eddy current computations, numerical computations in quantum chromodynamics, and numerical conformal mapping. Typically, the resulting coefficient matrices A exhibit special structures, such as complex symmetry, or they are shifted Hermitian matrices. In this paper, we first describe a Krylov subspace approach with iterates defined by a quasi-minimal residual property, the QMR method, for solving general complex non-Hermitian linear systems. Then, we study special Krylov subspace methods designed for the two families of complex symmetric respectively shifted Hermitian linear systems. We also include some results concerning the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.

Joint sparse representation for robust multimodal biometrics recognition.

PubMed

Shekhar, Sumit; Patel, Vishal M; Nasrabadi, Nasser M; Chellappa, Rama

2014-01-01

Traditional biometric recognition systems rely on a single biometric signature for authentication. While the advantage of using multiple sources of information for establishing the identity has been widely recognized, computational models for multimodal biometrics recognition have only recently received attention. We propose a multimodal sparse representation method, which represents the test data by a sparse linear combination of training data, while constraining the observations from different modalities of the test subject to share their sparse representations. Thus, we simultaneously take into account correlations as well as coupling information among biometric modalities. A multimodal quality measure is also proposed to weigh each modality as it gets fused. Furthermore, we also kernelize the algorithm to handle nonlinearity in data. The optimization problem is solved using an efficient alternative direction method. Various experiments show that the proposed method compares favorably with competing fusion-based methods.

A variant of nested dissection for solving n by n grid problems

NASA Technical Reports Server (NTRS)

George, A.; Poole, W. G., Jr.; Voigt, R. G.

1976-01-01

Nested dissection orderings are known to be very effective for solving the sparse positive definite linear systems which arise from n by n grid problems. In this paper nested dissection is shown to be the final step of incomplete nested dissection, an ordering which corresponds to the premature termination of dissection. Analyses of the arithmetic and storage requirements for incomplete nested dissection are given, and the ordering is shown to be competitive with nested dissection under certain conditions.

An accurate method for solving a class of fractional Sturm-Liouville eigenvalue problems

NASA Astrophysics Data System (ADS)

Kashkari, Bothayna S. H.; Syam, Muhammed I.

2018-06-01

This article is devoted to both theoretical and numerical study of the eigenvalues of nonsingular fractional second-order Sturm-Liouville problem. In this paper, we implement a fractional-order Legendre Tau method to approximate the eigenvalues. This method transforms the Sturm-Liouville problem to a sparse nonsingular linear system which is solved using the continuation method. Theoretical results for the considered problem are provided and proved. Numerical results are presented to show the efficiency of the proposed method.

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.

An empirical investigation of methods for nonsymmetric linear systems

NASA Technical Reports Server (NTRS)

Sherman, A. H.

1981-01-01

The present investigation is concerned with a comparison of methods for solving linear algebraic systems which arise from finite difference discretizations of the elliptic convection-diffusion equation in a planar region Omega with Dirichlet boundary conditions. Such linear systems are typically of the form Ax = b where A is an N x N sparse nonsymmetric matrix. In a discussion of discretizations, it is assumed that a regular rectilinear mesh of width h has been imposed on Omega. The discretizations considered include central differences, upstream differences, and modified upstream differences. Six methods for solving Ax = b are considered. Three variants of Gaussian elimination have been chosen as representatives of state-of-the-art software for direct methods under different assumptions about pivoting. Three iterative methods are also included.

Orthogonal sparse linear discriminant analysis

NASA Astrophysics Data System (ADS)

Liu, Zhonghua; Liu, Gang; Pu, Jiexin; Wang, Xiaohong; Wang, Haijun

2018-03-01

Linear discriminant analysis (LDA) is a linear feature extraction approach, and it has received much attention. On the basis of LDA, researchers have done a lot of research work on it, and many variant versions of LDA were proposed. However, the inherent problem of LDA cannot be solved very well by the variant methods. The major disadvantages of the classical LDA are as follows. First, it is sensitive to outliers and noises. Second, only the global discriminant structure is preserved, while the local discriminant information is ignored. In this paper, we present a new orthogonal sparse linear discriminant analysis (OSLDA) algorithm. The k nearest neighbour graph is first constructed to preserve the locality discriminant information of sample points. Then, L2,1-norm constraint on the projection matrix is used to act as loss function, which can make the proposed method robust to outliers in data points. Extensive experiments have been performed on several standard public image databases, and the experiment results demonstrate the performance of the proposed OSLDA algorithm.

Iterative-method performance evaluation for multiple vectors associated with a large-scale sparse matrix

NASA Astrophysics Data System (ADS)

Imamura, Seigo; Ono, Kenji; Yokokawa, Mitsuo

2016-07-01

Ensemble computing, which is an instance of capacity computing, is an effective computing scenario for exascale parallel supercomputers. In ensemble computing, there are multiple linear systems associated with a common coefficient matrix. We improve the performance of iterative solvers for multiple vectors by solving them at the same time, that is, by solving for the product of the matrices. We implemented several iterative methods and compared their performance. The maximum performance on Sparc VIIIfx was 7.6 times higher than that of a naïve implementation. Finally, to deal with the different convergence processes of linear systems, we introduced a control method to eliminate the calculation of already converged vectors.

Sparsity-Cognizant Algorithms with Applications to Communications, Signal Processing, and the Smart Grid

NASA Astrophysics Data System (ADS)

Zhu, Hao

Sparsity plays an instrumental role in a plethora of scientific fields, including statistical inference for variable selection, parsimonious signal representations, and solving under-determined systems of linear equations - what has led to the ground-breaking result of compressive sampling (CS). This Thesis leverages exciting ideas of sparse signal reconstruction to develop sparsity-cognizant algorithms, and analyze their performance. The vision is to devise tools exploiting the 'right' form of sparsity for the 'right' application domain of multiuser communication systems, array signal processing systems, and the emerging challenges in the smart power grid. Two important power system monitoring tasks are addressed first by capitalizing on the hidden sparsity. To robustify power system state estimation, a sparse outlier model is leveraged to capture the possible corruption in every datum, while the problem nonconvexity due to nonlinear measurements is handled using the semidefinite relaxation technique. Different from existing iterative methods, the proposed algorithm approximates well the global optimum regardless of the initialization. In addition, for enhanced situational awareness, a novel sparse overcomplete representation is introduced to capture (possibly multiple) line outages, and develop real-time algorithms for solving the combinatorially complex identification problem. The proposed algorithms exhibit near-optimal performance while incurring only linear complexity in the number of lines, which makes it possible to quickly bring contingencies to attention. This Thesis also accounts for two basic issues in CS, namely fully-perturbed models and the finite alphabet property. The sparse total least-squares (S-TLS) approach is proposed to furnish CS algorithms for fully-perturbed linear models, leading to statistically optimal and computationally efficient solvers. The S-TLS framework is well motivated for grid-based sensing applications and exhibits higher accuracy than existing sparse algorithms. On the other hand, exploiting the finite alphabet of unknown signals emerges naturally in communication systems, along with sparsity coming from the low activity of each user. Compared to approaches only accounting for either one of the two, joint exploitation of both leads to statistically optimal detectors with improved error performance.

Parallel Finite Element Domain Decomposition for Structural/Acoustic Analysis

NASA Technical Reports Server (NTRS)

Nguyen, Duc T.; Tungkahotara, Siroj; Watson, Willie R.; Rajan, Subramaniam D.

2005-01-01

A domain decomposition (DD) formulation for solving sparse linear systems of equations resulting from finite element analysis is presented. The formulation incorporates mixed direct and iterative equation solving strategics and other novel algorithmic ideas that are optimized to take advantage of sparsity and exploit modern computer architecture, such as memory and parallel computing. The most time consuming part of the formulation is identified and the critical roles of direct sparse and iterative solvers within the framework of the formulation are discussed. Experiments on several computer platforms using several complex test matrices are conducted using software based on the formulation. Small-scale structural examples are used to validate thc steps in the formulation and large-scale (l,000,000+ unknowns) duct acoustic examples are used to evaluate the ORIGIN 2000 processors, and a duster of 6 PCs (running under the Windows environment). Statistics show that the formulation is efficient in both sequential and parallel computing environmental and that the formulation is significantly faster and consumes less memory than that based on one of the best available commercialized parallel sparse solvers.

A Relaxation Method for Nonlocal and Non-Hermitian Operators

NASA Astrophysics Data System (ADS)

Lagaris, I. E.; Papageorgiou, D. G.; Braun, M.; Sofianos, S. A.

1996-06-01

We present a grid method to solve the time dependent Schrödinger equation (TDSE). It uses the Crank-Nicholson scheme to propagate the wavefunction forward in time and finite differences to approximate the derivative operators. The resulting sparse linear system is solved by the symmetric successive overrelaxation iterative technique. The method handles local and nonlocal interactions and Hamiltonians that correspond to either Hermitian or to non-Hermitian matrices with real eigenvalues. We test the method by solving the TDSE in the imaginary time domain, thus converting the time propagation to asymptotic relaxation. Benchmark problems solved are both in one and two dimensions, with local, nonlocal, Hermitian and non-Hermitian Hamiltonians.

An M-step preconditioned conjugate gradient method for parallel computation

NASA Technical Reports Server (NTRS)

Adams, L.

1983-01-01

This paper describes a preconditioned conjugate gradient method that can be effectively implemented on both vector machines and parallel arrays to solve sparse symmetric and positive definite systems of linear equations. The implementation on the CYBER 203/205 and on the Finite Element Machine is discussed and results obtained using the method on these machines are given.

Folded concave penalized sparse linear regression: sparsity, statistical performance, and algorithmic theory for local solutions.

PubMed

Liu, Hongcheng; Yao, Tao; Li, Runze; Ye, Yinyu

2017-11-01

This paper concerns the folded concave penalized sparse linear regression (FCPSLR), a class of popular sparse recovery methods. Although FCPSLR yields desirable recovery performance when solved globally, computing a global solution is NP-complete. Despite some existing statistical performance analyses on local minimizers or on specific FCPSLR-based learning algorithms, it still remains open questions whether local solutions that are known to admit fully polynomial-time approximation schemes (FPTAS) may already be sufficient to ensure the statistical performance, and whether that statistical performance can be non-contingent on the specific designs of computing procedures. To address the questions, this paper presents the following threefold results: (i) Any local solution (stationary point) is a sparse estimator, under some conditions on the parameters of the folded concave penalties. (ii) Perhaps more importantly, any local solution satisfying a significant subspace second-order necessary condition (S 3 ONC), which is weaker than the second-order KKT condition, yields a bounded error in approximating the true parameter with high probability. In addition, if the minimal signal strength is sufficient, the S 3 ONC solution likely recovers the oracle solution. This result also explicates that the goal of improving the statistical performance is consistent with the optimization criteria of minimizing the suboptimality gap in solving the non-convex programming formulation of FCPSLR. (iii) We apply (ii) to the special case of FCPSLR with minimax concave penalty (MCP) and show that under the restricted eigenvalue condition, any S 3 ONC solution with a better objective value than the Lasso solution entails the strong oracle property. In addition, such a solution generates a model error (ME) comparable to the optimal but exponential-time sparse estimator given a sufficient sample size, while the worst-case ME is comparable to the Lasso in general. Furthermore, to guarantee the S 3 ONC admits FPTAS.

Sparse distributed memory: understanding the speed and robustness of expert memory

PubMed Central

Brogliato, Marcelo S.; Chada, Daniel M.; Linhares, Alexandre

2014-01-01

How can experts, sometimes in exacting detail, almost immediately and very precisely recall memory items from a vast repertoire? The problem in which we will be interested concerns models of theoretical neuroscience that could explain the speed and robustness of an expert's recollection. The approach is based on Sparse Distributed Memory, which has been shown to be plausible, both in a neuroscientific and in a psychological manner, in a number of ways. A crucial characteristic concerns the limits of human recollection, the “tip-of-tongue” memory event—which is found at a non-linearity in the model. We expand the theoretical framework, deriving an optimization formula to solve this non-linearity. Numerical results demonstrate how the higher frequency of rehearsal, through work or study, immediately increases the robustness and speed associated with expert memory. PMID:24808842

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]!

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.

Impact of view reduction in CT on radiation dose for patients

NASA Astrophysics Data System (ADS)

Parcero, E.; Flores, L.; Sánchez, M. G.; Vidal, V.; Verdú, G.

2017-08-01

Iterative methods have become a hot topic of research in computed tomography (CT) imaging because of their capacity to resolve the reconstruction problem from a limited number of projections. This allows the reduction of radiation exposure on patients during the data acquisition. The reconstruction time and the high radiation dose imposed on patients are the two major drawbacks in CT. To solve them effectively we adapted the method for sparse linear equations and sparse least squares (LSQR) with soft threshold filtering (STF) and the fast iterative shrinkage-thresholding algorithm (FISTA) to computed tomography reconstruction. The feasibility of the proposed methods is demonstrated numerically.

Learning Incoherent Sparse and Low-Rank Patterns from Multiple Tasks

PubMed Central

Chen, Jianhui; Liu, Ji; Ye, Jieping

2013-01-01

We consider the problem of learning incoherent sparse and low-rank patterns from multiple tasks. Our approach is based on a linear multi-task learning formulation, in which the sparse and low-rank patterns are induced by a cardinality regularization term and a low-rank constraint, respectively. This formulation is non-convex; we convert it into its convex surrogate, which can be routinely solved via semidefinite programming for small-size problems. We propose to employ the general projected gradient scheme to efficiently solve such a convex surrogate; however, in the optimization formulation, the objective function is non-differentiable and the feasible domain is non-trivial. We present the procedures for computing the projected gradient and ensuring the global convergence of the projected gradient scheme. The computation of projected gradient involves a constrained optimization problem; we show that the optimal solution to such a problem can be obtained via solving an unconstrained optimization subproblem and an Euclidean projection subproblem. We also present two projected gradient algorithms and analyze their rates of convergence in details. In addition, we illustrate the use of the presented projected gradient algorithms for the proposed multi-task learning formulation using the least squares loss. Experimental results on a collection of real-world data sets demonstrate the effectiveness of the proposed multi-task learning formulation and the efficiency of the proposed projected gradient algorithms. PMID:24077658

Learning Incoherent Sparse and Low-Rank Patterns from Multiple Tasks.

PubMed

Chen, Jianhui; Liu, Ji; Ye, Jieping

2012-02-01

We consider the problem of learning incoherent sparse and low-rank patterns from multiple tasks. Our approach is based on a linear multi-task learning formulation, in which the sparse and low-rank patterns are induced by a cardinality regularization term and a low-rank constraint, respectively. This formulation is non-convex; we convert it into its convex surrogate, which can be routinely solved via semidefinite programming for small-size problems. We propose to employ the general projected gradient scheme to efficiently solve such a convex surrogate; however, in the optimization formulation, the objective function is non-differentiable and the feasible domain is non-trivial. We present the procedures for computing the projected gradient and ensuring the global convergence of the projected gradient scheme. The computation of projected gradient involves a constrained optimization problem; we show that the optimal solution to such a problem can be obtained via solving an unconstrained optimization subproblem and an Euclidean projection subproblem. We also present two projected gradient algorithms and analyze their rates of convergence in details. In addition, we illustrate the use of the presented projected gradient algorithms for the proposed multi-task learning formulation using the least squares loss. Experimental results on a collection of real-world data sets demonstrate the effectiveness of the proposed multi-task learning formulation and the efficiency of the proposed projected gradient algorithms.

Sparse Coding and Counting for Robust Visual Tracking

PubMed Central

Liu, Risheng; Wang, Jing; Shang, Xiaoke; Wang, Yiyang; Su, Zhixun; Cai, Yu

2016-01-01

In this paper, we propose a novel sparse coding and counting method under Bayesian framework for visual tracking. In contrast to existing methods, the proposed method employs the combination of L0 and L1 norm to regularize the linear coefficients of incrementally updated linear basis. The sparsity constraint enables the tracker to effectively handle difficult challenges, such as occlusion or image corruption. To achieve real-time processing, we propose a fast and efficient numerical algorithm for solving the proposed model. Although it is an NP-hard problem, the proposed accelerated proximal gradient (APG) approach is guaranteed to converge to a solution quickly. Besides, we provide a closed solution of combining L0 and L1 regularized representation to obtain better sparsity. Experimental results on challenging video sequences demonstrate that the proposed method achieves state-of-the-art results both in accuracy and speed. PMID:27992474

Typed Linear Chain Conditional Random Fields and Their Application to Intrusion Detection

NASA Astrophysics Data System (ADS)

Elfers, Carsten; Horstmann, Mirko; Sohr, Karsten; Herzog, Otthein

Intrusion detection in computer networks faces the problem of a large number of both false alarms and unrecognized attacks. To improve the precision of detection, various machine learning techniques have been proposed. However, one critical issue is that the amount of reference data that contains serious intrusions is very sparse. In this paper we present an inference process with linear chain conditional random fields that aims to solve this problem by using domain knowledge about the alerts of different intrusion sensors represented in an ontology.

M-step preconditioned conjugate gradient methods

NASA Technical Reports Server (NTRS)

Adams, L.

1983-01-01

Preconditioned conjugate gradient methods for solving sparse symmetric and positive finite systems of linear equations are described. Necessary and sufficient conditions are given for when these preconditioners can be used and an analysis of their effectiveness is given. Efficient computer implementations of these methods are discussed and results on the CYBER 203 and the Finite Element Machine under construction at NASA Langley Research Center are included.

Linear SFM: A hierarchical approach to solving structure-from-motion problems by decoupling the linear and nonlinear components

NASA Astrophysics Data System (ADS)

Zhao, Liang; Huang, Shoudong; Dissanayake, Gamini

2018-07-01

This paper presents a novel hierarchical approach to solving structure-from-motion (SFM) problems. The algorithm begins with small local reconstructions based on nonlinear bundle adjustment (BA). These are then joined in a hierarchical manner using a strategy that requires solving a linear least squares optimization problem followed by a nonlinear transform. The algorithm can handle ordered monocular and stereo image sequences. Two stereo images or three monocular images are adequate for building each initial reconstruction. The bulk of the computation involves solving a linear least squares problem and, therefore, the proposed algorithm avoids three major issues associated with most of the nonlinear optimization algorithms currently used for SFM: the need for a reasonably accurate initial estimate, the need for iterations, and the possibility of being trapped in a local minimum. Also, by summarizing all the original observations into the small local reconstructions with associated information matrices, the proposed Linear SFM manages to preserve all the information contained in the observations. The paper also demonstrates that the proposed problem formulation results in a sparse structure that leads to an efficient numerical implementation. The experimental results using publicly available datasets show that the proposed algorithm yields solutions that are very close to those obtained using a global BA starting with an accurate initial estimate. The C/C++ source code of the proposed algorithm is publicly available at https://github.com/LiangZhaoPKUImperial/LinearSFM.

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.

An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Gutknecht, Martin H.; Nachtigal, Noel M.

1991-01-01

The nonsymmetric Lanczos method can be used to compute eigenvalues of large sparse non-Hermitian matrices or to solve large sparse non-Hermitian linear systems. However, the original Lanczos algorithm is susceptible to possible breakdowns and potential instabilities. An implementation is presented of a look-ahead version of the Lanczos algorithm that, except for the very special situation of an incurable breakdown, overcomes these problems by skipping over those steps in which a breakdown or near-breakdown would occur in the standard process. The proposed algorithm can handle look-ahead steps of any length and requires the same number of matrix-vector products and inner products as the standard Lanczos process without look-ahead.

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.

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.

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.

Conic Sampling: An Efficient Method for Solving Linear and Quadratic Programming by Randomly Linking Constraints within the Interior

PubMed Central

Serang, Oliver

2012-01-01

Linear programming (LP) problems are commonly used in analysis and resource allocation, frequently surfacing as approximations to more difficult problems. Existing approaches to LP have been dominated by a small group of methods, and randomized algorithms have not enjoyed popularity in practice. This paper introduces a novel randomized method of solving LP problems by moving along the facets and within the interior of the polytope along rays randomly sampled from the polyhedral cones defined by the bounding constraints. This conic sampling method is then applied to randomly sampled LPs, and its runtime performance is shown to compare favorably to the simplex and primal affine-scaling algorithms, especially on polytopes with certain characteristics. The conic sampling method is then adapted and applied to solve a certain quadratic program, which compute a projection onto a polytope; the proposed method is shown to outperform the proprietary software Mathematica on large, sparse QP problems constructed from mass spectometry-based proteomics. PMID:22952741

A robust real-time surface reconstruction method on point clouds captured from a 3D surface photogrammetry system.

PubMed

Liu, Wenyang; Cheung, Yam; Sawant, Amit; Ruan, Dan

2016-05-01

To develop a robust and real-time surface reconstruction method on point clouds captured from a 3D surface photogrammetry system. The authors have developed a robust and fast surface reconstruction method on point clouds acquired by the photogrammetry system, without explicitly solving the partial differential equation required by a typical variational approach. Taking advantage of the overcomplete nature of the acquired point clouds, their method solves and propagates a sparse linear relationship from the point cloud manifold to the surface manifold, assuming both manifolds share similar local geometry. With relatively consistent point cloud acquisitions, the authors propose a sparse regression (SR) model to directly approximate the target point cloud as a sparse linear combination from the training set, assuming that the point correspondences built by the iterative closest point (ICP) is reasonably accurate and have residual errors following a Gaussian distribution. To accommodate changing noise levels and/or presence of inconsistent occlusions during the acquisition, the authors further propose a modified sparse regression (MSR) model to model the potentially large and sparse error built by ICP with a Laplacian prior. The authors evaluated the proposed method on both clinical point clouds acquired under consistent acquisition conditions and on point clouds with inconsistent occlusions. The authors quantitatively evaluated the reconstruction performance with respect to root-mean-squared-error, by comparing its reconstruction results against that from the variational method. On clinical point clouds, both the SR and MSR models have achieved sub-millimeter reconstruction accuracy and reduced the reconstruction time by two orders of magnitude to a subsecond reconstruction time. On point clouds with inconsistent occlusions, the MSR model has demonstrated its advantage in achieving consistent and robust performance despite the introduced occlusions. The authors have developed a fast and robust surface reconstruction method on point clouds captured from a 3D surface photogrammetry system, with demonstrated sub-millimeter reconstruction accuracy and subsecond reconstruction time. It is suitable for real-time motion tracking in radiotherapy, with clear surface structures for better quantifications.

A robust real-time surface reconstruction method on point clouds captured from a 3D surface photogrammetry system

PubMed Central

Liu, Wenyang; Cheung, Yam; Sawant, Amit; Ruan, Dan

2016-01-01

Purpose: To develop a robust and real-time surface reconstruction method on point clouds captured from a 3D surface photogrammetry system. Methods: The authors have developed a robust and fast surface reconstruction method on point clouds acquired by the photogrammetry system, without explicitly solving the partial differential equation required by a typical variational approach. Taking advantage of the overcomplete nature of the acquired point clouds, their method solves and propagates a sparse linear relationship from the point cloud manifold to the surface manifold, assuming both manifolds share similar local geometry. With relatively consistent point cloud acquisitions, the authors propose a sparse regression (SR) model to directly approximate the target point cloud as a sparse linear combination from the training set, assuming that the point correspondences built by the iterative closest point (ICP) is reasonably accurate and have residual errors following a Gaussian distribution. To accommodate changing noise levels and/or presence of inconsistent occlusions during the acquisition, the authors further propose a modified sparse regression (MSR) model to model the potentially large and sparse error built by ICP with a Laplacian prior. The authors evaluated the proposed method on both clinical point clouds acquired under consistent acquisition conditions and on point clouds with inconsistent occlusions. The authors quantitatively evaluated the reconstruction performance with respect to root-mean-squared-error, by comparing its reconstruction results against that from the variational method. Results: On clinical point clouds, both the SR and MSR models have achieved sub-millimeter reconstruction accuracy and reduced the reconstruction time by two orders of magnitude to a subsecond reconstruction time. On point clouds with inconsistent occlusions, the MSR model has demonstrated its advantage in achieving consistent and robust performance despite the introduced occlusions. Conclusions: The authors have developed a fast and robust surface reconstruction method on point clouds captured from a 3D surface photogrammetry system, with demonstrated sub-millimeter reconstruction accuracy and subsecond reconstruction time. It is suitable for real-time motion tracking in radiotherapy, with clear surface structures for better quantifications. PMID:27147347

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.

Enhancing sparsity of Hermite polynomial expansions by iterative rotations

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

Yang, Xiu; Lei, Huan; Baker, Nathan A.

2016-02-01

Compressive sensing has become a powerful addition to uncertainty quantification in recent years. This paper identifies new bases for random variables through linear mappings such that the representation of the quantity of interest is more sparse with new basis functions associated with the new random variables. This sparsity increases both the efficiency and accuracy of the compressive sensing-based uncertainty quantification method. Specifically, we consider rotation- based linear mappings which are determined iteratively for Hermite polynomial expansions. We demonstrate the effectiveness of the new method with applications in solving stochastic partial differential equations and high-dimensional (O(100)) problems.

One-shot 3D scanning by combining sparse landmarks with dense gradient information

NASA Astrophysics Data System (ADS)

Di Martino, Matías; Flores, Jorge; Ferrari, José A.

2018-06-01

Scene understanding is one of the most challenging and popular problems in the field of robotics and computer vision and the estimation of 3D information is at the core of most of these applications. In order to retrieve the 3D structure of a test surface we propose a single shot approach that combines dense gradient information with sparse absolute measurements. To that end, we designed a colored pattern that codes fine horizontal and vertical fringes, with sparse corners landmarks. By measuring the deformation (bending) of horizontal and vertical fringes, we are able to estimate surface local variations (i.e. its gradient field). Then corner sparse landmarks are detected and matched to infer spare absolute information about the test surface height. Local gradient information is combined with the sparse absolute values which work as anchors to guide the integration process. We show that this can be mathematically done in a very compact and intuitive way by properly defining a Poisson-like partial differential equation. Then we address in detail how the problem can be formulated in a discrete domain and how it can be practically solved by straight forward linear numerical solvers. Finally, validation experiment are presented.

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.

Communications oriented programming of parallel iterative solutions of sparse linear systems

NASA Technical Reports Server (NTRS)

Patrick, M. L.; Pratt, T. W.

1986-01-01

Parallel algorithms are developed for a class of scientific computational problems by partitioning the problems into smaller problems which may be solved concurrently. The effectiveness of the resulting parallel solutions is determined by the amount and frequency of communication and synchronization and the extent to which communication can be overlapped with computation. Three different parallel algorithms for solving the same class of problems are presented, and their effectiveness is analyzed from this point of view. The algorithms are programmed using a new programming environment. Run-time statistics and experience obtained from the execution of these programs assist in measuring the effectiveness of these algorithms.

Non-uniform sampling: post-Fourier era of NMR data collection and processing.

PubMed

Kazimierczuk, Krzysztof; Orekhov, Vladislav

2015-11-01

The invention of multidimensional techniques in the 1970s revolutionized NMR, making it the general tool of structural analysis of molecules and materials. In the most straightforward approach, the signal sampling in the indirect dimensions of a multidimensional experiment is performed in the same manner as in the direct dimension, i.e. with a grid of equally spaced points. This results in lengthy experiments with a resolution often far from optimum. To circumvent this problem, numerous sparse-sampling techniques have been developed in the last three decades, including two traditionally distinct approaches: the radial sampling and non-uniform sampling. This mini review discusses the sparse signal sampling and reconstruction techniques from the point of view of an underdetermined linear algebra problem that arises when a full, equally spaced set of sampled points is replaced with sparse sampling. Additional assumptions that are introduced to solve the problem, as well as the shape of the undersampled Fourier transform operator (visualized as so-called point spread function), are shown to be the main differences between various sparse-sampling methods. Copyright © 2015 John Wiley & Sons, Ltd.

Multi-objective based spectral unmixing for hyperspectral images

NASA Astrophysics Data System (ADS)

Xu, Xia; Shi, Zhenwei

2017-02-01

Sparse hyperspectral unmixing assumes that each observed pixel can be expressed by a linear combination of several pure spectra in a priori library. Sparse unmixing is challenging, since it is usually transformed to a NP-hard l0 norm based optimization problem. Existing methods usually utilize a relaxation to the original l0 norm. However, the relaxation may bring in sensitive weighted parameters and additional calculation error. In this paper, we propose a novel multi-objective based algorithm to solve the sparse unmixing problem without any relaxation. We transform sparse unmixing to a multi-objective optimization problem, which contains two correlative objectives: minimizing the reconstruction error and controlling the endmember sparsity. To improve the efficiency of multi-objective optimization, a population-based randomly flipping strategy is designed. Moreover, we theoretically prove that the proposed method is able to recover a guaranteed approximate solution from the spectral library within limited iterations. The proposed method can directly deal with l0 norm via binary coding for the spectral signatures in the library. Experiments on both synthetic and real hyperspectral datasets demonstrate the effectiveness of the proposed method.

An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices, part 1

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Gutknecht, Martin H.; Nachtigal, Noel M.

1990-01-01

The nonsymmetric Lanczos method can be used to compute eigenvalues of large sparse non-Hermitian matrices or to solve large sparse non-Hermitian linear systems. However, the original Lanczos algorithm is susceptible to possible breakdowns and potential instabilities. We present an implementation of a look-ahead version of the Lanczos algorithm which overcomes these problems by skipping over those steps in which a breakdown or near-breakdown would occur in the standard process. The proposed algorithm can handle look-ahead steps of any length and is not restricted to steps of length 2, as earlier implementations are. Also, our implementation has the feature that it requires roughly the same number of inner products as the standard Lanczos process without look-ahead.

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.

Conjugate gradient type methods for linear systems with complex symmetric coefficient matrices

NASA Technical Reports Server (NTRS)

Freund, Roland

1989-01-01

We consider conjugate gradient type methods for the solution of large sparse linear system Ax equals b with complex symmetric coefficient matrices A equals A(T). Such linear systems arise in important applications, such as the numerical solution of the complex Helmholtz equation. Furthermore, most complex non-Hermitian linear systems which occur in practice are actually complex symmetric. We investigate conjugate gradient type iterations which are based on a variant of the nonsymmetric Lanczos algorithm for complex symmetric matrices. We propose a new approach with iterates defined by a quasi-minimal residual property. The resulting algorithm presents several advantages over the standard biconjugate gradient method. We also include some remarks on the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.

Weighted least squares phase unwrapping based on the wavelet transform

NASA Astrophysics Data System (ADS)

Chen, Jiafeng; Chen, Haiqin; Yang, Zhengang; Ren, Haixia

2007-01-01

The weighted least squares phase unwrapping algorithm is a robust and accurate method to solve phase unwrapping problem. This method usually leads to a large sparse linear equation system. Gauss-Seidel relaxation iterative method is usually used to solve this large linear equation. However, this method is not practical due to its extremely slow convergence. The multigrid method is an efficient algorithm to improve convergence rate. However, this method needs an additional weight restriction operator which is very complicated. For this reason, the multiresolution analysis method based on the wavelet transform is proposed. By applying the wavelet transform, the original system is decomposed into its coarse and fine resolution levels and an equivalent equation system with better convergence condition can be obtained. Fast convergence in separate coarse resolution levels speeds up the overall system convergence rate. The simulated experiment shows that the proposed method converges faster and provides better result than the multigrid method.

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

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.

Modeling Alzheimer's disease cognitive scores using multi-task sparse group lasso.

PubMed

Liu, Xiaoli; Goncalves, André R; Cao, Peng; Zhao, Dazhe; Banerjee, Arindam

2018-06-01

Alzheimer's disease (AD) is a severe neurodegenerative disorder characterized by loss of memory and reduction in cognitive functions due to progressive degeneration of neurons and their connections, eventually leading to death. In this paper, we consider the problem of simultaneously predicting several different cognitive scores associated with categorizing subjects as normal, mild cognitive impairment (MCI), or Alzheimer's disease (AD) in a multi-task learning framework using features extracted from brain images obtained from ADNI (Alzheimer's Disease Neuroimaging Initiative). To solve the problem, we present a multi-task sparse group lasso (MT-SGL) framework, which estimates sparse features coupled across tasks, and can work with loss functions associated with any Generalized Linear Models. Through comparisons with a variety of baseline models using multiple evaluation metrics, we illustrate the promising predictive performance of MT-SGL on ADNI along with its ability to identify brain regions more likely to help the characterization Alzheimer's disease progression. Copyright © 2017 Elsevier Ltd. All rights reserved.

ML 3.0 smoothed aggregation user's guide.

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

Sala, Marzio; Hu, Jonathan Joseph; Tuminaro, Raymond Stephen

2004-05-01

ML is a multigrid preconditioning package intended to solve linear systems of equations Az = 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. ML should be used on large sparse linear systems arising from partial differential equation (PDE) discretizations. While technically any linear system can be considered, ML should be used on linear systems that correspond to things that work well with multigrid methods (e.g. elliptic PDEs). ML can be used as a stand-alone package ormore » to generate preconditioners for a traditional iterative solver package (e.g. Krylov methods). We have supplied support for working with the AZTEC 2.1 and AZTECOO iterative package [15]. However, other solvers can be used by supplying a few functions. This document describes one specific algebraic multigrid approach: smoothed aggregation. This approach is used within several specialized multigrid methods: one for the eddy current formulation for Maxwell's equations, and a multilevel and domain decomposition method for symmetric and non-symmetric systems of equations (like elliptic equations, or compressible and incompressible fluid dynamics problems). Other methods exist within ML but are not described in this document. Examples are given illustrating the problem definition and exercising multigrid options.« less

ML 3.1 smoothed aggregation user's guide.

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

Sala, Marzio; Hu, Jonathan Joseph; Tuminaro, Raymond Stephen

2004-10-01

ML is a multigrid preconditioning package intended to solve 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. ML should be used on large sparse linear systems arising from partial differential equation (PDE) discretizations. While technically any linear system can be considered, ML should be used on linear systems that correspond to things that work well with multigrid methods (e.g. elliptic PDEs). ML can be used as a stand-alone package ormore » to generate preconditioners for a traditional iterative solver package (e.g. Krylov methods). We have supplied support for working with the Aztec 2.1 and AztecOO iterative package [16]. However, other solvers can be used by supplying a few functions. This document describes one specific algebraic multigrid approach: smoothed aggregation. This approach is used within several specialized multigrid methods: one for the eddy current formulation for Maxwell's equations, and a multilevel and domain decomposition method for symmetric and nonsymmetric systems of equations (like elliptic equations, or compressible and incompressible fluid dynamics problems). Other methods exist within ML but are not described in this document. Examples are given illustrating the problem definition and exercising multigrid options.« less

Off-Grid Direction of Arrival Estimation Based on Joint Spatial Sparsity for Distributed Sparse Linear Arrays

PubMed Central

Liang, Yujie; Ying, Rendong; Lu, Zhenqi; Liu, Peilin

2014-01-01

In the design phase of sensor arrays during array signal processing, the estimation performance and system cost are largely determined by array aperture size. In this article, we address the problem of joint direction-of-arrival (DOA) estimation with distributed sparse linear arrays (SLAs) and propose an off-grid synchronous approach based on distributed compressed sensing to obtain larger array aperture. We focus on the complex source distribution in the practical applications and classify the sources into common and innovation parts according to whether a signal of source can impinge on all the SLAs or a specific one. For each SLA, we construct a corresponding virtual uniform linear array (ULA) to create the relationship of random linear map between the signals respectively observed by these two arrays. The signal ensembles including the common/innovation sources for different SLAs are abstracted as a joint spatial sparsity model. And we use the minimization of concatenated atomic norm via semidefinite programming to solve the problem of joint DOA estimation. Joint calculation of the signals observed by all the SLAs exploits their redundancy caused by the common sources and decreases the requirement of array size. The numerical results illustrate the advantages of the proposed approach. PMID:25420150

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.

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.

Deep and Structured Robust Information Theoretic Learning for Image Analysis.

PubMed

Deng, Yue; Bao, Feng; Deng, Xuesong; Wang, Ruiping; Kong, Youyong; Dai, Qionghai

2016-07-07

This paper presents a robust information theoretic (RIT) model to reduce the uncertainties, i.e. missing and noisy labels, in general discriminative data representation tasks. The fundamental pursuit of our model is to simultaneously learn a transformation function and a discriminative classifier that maximize the mutual information of data and their labels in the latent space. In this general paradigm, we respectively discuss three types of the RIT implementations with linear subspace embedding, deep transformation and structured sparse learning. In practice, the RIT and deep RIT are exploited to solve the image categorization task whose performances will be verified on various benchmark datasets. The structured sparse RIT is further applied to a medical image analysis task for brain MRI segmentation that allows group-level feature selections on the brain tissues.

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.

Incomplete Gröbner basis as a preconditioner for polynomial systems

NASA Astrophysics Data System (ADS)

Sun, Yang; Tao, Yu-Hui; Bai, Feng-Shan

2009-04-01

Precondition plays a critical role in the numerical methods for large and sparse linear systems. It is also true for nonlinear algebraic systems. In this paper incomplete Gröbner basis (IGB) is proposed as a preconditioner of homotopy methods for polynomial systems of equations, which transforms a deficient system into a system with the same finite solutions, but smaller degree. The reduced system can thus be solved faster. Numerical results show the efficiency of the preconditioner.

Reconstruction of finite-valued sparse signals

NASA Astrophysics Data System (ADS)

Keiper, Sandra; Kutyniok, Gitta; Lee, Dae Gwan; Pfander, Götz

2017-08-01

The need of reconstructing discrete-valued sparse signals from few measurements, that is solving an undetermined system of linear equations, appears frequently in science and engineering. Those signals appear, for example, in error correcting codes as well as massive Multiple-Input Multiple-Output (MIMO) channel and wideband spectrum sensing. A particular example is given by wireless communications, where the transmitted signals are sequences of bits, i.e., with entries in f0; 1g. Whereas classical compressed sensing algorithms do not incorporate the additional knowledge of the discrete nature of the signal, classical lattice decoding approaches do not utilize sparsity constraints. In this talk, we present an approach that incorporates a discrete values prior into basis pursuit. In particular, we address finite-valued sparse signals, i.e., sparse signals with entries in a finite alphabet. We will introduce an equivalent null space characterization and show that phase transition takes place earlier than when using the classical basis pursuit approach. We will further discuss robustness of the algorithm and show that the nonnegative case is very different from the bipolar one. One of our findings is that the positioning of the zero in the alphabet - i.e., whether it is a boundary element or not - is crucial.

An efficient implementation of a high-order filter for a cubed-sphere spectral element model

NASA Astrophysics Data System (ADS)

Kang, Hyun-Gyu; Cheong, Hyeong-Bin

2017-03-01

A parallel-scalable, isotropic, scale-selective spatial filter was developed for the cubed-sphere spectral element model on the sphere. The filter equation is a high-order elliptic (Helmholtz) equation based on the spherical Laplacian operator, which is transformed into cubed-sphere local coordinates. The Laplacian operator is discretized on the computational domain, i.e., on each cell, by the spectral element method with Gauss-Lobatto Lagrange interpolating polynomials (GLLIPs) as the orthogonal basis functions. On the global domain, the discrete filter equation yielded a linear system represented by a highly sparse matrix. The density of this matrix increases quadratically (linearly) with the order of GLLIP (order of the filter), and the linear system is solved in only O (Ng) operations, where Ng is the total number of grid points. The solution, obtained by a row reduction method, demonstrated the typical accuracy and convergence rate of the cubed-sphere spectral element method. To achieve computational efficiency on parallel computers, the linear system was treated by an inverse matrix method (a sparse matrix-vector multiplication). The density of the inverse matrix was lowered to only a few times of the original sparse matrix without degrading the accuracy of the solution. For better computational efficiency, a local-domain high-order filter was introduced: The filter equation is applied to multiple cells, and then the central cell was only used to reconstruct the filtered field. The parallel efficiency of applying the inverse matrix method to the global- and local-domain filter was evaluated by the scalability on a distributed-memory parallel computer. The scale-selective performance of the filter was demonstrated on Earth topography. The usefulness of the filter as a hyper-viscosity for the vorticity equation was also demonstrated.

A robust real-time surface reconstruction method on point clouds captured from a 3D surface photogrammetry system

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

Liu, Wenyang; Cheung, Yam; Sawant, Amit

2016-05-15

Purpose: To develop a robust and real-time surface reconstruction method on point clouds captured from a 3D surface photogrammetry system. Methods: The authors have developed a robust and fast surface reconstruction method on point clouds acquired by the photogrammetry system, without explicitly solving the partial differential equation required by a typical variational approach. Taking advantage of the overcomplete nature of the acquired point clouds, their method solves and propagates a sparse linear relationship from the point cloud manifold to the surface manifold, assuming both manifolds share similar local geometry. With relatively consistent point cloud acquisitions, the authors propose a sparsemore » regression (SR) model to directly approximate the target point cloud as a sparse linear combination from the training set, assuming that the point correspondences built by the iterative closest point (ICP) is reasonably accurate and have residual errors following a Gaussian distribution. To accommodate changing noise levels and/or presence of inconsistent occlusions during the acquisition, the authors further propose a modified sparse regression (MSR) model to model the potentially large and sparse error built by ICP with a Laplacian prior. The authors evaluated the proposed method on both clinical point clouds acquired under consistent acquisition conditions and on point clouds with inconsistent occlusions. The authors quantitatively evaluated the reconstruction performance with respect to root-mean-squared-error, by comparing its reconstruction results against that from the variational method. Results: On clinical point clouds, both the SR and MSR models have achieved sub-millimeter reconstruction accuracy and reduced the reconstruction time by two orders of magnitude to a subsecond reconstruction time. On point clouds with inconsistent occlusions, the MSR model has demonstrated its advantage in achieving consistent and robust performance despite the introduced occlusions. Conclusions: The authors have developed a fast and robust surface reconstruction method on point clouds captured from a 3D surface photogrammetry system, with demonstrated sub-millimeter reconstruction accuracy and subsecond reconstruction time. It is suitable for real-time motion tracking in radiotherapy, with clear surface structures for better quantifications.« less

Extending the eigCG algorithm to nonsymmetric Lanczos for linear systems with multiple right-hand sides

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

Abdel-Rehim, A M; Stathopoulos, Andreas; Orginos, Kostas

2014-08-01

The technique that was used to build the EigCG algorithm for sparse symmetric linear systems is extended to the nonsymmetric case using the BiCG algorithm. We show that, similarly to the symmetric case, we can build an algorithm that is capable of computing a few smallest magnitude eigenvalues and their corresponding left and right eigenvectors of a nonsymmetric matrix using only a small window of the BiCG residuals while simultaneously solving a linear system with that matrix. For a system with multiple right-hand sides, we give an algorithm that computes incrementally more eigenvalues while solving the first few systems andmore » then uses the computed eigenvectors to deflate BiCGStab for the remaining systems. Our experiments on various test problems, including Lattice QCD, show the remarkable ability of EigBiCG to compute spectral approximations with accuracy comparable to that of the unrestarted, nonsymmetric Lanczos. Furthermore, our incremental EigBiCG followed by appropriately restarted and deflated BiCGStab provides a competitive method for systems with multiple right-hand sides.« less

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.

Analysis of programming properties and the row-column generation method for 1-norm support vector machines.

PubMed

Zhang, Li; Zhou, WeiDa

2013-12-01

This paper deals with fast methods for training a 1-norm support vector machine (SVM). First, we define a specific class of linear programming with many sparse constraints, i.e., row-column sparse constraint linear programming (RCSC-LP). In nature, the 1-norm SVM is a sort of RCSC-LP. In order to construct subproblems for RCSC-LP and solve them, a family of row-column generation (RCG) methods is introduced. RCG methods belong to a category of decomposition techniques, and perform row and column generations in a parallel fashion. Specially, for the 1-norm SVM, the maximum size of subproblems of RCG is identical with the number of Support Vectors (SVs). We also introduce a semi-deleting rule for RCG methods and prove the convergence of RCG methods when using the semi-deleting rule. Experimental results on toy data and real-world datasets illustrate that it is efficient to use RCG to train the 1-norm SVM, especially in the case of small SVs. Copyright © 2013 Elsevier Ltd. All rights reserved.

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.

Temporally-Constrained Group Sparse Learning for Longitudinal Data Analysis in Alzheimer’s Disease

PubMed Central

Jie, Biao; Liu, Mingxia; Liu, Jun

2016-01-01

Sparse learning has been widely investigated for analysis of brain images to assist the diagnosis of Alzheimer’s disease (AD) and its prodromal stage, i.e., mild cognitive impairment (MCI). However, most existing sparse learning-based studies only adopt cross-sectional analysis methods, where the sparse model is learned using data from a single time-point. Actually, multiple time-points of data are often available in brain imaging applications, which can be used in some longitudinal analysis methods to better uncover the disease progression patterns. Accordingly, in this paper we propose a novel temporally-constrained group sparse learning method aiming for longitudinal analysis with multiple time-points of data. Specifically, we learn a sparse linear regression model by using the imaging data from multiple time-points, where a group regularization term is first employed to group the weights for the same brain region across different time-points together. Furthermore, to reflect the smooth changes between data derived from adjacent time-points, we incorporate two smoothness regularization terms into the objective function, i.e., one fused smoothness term which requires that the differences between two successive weight vectors from adjacent time-points should be small, and another output smoothness term which requires the differences between outputs of two successive models from adjacent time-points should also be small. We develop an efficient optimization algorithm to solve the proposed objective function. Experimental results on ADNI database demonstrate that, compared with conventional sparse learning-based methods, our proposed method can achieve improved regression performance and also help in discovering disease-related biomarkers. PMID:27093313

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.

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.

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.

Methodology for sensitivity analysis, approximate analysis, and design optimization in CFD for multidisciplinary applications

NASA Technical Reports Server (NTRS)

Taylor, Arthur C., III; Hou, Gene W.

1993-01-01

In this study involving advanced fluid flow codes, an incremental iterative formulation (also known as the delta or correction form) together with the well-known spatially-split approximate factorization algorithm, is presented for solving the very large sparse systems of linear equations which are associated with aerodynamic sensitivity analysis. For smaller 2D problems, a direct method can be applied to solve these linear equations in either the standard or the incremental form, in which case the two are equivalent. Iterative methods are needed for larger 2D and future 3D applications, however, because direct methods require much more computer memory than is currently available. Iterative methods for solving these equations in the standard form are generally unsatisfactory due to an ill-conditioning of the coefficient matrix; this problem can be overcome when these equations are cast in the incremental form. These and other benefits are discussed. The methodology is successfully implemented and tested in 2D using an upwind, cell-centered, finite volume formulation applied to the thin-layer Navier-Stokes equations. Results are presented for two sample airfoil problems: (1) subsonic low Reynolds number laminar flow; and (2) transonic high Reynolds number turbulent flow.

Review on solving the forward problem in EEG source analysis

PubMed Central

Hallez, Hans; Vanrumste, Bart; Grech, Roberta; Muscat, Joseph; De Clercq, Wim; Vergult, Anneleen; D'Asseler, Yves; Camilleri, Kenneth P; Fabri, Simon G; Van Huffel, Sabine; Lemahieu, Ignace

2007-01-01

Background The aim of electroencephalogram (EEG) source localization is to find the brain areas responsible for EEG waves of interest. It consists of solving forward and inverse problems. The forward problem is solved by starting from a given electrical source and calculating the potentials at the electrodes. These evaluations are necessary to solve the inverse problem which is defined as finding brain sources which are responsible for the measured potentials at the EEG electrodes. Methods While other reviews give an extensive summary of the both forward and inverse problem, this review article focuses on different aspects of solving the forward problem and it is intended for newcomers in this research field. Results It starts with focusing on the generators of the EEG: the post-synaptic potentials in the apical dendrites of pyramidal neurons. These cells generate an extracellular current which can be modeled by Poisson's differential equation, and Neumann and Dirichlet boundary conditions. The compartments in which these currents flow can be anisotropic (e.g. skull and white matter). In a three-shell spherical head model an analytical expression exists to solve the forward problem. During the last two decades researchers have tried to solve Poisson's equation in a realistically shaped head model obtained from 3D medical images, which requires numerical methods. The following methods are compared with each other: the boundary element method (BEM), the finite element method (FEM) and the finite difference method (FDM). In the last two methods anisotropic conducting compartments can conveniently be introduced. Then the focus will be set on the use of reciprocity in EEG source localization. It is introduced to speed up the forward calculations which are here performed for each electrode position rather than for each dipole position. Solving Poisson's equation utilizing FEM and FDM corresponds to solving a large sparse linear system. Iterative methods are required to solve these sparse linear systems. The following iterative methods are discussed: successive over-relaxation, conjugate gradients method and algebraic multigrid method. Conclusion Solving the forward problem has been well documented in the past decades. In the past simplified spherical head models are used, whereas nowadays a combination of imaging modalities are used to accurately describe the geometry of the head model. Efforts have been done on realistically describing the shape of the head model, as well as the heterogenity of the tissue types and realistically determining the conductivity. However, the determination and validation of the in vivo conductivity values is still an important topic in this field. In addition, more studies have to be done on the influence of all the parameters of the head model and of the numerical techniques on the solution of the forward problem. PMID:18053144

Learning Sparse Feature Representations using Probabilistic Quadtrees and Deep Belief Nets

DTIC Science & Technology

2015-04-24

Feature Representations usingProbabilistic Quadtrees and Deep Belief Nets Learning sparse feature representations is a useful instru- ment for solving an...novel framework for the classifi cation of handwritten digits that learns sparse representations using probabilistic quadtrees and Deep Belief Nets... Learning Sparse Feature Representations usingProbabilistic Quadtrees and Deep Belief Nets Report Title Learning sparse feature representations is a useful

Sparse 4D TomoSAR imaging in the presence of non-linear deformation

NASA Astrophysics Data System (ADS)

Khwaja, Ahmed Shaharyar; ćetin, Müjdat

2018-04-01

In this paper, we present a sparse four-dimensional tomographic synthetic aperture radar (4D TomoSAR) imaging scheme that can estimate elevation and linear as well as non-linear seasonal deformation rates of scatterers using the interferometric phase. Unlike existing sparse processing techniques that use fixed dictionaries based on a linear deformation model, we use a variable dictionary for the non-linear deformation in the form of seasonal sinusoidal deformation, in addition to the fixed dictionary for the linear deformation. We estimate the amplitude of the sinusoidal deformation using an optimization method and create the variable dictionary using the estimated amplitude. We show preliminary results using simulated data that demonstrate the soundness of our proposed technique for sparse 4D TomoSAR imaging in the presence of non-linear deformation.

Sequential Designs Based on Bayesian Uncertainty Quantification in Sparse Representation Surrogate Modeling

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

Chen, Ray -Bing; Wang, Weichung; Jeff Wu, C. F.

A numerical method, called OBSM, was recently proposed which employs overcomplete basis functions to achieve sparse representations. While the method can handle non-stationary response without the need of inverting large covariance matrices, it lacks the capability to quantify uncertainty in predictions. We address this issue by proposing a Bayesian approach which first imposes a normal prior on the large space of linear coefficients, then applies the MCMC algorithm to generate posterior samples for predictions. From these samples, Bayesian credible intervals can then be obtained to assess prediction uncertainty. A key application for the proposed method is the efficient construction ofmore » sequential designs. Several sequential design procedures with different infill criteria are proposed based on the generated posterior samples. As a result, numerical studies show that the proposed schemes are capable of solving problems of positive point identification, optimization, and surrogate fitting.« less

Sequential Designs Based on Bayesian Uncertainty Quantification in Sparse Representation Surrogate Modeling

DOE PAGES

Chen, Ray -Bing; Wang, Weichung; Jeff Wu, C. F.

2017-04-12

A numerical method, called OBSM, was recently proposed which employs overcomplete basis functions to achieve sparse representations. While the method can handle non-stationary response without the need of inverting large covariance matrices, it lacks the capability to quantify uncertainty in predictions. We address this issue by proposing a Bayesian approach which first imposes a normal prior on the large space of linear coefficients, then applies the MCMC algorithm to generate posterior samples for predictions. From these samples, Bayesian credible intervals can then be obtained to assess prediction uncertainty. A key application for the proposed method is the efficient construction ofmore » sequential designs. Several sequential design procedures with different infill criteria are proposed based on the generated posterior samples. As a result, numerical studies show that the proposed schemes are capable of solving problems of positive point identification, optimization, and surrogate fitting.« less

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

Discretized energy minimization in a wave guide with point sources

NASA Technical Reports Server (NTRS)

Propst, G.

1994-01-01

An anti-noise problem on a finite time interval is solved by minimization of a quadratic functional on the Hilbert space of square integrable controls. To this end, the one-dimensional wave equation with point sources and pointwise reflecting boundary conditions is decomposed into a system for the two propagating components of waves. Wellposedness of this system is proved for a class of data that includes piecewise linear initial conditions and piecewise constant forcing functions. It is shown that for such data the optimal piecewise constant control is the solution of a sparse linear system. Methods for its computational treatment are presented as well as examples of their applicability. The convergence of discrete approximations to the general optimization problem is demonstrated by finite element methods.

Numerical simulation of heat and mass transfer in unsteady nanofluid between two orthogonally moving porous coaxial disks

NASA Astrophysics Data System (ADS)

Ali, Kashif; Akbar, Muhammad Zubair; Iqbal, Muhammad Farooq; Ashraf, Muhammad

2014-10-01

The paper deals with the study of heat and mass transfer in an unsteady viscous incompressible water-based nanofluid (containing Titanium dioxide nanoparticles) between two orthogonally moving porous coaxial disks with suction. A combination of iterative (successive over relaxation) and a direct method is employed for solving the sparse systems of linear algebraic equations arising from the FD discretization of the linearized self similar ODEs. It has been noticed that the rate of mass transfer at the disks decreases with the permeability Reynolds number whether the disks are approaching or receding. The findings of the present investigation may be beneficial for the electronic industry in maintaining the electronic components under effective and safe operational conditions.

Quantum algorithms for Gibbs sampling and hitting-time estimation

DOE PAGES

Chowdhury, Anirban Narayan; Somma, Rolando D.

2017-02-01

In this paper, we present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in √Nβ/Ζ and polynomial in log(1/ϵ), where N is the Hilbert space dimension, β is the inverse temperature, Ζ is the partition function, and ϵ is the desired precision of the output state. Our quantum algorithm exponentially improves the dependence on 1/ϵ and quadratically improves the dependence on β of known quantum algorithms for this problem. The second algorithm estimates the hitting time of a Markov chain. Formore » a sparse stochastic matrix Ρ, it runs in time almost linear in 1/(ϵΔ 3/2), where ϵ is the absolute precision in the estimation and Δ is a parameter determined by Ρ, and whose inverse is an upper bound of the hitting time. Our quantum algorithm quadratically improves the dependence on 1/ϵ and 1/Δ of the analog classical algorithm for hitting-time estimation. Finally, both algorithms use tools recently developed in the context of Hamiltonian simulation, spectral gap amplification, and solving linear systems of equations.« less

A Multilevel Algorithm for the Solution of Second Order Elliptic Differential Equations on Sparse Grids

NASA Technical Reports Server (NTRS)

Pflaum, Christoph

1996-01-01

A multilevel algorithm is presented that solves general second order elliptic partial differential equations on adaptive sparse grids. The multilevel algorithm consists of several V-cycles. Suitable discretizations provide that the discrete equation system can be solved in an efficient way. Numerical experiments show a convergence rate of order Omicron(1) for the multilevel algorithm.

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.

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

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.

A survey of packages for large linear systems

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

Wu, Kesheng; Milne, Brent

2000-02-11

This paper evaluates portable software packages for the iterative solution of very large sparse linear systems on parallel architectures. While we cannot hope to tell individual users which package will best suit their needs, we do hope that our systematic evaluation provides essential unbiased information about the packages and the evaluation process may serve as an example on how to evaluate these packages. The information contained here include feature comparisons, usability evaluations and performance characterizations. This review is primarily focused on self-contained packages that can be easily integrated into an existing program and are capable of computing solutions to verymore » large sparse linear systems of equations. More specifically, it concentrates on portable parallel linear system solution packages that provide iterative solution schemes and related preconditioning schemes because iterative methods are more frequently used than competing schemes such as direct methods. The eight packages evaluated are: Aztec, BlockSolve,ISIS++, LINSOL, P-SPARSLIB, PARASOL, PETSc, and PINEAPL. Among the eight portable parallel iterative linear system solvers reviewed, we recommend PETSc and Aztec for most application programmers because they have well designed user interface, extensive documentation and very responsive user support. Both PETSc and Aztec are written in the C language and are callable from Fortran. For those users interested in using Fortran 90, PARASOL is a good alternative. ISIS++is a good alternative for those who prefer the C++ language. Both PARASOL and ISIS++ are relatively new and are continuously evolving. Thus their user interface may change. In general, those packages written in Fortran 77 are more cumbersome to use because the user may need to directly deal with a number of arrays of varying sizes. Languages like C++ and Fortran 90 offer more convenient data encapsulation mechanisms which make it easier to implement a clean and intuitive user interface. In addition to reviewing these portable parallel iterative solver packages, we also provide a more cursory assessment of a range of related packages, from specialized parallel preconditioners to direct methods for sparse linear systems.« less

A Sparse Reconstruction Approach for Identifying Gene Regulatory Networks Using Steady-State Experiment Data

PubMed Central

Zhang, Wanhong; Zhou, Tong

2015-01-01

Motivation Identifying gene regulatory networks (GRNs) which consist of a large number of interacting units has become a problem of paramount importance in systems biology. Situations exist extensively in which causal interacting relationships among these units are required to be reconstructed from measured expression data and other a priori information. Though numerous classical methods have been developed to unravel the interactions of GRNs, these methods either have higher computing complexities or have lower estimation accuracies. Note that great similarities exist between identification of genes that directly regulate a specific gene and a sparse vector reconstruction, which often relates to the determination of the number, location and magnitude of nonzero entries of an unknown vector by solving an underdetermined system of linear equations y = Φx. Based on these similarities, we propose a novel framework of sparse reconstruction to identify the structure of a GRN, so as to increase accuracy of causal regulation estimations, as well as to reduce their computational complexity. Results In this paper, a sparse reconstruction framework is proposed on basis of steady-state experiment data to identify GRN structure. Different from traditional methods, this approach is adopted which is well suitable for a large-scale underdetermined problem in inferring a sparse vector. We investigate how to combine the noisy steady-state experiment data and a sparse reconstruction algorithm to identify causal relationships. Efficiency of this method is tested by an artificial linear network, a mitogen-activated protein kinase (MAPK) pathway network and the in silico networks of the DREAM challenges. The performance of the suggested approach is compared with two state-of-the-art algorithms, the widely adopted total least-squares (TLS) method and those available results on the DREAM project. Actual results show that, with a lower computational cost, the proposed method can significantly enhance estimation accuracy and greatly reduce false positive and negative errors. Furthermore, numerical calculations demonstrate that the proposed algorithm may have faster convergence speed and smaller fluctuation than other methods when either estimate error or estimate bias is considered. PMID:26207991

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

An Optimized Multicolor Point-Implicit Solver for Unstructured Grid Applications on Graphics Processing Units

NASA Technical Reports Server (NTRS)

Zubair, Mohammad; Nielsen, Eric; Luitjens, Justin; Hammond, Dana

2016-01-01

In the field of computational fluid dynamics, the Navier-Stokes equations are often solved using an unstructuredgrid approach to accommodate geometric complexity. Implicit solution methodologies for such spatial discretizations generally require frequent solution of large tightly-coupled systems of block-sparse linear equations. The multicolor point-implicit solver used in the current work typically requires a significant fraction of the overall application run time. In this work, an efficient implementation of the solver for graphics processing units is proposed. Several factors present unique challenges to achieving an efficient implementation in this environment. These include the variable amount of parallelism available in different kernel calls, indirect memory access patterns, low arithmetic intensity, and the requirement to support variable block sizes. In this work, the solver is reformulated to use standard sparse and dense Basic Linear Algebra Subprograms (BLAS) functions. However, numerical experiments show that the performance of the BLAS functions available in existing CUDA libraries is suboptimal for matrices representative of those encountered in actual simulations. Instead, optimized versions of these functions are developed. Depending on block size, the new implementations show performance gains of up to 7x over the existing CUDA library functions.

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.

Analog "neuronal" networks in early vision.

PubMed Central

Koch, C; Marroquin, J; Yuille, A

1986-01-01

Many problems in early vision can be formulated in terms of minimizing a cost function. Examples are shape from shading, edge detection, motion analysis, structure from motion, and surface interpolation. As shown by Poggio and Koch [Poggio, T. & Koch, C. (1985) Proc. R. Soc. London, Ser. B 226, 303-323], quadratic variational problems, an important subset of early vision tasks, can be "solved" by linear, analog electrical, or chemical networks. However, in the presence of discontinuities, the cost function is nonquadratic, raising the question of designing efficient algorithms for computing the optimal solution. Recently, Hopfield and Tank [Hopfield, J. J. & Tank, D. W. (1985) Biol. Cybern. 52, 141-152] have shown that networks of nonlinear analog "neurons" can be effective in computing the solution of optimization problems. We show how these networks can be generalized to solve the nonconvex energy functionals of early vision. We illustrate this approach by implementing a specific analog network, solving the problem of reconstructing a smooth surface from sparse data while preserving its discontinuities. These results suggest a novel computational strategy for solving early vision problems in both biological and real-time artificial vision systems. PMID:3459172

Group Sparse Optimization by Alternating Direction Method

DTIC Science & Technology

2012-11-22

to solving the following linear system: (β1G TG+ β2A TA)x = β1G T z −GTλ1 + β2AT b+ATλ2. (3.5) Note that GTG ∈ Rn×n is a diagonal matrix whose i-th...diagonal entry is the number of repetitions of xi in x̃. When the groups form an complete cover of the solution, the diagonal entries of GTG will be...positive, so GTG is invertible. In the next subsection, we will show that an incomplete cover case can be converted to a complete cover case by

Using dynamic mode decomposition for real-time background/foreground separation in video

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

Kutz, Jose Nathan; Grosek, Jacob; Brunton, Steven

The technique of dynamic mode decomposition (DMD) is disclosed herein for the purpose of robustly separating video frames into background (low-rank) and foreground (sparse) components in real-time. Foreground/background separation is achieved at the computational cost of just one singular value decomposition (SVD) and one linear equation solve, thus producing results orders of magnitude faster than robust principal component analysis (RPCA). Additional techniques, including techniques for analyzing the video for multi-resolution time-scale components, and techniques for reusing computations to allow processing of streaming video in real time, are also described herein.

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

Application of Fast Multipole Methods to the NASA Fast Scattering Code

NASA Technical Reports Server (NTRS)

Dunn, Mark H.; Tinetti, Ana F.

2008-01-01

The NASA Fast Scattering Code (FSC) is a versatile noise prediction program designed to conduct aeroacoustic noise reduction studies. The equivalent source method is used to solve an exterior Helmholtz boundary value problem with an impedance type boundary condition. The solution process in FSC v2.0 requires direct manipulation of a large, dense system of linear equations, limiting the applicability of the code to small scales and/or moderate excitation frequencies. Recent advances in the use of Fast Multipole Methods (FMM) for solving scattering problems, coupled with sparse linear algebra techniques, suggest that a substantial reduction in computer resource utilization over conventional solution approaches can be obtained. Implementation of the single level FMM (SLFMM) and a variant of the Conjugate Gradient Method (CGM) into the FSC is discussed in this paper. The culmination of this effort, FSC v3.0, was used to generate solutions for three configurations of interest. Benchmarking against previously obtained simulations indicate that a twenty-fold reduction in computational memory and up to a four-fold reduction in computer time have been achieved on a single processor.

Learning to read aloud: A neural network approach using sparse distributed memory

NASA Technical Reports Server (NTRS)

Joglekar, Umesh Dwarkanath

1989-01-01

An attempt to solve a problem of text-to-phoneme mapping is described which does not appear amenable to solution by use of standard algorithmic procedures. Experiments based on a model of distributed processing are also described. This model (sparse distributed memory (SDM)) can be used in an iterative supervised learning mode to solve the problem. Additional improvements aimed at obtaining better performance are suggested.

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).

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.

Solving Constraint-Satisfaction Problems with Distributed Neocortical-Like Neuronal Networks.

PubMed

Rutishauser, Ueli; Slotine, Jean-Jacques; Douglas, Rodney J

2018-05-01

Finding actions that satisfy the constraints imposed by both external inputs and internal representations is central to decision making. We demonstrate that some important classes of constraint satisfaction problems (CSPs) can be solved by networks composed of homogeneous cooperative-competitive modules that have connectivity similar to motifs observed in the superficial layers of neocortex. The winner-take-all modules are sparsely coupled by programming neurons that embed the constraints onto the otherwise homogeneous modular computational substrate. We show rules that embed any instance of the CSP's planar four-color graph coloring, maximum independent set, and sudoku on this substrate and provide mathematical proofs that guarantee these graph coloring problems will convergence to a solution. The network is composed of nonsaturating linear threshold neurons. Their lack of right saturation allows the overall network to explore the problem space driven through the unstable dynamics generated by recurrent excitation. The direction of exploration is steered by the constraint neurons. While many problems can be solved using only linear inhibitory constraints, network performance on hard problems benefits significantly when these negative constraints are implemented by nonlinear multiplicative inhibition. Overall, our results demonstrate the importance of instability rather than stability in network computation and offer insight into the computational role of dual inhibitory mechanisms in neural circuits.

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.

An Efficient Scheme for Updating Sparse Cholesky Factors

NASA Technical Reports Server (NTRS)

Raghavan, Padma

2002-01-01

Raghavan had earlier developed the software package DCSPACK which can be used for solving sparse linear systems where the coefficient matrix is symmetric and positive definite (this project was not funded by NASA but by agencies such as NSF). DSCPACK-S is the serial code and DSCPACK-P is a parallel implementation suitable for multiprocessors or networks-of-workstations with message passing using MCI. The main algorithm used is the Cholesky factorization of a sparse symmetric positive positive definite matrix A = LL(T). The code can also compute the factorization A = LDL(T). The complexity of the software arises from several factors relating to the sparsity of the matrix A. A sparse N x N matrix A has typically less that cN nonzeroes where c is a small constant. If the matrix were dense, it would have O(N2) nonzeroes. The most complicated part of such sparse Cholesky factorization relates to fill-in, i.e., zeroes in the original matrix that become nonzeroes in the factor L. An efficient implementation depends to a large extent on complex data structures and on techniques from graph theory to reduce, identify, and manage fill. DSCPACK is based on an efficient multifrontal implementation with fill-managing algorithms and implementation arising from earlier research by Raghavan and others. Sparse Cholesky factorization is typically a four step process: (1) ordering to compute a fill-reducing numbering, (2) symbolic factorization to determine the nonzero structure of L, (3) numeric factorization to compute L, and, (4) triangular solution to solve L(T)x = y and Ly = b. The first two steps are symbolic and are performed using the graph of the matrix. The numeric factorization step is of dominant cost and there are several schemes for improving performance by exploiting the nested and dense structure of groups of columns in the factor. The latter are aimed at better utilization of the cache-memory hierarchy on modem processors to prevent cache-misses and provide execution rates (operations/second) that are close to the peak rates for dense matrix computations. Currently, EPISCOPACY is being used in an application at NASA directed by J. Newman and M. James. We propose the implementation of efficient schemes for updating the LL(T) or LDL(T) factors computed in DSCPACK-S to meet the computational requirements of their project. A brief description is provided in the next section.

An incremental strategy for calculating consistent discrete CFD sensitivity derivatives

NASA Technical Reports Server (NTRS)

Korivi, Vamshi Mohan; Taylor, Arthur C., III; Newman, Perry A.; Hou, Gene W.; Jones, Henry E.

1992-01-01

In this preliminary study involving advanced computational fluid dynamic (CFD) codes, an incremental formulation, also known as the 'delta' or 'correction' form, is presented for solving the very large sparse systems of linear equations which are associated with aerodynamic sensitivity analysis. For typical problems in 2D, a direct solution method can be applied to these linear equations which are associated with aerodynamic sensitivity analysis. For typical problems in 2D, a direct solution method can be applied to these linear equations in either the standard or the incremental form, in which case the two are equivalent. Iterative methods appear to be needed for future 3D applications; however, because direct solver methods require much more computer memory than is currently available. Iterative methods for solving these equations in the standard form result in certain difficulties, such as ill-conditioning of the coefficient matrix, which can be overcome when these equations are cast in the incremental form; these and other benefits are discussed. The methodology is successfully implemented and tested in 2D using an upwind, cell-centered, finite volume formulation applied to the thin-layer Navier-Stokes equations. Results are presented for two laminar sample problems: (1) transonic flow through a double-throat nozzle; and (2) flow over an isolated airfoil.

Improving the Performance of Temperature Index Snowmelt Model of SWAT by Using MODIS Land Surface Temperature Data

PubMed Central

Yang, Yan; Onishi, Takeo; Hiramatsu, Ken

2014-01-01

Simulation results of the widely used temperature index snowmelt model are greatly influenced by input air temperature data. Spatially sparse air temperature data remain the main factor inducing uncertainties and errors in that model, which limits its applications. Thus, to solve this problem, we created new air temperature data using linear regression relationships that can be formulated based on MODIS land surface temperature data. The Soil Water Assessment Tool model, which includes an improved temperature index snowmelt module, was chosen to test the newly created data. By evaluating simulation performance for daily snowmelt in three test basins of the Amur River, performance of the newly created data was assessed. The coefficient of determination (R 2) and Nash-Sutcliffe efficiency (NSE) were used for evaluation. The results indicate that MODIS land surface temperature data can be used as a new source for air temperature data creation. This will improve snow simulation using the temperature index model in an area with sparse air temperature observations. PMID:25165746

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.

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.

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

TH-AB-202-08: A Robust Real-Time Surface Reconstruction Method On Point Clouds Captured From a 3D Surface Photogrammetry System

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

Liu, W; Sawant, A; Ruan, D

2016-06-15

Purpose: Surface photogrammetry (e.g. VisionRT, C-Rad) provides a noninvasive way to obtain high-frequency measurement for patient motion monitoring in radiotherapy. This work aims to develop a real-time surface reconstruction method on the acquired point clouds, whose acquisitions are subject to noise and missing measurements. In contrast to existing surface reconstruction methods that are usually computationally expensive, the proposed method reconstructs continuous surfaces with comparable accuracy in real-time. Methods: The key idea in our method is to solve and propagate a sparse linear relationship from the point cloud (measurement) manifold to the surface (reconstruction) manifold, taking advantage of the similarity inmore » local geometric topology in both manifolds. With consistent point cloud acquisition, we propose a sparse regression (SR) model to directly approximate the target point cloud as a sparse linear combination from the training set, building the point correspondences by the iterative closest point (ICP) method. To accommodate changing noise levels and/or presence of inconsistent occlusions, we further propose a modified sparse regression (MSR) model to account for the large and sparse error built by ICP, with a Laplacian prior. We evaluated our method on both clinical acquired point clouds under consistent conditions and simulated point clouds with inconsistent occlusions. The reconstruction accuracy was evaluated w.r.t. root-mean-squared-error, by comparing the reconstructed surfaces against those from the variational reconstruction method. Results: On clinical point clouds, both the SR and MSR models achieved sub-millimeter accuracy, with mean reconstruction time reduced from 82.23 seconds to 0.52 seconds and 0.94 seconds, respectively. On simulated point cloud with inconsistent occlusions, the MSR model has demonstrated its advantage in achieving consistent performance despite the introduced occlusions. Conclusion: We have developed a real-time and robust surface reconstruction method on point clouds acquired by photogrammetry systems. It serves an important enabling step for real-time motion tracking in radiotherapy. This work is supported in part by NIH grant R01 CA169102-02.« less

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.

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.

Sparse matrix multiplications for linear scaling electronic structure calculations in an atom-centered basis set using multiatom blocks.

PubMed

Saravanan, Chandra; Shao, Yihan; Baer, Roi; Ross, Philip N; Head-Gordon, Martin

2003-04-15

A sparse matrix multiplication scheme with multiatom blocks is reported, a tool that can be very useful for developing linear-scaling methods with atom-centered basis functions. Compared to conventional element-by-element sparse matrix multiplication schemes, efficiency is gained by the use of the highly optimized basic linear algebra subroutines (BLAS). However, some sparsity is lost in the multiatom blocking scheme because these matrix blocks will in general contain negligible elements. As a result, an optimal block size that minimizes the CPU time by balancing these two effects is recovered. In calculations on linear alkanes, polyglycines, estane polymers, and water clusters the optimal block size is found to be between 40 and 100 basis functions, where about 55-75% of the machine peak performance was achieved on an IBM RS6000 workstation. In these calculations, the blocked sparse matrix multiplications can be 10 times faster than a standard element-by-element sparse matrix package. Copyright 2003 Wiley Periodicals, Inc. J Comput Chem 24: 618-622, 2003

Implicit solvers for unstructured meshes

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.; Mavriplis, Dimitri J.

1991-01-01

Implicit methods for unstructured mesh computations are developed and tested. The approximate system which arises from the Newton-linearization of the nonlinear evolution operator is solved by using the preconditioned generalized minimum residual technique. These different preconditioners are investigated: the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over-relaxation (SSOR). The preconditioners have been optimized to have good vectorization properties. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also investigated. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

Image restoration by minimizing zero norm of wavelet frame coefficients

NASA Astrophysics Data System (ADS)

Bao, Chenglong; Dong, Bin; Hou, Likun; Shen, Zuowei; Zhang, Xiaoqun; Zhang, Xue

2016-11-01

In this paper, we propose two algorithms, namely the extrapolated proximal iterative hard thresholding (EPIHT) algorithm and the EPIHT algorithm with line-search, for solving the {{\\ell }}0-norm regularized wavelet frame balanced approach for image restoration. Under the theoretical framework of Kurdyka-Łojasiewicz property, we show that the sequences generated by the two algorithms converge to a local minimizer with linear convergence rate. Moreover, extensive numerical experiments on sparse signal reconstruction and wavelet frame based image restoration problems including CT reconstruction, image deblur, demonstrate the improvement of {{\\ell }}0-norm based regularization models over some prevailing ones, as well as the computational efficiency of the proposed algorithms.

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.

Discriminant WSRC for Large-Scale Plant Species Recognition.

PubMed

Zhang, Shanwen; Zhang, Chuanlei; Zhu, Yihai; You, Zhuhong

2017-01-01

In sparse representation based classification (SRC) and weighted SRC (WSRC), it is time-consuming to solve the global sparse representation problem. A discriminant WSRC (DWSRC) is proposed for large-scale plant species recognition, including two stages. Firstly, several subdictionaries are constructed by dividing the dataset into several similar classes, and a subdictionary is chosen by the maximum similarity between the test sample and the typical sample of each similar class. Secondly, the weighted sparse representation of the test image is calculated with respect to the chosen subdictionary, and then the leaf category is assigned through the minimum reconstruction error. Different from the traditional SRC and its improved approaches, we sparsely represent the test sample on a subdictionary whose base elements are the training samples of the selected similar class, instead of using the generic overcomplete dictionary on the entire training samples. Thus, the complexity to solving the sparse representation problem is reduced. Moreover, DWSRC is adapted to newly added leaf species without rebuilding the dictionary. Experimental results on the ICL plant leaf database show that the method has low computational complexity and high recognition rate and can be clearly interpreted.

Methodology for Sensitivity Analysis, Approximate Analysis, and Design Optimization in CFD for Multidisciplinary Applications

NASA Technical Reports Server (NTRS)

Taylor, Arthur C., III; Hou, Gene W.

1996-01-01

An incremental iterative formulation together with the well-known spatially split approximate-factorization algorithm, is presented for solving the large, sparse systems of linear equations that are associated with aerodynamic sensitivity analysis. This formulation is also known as the 'delta' or 'correction' form. For the smaller two dimensional problems, a direct method can be applied to solve these linear equations in either the standard or the incremental form, in which case the two are equivalent. However, iterative methods are needed for larger two-dimensional and three dimensional applications because direct methods require more computer memory than is currently available. Iterative methods for solving these equations in the standard form are generally unsatisfactory due to an ill-conditioned coefficient matrix; this problem is overcome when these equations are cast in the incremental form. The methodology is successfully implemented and tested using an upwind cell-centered finite-volume formulation applied in two dimensions to the thin-layer Navier-Stokes equations for external flow over an airfoil. In three dimensions this methodology is demonstrated with a marching-solution algorithm for the Euler equations to calculate supersonic flow over the High-Speed Civil Transport configuration (HSCT 24E). The sensitivity derivatives obtained with the incremental iterative method from a marching Euler code are used in a design-improvement study of the HSCT configuration that involves thickness. camber, and planform design variables.

Configurable hardware integrate and fire neurons for sparse approximation.

PubMed

Shapero, Samuel; Rozell, Christopher; Hasler, Paul

2013-09-01

Sparse approximation is an important optimization problem in signal and image processing applications. A Hopfield-Network-like system of integrate and fire (IF) neurons is proposed as a solution, using the Locally Competitive Algorithm (LCA) to solve an overcomplete L1 sparse approximation problem. A scalable system architecture is described, including IF neurons with a nonlinear firing function, and current-based synapses to provide linear computation. A network of 18 neurons with 12 inputs is implemented on the RASP 2.9v chip, a Field Programmable Analog Array (FPAA) with directly programmable floating gate elements. Said system uses over 1400 floating gates, the largest system programmed on a FPAA to date. The circuit successfully reproduced the outputs of a digital optimization program, converging to within 4.8% RMS, and an objective cost only 1.7% higher on average. The active circuit consumed 559 μA of current at 2.4 V and converges on solutions in 25 μs, with measurement of the converged spike rate taking an additional 1 ms. Extrapolating the scaling trends to a N=1000 node system, the spiking LCA compares favorably with state-of-the-art digital solutions, and analog solutions using a non-spiking approach. Copyright © 2013 Elsevier Ltd. All rights reserved.

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.

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.

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.

Multi-frame linear regressive filter for the measurement of infrared pixel spatial response and MTF from sparse data.

PubMed

Huard, Edouard; Derelle, Sophie; Jaeck, Julien; Nghiem, Jean; Haïdar, Riad; Primot, Jérôme

2018-03-05

A challenging point in the prediction of the image quality of infrared imaging systems is the evaluation of the detector modulation transfer function (MTF). In this paper, we present a linear method to get a 2D continuous MTF from sparse spectral data. Within the method, an object with a predictable sparse spatial spectrum is imaged by the focal plane array. The sparse data is then treated to return the 2D continuous MTF with the hypothesis that all the pixels have an identical spatial response. The linearity of the treatment is a key point to estimate directly the error bars of the resulting detector MTF. The test bench will be presented along with measurement tests on a 25 μm pitch InGaAs detector.

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

LANZ: Software solving the large sparse symmetric generalized eigenproblem

NASA Technical Reports Server (NTRS)

Jones, Mark T.; Patrick, Merrell L.

1990-01-01

A package, LANZ, for solving the large symmetric generalized eigenproblem is described. The package was tested on four different architectures: Convex 200, CRAY Y-MP, Sun-3, and Sun-4. The package uses a Lanczos' method and is based on recent research into solving the generalized eigenproblem.

An adaptive sparse deconvolution method for distinguishing the overlapping echoes of ultrasonic guided waves for pipeline crack inspection

NASA Astrophysics Data System (ADS)

Chang, Yong; Zi, Yanyang; Zhao, Jiyuan; Yang, Zhe; He, Wangpeng; Sun, Hailiang

2017-03-01

In guided wave pipeline inspection, echoes reflected from closely spaced reflectors generally overlap, meaning useful information is lost. To solve the overlapping problem, sparse deconvolution methods have been developed in the past decade. However, conventional sparse deconvolution methods have limitations in handling guided wave signals, because the input signal is directly used as the prototype of the convolution matrix, without considering the waveform change caused by the dispersion properties of the guided wave. In this paper, an adaptive sparse deconvolution (ASD) method is proposed to overcome these limitations. First, the Gaussian echo model is employed to adaptively estimate the column prototype of the convolution matrix instead of directly using the input signal as the prototype. Then, the convolution matrix is constructed upon the estimated results. Third, the split augmented Lagrangian shrinkage (SALSA) algorithm is introduced to solve the deconvolution problem with high computational efficiency. To verify the effectiveness of the proposed method, guided wave signals obtained from pipeline inspection are investigated numerically and experimentally. Compared to conventional sparse deconvolution methods, e.g. the {{l}1} -norm deconvolution method, the proposed method shows better performance in handling the echo overlap problem in the guided wave signal.

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.

A Two-Layer Least Squares Support Vector Machine Approach to Credit Risk Assessment

NASA Astrophysics Data System (ADS)

Liu, Jingli; Li, Jianping; Xu, Weixuan; Shi, Yong

Least squares support vector machine (LS-SVM) is a revised version of support vector machine (SVM) and has been proved to be a useful tool for pattern recognition. LS-SVM had excellent generalization performance and low computational cost. In this paper, we propose a new method called two-layer least squares support vector machine which combines kernel principle component analysis (KPCA) and linear programming form of least square support vector machine. With this method sparseness and robustness is obtained while solving large dimensional and large scale database. A U.S. commercial credit card database is used to test the efficiency of our method and the result proved to be a satisfactory one.

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.

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.

Three-Dimensional Inverse Transport Solver Based on Compressive Sensing Technique

NASA Astrophysics Data System (ADS)

Cheng, Yuxiong; Wu, Hongchun; Cao, Liangzhi; Zheng, Youqi

2013-09-01

According to the direct exposure measurements from flash radiographic image, a compressive sensing-based method for three-dimensional inverse transport problem is presented. The linear absorption coefficients and interface locations of objects are reconstructed directly at the same time. It is always very expensive to obtain enough measurements. With limited measurements, compressive sensing sparse reconstruction technique orthogonal matching pursuit is applied to obtain the sparse coefficients by solving an optimization problem. A three-dimensional inverse transport solver is developed based on a compressive sensing-based technique. There are three features in this solver: (1) AutoCAD is employed as a geometry preprocessor due to its powerful capacity in graphic. (2) The forward projection matrix rather than Gauss matrix is constructed by the visualization tool generator. (3) Fourier transform and Daubechies wavelet transform are adopted to convert an underdetermined system to a well-posed system in the algorithm. Simulations are performed and numerical results in pseudo-sine absorption problem, two-cube problem and two-cylinder problem when using compressive sensing-based solver agree well with the reference value.

Signal-Preserving Erratic Noise Attenuation via Iterative Robust Sparsity-Promoting Filter

DOE PAGES

Zhao, Qiang; Du, Qizhen; Gong, Xufei; ...

2018-04-06

Sparse domain thresholding filters operating in a sparse domain are highly effective in removing Gaussian random noise under Gaussian distribution assumption. Erratic noise, which designates non-Gaussian noise that consists of large isolated events with known or unknown distribution, also needs to be explicitly taken into account. However, conventional sparse domain thresholding filters based on the least-squares (LS) criterion are severely sensitive to data with high-amplitude and non-Gaussian noise, i.e., the erratic noise, which makes the suppression of this type of noise extremely challenging. Here, in this paper, we present a robust sparsity-promoting denoising model, in which the LS criterion ismore » replaced by the Huber criterion to weaken the effects of erratic noise. The random and erratic noise is distinguished by using a data-adaptive parameter in the presented method, where random noise is described by mean square, while the erratic noise is downweighted through a damped weight. Different from conventional sparse domain thresholding filters, definition of the misfit between noisy data and recovered signal via the Huber criterion results in a nonlinear optimization problem. With the help of theoretical pseudoseismic data, an iterative robust sparsity-promoting filter is proposed to transform the nonlinear optimization problem into a linear LS problem through an iterative procedure. The main advantage of this transformation is that the nonlinear denoising filter can be solved by conventional LS solvers. Lastly, tests with several data sets demonstrate that the proposed denoising filter can successfully attenuate the erratic noise without damaging useful signal when compared with conventional denoising approaches based on the LS criterion.« less

Signal-Preserving Erratic Noise Attenuation via Iterative Robust Sparsity-Promoting Filter

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

Zhao, Qiang; Du, Qizhen; Gong, Xufei

Sparse domain thresholding filters operating in a sparse domain are highly effective in removing Gaussian random noise under Gaussian distribution assumption. Erratic noise, which designates non-Gaussian noise that consists of large isolated events with known or unknown distribution, also needs to be explicitly taken into account. However, conventional sparse domain thresholding filters based on the least-squares (LS) criterion are severely sensitive to data with high-amplitude and non-Gaussian noise, i.e., the erratic noise, which makes the suppression of this type of noise extremely challenging. Here, in this paper, we present a robust sparsity-promoting denoising model, in which the LS criterion ismore » replaced by the Huber criterion to weaken the effects of erratic noise. The random and erratic noise is distinguished by using a data-adaptive parameter in the presented method, where random noise is described by mean square, while the erratic noise is downweighted through a damped weight. Different from conventional sparse domain thresholding filters, definition of the misfit between noisy data and recovered signal via the Huber criterion results in a nonlinear optimization problem. With the help of theoretical pseudoseismic data, an iterative robust sparsity-promoting filter is proposed to transform the nonlinear optimization problem into a linear LS problem through an iterative procedure. The main advantage of this transformation is that the nonlinear denoising filter can be solved by conventional LS solvers. Lastly, tests with several data sets demonstrate that the proposed denoising filter can successfully attenuate the erratic noise without damaging useful signal when compared with conventional denoising approaches based on the LS criterion.« 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

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.

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.

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

A compressed sensing based 3D resistivity inversion algorithm for hydrogeological applications

NASA Astrophysics Data System (ADS)

Ranjan, Shashi; Kambhammettu, B. V. N. P.; Peddinti, Srinivasa Rao; Adinarayana, J.

2018-04-01

Image reconstruction from discrete electrical responses pose a number of computational and mathematical challenges. Application of smoothness constrained regularized inversion from limited measurements may fail to detect resistivity anomalies and sharp interfaces separated by hydro stratigraphic units. Under favourable conditions, compressed sensing (CS) can be thought of an alternative to reconstruct the image features by finding sparse solutions to highly underdetermined linear systems. This paper deals with the development of a CS assisted, 3-D resistivity inversion algorithm for use with hydrogeologists and groundwater scientists. CS based l1-regularized least square algorithm was applied to solve the resistivity inversion problem. Sparseness in the model update vector is introduced through block oriented discrete cosine transformation, with recovery of the signal achieved through convex optimization. The equivalent quadratic program was solved using primal-dual interior point method. Applicability of the proposed algorithm was demonstrated using synthetic and field examples drawn from hydrogeology. The proposed algorithm has outperformed the conventional (smoothness constrained) least square method in recovering the model parameters with much fewer data, yet preserving the sharp resistivity fronts separated by geologic layers. Resistivity anomalies represented by discrete homogeneous blocks embedded in contrasting geologic layers were better imaged using the proposed algorithm. In comparison to conventional algorithm, CS has resulted in an efficient (an increase in R2 from 0.62 to 0.78; a decrease in RMSE from 125.14 Ω-m to 72.46 Ω-m), reliable, and fast converging (run time decreased by about 25%) solution.

Load identification approach based on basis pursuit denoising algorithm

NASA Astrophysics Data System (ADS)

Ginsberg, D.; Ruby, M.; Fritzen, C. P.

2015-07-01

The information of the external loads is of great interest in many fields of structural analysis, such as structural health monitoring (SHM) systems or assessment of damage after extreme events. However, in most cases it is not possible to measure the external forces directly, so they need to be reconstructed. Load reconstruction refers to the problem of estimating an input to a dynamic system when the system output and the impulse response functions are usually the knowns. Generally, this leads to a so called ill-posed inverse problem, which involves solving an underdetermined linear system of equations. For most practical applications it can be assumed that the applied loads are not arbitrarily distributed in time and space, at least some specific characteristics about the external excitation are known a priori. In this contribution this knowledge was used to develop a more suitable force reconstruction method, which allows identifying the time history and the force location simultaneously by employing significantly fewer sensors compared to other reconstruction approaches. The properties of the external force are used to transform the ill-posed problem into a sparse recovery task. The sparse solution is acquired by solving a minimization problem known as basis pursuit denoising (BPDN). The possibility of reconstructing loads based on noisy structural measurement signals will be demonstrated by considering two frequently occurring loading conditions: harmonic excitation and impact events, separately and combined. First a simulation study of a simple plate structure is carried out and thereafter an experimental investigation of a real beam is performed.

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.

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.

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.

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.

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.

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.

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).

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.

Exhaustive Search for Sparse Variable Selection in Linear Regression

NASA Astrophysics Data System (ADS)

Igarashi, Yasuhiko; Takenaka, Hikaru; Nakanishi-Ohno, Yoshinori; Uemura, Makoto; Ikeda, Shiro; Okada, Masato

2018-04-01

We propose a K-sparse exhaustive search (ES-K) method and a K-sparse approximate exhaustive search method (AES-K) for selecting variables in linear regression. With these methods, K-sparse combinations of variables are tested exhaustively assuming that the optimal combination of explanatory variables is K-sparse. By collecting the results of exhaustively computing ES-K, various approximate methods for selecting sparse variables can be summarized as density of states. With this density of states, we can compare different methods for selecting sparse variables such as relaxation and sampling. For large problems where the combinatorial explosion of explanatory variables is crucial, the AES-K method enables density of states to be effectively reconstructed by using the replica-exchange Monte Carlo method and the multiple histogram method. Applying the ES-K and AES-K methods to type Ia supernova data, we confirmed the conventional understanding in astronomy when an appropriate K is given beforehand. However, we found the difficulty to determine K from the data. Using virtual measurement and analysis, we argue that this is caused by data shortage.

A meshless approach to thermomechanics of DC casting of aluminium billets

NASA Astrophysics Data System (ADS)

Mavrič, B.; Šarler, B.

2016-03-01

The ability to model thermomechanics in DC casting is important due to the technological challenges caused by physical phenomena such as different ingot distortions, cracking, hot tearing and residual stress. Many thermomechanical models already exist and usually take into account three contributions: elastic, thermal expansion, and viscoplastic to model the mushy zone. These models are, in a vast majority, solved by the finite element method. In the present work the elastic model that accounts for linear thermal expansion is considered. The method used for solving the model is of a novel meshless type and extends our previous meshless attempts in solving fluid mechanics problems. The solution to the problem is constructed using collocation on the overlapping subdomains, which are composed of computational nodes. Multiquadric radial basis functions, augmented by monomials, are used for the displacement interpolation. The interpolation is constructed in such a manner that it readily satisfies the boundary conditions. The discretization results in construction of a global square sparse matrix representing the system of linear equations for the displacement field. The developed method has many advantages. The system of equations can be easily constructed and efficiently solved. There is no need to perform expensive meshing of the domain and the formulation of the method is similar in two and three dimensions. Since no meshing is required, the nodes can easily be added or removed, which allows for efficient adaption of the node arrangement density. The order of convergence, estimated through an analytically solvable test, can be adjusted through the number of interpolation nodes in the subdomain, with 6 nodes being enough for the second order convergence. Simulations of axisymmetric mechanical problems, associated with low frequency electromagnetic DC casting are presented.

Reducing computational costs in large scale 3D EIT by using a sparse Jacobian matrix with block-wise CGLS reconstruction.

PubMed

Yang, C L; Wei, H Y; Adler, A; Soleimani, M

2013-06-01

Electrical impedance tomography (EIT) is a fast and cost-effective technique to provide a tomographic conductivity image of a subject from boundary current-voltage data. This paper proposes a time and memory efficient method for solving a large scale 3D EIT inverse problem using a parallel conjugate gradient (CG) algorithm. The 3D EIT system with a large number of measurement data can produce a large size of Jacobian matrix; this could cause difficulties in computer storage and the inversion process. One of challenges in 3D EIT is to decrease the reconstruction time and memory usage, at the same time retaining the image quality. Firstly, a sparse matrix reduction technique is proposed using thresholding to set very small values of the Jacobian matrix to zero. By adjusting the Jacobian matrix into a sparse format, the element with zeros would be eliminated, which results in a saving of memory requirement. Secondly, a block-wise CG method for parallel reconstruction has been developed. The proposed method has been tested using simulated data as well as experimental test samples. Sparse Jacobian with a block-wise CG enables the large scale EIT problem to be solved efficiently. Image quality measures are presented to quantify the effect of sparse matrix reduction in reconstruction results.

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.

Full Wave Parallel Code for Modeling RF Fields in Hot Plasmas

NASA Astrophysics Data System (ADS)

Spencer, Joseph; Svidzinski, Vladimir; Evstatiev, Evstati; Galkin, Sergei; Kim, Jin-Soo

2015-11-01

FAR-TECH, Inc. is developing a suite of full wave RF codes in hot plasmas. It is based on a formulation in configuration space with grid adaptation capability. The conductivity kernel (which includes a nonlocal dielectric response) is calculated by integrating the linearized Vlasov equation along unperturbed test particle orbits. For Tokamak applications a 2-D version of the code is being developed. Progress of this work will be reported. This suite of codes has the following advantages over existing spectral codes: 1) It utilizes the localized nature of plasma dielectric response to the RF field and calculates this response numerically without approximations. 2) It uses an adaptive grid to better resolve resonances in plasma and antenna structures. 3) It uses an efficient sparse matrix solver to solve the formulated linear equations. The linear wave equation is formulated using two approaches: for cold plasmas the local cold plasma dielectric tensor is used (resolving resonances by particle collisions), while for hot plasmas the conductivity kernel is calculated. Work is supported by the U.S. DOE SBIR program.

High-SNR spectrum measurement based on Hadamard encoding and sparse reconstruction

NASA Astrophysics Data System (ADS)

Wang, Zhaoxin; Yue, Jiang; Han, Jing; Li, Long; Jin, Yong; Gao, Yuan; Li, Baoming

2017-12-01

The denoising capabilities of the H-matrix and cyclic S-matrix based on the sparse reconstruction, employed in the Pixel of Focal Plane Coded Visible Spectrometer for spectrum measurement are investigated, where the spectrum is sparse in a known basis. In the measurement process, the digital micromirror device plays an important role, which implements the Hadamard coding. In contrast with Hadamard transform spectrometry, based on the shift invariability, this spectrometer may have the advantage of a high efficiency. Simulations and experiments show that the nonlinear solution with a sparse reconstruction has a better signal-to-noise ratio than the linear solution and the H-matrix outperforms the cyclic S-matrix whether the reconstruction method is nonlinear or linear.

Algebraic multigrid preconditioners for two-phase flow in porous media with phase transitions

NASA Astrophysics Data System (ADS)

Bui, Quan M.; Wang, Lu; Osei-Kuffuor, Daniel

2018-04-01

Multiphase flow is a critical process in a wide range of applications, including oil and gas recovery, carbon sequestration, and contaminant remediation. Numerical simulation of multiphase flow requires solving of a large, sparse linear system resulting from the discretization of the partial differential equations modeling the flow. In the case of multiphase multicomponent flow with miscible effect, this is a very challenging task. The problem becomes even more difficult if phase transitions are taken into account. A new approach to handle phase transitions is to formulate the system as a nonlinear complementarity problem (NCP). Unlike in the primary variable switching technique, the set of primary variables in this approach is fixed even when there is phase transition. Not only does this improve the robustness of the nonlinear solver, it opens up the possibility to use multigrid methods to solve the resulting linear system. The disadvantage of the complementarity approach, however, is that when a phase disappears, the linear system has the structure of a saddle point problem and becomes indefinite, and current algebraic multigrid (AMG) algorithms cannot be applied directly. In this study, we explore the effectiveness of a new multilevel strategy, based on the multigrid reduction technique, to deal with problems of this type. We demonstrate the effectiveness of the method through numerical results for the case of two-phase, two-component flow with phase appearance/disappearance. We also show that the strategy is efficient and scales optimally with problem size.

Implicit solvers for unstructured meshes

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.; Mavriplis, Dimitri J.

1991-01-01

Implicit methods were developed and tested for unstructured mesh computations. The approximate system which arises from the Newton linearization of the nonlinear evolution operator is solved by using the preconditioned GMRES (Generalized Minimum Residual) technique. Three different preconditioners were studied, namely, the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over relaxation (SSOR). The preconditioners were optimized to have good vectorization properties. SSOR and ILU were also studied as iterative schemes. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also studied. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

Functional fixedness in a technologically sparse culture.

PubMed

German, Tim P; Barrett, H Clark

2005-01-01

Problem solving can be inefficient when the solution requires subjects to generate an atypical function for an object and the object's typical function has been primed. Subjects become "fixed" on the design function of the object, and problem solving suffers relative to control conditions in which the object's function is not demonstrated. In the current study, such functional fixedness was demonstrated in a sample of adolescents (mean age of 16 years) among the Shuar of Ecuadorian Amazonia, whose technologically sparse culture provides limited access to large numbers of artifacts with highly specialized functions. This result suggests that design function may universally be the core property of artifact concepts in human semantic memory.

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.

Constructing the L2-Graph for Robust Subspace Learning and Subspace Clustering.

PubMed

Peng, Xi; Yu, Zhiding; Yi, Zhang; Tang, Huajin

2017-04-01

Under the framework of graph-based learning, the key to robust subspace clustering and subspace learning is to obtain a good similarity graph that eliminates the effects of errors and retains only connections between the data points from the same subspace (i.e., intrasubspace data points). Recent works achieve good performance by modeling errors into their objective functions to remove the errors from the inputs. However, these approaches face the limitations that the structure of errors should be known prior and a complex convex problem must be solved. In this paper, we present a novel method to eliminate the effects of the errors from the projection space (representation) rather than from the input space. We first prove that l 1 -, l 2 -, l ∞ -, and nuclear-norm-based linear projection spaces share the property of intrasubspace projection dominance, i.e., the coefficients over intrasubspace data points are larger than those over intersubspace data points. Based on this property, we introduce a method to construct a sparse similarity graph, called L2-graph. The subspace clustering and subspace learning algorithms are developed upon L2-graph. We conduct comprehensive experiment on subspace learning, image clustering, and motion segmentation and consider several quantitative benchmarks classification/clustering accuracy, normalized mutual information, and running time. Results show that L2-graph outperforms many state-of-the-art methods in our experiments, including L1-graph, low rank representation (LRR), and latent LRR, least square regression, sparse subspace clustering, and locally linear representation.

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.

Analog system for computing sparse codes

DOEpatents

Rozell, Christopher John; Johnson, Don Herrick; Baraniuk, Richard Gordon; Olshausen, Bruno A.; Ortman, Robert Lowell

2010-08-24

A parallel dynamical system for computing sparse representations of data, i.e., where the data can be fully represented in terms of a small number of non-zero code elements, and for reconstructing compressively sensed images. The system is based on the principles of thresholding and local competition that solves a family of sparse approximation problems corresponding to various sparsity metrics. The system utilizes Locally Competitive Algorithms (LCAs), nodes in a population continually compete with neighboring units using (usually one-way) lateral inhibition to calculate coefficients representing an input in an over complete dictionary.

Quantum algorithm for linear systems of equations.

PubMed

Harrow, Aram W; Hassidim, Avinatan; Lloyd, Seth

2009-10-09

Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b(-->), find a vector x(-->) such that Ax(-->) = b(-->). We consider the case where one does not need to know the solution x(-->) itself, but rather an approximation of the expectation value of some operator associated with x(-->), e.g., x(-->)(dagger) Mx(-->) for some matrix M. In this case, when A is sparse, N x N and has condition number kappa, the fastest known classical algorithms can find x(-->) and estimate x(-->)(dagger) Mx(-->) in time scaling roughly as N square root(kappa). Here, we exhibit a quantum algorithm for estimating x(-->)(dagger) Mx(-->) whose runtime is a polynomial of log(N) and kappa. Indeed, for small values of kappa [i.e., poly log(N)], we prove (using some common complexity-theoretic assumptions) that any classical algorithm for this problem generically requires exponentially more time than our quantum algorithm.

The solution of linear systems of equations with a structural analysis code on the NAS CRAY-2

NASA Technical Reports Server (NTRS)

Poole, Eugene L.; Overman, Andrea L.

1988-01-01

Two methods for solving linear systems of equations on the NAS Cray-2 are described. One is a direct method; the other is an iterative method. Both methods exploit the architecture of the Cray-2, particularly the vectorization, and are aimed at structural analysis applications. To demonstrate and evaluate the methods, they were installed in a finite element structural analysis code denoted the Computational Structural Mechanics (CSM) Testbed. A description of the techniques used to integrate the two solvers into the Testbed is given. Storage schemes, memory requirements, operation counts, and reformatting procedures are discussed. Finally, results from the new methods are compared with results from the initial Testbed sparse Choleski equation solver for three structural analysis problems. The new direct solvers described achieve the highest computational rates of the methods compared. The new iterative methods are not able to achieve as high computation rates as the vectorized direct solvers but are best for well conditioned problems which require fewer iterations to converge to the solution.

High Performance Radiation Transport Simulations on TITAN

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

Baker, Christopher G; Davidson, Gregory G; Evans, Thomas M

2012-01-01

In this paper we describe the Denovo code system. Denovo solves the six-dimensional, steady-state, linear Boltzmann transport equation, of central importance to nuclear technology applications such as reactor core analysis (neutronics), radiation shielding, nuclear forensics and radiation detection. The code features multiple spatial differencing schemes, state-of-the-art linear solvers, the Koch-Baker-Alcouffe (KBA) parallel-wavefront sweep algorithm for inverting the transport operator, a new multilevel energy decomposition method scaling to hundreds of thousands of processing cores, and a modern, novel code architecture that supports straightforward integration of new features. In this paper we discuss the performance of Denovo on the 10--20 petaflop ORNLmore » GPU-based system, Titan. We describe algorithms and techniques used to exploit the capabilities of Titan's heterogeneous compute node architecture and the challenges of obtaining good parallel performance for this sparse hyperbolic PDE solver containing inherently sequential computations. Numerical results demonstrating Denovo performance on early Titan hardware are presented.« less

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

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.

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

Blockwise conjugate gradient methods for image reconstruction in volumetric CT.

PubMed

Qiu, W; Titley-Peloquin, D; Soleimani, M

2012-11-01

Cone beam computed tomography (CBCT) enables volumetric image reconstruction from 2D projection data and plays an important role in image guided radiation therapy (IGRT). Filtered back projection is still the most frequently used algorithm in applications. The algorithm discretizes the scanning process (forward projection) into a system of linear equations, which must then be solved to recover images from measured projection data. The conjugate gradients (CG) algorithm and its variants can be used to solve (possibly regularized) linear systems of equations Ax=b and linear least squares problems minx∥b-Ax∥2, especially when the matrix A is very large and sparse. Their applications can be found in a general CT context, but in tomography problems (e.g. CBCT reconstruction) they have not widely been used. Hence, CBCT reconstruction using the CG-type algorithm LSQR was implemented and studied in this paper. In CBCT reconstruction, the main computational challenge is that the matrix A usually is very large, and storing it in full requires an amount of memory well beyond the reach of commodity computers. Because of these memory capacity constraints, only a small fraction of the weighting matrix A is typically used, leading to a poor reconstruction. In this paper, to overcome this difficulty, the matrix A is partitioned and stored blockwise, and blockwise matrix-vector multiplications are implemented within LSQR. This implementation allows us to use the full weighting matrix A for CBCT reconstruction without further enhancing computer standards. Tikhonov regularization can also be implemented in this fashion, and can produce significant improvement in the reconstructed images. Copyright © 2011 Elsevier Ireland Ltd. All rights reserved.

Algebraic multigrid preconditioners for two-phase flow in porous media with phase transitions [Algebraic multigrid preconditioners for multiphase flow in porous media with phase transitions

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

Bui, Quan M.; Wang, Lu; Osei-Kuffuor, Daniel

Multiphase flow is a critical process in a wide range of applications, including oil and gas recovery, carbon sequestration, and contaminant remediation. Numerical simulation of multiphase flow requires solving of a large, sparse linear system resulting from the discretization of the partial differential equations modeling the flow. In the case of multiphase multicomponent flow with miscible effect, this is a very challenging task. The problem becomes even more difficult if phase transitions are taken into account. A new approach to handle phase transitions is to formulate the system as a nonlinear complementarity problem (NCP). Unlike in the primary variable switchingmore » technique, the set of primary variables in this approach is fixed even when there is phase transition. Not only does this improve the robustness of the nonlinear solver, it opens up the possibility to use multigrid methods to solve the resulting linear system. The disadvantage of the complementarity approach, however, is that when a phase disappears, the linear system has the structure of a saddle point problem and becomes indefinite, and current algebraic multigrid (AMG) algorithms cannot be applied directly. In this study, we explore the effectiveness of a new multilevel strategy, based on the multigrid reduction technique, to deal with problems of this type. We demonstrate the effectiveness of the method through numerical results for the case of two-phase, two-component flow with phase appearance/disappearance. In conclusion, we also show that the strategy is efficient and scales optimally with problem size.« less

Algebraic multigrid preconditioners for two-phase flow in porous media with phase transitions [Algebraic multigrid preconditioners for multiphase flow in porous media with phase transitions

DOE PAGES

Bui, Quan M.; Wang, Lu; Osei-Kuffuor, Daniel

2018-02-06

Multiphase flow is a critical process in a wide range of applications, including oil and gas recovery, carbon sequestration, and contaminant remediation. Numerical simulation of multiphase flow requires solving of a large, sparse linear system resulting from the discretization of the partial differential equations modeling the flow. In the case of multiphase multicomponent flow with miscible effect, this is a very challenging task. The problem becomes even more difficult if phase transitions are taken into account. A new approach to handle phase transitions is to formulate the system as a nonlinear complementarity problem (NCP). Unlike in the primary variable switchingmore » technique, the set of primary variables in this approach is fixed even when there is phase transition. Not only does this improve the robustness of the nonlinear solver, it opens up the possibility to use multigrid methods to solve the resulting linear system. The disadvantage of the complementarity approach, however, is that when a phase disappears, the linear system has the structure of a saddle point problem and becomes indefinite, and current algebraic multigrid (AMG) algorithms cannot be applied directly. In this study, we explore the effectiveness of a new multilevel strategy, based on the multigrid reduction technique, to deal with problems of this type. We demonstrate the effectiveness of the method through numerical results for the case of two-phase, two-component flow with phase appearance/disappearance. In conclusion, we also show that the strategy is efficient and scales optimally with problem size.« less

A fast and well-conditioned spectral method for singular integral equations

NASA Astrophysics Data System (ADS)

Slevinsky, Richard Mikael; Olver, Sheehan

2017-03-01

We develop a spectral method for solving univariate singular integral equations over unions of intervals by utilizing Chebyshev and ultraspherical polynomials to reformulate the equations as almost-banded infinite-dimensional systems. This is accomplished by utilizing low rank approximations for sparse representations of the bivariate kernels. The resulting system can be solved in O (m2 n) operations using an adaptive QR factorization, where m is the bandwidth and n is the optimal number of unknowns needed to resolve the true solution. The complexity is reduced to O (mn) operations by pre-caching the QR factorization when the same operator is used for multiple right-hand sides. Stability is proved by showing that the resulting linear operator can be diagonally preconditioned to be a compact perturbation of the identity. Applications considered include the Faraday cage, and acoustic scattering for the Helmholtz and gravity Helmholtz equations, including spectrally accurate numerical evaluation of the far- and near-field solution. The JULIA software package SingularIntegralEquations.jl implements our method with a convenient, user-friendly interface.

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.

Efficient Implementation of an Optimal Interpolator for Large Spatial Data Sets

NASA Technical Reports Server (NTRS)

Memarsadeghi, Nargess; Mount, David M.

2007-01-01

Interpolating scattered data points is a problem of wide ranging interest. A number of approaches for interpolation have been proposed both from theoretical domains such as computational geometry and in applications' fields such as geostatistics. Our motivation arises from geological and mining applications. In many instances data can be costly to compute and are available only at nonuniformly scattered positions. Because of the high cost of collecting measurements, high accuracy is required in the interpolants. One of the most popular interpolation methods in this field is called ordinary kriging. It is popular because it is a best linear unbiased estimator. The price for its statistical optimality is that the estimator is computationally very expensive. This is because the value of each interpolant is given by the solution of a large dense linear system. In practice, kriging problems have been solved approximately by restricting the domain to a small local neighborhood of points that lie near the query point. Determining the proper size for this neighborhood is a solved by ad hoc methods, and it has been shown that this approach leads to undesirable discontinuities in the interpolant. Recently a more principled approach to approximating kriging has been proposed based on a technique called covariance tapering. This process achieves its efficiency by replacing the large dense kriging system with a much sparser linear system. This technique has been applied to a restriction of our problem, called simple kriging, which is not unbiased for general data sets. In this paper we generalize these results by showing how to apply covariance tapering to the more general problem of ordinary kriging. Through experimentation we demonstrate the space and time efficiency and accuracy of approximating ordinary kriging through the use of covariance tapering combined with iterative methods for solving large sparse systems. We demonstrate our approach on large data sizes arising both from synthetic sources and from real applications.

Three-dimensional forward modeling of DC resistivity using the aggregation-based algebraic multigrid method

NASA Astrophysics Data System (ADS)

Chen, Hui; Deng, Ju-Zhi; Yin, Min; Yin, Chang-Chun; Tang, Wen-Wu

2017-03-01

To speed up three-dimensional (3D) DC resistivity modeling, we present a new multigrid method, the aggregation-based algebraic multigrid method (AGMG). We first discretize the differential equation of the secondary potential field with mixed boundary conditions by using a seven-point finite-difference method to obtain a large sparse system of linear equations. Then, we introduce the theory behind the pairwise aggregation algorithms for AGMG and use the conjugate-gradient method with the V-cycle AGMG preconditioner (AGMG-CG) to solve the linear equations. We use typical geoelectrical models to test the proposed AGMG-CG method and compare the results with analytical solutions and the 3DDCXH algorithm for 3D DC modeling (3DDCXH). In addition, we apply the AGMG-CG method to different grid sizes and geoelectrical models and compare it to different iterative methods, such as ILU-BICGSTAB, ILU-GCR, and SSOR-CG. The AGMG-CG method yields nearly linearly decreasing errors, whereas the number of iterations increases slowly with increasing grid size. The AGMG-CG method is precise and converges fast, and thus can improve the computational efficiency in forward modeling of three-dimensional DC resistivity.

Linear-scaling implementation of molecular response theory in self-consistent field electronic-structure theory.

PubMed

Coriani, Sonia; Høst, Stinne; Jansík, Branislav; Thøgersen, Lea; Olsen, Jeppe; Jørgensen, Poul; Reine, Simen; Pawłowski, Filip; Helgaker, Trygve; Sałek, Paweł

2007-04-21

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field theories for the calculation of frequency-dependent molecular response properties and excitation energies is presented, based on a nonredundant exponential parametrization of the one-electron density matrix in the atomic-orbital basis, avoiding the use of canonical orbitals. The response equations are solved iteratively, by an atomic-orbital subspace method equivalent to that of molecular-orbital theory. Important features of the subspace method are the use of paired trial vectors (to preserve the algebraic structure of the response equations), a nondiagonal preconditioner (for rapid convergence), and the generation of good initial guesses (for robust solution). As a result, the performance of the iterative method is the same as in canonical molecular-orbital theory, with five to ten iterations needed for convergence. As in traditional direct Hartree-Fock and Kohn-Sham theories, the calculations are dominated by the construction of the effective Fock/Kohn-Sham matrix, once in each iteration. Linear complexity is achieved by using sparse-matrix algebra, as illustrated in calculations of excitation energies and frequency-dependent polarizabilities of polyalanine peptides containing up to 1400 atoms.

Sampling schemes and parameter estimation for nonlinear Bernoulli-Gaussian sparse models

NASA Astrophysics Data System (ADS)

Boudineau, Mégane; Carfantan, Hervé; Bourguignon, Sébastien; Bazot, Michael

2016-06-01

We address the sparse approximation problem in the case where the data are approximated by the linear combination of a small number of elementary signals, each of these signals depending non-linearly on additional parameters. Sparsity is explicitly expressed through a Bernoulli-Gaussian hierarchical model in a Bayesian framework. Posterior mean estimates are computed using Markov Chain Monte-Carlo algorithms. We generalize the partially marginalized Gibbs sampler proposed in the linear case in [1], and build an hybrid Hastings-within-Gibbs algorithm in order to account for the nonlinear parameters. All model parameters are then estimated in an unsupervised procedure. The resulting method is evaluated on a sparse spectral analysis problem. It is shown to converge more efficiently than the classical joint estimation procedure, with only a slight increase of the computational cost per iteration, consequently reducing the global cost of the estimation procedure.

Sparse brain network using penalized linear regression

NASA Astrophysics Data System (ADS)

Lee, Hyekyoung; Lee, Dong Soo; Kang, Hyejin; Kim, Boong-Nyun; Chung, Moo K.

2011-03-01

Sparse partial correlation is a useful connectivity measure for brain networks when it is difficult to compute the exact partial correlation in the small-n large-p setting. In this paper, we formulate the problem of estimating partial correlation as a sparse linear regression with a l1-norm penalty. The method is applied to brain network consisting of parcellated regions of interest (ROIs), which are obtained from FDG-PET images of the autism spectrum disorder (ASD) children and the pediatric control (PedCon) subjects. To validate the results, we check their reproducibilities of the obtained brain networks by the leave-one-out cross validation and compare the clustered structures derived from the brain networks of ASD and PedCon.

Sparse representation based SAR vehicle recognition along with aspect angle.

PubMed

Xing, Xiangwei; Ji, Kefeng; Zou, Huanxin; Sun, Jixiang

2014-01-01

As a method of representing the test sample with few training samples from an overcomplete dictionary, sparse representation classification (SRC) has attracted much attention in synthetic aperture radar (SAR) automatic target recognition (ATR) recently. In this paper, we develop a novel SAR vehicle recognition method based on sparse representation classification along with aspect information (SRCA), in which the correlation between the vehicle's aspect angle and the sparse representation vector is exploited. The detailed procedure presented in this paper can be summarized as follows. Initially, the sparse representation vector of a test sample is solved by sparse representation algorithm with a principle component analysis (PCA) feature-based dictionary. Then, the coefficient vector is projected onto a sparser one within a certain range of the vehicle's aspect angle. Finally, the vehicle is classified into a certain category that minimizes the reconstruction error with the novel sparse representation vector. Extensive experiments are conducted on the moving and stationary target acquisition and recognition (MSTAR) dataset and the results demonstrate that the proposed method performs robustly under the variations of depression angle and target configurations, as well as incomplete observation.

Magnetic Resonance Super-resolution Imaging Measurement with Dictionary-optimized Sparse Learning

NASA Astrophysics Data System (ADS)

Li, Jun-Bao; Liu, Jing; Pan, Jeng-Shyang; Yao, Hongxun

2017-06-01

Magnetic Resonance Super-resolution Imaging Measurement (MRIM) is an effective way of measuring materials. MRIM has wide applications in physics, chemistry, biology, geology, medical and material science, especially in medical diagnosis. It is feasible to improve the resolution of MR imaging through increasing radiation intensity, but the high radiation intensity and the longtime of magnetic field harm the human body. Thus, in the practical applications the resolution of hardware imaging reaches the limitation of resolution. Software-based super-resolution technology is effective to improve the resolution of image. This work proposes a framework of dictionary-optimized sparse learning based MR super-resolution method. The framework is to solve the problem of sample selection for dictionary learning of sparse reconstruction. The textural complexity-based image quality representation is proposed to choose the optimal samples for dictionary learning. Comprehensive experiments show that the dictionary-optimized sparse learning improves the performance of sparse representation.

Return probabilities and hitting times of random walks on sparse Erdös-Rényi graphs.

PubMed

Martin, O C; Sulc, P

2010-03-01

We consider random walks on random graphs, focusing on return probabilities and hitting times for sparse Erdös-Rényi graphs. Using the tree approach, which is expected to be exact in the large graph limit, we show how to solve for the distribution of these quantities and we find that these distributions exhibit a form of self-similarity.

Architecting the Finite Element Method Pipeline for the GPU.

PubMed

Fu, Zhisong; Lewis, T James; Kirby, Robert M; Whitaker, Ross T

2014-02-01

The finite element method (FEM) is a widely employed numerical technique for approximating the solution of partial differential equations (PDEs) in various science and engineering applications. Many of these applications benefit from fast execution of the FEM pipeline. One way to accelerate the FEM pipeline is by exploiting advances in modern computational hardware, such as the many-core streaming processors like the graphical processing unit (GPU). In this paper, we present the algorithms and data-structures necessary to move the entire FEM pipeline to the GPU. First we propose an efficient GPU-based algorithm to generate local element information and to assemble the global linear system associated with the FEM discretization of an elliptic PDE. To solve the corresponding linear system efficiently on the GPU, we implement a conjugate gradient method preconditioned with a geometry-informed algebraic multi-grid (AMG) method preconditioner. We propose a new fine-grained parallelism strategy, a corresponding multigrid cycling stage and efficient data mapping to the many-core architecture of GPU. Comparison of our on-GPU assembly versus a traditional serial implementation on the CPU achieves up to an 87 × speedup. Focusing on the linear system solver alone, we achieve a speedup of up to 51 × versus use of a comparable state-of-the-art serial CPU linear system solver. Furthermore, the method compares favorably with other GPU-based, sparse, linear solvers.

Accelerating scientific computations with mixed precision algorithms

NASA Astrophysics Data System (ADS)

Baboulin, Marc; Buttari, Alfredo; Dongarra, Jack; Kurzak, Jakub; Langou, Julie; Langou, Julien; Luszczek, Piotr; Tomov, Stanimire

2009-12-01

On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and sparse linear algebra algorithms can be significantly enhanced while maintaining the 64-bit accuracy of the resulting solution. The approach presented here can apply not only to conventional processors but also to other technologies such as Field Programmable Gate Arrays (FPGA), Graphical Processing Units (GPU), and the STI Cell BE processor. Results on modern processor architectures and the STI Cell BE are presented. Program summaryProgram title: ITER-REF Catalogue identifier: AECO_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECO_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 7211 No. of bytes in distributed program, including test data, etc.: 41 862 Distribution format: tar.gz Programming language: FORTRAN 77 Computer: desktop, server Operating system: Unix/Linux RAM: 512 Mbytes Classification: 4.8 External routines: BLAS (optional) Nature of problem: On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and sparse linear algebra algorithms can be significantly enhanced while maintaining the 64-bit accuracy of the resulting solution. Solution method: Mixed precision algorithms stem from the observation that, in many cases, a single precision solution of a problem can be refined to the point where double precision accuracy is achieved. A common approach to the solution of linear systems, either dense or sparse, is to perform the LU factorization of the coefficient matrix using Gaussian elimination. First, the coefficient matrix A is factored into the product of a lower triangular matrix L and an upper triangular matrix U. Partial row pivoting is in general used to improve numerical stability resulting in a factorization PA=LU, where P is a permutation matrix. The solution for the system is achieved by first solving Ly=Pb (forward substitution) and then solving Ux=y (backward substitution). Due to round-off errors, the computed solution, x, carries a numerical error magnified by the condition number of the coefficient matrix A. In order to improve the computed solution, an iterative process can be applied, which produces a correction to the computed solution at each iteration, which then yields the method that is commonly known as the iterative refinement algorithm. Provided that the system is not too ill-conditioned, the algorithm produces a solution correct to the working precision. Running time: seconds/minutes

Recovery of sparse translation-invariant signals with continuous basis pursuit

PubMed Central

Ekanadham, Chaitanya; Tranchina, Daniel; Simoncelli, Eero

2013-01-01

We consider the problem of decomposing a signal into a linear combination of features, each a continuously translated version of one of a small set of elementary features. Although these constituents are drawn from a continuous family, most current signal decomposition methods rely on a finite dictionary of discrete examples selected from this family (e.g., shifted copies of a set of basic waveforms), and apply sparse optimization methods to select and solve for the relevant coefficients. Here, we generate a dictionary that includes auxiliary interpolation functions that approximate translates of features via adjustment of their coefficients. We formulate a constrained convex optimization problem, in which the full set of dictionary coefficients represents a linear approximation of the signal, the auxiliary coefficients are constrained so as to only represent translated features, and sparsity is imposed on the primary coefficients using an L1 penalty. The basis pursuit denoising (BP) method may be seen as a special case, in which the auxiliary interpolation functions are omitted, and we thus refer to our methodology as continuous basis pursuit (CBP). We develop two implementations of CBP for a one-dimensional translation-invariant source, one using a first-order Taylor approximation, and another using a form of trigonometric spline. We examine the tradeoff between sparsity and signal reconstruction accuracy in these methods, demonstrating empirically that trigonometric CBP substantially outperforms Taylor CBP, which in turn offers substantial gains over ordinary BP. In addition, the CBP bases can generally achieve equally good or better approximations with much coarser sampling than BP, leading to a reduction in dictionary dimensionality. PMID:24352562

MGMRES: A generalization of GMRES for solving large sparse nonsymmetric linear systems

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

Young, D.M.; Chen, J.Y.

1994-12-31

The authors are concerned with the solution of the linear system (1): Au = b, where A is a real square nonsingular matrix which is large, sparse and non-symmetric. They consider the use of Krylov subspace methods. They first choose an initial approximation u{sup (0)} to the solution {bar u} = A{sup {minus}1}B of (1). They also choose an auxiliary matrix Z which is nonsingular. For n = 1,2,{hor_ellipsis} they determine u{sup (n)} such that u{sup (n)} {minus} u{sup (0)}{epsilon}K{sub n}(r{sup (0)},A) where K{sub n}(r{sup (0)},A) is the (Krylov) subspace spanned by the Krylov vectors r{sup (0)}, Ar{sup (0)}, {hor_ellipsis},more » A{sup n{minus}1}r{sup 0} and where r{sup (0)} = b{minus}Au{sup (0)}. If ZA is SPD they also require that (u{sup (n)}{minus}{bar u}, ZA(u{sup (n)}{minus}{bar u})) be minimized. If, on the other hand, ZA is not SPD, then they require that the Galerkin condition, (Zr{sup n}, v) = 0, be satisfied for all v{epsilon}K{sub n}(r{sup (0)}, A) where r{sup n} = b{minus}Au{sup (n)}. In this paper the authors consider a generalization of GMRES. This generalized method, which they refer to as `MGMRES`, is very similar to GMRES except that they let Z = A{sup T}Y where Y is a nonsingular matrix which is symmetric by not necessarily SPD.« 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.

Liver segmentation from CT images using a sparse priori statistical shape model (SP-SSM).

PubMed

Wang, Xuehu; Zheng, Yongchang; Gan, Lan; Wang, Xuan; Sang, Xinting; Kong, Xiangfeng; Zhao, Jie

2017-01-01

This study proposes a new liver segmentation method based on a sparse a priori statistical shape model (SP-SSM). First, mark points are selected in the liver a priori model and the original image. Then, the a priori shape and its mark points are used to obtain a dictionary for the liver boundary information. Second, the sparse coefficient is calculated based on the correspondence between mark points in the original image and those in the a priori model, and then the sparse statistical model is established by combining the sparse coefficients and the dictionary. Finally, the intensity energy and boundary energy models are built based on the intensity information and the specific boundary information of the original image. Then, the sparse matching constraint model is established based on the sparse coding theory. These models jointly drive the iterative deformation of the sparse statistical model to approximate and accurately extract the liver boundaries. This method can solve the problems of deformation model initialization and a priori method accuracy using the sparse dictionary. The SP-SSM can achieve a mean overlap error of 4.8% and a mean volume difference of 1.8%, whereas the average symmetric surface distance and the root mean square symmetric surface distance can reach 0.8 mm and 1.4 mm, respectively.

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.

A two-stage adaptive stochastic collocation method on nested sparse grids for multiphase flow in randomly heterogeneous porous media

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

Liao, Qinzhuo, E-mail: liaoqz@pku.edu.cn; Zhang, Dongxiao; Tchelepi, Hamdi

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 efficiencymore » of the proposed two-stage adaptive stochastic collocation method on nested sparse grids.« less

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.

Estimating the size of an open population using sparse capture-recapture data.

PubMed

Huggins, Richard; Stoklosa, Jakub; Roach, Cameron; Yip, Paul

2018-03-01

Sparse capture-recapture data from open populations are difficult to analyze using currently available frequentist statistical methods. However, in closed capture-recapture experiments, the Chao sparse estimator (Chao, 1989, Biometrics 45, 427-438) may be used to estimate population sizes when there are few recaptures. Here, we extend the Chao (1989) closed population size estimator to the open population setting by using linear regression and extrapolation techniques. We conduct a small simulation study and apply the models to several sparse capture-recapture data sets. © 2017, The International Biometric Society.

An Assessment of Iterative Reconstruction Methods for Sparse Ultrasound Imaging

PubMed Central

Valente, Solivan A.; Zibetti, Marcelo V. W.; Pipa, Daniel R.; Maia, Joaquim M.; Schneider, Fabio K.

2017-01-01

Ultrasonic image reconstruction using inverse problems has recently appeared as an alternative to enhance ultrasound imaging over beamforming methods. This approach depends on the accuracy of the acquisition model used to represent transducers, reflectivity, and medium physics. Iterative methods, well known in general sparse signal reconstruction, are also suited for imaging. In this paper, a discrete acquisition model is assessed by solving a linear system of equations by an ℓ1-regularized least-squares minimization, where the solution sparsity may be adjusted as desired. The paper surveys 11 variants of four well-known algorithms for sparse reconstruction, and assesses their optimization parameters with the goal of finding the best approach for iterative ultrasound imaging. The strategy for the model evaluation consists of using two distinct datasets. We first generate data from a synthetic phantom that mimics real targets inside a professional ultrasound phantom device. This dataset is contaminated with Gaussian noise with an estimated SNR, and all methods are assessed by their resulting images and performances. The model and methods are then assessed with real data collected by a research ultrasound platform when scanning the same phantom device, and results are compared with beamforming. A distinct real dataset is finally used to further validate the proposed modeling. Although high computational effort is required by iterative methods, results show that the discrete model may lead to images closer to ground-truth than traditional beamforming. However, computing capabilities of current platforms need to evolve before frame rates currently delivered by ultrasound equipments are achievable. PMID:28282862

M-estimation for robust sparse unmixing of hyperspectral images

NASA Astrophysics Data System (ADS)

Toomik, Maria; Lu, Shijian; Nelson, James D. B.

2016-10-01

Hyperspectral unmixing methods often use a conventional least squares based lasso which assumes that the data follows the Gaussian distribution. The normality assumption is an approximation which is generally invalid for real imagery data. We consider a robust (non-Gaussian) approach to sparse spectral unmixing of remotely sensed imagery which reduces the sensitivity of the estimator to outliers and relaxes the linearity assumption. The method consists of several appropriate penalties. We propose to use an lp norm with 0 < p < 1 in the sparse regression problem, which induces more sparsity in the results, but makes the problem non-convex. On the other hand, the problem, though non-convex, can be solved quite straightforwardly with an extensible algorithm based on iteratively reweighted least squares. To deal with the huge size of modern spectral libraries we introduce a library reduction step, similar to the multiple signal classification (MUSIC) array processing algorithm, which not only speeds up unmixing but also yields superior results. In the hyperspectral setting we extend the traditional least squares method to the robust heavy-tailed case and propose a generalised M-lasso solution. M-estimation replaces the Gaussian likelihood with a fixed function ρ(e) that restrains outliers. The M-estimate function reduces the effect of errors with large amplitudes or even assigns the outliers zero weights. Our experimental results on real hyperspectral data show that noise with large amplitudes (outliers) often exists in the data. This ability to mitigate the influence of such outliers can therefore offer greater robustness. Qualitative hyperspectral unmixing results on real hyperspectral image data corroborate the efficacy of the proposed method.

Limited-memory trust-region methods for sparse relaxation

NASA Astrophysics Data System (ADS)

Adhikari, Lasith; DeGuchy, Omar; Erway, Jennifer B.; Lockhart, Shelby; Marcia, Roummel F.

2017-08-01

In this paper, we solve the l2-l1 sparse recovery problem by transforming the objective function of this problem into an unconstrained differentiable function and applying a limited-memory trust-region method. Unlike gradient projection-type methods, which uses only the current gradient, our approach uses gradients from previous iterations to obtain a more accurate Hessian approximation. Numerical experiments show that our proposed approach eliminates spurious solutions more effectively while improving computational time.

Application of Four-Point Newton-EGSOR iteration for the numerical solution of 2D Porous Medium Equations

NASA Astrophysics Data System (ADS)

Chew, J. V. L.; Sulaiman, J.

2017-09-01

Partial differential equations that are used in describing the nonlinear heat and mass transfer phenomena are difficult to be solved. For the case where the exact solution is difficult to be obtained, it is necessary to use a numerical procedure such as the finite difference method to solve a particular partial differential equation. In term of numerical procedure, a particular method can be considered as an efficient method if the method can give an approximate solution within the specified error with the least computational complexity. Throughout this paper, the two-dimensional Porous Medium Equation (2D PME) is discretized by using the implicit finite difference scheme to construct the corresponding approximation equation. Then this approximation equation yields a large-sized and sparse nonlinear system. By using the Newton method to linearize the nonlinear system, this paper deals with the application of the Four-Point Newton-EGSOR (4NEGSOR) iterative method for solving the 2D PMEs. In addition to that, the efficiency of the 4NEGSOR iterative method is studied by solving three examples of the problems. Based on the comparative analysis, the Newton-Gauss-Seidel (NGS) and the Newton-SOR (NSOR) iterative methods are also considered. The numerical findings show that the 4NEGSOR method is superior to the NGS and the NSOR methods in terms of the number of iterations to get the converged solutions, the time of computation and the maximum absolute errors produced by the methods.

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.

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.

Prediction of siRNA potency using sparse logistic regression.

PubMed

Hu, Wei; Hu, John

2014-06-01

RNA interference (RNAi) can modulate gene expression at post-transcriptional as well as transcriptional levels. Short interfering RNA (siRNA) serves as a trigger for the RNAi gene inhibition mechanism, and therefore is a crucial intermediate step in RNAi. There have been extensive studies to identify the sequence characteristics of potent siRNAs. One such study built a linear model using LASSO (Least Absolute Shrinkage and Selection Operator) to measure the contribution of each siRNA sequence feature. This model is simple and interpretable, but it requires a large number of nonzero weights. We have introduced a novel technique, sparse logistic regression, to build a linear model using single-position specific nucleotide compositions which has the same prediction accuracy of the linear model based on LASSO. The weights in our new model share the same general trend as those in the previous model, but have only 25 nonzero weights out of a total 84 weights, a 54% reduction compared to the previous model. Contrary to the linear model based on LASSO, our model suggests that only a few positions are influential on the efficacy of the siRNA, which are the 5' and 3' ends and the seed region of siRNA sequences. We also employed sparse logistic regression to build a linear model using dual-position specific nucleotide compositions, a task LASSO is not able to accomplish well due to its high dimensional nature. Our results demonstrate the superiority of sparse logistic regression as a technique for both feature selection and regression over LASSO in the context of siRNA design.

Human mobility prediction from region functions with taxi trajectories.

PubMed

Wang, Minjie; Yang, Su; Sun, Yi; Gao, Jun

2017-01-01

People in cities nowadays suffer from increasingly severe traffic jams due to less awareness of how collective human mobility is affected by urban planning. Besides, understanding how region functions shape human mobility is critical for business planning but remains unsolved so far. This study aims to discover the association between region functions and resulting human mobility. We establish a linear regression model to predict the traffic flows of Beijing based on the input referred to as bag of POIs. By solving the predictor in the sense of sparse representation, we find that the average prediction precision is over 74% and each type of POI contributes differently in the predictor, which accounts for what factors and how such region functions attract people visiting. Based on these findings, predictive human mobility could be taken into account when planning new regions and region functions.

New numerical method for radiation heat transfer in nonhomogeneous participating media

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

Howell, J.R.; Tan, Zhiqiang

A new numerical method, which solves the exact integral equations of distance-angular integration form for radiation transfer, is introduced in this paper. By constructing and prestoring the numerical integral formulas for the distance integral for appropriate kernel functions, this method eliminates the time consuming evaluations of the kernels of the space integrals in the formal computations. In addition, when the number of elements in the system is large, the resulting coefficient matrix is quite sparse. Thus, either considerable time or much storage can be saved. A weakness of the method is discussed, and some remedies are suggested. As illustrations, somemore » one-dimensional and two-dimensional problems in both homogeneous and inhomogeneous emitting, absorbing, and linear anisotropic scattering media are studied. Some results are compared with available data. 13 refs.« less

Numerical simulations of microwave heating of liquids: enhancements using Krylov subspace methods

NASA Astrophysics Data System (ADS)

Lollchund, M. R.; Dookhitram, K.; Sunhaloo, M. S.; Boojhawon, R.

2013-04-01

In this paper, we compare the performances of three iterative solvers for large sparse linear systems arising in the numerical computations of incompressible Navier-Stokes (NS) equations. These equations are employed mainly in the simulation of microwave heating of liquids. The emphasis of this work is on the application of Krylov projection techniques such as Generalized Minimal Residual (GMRES) to solve the Pressure Poisson Equations that result from discretisation of the NS equations. The performance of the GMRES method is compared with the traditional Gauss-Seidel (GS) and point successive over relaxation (PSOR) techniques through their application to simulate the dynamics of water housed inside a vertical cylindrical vessel which is subjected to microwave radiation. It is found that as the mesh size increases, GMRES gives the fastest convergence rate in terms of computational times and number of iterations.

CSI feedback-based CS for underwater acoustic adaptive modulation OFDM system with channel prediction

NASA Astrophysics Data System (ADS)

Kuai, Xiao-yan; Sun, Hai-xin; Qi, Jie; Cheng, En; Xu, Xiao-ka; Guo, Yu-hui; Chen, You-gan

2014-06-01

In this paper, we investigate the performance of adaptive modulation (AM) orthogonal frequency division multiplexing (OFDM) system in underwater acoustic (UWA) communications. The aim is to solve the problem of large feedback overhead for channel state information (CSI) in every subcarrier. A novel CSI feedback scheme is proposed based on the theory of compressed sensing (CS). We propose a feedback from the receiver that only feedback the sparse channel parameters. Additionally, prediction of the channel state is proposed every several symbols to realize the AM in practice. We describe a linear channel prediction algorithm which is used in adaptive transmission. This system has been tested in the real underwater acoustic channel. The linear channel prediction makes the AM transmission techniques more feasible for acoustic channel communications. The simulation and experiment show that significant improvements can be obtained both in bit error rate (BER) and throughput in the AM scheme compared with the fixed Quadrature Phase Shift Keying (QPSK) modulation scheme. Moreover, the performance with standard CS outperforms the Discrete Cosine Transform (DCT) method.

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

Kitanidis, Peter

As large-scale, commercial storage projects become operational, the problem of utilizing information from diverse sources becomes more critically important. In this project, we developed, tested, and applied an advanced joint data inversion system for CO 2 storage modeling with large data sets for use in site characterization and real-time monitoring. Emphasis was on the development of advanced and efficient computational algorithms for joint inversion of hydro-geophysical data, coupled with state-of-the-art forward process simulations. The developed system consists of (1) inversion tools using characterization data, such as 3D seismic survey (amplitude images), borehole log and core data, as well as hydraulic,more » tracer and thermal tests before CO 2 injection, (2) joint inversion tools for updating the geologic model with the distribution of rock properties, thus reducing uncertainty, using hydro-geophysical monitoring data, and (3) highly efficient algorithms for directly solving the dense or sparse linear algebra systems derived from the joint inversion. The system combines methods from stochastic analysis, fast linear algebra, and high performance computing. The developed joint inversion tools have been tested through synthetic CO 2 storage examples.« less

Nonlinear spike-and-slab sparse coding for interpretable image encoding.

PubMed

Shelton, Jacquelyn A; Sheikh, Abdul-Saboor; Bornschein, Jörg; Sterne, Philip; Lücke, Jörg

2015-01-01

Sparse coding is a popular approach to model natural images but has faced two main challenges: modelling low-level image components (such as edge-like structures and their occlusions) and modelling varying pixel intensities. Traditionally, images are modelled as a sparse linear superposition of dictionary elements, where the probabilistic view of this problem is that the coefficients follow a Laplace or Cauchy prior distribution. We propose a novel model that instead uses a spike-and-slab prior and nonlinear combination of components. With the prior, our model can easily represent exact zeros for e.g. the absence of an image component, such as an edge, and a distribution over non-zero pixel intensities. With the nonlinearity (the nonlinear max combination rule), the idea is to target occlusions; dictionary elements correspond to image components that can occlude each other. There are major consequences of the model assumptions made by both (non)linear approaches, thus the main goal of this paper is to isolate and highlight differences between them. Parameter optimization is analytically and computationally intractable in our model, thus as a main contribution we design an exact Gibbs sampler for efficient inference which we can apply to higher dimensional data using latent variable preselection. Results on natural and artificial occlusion-rich data with controlled forms of sparse structure show that our model can extract a sparse set of edge-like components that closely match the generating process, which we refer to as interpretable components. Furthermore, the sparseness of the solution closely follows the ground-truth number of components/edges in the images. The linear model did not learn such edge-like components with any level of sparsity. This suggests that our model can adaptively well-approximate and characterize the meaningful generation process.

Nonlinear Spike-And-Slab Sparse Coding for Interpretable Image Encoding

PubMed Central

Shelton, Jacquelyn A.; Sheikh, Abdul-Saboor; Bornschein, Jörg; Sterne, Philip; Lücke, Jörg

2015-01-01

Sparse coding is a popular approach to model natural images but has faced two main challenges: modelling low-level image components (such as edge-like structures and their occlusions) and modelling varying pixel intensities. Traditionally, images are modelled as a sparse linear superposition of dictionary elements, where the probabilistic view of this problem is that the coefficients follow a Laplace or Cauchy prior distribution. We propose a novel model that instead uses a spike-and-slab prior and nonlinear combination of components. With the prior, our model can easily represent exact zeros for e.g. the absence of an image component, such as an edge, and a distribution over non-zero pixel intensities. With the nonlinearity (the nonlinear max combination rule), the idea is to target occlusions; dictionary elements correspond to image components that can occlude each other. There are major consequences of the model assumptions made by both (non)linear approaches, thus the main goal of this paper is to isolate and highlight differences between them. Parameter optimization is analytically and computationally intractable in our model, thus as a main contribution we design an exact Gibbs sampler for efficient inference which we can apply to higher dimensional data using latent variable preselection. Results on natural and artificial occlusion-rich data with controlled forms of sparse structure show that our model can extract a sparse set of edge-like components that closely match the generating process, which we refer to as interpretable components. Furthermore, the sparseness of the solution closely follows the ground-truth number of components/edges in the images. The linear model did not learn such edge-like components with any level of sparsity. This suggests that our model can adaptively well-approximate and characterize the meaningful generation process. PMID:25954947

Track monitoring from the dynamic response of a passing train: A sparse approach

NASA Astrophysics Data System (ADS)

Lederman, George; Chen, Siheng; Garrett, James H.; Kovačević, Jelena; Noh, Hae Young; Bielak, Jacobo

2017-06-01

Collecting vibration data from revenue service trains could be a low-cost way to more frequently monitor railroad tracks, yet operational variability makes robust analysis a challenge. We propose a novel analysis technique for track monitoring that exploits the sparsity inherent in train-vibration data. This sparsity is based on the observation that large vertical train vibrations typically involve the excitation of the train's fundamental mode due to track joints, switchgear, or other discrete hardware. Rather than try to model the entire rail profile, in this study we examine a sparse approach to solving an inverse problem where (1) the roughness is constrained to a discrete and limited set of "bumps"; and (2) the train system is idealized as a simple damped oscillator that models the train's vibration in the fundamental mode. We use an expectation maximization (EM) approach to iteratively solve for the track profile and the train system properties, using orthogonal matching pursuit (OMP) to find the sparse approximation within each step. By enforcing sparsity, the inverse problem is well posed and the train's position can be found relative to the sparse bumps, thus reducing the uncertainty in the GPS data. We validate the sparse approach on two sections of track monitored from an operational train over a 16 month period of time, one where track changes did not occur during this period and another where changes did occur. We show that this approach can not only detect when track changes occur, but also offers insight into the type of such changes.

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.

A General Iterative Shrinkage and Thresholding Algorithm for Non-convex Regularized Optimization Problems.

PubMed

Gong, Pinghua; Zhang, Changshui; Lu, Zhaosong; Huang, Jianhua Z; Ye, Jieping

2013-01-01

Non-convex sparsity-inducing penalties have recently received considerable attentions in sparse learning. Recent theoretical investigations have demonstrated their superiority over the convex counterparts in several sparse learning settings. However, solving the non-convex optimization problems associated with non-convex penalties remains a big challenge. A commonly used approach is the Multi-Stage (MS) convex relaxation (or DC programming), which relaxes the original non-convex problem to a sequence of convex problems. This approach is usually not very practical for large-scale problems because its computational cost is a multiple of solving a single convex problem. In this paper, we propose a General Iterative Shrinkage and Thresholding (GIST) algorithm to solve the nonconvex optimization problem for a large class of non-convex penalties. The GIST algorithm iteratively solves a proximal operator problem, which in turn has a closed-form solution for many commonly used penalties. At each outer iteration of the algorithm, we use a line search initialized by the Barzilai-Borwein (BB) rule that allows finding an appropriate step size quickly. The paper also presents a detailed convergence analysis of the GIST algorithm. The efficiency of the proposed algorithm is demonstrated by extensive experiments on large-scale data sets.

Multi-color incomplete Cholesky conjugate gradient methods for vector computers

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

Poole, E.L.

1986-01-01

This research is concerned with the solution on vector computers of linear systems of equations. Ax = b, where A is a large, sparse symmetric positive definite matrix with non-zero elements lying only along a few diagonals of the matrix. The system is solved using the incomplete Cholesky conjugate gradient method (ICCG). Multi-color orderings are used of the unknowns in the linear system to obtain p-color matrices for which a no-fill block ICCG method is implemented on the CYBER 205 with O(N/p) length vector operations in both the decomposition of A and, more importantly, in the forward and back solvesmore » necessary at each iteration of the method. (N is the number of unknowns and p is a small constant). A p-colored matrix is a matrix that can be partitioned into a p x p block matrix where the diagonal blocks are diagonal matrices. The matrix is stored by diagonals and matrix multiplication by diagonals is used to carry out the decomposition of A and the forward and back solves. Additionally, if the vectors across adjacent blocks line up, then some of the overhead associated with vector startups can be eliminated in the matrix vector multiplication necessary at each conjugate gradient iteration. Necessary and sufficient conditions are given to determine which multi-color orderings of the unknowns correspond to p-color matrices, and a process is indicated for choosing multi-color orderings.« less

AITRAC: Augmented Interactive Transient Radiation Analysis by Computer. User's information manual

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

Not Available

1977-10-01

AITRAC is a program designed for on-line, interactive, DC, and transient analysis of electronic circuits. The program solves linear and nonlinear simultaneous equations which characterize the mathematical models used to predict circuit response. The program features 100 external node--200 branch capability; conversional, free-format input language; built-in junction, FET, MOS, and switch models; sparse matrix algorithm with extended-precision H matrix and T vector calculations, for fast and accurate execution; linear transconductances: beta, GM, MU, ZM; accurate and fast radiation effects analysis; special interface for user-defined equations; selective control of multiple outputs; graphical outputs in wide and narrow formats; and on-line parametermore » modification capability. The user describes the problem by entering the circuit topology and part parameters. The program then automatically generates and solves the circuit equations, providing the user with printed or plotted output. The circuit topology and/or part values may then be changed by the user, and a new analysis, requested. Circuit descriptions may be saved on disk files for storage and later use. The program contains built-in standard models for resistors, voltage and current sources, capacitors, inductors including mutual couplings, switches, junction diodes and transistors, FETS, and MOS devices. Nonstandard models may be constructed from standard models or by using the special equations interface. Time functions may be described by straight-line segments or by sine, damped sine, and exponential functions. 42 figures, 1 table. (RWR)« less

Automatic correction of intensity nonuniformity from sparseness of gradient distribution in medical images.

PubMed

Zheng, Yuanjie; Grossman, Murray; Awate, Suyash P; Gee, James C

2009-01-01

We propose to use the sparseness property of the gradient probability distribution to estimate the intensity nonuniformity in medical images, resulting in two novel automatic methods: a non-parametric method and a parametric method. Our methods are easy to implement because they both solve an iteratively re-weighted least squares problem. They are remarkably accurate as shown by our experiments on images of different imaged objects and from different imaging modalities.

Automatic Correction of Intensity Nonuniformity from Sparseness of Gradient Distribution in Medical Images

PubMed Central

Zheng, Yuanjie; Grossman, Murray; Awate, Suyash P.; Gee, James C.

2013-01-01

We propose to use the sparseness property of the gradient probability distribution to estimate the intensity nonuniformity in medical images, resulting in two novel automatic methods: a non-parametric method and a parametric method. Our methods are easy to implement because they both solve an iteratively re-weighted least squares problem. They are remarkably accurate as shown by our experiments on images of different imaged objects and from different imaging modalities. PMID:20426191

Integrative approach for inference of gene regulatory networks using lasso-based random featuring and application to psychiatric disorders.

PubMed

Kim, Dongchul; Kang, Mingon; Biswas, Ashis; Liu, Chunyu; Gao, Jean

2016-08-10

Inferring gene regulatory networks is one of the most interesting research areas in the systems biology. Many inference methods have been developed by using a variety of computational models and approaches. However, there are two issues to solve. First, depending on the structural or computational model of inference method, the results tend to be inconsistent due to innately different advantages and limitations of the methods. Therefore the combination of dissimilar approaches is demanded as an alternative way in order to overcome the limitations of standalone methods through complementary integration. Second, sparse linear regression that is penalized by the regularization parameter (lasso) and bootstrapping-based sparse linear regression methods were suggested in state of the art methods for network inference but they are not effective for a small sample size data and also a true regulator could be missed if the target gene is strongly affected by an indirect regulator with high correlation or another true regulator. We present two novel network inference methods based on the integration of three different criteria, (i) z-score to measure the variation of gene expression from knockout data, (ii) mutual information for the dependency between two genes, and (iii) linear regression-based feature selection. Based on these criterion, we propose a lasso-based random feature selection algorithm (LARF) to achieve better performance overcoming the limitations of bootstrapping as mentioned above. In this work, there are three main contributions. First, our z score-based method to measure gene expression variations from knockout data is more effective than similar criteria of related works. Second, we confirmed that the true regulator selection can be effectively improved by LARF. Lastly, we verified that an integrative approach can clearly outperform a single method when two different methods are effectively jointed. In the experiments, our methods were validated by outperforming the state of the art methods on DREAM challenge data, and then LARF was applied to inferences of gene regulatory network associated with psychiatric disorders.

Robust parallel iterative solvers for linear and least-squares problems, Final Technical Report

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

Saad, Yousef

2014-01-16

The primary goal of this project is to study and develop robust iterative methods for solving linear systems of equations and least squares systems. The focus of the Minnesota team is on algorithms development, robustness issues, and on tests and validation of the methods on realistic problems. 1. The project begun with an investigation on how to practically update a preconditioner obtained from an ILU-type factorization, when the coefficient matrix changes. 2. We investigated strategies to improve robustness in parallel preconditioners in a specific case of a PDE with discontinuous coefficients. 3. We explored ways to adapt standard preconditioners formore » solving linear systems arising from the Helmholtz equation. These are often difficult linear systems to solve by iterative methods. 4. We have also worked on purely theoretical issues related to the analysis of Krylov subspace methods for linear systems. 5. We developed an effective strategy for performing ILU factorizations for the case when the matrix is highly indefinite. The strategy uses shifting in some optimal way. The method was extended to the solution of Helmholtz equations by using complex shifts, yielding very good results in many cases. 6. We addressed the difficult problem of preconditioning sparse systems of equations on GPUs. 7. A by-product of the above work is a software package consisting of an iterative solver library for GPUs based on CUDA. This was made publicly available. It was the first such library that offers complete iterative solvers for GPUs. 8. We considered another form of ILU which blends coarsening techniques from Multigrid with algebraic multilevel methods. 9. We have released a new version on our parallel solver - called pARMS [new version is version 3]. As part of this we have tested the code in complex settings - including the solution of Maxwell and Helmholtz equations and for a problem of crystal growth.10. As an application of polynomial preconditioning we considered the problem of evaluating f(A)v which arises in statistical sampling. 11. As an application to the methods we developed, we tackled the problem of computing the diagonal of the inverse of a matrix. This arises in statistical applications as well as in many applications in physics. We explored probing methods as well as domain-decomposition type methods. 12. A collaboration with researchers from Toulouse, France, considered the important problem of computing the Schur complement in a domain-decomposition approach. 13. We explored new ways of preconditioning linear systems, based on low-rank approximations.« less

Source term identification in atmospheric modelling via sparse optimization

NASA Astrophysics Data System (ADS)

Adam, Lukas; Branda, Martin; Hamburger, Thomas

2015-04-01

Inverse modelling plays an important role in identifying the amount of harmful substances released into atmosphere during major incidents such as power plant accidents or volcano eruptions. Another possible application of inverse modelling lies in the monitoring the CO2 emission limits where only observations at certain places are available and the task is to estimate the total releases at given locations. This gives rise to minimizing the discrepancy between the observations and the model predictions. There are two standard ways of solving such problems. In the first one, this discrepancy is regularized by adding additional terms. Such terms may include Tikhonov regularization, distance from a priori information or a smoothing term. The resulting, usually quadratic, problem is then solved via standard optimization solvers. The second approach assumes that the error term has a (normal) distribution and makes use of Bayesian modelling to identify the source term. Instead of following the above-mentioned approaches, we utilize techniques from the field of compressive sensing. Such techniques look for a sparsest solution (solution with the smallest number of nonzeros) of a linear system, where a maximal allowed error term may be added to this system. Even though this field is a developed one with many possible solution techniques, most of them do not consider even the simplest constraints which are naturally present in atmospheric modelling. One of such examples is the nonnegativity of release amounts. We believe that the concept of a sparse solution is natural in both problems of identification of the source location and of the time process of the source release. In the first case, it is usually assumed that there are only few release points and the task is to find them. In the second case, the time window is usually much longer than the duration of the actual release. In both cases, the optimal solution should contain a large amount of zeros, giving rise to the concept of sparsity. In the paper, we summarize several optimization techniques which are used for finding sparse solutions and propose their modifications to handle selected constraints such as nonnegativity constraints and simple linear constraints, for example the minimal or maximal amount of total release. These techniques range from successive convex approximations to solution of one nonconvex problem. On simple examples, we explain these techniques and compare them from the point of implementation simplicity, approximation capability and convergence properties. Finally, these methods will be applied on the European Tracer Experiment (ETEX) data and the results will be compared with the current state of arts techniques such as regularized least squares or Bayesian approach. The obtained results show the surprisingly good results of these techniques. This research is supported by EEA/Norwegian Financial Mechanism under project 7F14287 STRADI.

Close Encounters of a Sparse Kind.

ERIC Educational Resources Information Center

Westerberg, Arthur W.

1980-01-01

By providing an example problem in solving sets of nonlinear algebraic equations, the advantages and disadvantages of two methods for its solution, the tearing approach v the Newton-Raphson approach, are elucidated. (CS)

Mapping visual stimuli to perceptual decisions via sparse decoding of mesoscopic neural activity.

PubMed

Sajda, Paul

2010-01-01

In this talk I will describe our work investigating sparse decoding of neural activity, given a realistic mapping of the visual scene to neuronal spike trains generated by a model of primary visual cortex (V1). We use a linear decoder which imposes sparsity via an L1 norm. The decoder can be viewed as a decoding neuron (linear summation followed by a sigmoidal nonlinearity) in which there are relatively few non-zero synaptic weights. We find: (1) the best decoding performance is for a representation that is sparse in both space and time, (2) decoding of a temporal code results in better performance than a rate code and is also a better fit to the psychophysical data, (3) the number of neurons required for decoding increases monotonically as signal-to-noise in the stimulus decreases, with as little as 1% of the neurons required for decoding at the highest signal-to-noise levels, and (4) sparse decoding results in a more accurate decoding of the stimulus and is a better fit to psychophysical performance than a distributed decoding, for example one imposed by an L2 norm. We conclude that sparse coding is well-justified from a decoding perspective in that it results in a minimum number of neurons and maximum accuracy when sparse representations can be decoded from the neural dynamics.

Time-Frequency Analysis of Non-Stationary Biological Signals with Sparse Linear Regression Based Fourier Linear Combiner.

PubMed

Wang, Yubo; Veluvolu, Kalyana C

2017-06-14

It is often difficult to analyze biological signals because of their nonlinear and non-stationary characteristics. This necessitates the usage of time-frequency decomposition methods for analyzing the subtle changes in these signals that are often connected to an underlying phenomena. This paper presents a new approach to analyze the time-varying characteristics of such signals by employing a simple truncated Fourier series model, namely the band-limited multiple Fourier linear combiner (BMFLC). In contrast to the earlier designs, we first identified the sparsity imposed on the signal model in order to reformulate the model to a sparse linear regression model. The coefficients of the proposed model are then estimated by a convex optimization algorithm. The performance of the proposed method was analyzed with benchmark test signals. An energy ratio metric is employed to quantify the spectral performance and results show that the proposed method Sparse-BMFLC has high mean energy (0.9976) ratio and outperforms existing methods such as short-time Fourier transfrom (STFT), continuous Wavelet transform (CWT) and BMFLC Kalman Smoother. Furthermore, the proposed method provides an overall 6.22% in reconstruction error.

Efficient parallel simulation of CO2 geologic sequestration insaline aquifers

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

Zhang, Keni; Doughty, Christine; Wu, Yu-Shu

2007-01-01

An efficient parallel simulator for large-scale, long-termCO2 geologic sequestration in saline aquifers has been developed. Theparallel simulator is a three-dimensional, fully implicit model thatsolves large, sparse linear systems arising from discretization of thepartial differential equations for mass and energy balance in porous andfractured media. The simulator is based on the ECO2N module of the TOUGH2code and inherits all the process capabilities of the single-CPU TOUGH2code, including a comprehensive description of the thermodynamics andthermophysical properties of H2O-NaCl- CO2 mixtures, modeling singleand/or two-phase isothermal or non-isothermal flow processes, two-phasemixtures, fluid phases appearing or disappearing, as well as saltprecipitation or dissolution. The newmore » parallel simulator uses MPI forparallel implementation, the METIS software package for simulation domainpartitioning, and the iterative parallel linear solver package Aztec forsolving linear equations by multiple processors. In addition, theparallel simulator has been implemented with an efficient communicationscheme. Test examples show that a linear or super-linear speedup can beobtained on Linux clusters as well as on supercomputers. Because of thesignificant improvement in both simulation time and memory requirement,the new simulator provides a powerful tool for tackling larger scale andmore complex problems than can be solved by single-CPU codes. Ahigh-resolution simulation example is presented that models buoyantconvection, induced by a small increase in brine density caused bydissolution of CO2.« less

Numerical study of heat transfer and fluid flow for steady crystal growth in a vertical Bridgman device

NASA Astrophysics Data System (ADS)

Pohlman, Matthew Michael

The study of heat transfer and fluid flow in a vertical Bridgman device is motivated by current industrial difficulties in growing crystals with as few defects as possible. For example, Gallium Arsenide (GaAs) is of great interest to the semiconductor industry but remains an uneconomical alternative to silicon because of the manufacturing problems. This dissertation is a two dimensional study of the fluid in an idealized Bridgman device. The model nonlinear PDEs are discretized using second order finite differencing. Newton's method solves the resulting nonlinear discrete equations. The large sparse linear systems involving the Jacobian are solved iteratively using the Generalized Minimum Residual method (GMRES). By adapting fast direct solvers for elliptic equations with simple boundary conditions, a good preconditioner is developed which is essential for GMRES to converge quickly. Trends of the fluid flow and heat transfer for typical ranges of the physical parameters are determined. Also, the size of the terms in the mathematical model are found by numerical investigation, in order to find what terms are in balance as the physical parameters vary. The results suggest the plausibility of simpler asymptotic solutions.

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.

Sparse representation-based image restoration via nonlocal supervised coding

NASA Astrophysics Data System (ADS)

Li, Ao; Chen, Deyun; Sun, Guanglu; Lin, Kezheng

2016-10-01

Sparse representation (SR) and nonlocal technique (NLT) have shown great potential in low-level image processing. However, due to the degradation of the observed image, SR and NLT may not be accurate enough to obtain a faithful restoration results when they are used independently. To improve the performance, in this paper, a nonlocal supervised coding strategy-based NLT for image restoration is proposed. The novel method has three main contributions. First, to exploit the useful nonlocal patches, a nonnegative sparse representation is introduced, whose coefficients can be utilized as the supervised weights among patches. Second, a novel objective function is proposed, which integrated the supervised weights learning and the nonlocal sparse coding to guarantee a more promising solution. Finally, to make the minimization tractable and convergence, a numerical scheme based on iterative shrinkage thresholding is developed to solve the above underdetermined inverse problem. The extensive experiments validate the effectiveness of the proposed method.

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.

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.

Multi-Source Multi-Target Dictionary Learning for Prediction of Cognitive Decline.

PubMed

Zhang, Jie; Li, Qingyang; Caselli, Richard J; Thompson, Paul M; Ye, Jieping; Wang, Yalin

2017-06-01

Alzheimer's Disease (AD) is the most common type of dementia. Identifying correct biomarkers may determine pre-symptomatic AD subjects and enable early intervention. Recently, Multi-task sparse feature learning has been successfully applied to many computer vision and biomedical informatics researches. It aims to improve the generalization performance by exploiting the shared features among different tasks. However, most of the existing algorithms are formulated as a supervised learning scheme. Its drawback is with either insufficient feature numbers or missing label information. To address these challenges, we formulate an unsupervised framework for multi-task sparse feature learning based on a novel dictionary learning algorithm. To solve the unsupervised learning problem, we propose a two-stage Multi-Source Multi-Target Dictionary Learning (MMDL) algorithm. In stage 1, we propose a multi-source dictionary learning method to utilize the common and individual sparse features in different time slots. In stage 2, supported by a rigorous theoretical analysis, we develop a multi-task learning method to solve the missing label problem. Empirical studies on an N = 3970 longitudinal brain image data set, which involves 2 sources and 5 targets, demonstrate the improved prediction accuracy and speed efficiency of MMDL in comparison with other state-of-the-art algorithms.

Group-sparse representation with dictionary learning for medical image denoising and fusion.

PubMed

Li, Shutao; Yin, Haitao; Fang, Leyuan

2012-12-01

Recently, sparse representation has attracted a lot of interest in various areas. However, the standard sparse representation does not consider the intrinsic structure, i.e., the nonzero elements occur in clusters, called group sparsity. Furthermore, there is no dictionary learning method for group sparse representation considering the geometrical structure of space spanned by atoms. In this paper, we propose a novel dictionary learning method, called Dictionary Learning with Group Sparsity and Graph Regularization (DL-GSGR). First, the geometrical structure of atoms is modeled as the graph regularization. Then, combining group sparsity and graph regularization, the DL-GSGR is presented, which is solved by alternating the group sparse coding and dictionary updating. In this way, the group coherence of learned dictionary can be enforced small enough such that any signal can be group sparse coded effectively. Finally, group sparse representation with DL-GSGR is applied to 3-D medical image denoising and image fusion. Specifically, in 3-D medical image denoising, a 3-D processing mechanism (using the similarity among nearby slices) and temporal regularization (to perverse the correlations across nearby slices) are exploited. The experimental results on 3-D image denoising and image fusion demonstrate the superiority of our proposed denoising and fusion approaches.

Human mobility prediction from region functions with taxi trajectories

PubMed Central

Wang, Minjie; Sun, Yi; Gao, Jun

2017-01-01

People in cities nowadays suffer from increasingly severe traffic jams due to less awareness of how collective human mobility is affected by urban planning. Besides, understanding how region functions shape human mobility is critical for business planning but remains unsolved so far. This study aims to discover the association between region functions and resulting human mobility. We establish a linear regression model to predict the traffic flows of Beijing based on the input referred to as bag of POIs. By solving the predictor in the sense of sparse representation, we find that the average prediction precision is over 74% and each type of POI contributes differently in the predictor, which accounts for what factors and how such region functions attract people visiting. Based on these findings, predictive human mobility could be taken into account when planning new regions and region functions. PMID:29190708

Sensor Network Localization by Eigenvector Synchronization Over the Euclidean Group

PubMed Central

CUCURINGU, MIHAI; LIPMAN, YARON; SINGER, AMIT

2013-01-01

We present a new approach to localization of sensors from noisy measurements of a subset of their Euclidean distances. Our algorithm starts by finding, embedding, and aligning uniquely realizable subsets of neighboring sensors called patches. In the noise-free case, each patch agrees with its global positioning up to an unknown rigid motion of translation, rotation, and possibly reflection. The reflections and rotations are estimated using the recently developed eigenvector synchronization algorithm, while the translations are estimated by solving an overdetermined linear system. The algorithm is scalable as the number of nodes increases and can be implemented in a distributed fashion. Extensive numerical experiments show that it compares favorably to other existing algorithms in terms of robustness to noise, sparse connectivity, and running time. While our approach is applicable to higher dimensions, in the current article, we focus on the two-dimensional case. PMID:23946700

Sparse distributed memory overview

NASA Technical Reports Server (NTRS)

Raugh, Mike

1990-01-01

The Sparse Distributed Memory (SDM) project is investigating the theory and applications of massively parallel computing architecture, called sparse distributed memory, that will support the storage and retrieval of sensory and motor patterns characteristic of autonomous systems. The immediate objectives of the project are centered in studies of the memory itself and in the use of the memory to solve problems in speech, vision, and robotics. Investigation of methods for encoding sensory data is an important part of the research. Examples of NASA missions that may benefit from this work are Space Station, planetary rovers, and solar exploration. Sparse distributed memory offers promising technology for systems that must learn through experience and be capable of adapting to new circumstances, and for operating any large complex system requiring automatic monitoring and control. Sparse distributed memory is a massively parallel architecture motivated by efforts to understand how the human brain works. Sparse distributed memory is an associative memory, able to retrieve information from cues that only partially match patterns stored in the memory. It is able to store long temporal sequences derived from the behavior of a complex system, such as progressive records of the system's sensory data and correlated records of the system's motor controls.

Sparse principal component analysis in medical shape modeling

NASA Astrophysics Data System (ADS)

Sjöstrand, Karl; Stegmann, Mikkel B.; Larsen, Rasmus

2006-03-01

Principal component analysis (PCA) is a widely used tool in medical image analysis for data reduction, model building, and data understanding and exploration. While PCA is a holistic approach where each new variable is a linear combination of all original variables, sparse PCA (SPCA) aims at producing easily interpreted models through sparse loadings, i.e. each new variable is a linear combination of a subset of the original variables. One of the aims of using SPCA is the possible separation of the results into isolated and easily identifiable effects. This article introduces SPCA for shape analysis in medicine. Results for three different data sets are given in relation to standard PCA and sparse PCA by simple thresholding of small loadings. Focus is on a recent algorithm for computing sparse principal components, but a review of other approaches is supplied as well. The SPCA algorithm has been implemented using Matlab and is available for download. The general behavior of the algorithm is investigated, and strengths and weaknesses are discussed. The original report on the SPCA algorithm argues that the ordering of modes is not an issue. We disagree on this point and propose several approaches to establish sensible orderings. A method that orders modes by decreasing variance and maximizes the sum of variances for all modes is presented and investigated in detail.

Multi-linear sparse reconstruction for SAR imaging based on higher-order SVD

NASA Astrophysics Data System (ADS)

Gao, Yu-Fei; Gui, Guan; Cong, Xun-Chao; Yang, Yue; Zou, Yan-Bin; Wan, Qun

2017-12-01

This paper focuses on the spotlight synthetic aperture radar (SAR) imaging for point scattering targets based on tensor modeling. In a real-world scenario, scatterers usually distribute in the block sparse pattern. Such a distribution feature has been scarcely utilized by the previous studies of SAR imaging. Our work takes advantage of this structure property of the target scene, constructing a multi-linear sparse reconstruction algorithm for SAR imaging. The multi-linear block sparsity is introduced into higher-order singular value decomposition (SVD) with a dictionary constructing procedure by this research. The simulation experiments for ideal point targets show the robustness of the proposed algorithm to the noise and sidelobe disturbance which always influence the imaging quality of the conventional methods. The computational resources requirement is further investigated in this paper. As a consequence of the algorithm complexity analysis, the present method possesses the superiority on resource consumption compared with the classic matching pursuit method. The imaging implementations for practical measured data also demonstrate the effectiveness of the algorithm developed in this paper.

Numerical Technology for Large-Scale Computational Electromagnetics

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

Sharpe, R; Champagne, N; White, D

The key bottleneck of implicit computational electromagnetics tools for large complex geometries is the solution of the resulting linear system of equations. The goal of this effort was to research and develop critical numerical technology that alleviates this bottleneck for large-scale computational electromagnetics (CEM). The mathematical operators and numerical formulations used in this arena of CEM yield linear equations that are complex valued, unstructured, and indefinite. Also, simultaneously applying multiple mathematical modeling formulations to different portions of a complex problem (hybrid formulations) results in a mixed structure linear system, further increasing the computational difficulty. Typically, these hybrid linear systems aremore » solved using a direct solution method, which was acceptable for Cray-class machines but does not scale adequately for ASCI-class machines. Additionally, LLNL's previously existing linear solvers were not well suited for the linear systems that are created by hybrid implicit CEM codes. Hence, a new approach was required to make effective use of ASCI-class computing platforms and to enable the next generation design capabilities. Multiple approaches were investigated, including the latest sparse-direct methods developed by our ASCI collaborators. In addition, approaches that combine domain decomposition (or matrix partitioning) with general-purpose iterative methods and special purpose pre-conditioners were investigated. Special-purpose pre-conditioners that take advantage of the structure of the matrix were adapted and developed based on intimate knowledge of the matrix properties. Finally, new operator formulations were developed that radically improve the conditioning of the resulting linear systems thus greatly reducing solution time. The goal was to enable the solution of CEM problems that are 10 to 100 times larger than our previous capability.« less

Hyperspherical Sparse Approximation Techniques for High-Dimensional Discontinuity Detection

DOE PAGES

Zhang, Guannan; Webster, Clayton G.; Gunzburger, Max; ...

2016-08-04

This work proposes a hyperspherical sparse approximation framework for detecting jump discontinuities in functions in high-dimensional spaces. The need for a novel approach results from the theoretical and computational inefficiencies of well-known approaches, such as adaptive sparse grids, for discontinuity detection. Our approach constructs the hyperspherical coordinate representation of the discontinuity surface of a function. Then sparse approximations of the transformed function are built in the hyperspherical coordinate system, with values at each point estimated by solving a one-dimensional discontinuity detection problem. Due to the smoothness of the hypersurface, the new technique can identify jump discontinuities with significantly reduced computationalmore » cost, compared to existing methods. Several approaches are used to approximate the transformed discontinuity surface in the hyperspherical system, including adaptive sparse grid and radial basis function interpolation, discrete least squares projection, and compressed sensing approximation. Moreover, hierarchical acceleration techniques are also incorporated to further reduce the overall complexity. In conclusion, rigorous complexity analyses of the new methods are provided, as are several numerical examples that illustrate the effectiveness of our approach.« less

Multi-layer sparse representation for weighted LBP-patches based facial expression recognition.

PubMed

Jia, Qi; Gao, Xinkai; Guo, He; Luo, Zhongxuan; Wang, Yi

2015-03-19

In this paper, a novel facial expression recognition method based on sparse representation is proposed. Most contemporary facial expression recognition systems suffer from limited ability to handle image nuisances such as low resolution and noise. Especially for low intensity expression, most of the existing training methods have quite low recognition rates. Motivated by sparse representation, the problem can be solved by finding sparse coefficients of the test image by the whole training set. Deriving an effective facial representation from original face images is a vital step for successful facial expression recognition. We evaluate facial representation based on weighted local binary patterns, and Fisher separation criterion is used to calculate the weighs of patches. A multi-layer sparse representation framework is proposed for multi-intensity facial expression recognition, especially for low-intensity expressions and noisy expressions in reality, which is a critical problem but seldom addressed in the existing works. To this end, several experiments based on low-resolution and multi-intensity expressions are carried out. Promising results on publicly available databases demonstrate the potential of the proposed approach.

A network of spiking neurons for computing sparse representations in an energy efficient way

PubMed Central

Hu, Tao; Genkin, Alexander; Chklovskii, Dmitri B.

2013-01-01

Computing sparse redundant representations is an important problem both in applied mathematics and neuroscience. In many applications, this problem must be solved in an energy efficient way. Here, we propose a hybrid distributed algorithm (HDA), which solves this problem on a network of simple nodes communicating via low-bandwidth channels. HDA nodes perform both gradient-descent-like steps on analog internal variables and coordinate-descent-like steps via quantized external variables communicated to each other. Interestingly, such operation is equivalent to a network of integrate-and-fire neurons, suggesting that HDA may serve as a model of neural computation. We compare the numerical performance of HDA with existing algorithms and show that in the asymptotic regime the representation error of HDA decays with time, t, as 1/t. We show that HDA is stable against time-varying noise, specifically, the representation error decays as 1/t for Gaussian white noise. PMID:22920853

Sparse Image Reconstruction on the Sphere: Analysis and Synthesis.

PubMed

Wallis, Christopher G R; Wiaux, Yves; McEwen, Jason D

2017-11-01

We develop techniques to solve ill-posed inverse problems on the sphere by sparse regularization, exploiting sparsity in both axisymmetric and directional scale-discretized wavelet space. Denoising, inpainting, and deconvolution problems and combinations thereof, are considered as examples. Inverse problems are solved in both the analysis and synthesis settings, with a number of different sampling schemes. The most effective approach is that with the most restricted solution-space, which depends on the interplay between the adopted sampling scheme, the selection of the analysis/synthesis problem, and any weighting of the l 1 norm appearing in the regularization problem. More efficient sampling schemes on the sphere improve reconstruction fidelity by restricting the solution-space and also by improving sparsity in wavelet space. We apply the technique to denoise Planck 353-GHz observations, improving the ability to extract the structure of Galactic dust emission, which is important for studying Galactic magnetism.

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.

A network of spiking neurons for computing sparse representations in an energy-efficient way.

PubMed

Hu, Tao; Genkin, Alexander; Chklovskii, Dmitri B

2012-11-01

Computing sparse redundant representations is an important problem in both applied mathematics and neuroscience. In many applications, this problem must be solved in an energy-efficient way. Here, we propose a hybrid distributed algorithm (HDA), which solves this problem on a network of simple nodes communicating by low-bandwidth channels. HDA nodes perform both gradient-descent-like steps on analog internal variables and coordinate-descent-like steps via quantized external variables communicated to each other. Interestingly, the operation is equivalent to a network of integrate-and-fire neurons, suggesting that HDA may serve as a model of neural computation. We show that the numerical performance of HDA is on par with existing algorithms. In the asymptotic regime, the representation error of HDA decays with time, t, as 1/t. HDA is stable against time-varying noise; specifically, the representation error decays as 1/√t for gaussian white noise.

A note on the blind deconvolution of multiple sparse signals from unknown subspaces

NASA Astrophysics Data System (ADS)

Cosse, Augustin

2017-08-01

This note studies the recovery of multiple sparse signals, xn ∈ ℝL, n = 1, . . . , N, from the knowledge of their convolution with an unknown point spread function h ∈ ℝL. When the point spread function is known to be nonzero, |h[k]| > 0, this blind deconvolution problem can be relaxed into a linear, ill-posed inverse problem in the vector concatenating the unknown inputs xn together with the inverse of the filter, d ∈ ℝL where d[k] := 1/h[k]. When prior information is given on the input subspaces, the resulting overdetermined linear system can be solved efficiently via least squares (see Ling et al. 20161). When no information is given on those subspaces, and the inputs are only known to be sparse, it still remains possible to recover these inputs along with the filter by considering an additional l1 penalty. This note certifies exact recovery of both the unknown PSF and unknown sparse inputs, from the knowledge of their convolutions, as soon as the number of inputs N and the dimension of each input, L , satisfy L ≳ N and N ≳ T2max, up to log factors. Here Tmax = maxn{Tn} and Tn, n = 1, . . . , N denote the supports of the inputs xn. Our proof system combines the recent results on blind deconvolution via least squares to certify invertibility of the linear map encoding the convolutions, with the construction of a dual certificate following the structure first suggested in Candés et al. 2007.2 Unlike in these papers, however, it is not possible to rely on the norm ||(A*TAT)-1|| to certify recovery. We instead use a combination of the Schur Complement and Neumann series to compute an expression for the inverse (A*TAT)-1. Given this expression, it is possible to show that the poorly scaled blocks in (A*TAT)-1 are multiplied by the better scaled ones or vanish in the construction of the certificate. Recovery is certified with high probablility on the choice of the supports and distribution of the signs of each input xn on the support. The paper follows the line of previous work by Wang et al. 20163 where the authors guarantee recovery for subgaussian × Bernoulli inputs satisfying 𝔼xn|k| ∈ [1/10, 1] as soon as N ≳ L. Examples of applications include seismic imaging with unknown source or marine seismic data deghosting, magnetic resonance autocalibration or multiple channel estimation in communication. Numerical experiments are provided along with a discussion on the sample complexity tightness.

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.

Locality-preserving sparse representation-based classification in hyperspectral imagery

NASA Astrophysics Data System (ADS)

Gao, Lianru; Yu, Haoyang; Zhang, Bing; Li, Qingting

2016-10-01

This paper proposes to combine locality-preserving projections (LPP) and sparse representation (SR) for hyperspectral image classification. The LPP is first used to reduce the dimensionality of all the training and testing data by finding the optimal linear approximations to the eigenfunctions of the Laplace Beltrami operator on the manifold, where the high-dimensional data lies. Then, SR codes the projected testing pixels as sparse linear combinations of all the training samples to classify the testing pixels by evaluating which class leads to the minimum approximation error. The integration of LPP and SR represents an innovative contribution to the literature. The proposed approach, called locality-preserving SR-based classification, addresses the imbalance between high dimensionality of hyperspectral data and the limited number of training samples. Experimental results on three real hyperspectral data sets demonstrate that the proposed approach outperforms the original counterpart, i.e., SR-based classification.

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.

Estimation of white matter fiber parameters from compressed multiresolution diffusion MRI using sparse Bayesian learning.

PubMed

Pisharady, Pramod Kumar; Sotiropoulos, Stamatios N; Duarte-Carvajalino, Julio M; Sapiro, Guillermo; Lenglet, Christophe

2018-02-15

We present a sparse Bayesian unmixing algorithm BusineX: Bayesian Unmixing for Sparse Inference-based Estimation of Fiber Crossings (X), for estimation of white matter fiber parameters from compressed (under-sampled) diffusion MRI (dMRI) data. BusineX combines compressive sensing with linear unmixing and introduces sparsity to the previously proposed multiresolution data fusion algorithm RubiX, resulting in a method for improved reconstruction, especially from data with lower number of diffusion gradients. We formulate the estimation of fiber parameters as a sparse signal recovery problem and propose a linear unmixing framework with sparse Bayesian learning for the recovery of sparse signals, the fiber orientations and volume fractions. The data is modeled using a parametric spherical deconvolution approach and represented using a dictionary created with the exponential decay components along different possible diffusion directions. Volume fractions of fibers along these directions define the dictionary weights. The proposed sparse inference, which is based on the dictionary representation, considers the sparsity of fiber populations and exploits the spatial redundancy in data representation, thereby facilitating inference from under-sampled q-space. The algorithm improves parameter estimation from dMRI through data-dependent local learning of hyperparameters, at each voxel and for each possible fiber orientation, that moderate the strength of priors governing the parameter variances. Experimental results on synthetic and in-vivo data show improved accuracy with a lower uncertainty in fiber parameter estimates. BusineX resolves a higher number of second and third fiber crossings. For under-sampled data, the algorithm is also shown to produce more reliable estimates. Copyright © 2017 Elsevier Inc. All rights reserved.

Object-Oriented Design for Sparse Direct Solvers

NASA Technical Reports Server (NTRS)

Dobrian, Florin; Kumfert, Gary; Pothen, Alex

1999-01-01

We discuss the object-oriented design of a software package for solving sparse, symmetric systems of equations (positive definite and indefinite) by direct methods. At the highest layers, we decouple data structure classes from algorithmic classes for flexibility. We describe the important structural and algorithmic classes in our design, and discuss the trade-offs we made for high performance. The kernels at the lower layers were optimized by hand. Our results show no performance loss from our object-oriented design, while providing flexibility, case of use, and extensibility over solvers using procedural design.

Local structure preserving sparse coding for infrared target recognition

PubMed Central

Han, Jing; Yue, Jiang; Zhang, Yi; Bai, Lianfa

2017-01-01

Sparse coding performs well in image classification. However, robust target recognition requires a lot of comprehensive template images and the sparse learning process is complex. We incorporate sparsity into a template matching concept to construct a local sparse structure matching (LSSM) model for general infrared target recognition. A local structure preserving sparse coding (LSPSc) formulation is proposed to simultaneously preserve the local sparse and structural information of objects. By adding a spatial local structure constraint into the classical sparse coding algorithm, LSPSc can improve the stability of sparse representation for targets and inhibit background interference in infrared images. Furthermore, a kernel LSPSc (K-LSPSc) formulation is proposed, which extends LSPSc to the kernel space to weaken the influence of the linear structure constraint in nonlinear natural data. Because of the anti-interference and fault-tolerant capabilities, both LSPSc- and K-LSPSc-based LSSM can implement target identification based on a simple template set, which just needs several images containing enough local sparse structures to learn a sufficient sparse structure dictionary of a target class. Specifically, this LSSM approach has stable performance in the target detection with scene, shape and occlusions variations. High performance is demonstrated on several datasets, indicating robust infrared target recognition in diverse environments and imaging conditions. PMID:28323824

Initial Simulations of RF Waves in Hot Plasmas Using the FullWave Code

NASA Astrophysics Data System (ADS)

Zhao, Liangji; Svidzinski, Vladimir; Spencer, Andrew; Kim, Jin-Soo

2017-10-01

FullWave is a simulation tool that models RF fields in hot inhomogeneous magnetized plasmas. The wave equations with linearized hot plasma dielectric response are solved in configuration space on adaptive cloud of computational points. The nonlocal hot plasma dielectric response is formulated by calculating the plasma conductivity kernel based on the solution of the linearized Vlasov equation in inhomogeneous magnetic field. In an rf field, the hot plasma dielectric response is limited to the distance of a few particles' Larmor radii, near the magnetic field line passing through the test point. The localization of the hot plasma dielectric response results in a sparse matrix of the problem thus significantly reduces the size of the problem and makes the simulations faster. We will present the initial results of modeling of rf waves using the Fullwave code, including calculation of nonlocal conductivity kernel in 2D Tokamak geometry; the interpolation of conductivity kernel from test points to adaptive cloud of computational points; and the results of self-consistent simulations of 2D rf fields using calculated hot plasma conductivity kernel in a tokamak plasma with reduced parameters. Work supported by the US DOE ``SBIR program.

ALPS: A Linear Program Solver

NASA Technical Reports Server (NTRS)

Ferencz, Donald C.; Viterna, Larry A.

1991-01-01

ALPS is a computer program which can be used to solve general linear program (optimization) problems. ALPS was designed for those who have minimal linear programming (LP) knowledge and features a menu-driven scheme to guide the user through the process of creating and solving LP formulations. Once created, the problems can be edited and stored in standard DOS ASCII files to provide portability to various word processors or even other linear programming packages. Unlike many math-oriented LP solvers, ALPS contains an LP parser that reads through the LP formulation and reports several types of errors to the user. ALPS provides a large amount of solution data which is often useful in problem solving. In addition to pure linear programs, ALPS can solve for integer, mixed integer, and binary type problems. Pure linear programs are solved with the revised simplex method. Integer or mixed integer programs are solved initially with the revised simplex, and the completed using the branch-and-bound technique. Binary programs are solved with the method of implicit enumeration. This manual describes how to use ALPS to create, edit, and solve linear programming problems. Instructions for installing ALPS on a PC compatible computer are included in the appendices along with a general introduction to linear programming. A programmers guide is also included for assistance in modifying and maintaining the program.

Sparse reconstruction for quantitative bioluminescence tomography based on the incomplete variables truncated conjugate gradient method.

PubMed

He, Xiaowei; Liang, Jimin; Wang, Xiaorui; Yu, Jingjing; Qu, Xiaochao; Wang, Xiaodong; Hou, Yanbin; Chen, Duofang; Liu, Fang; Tian, Jie

2010-11-22

In this paper, we present an incomplete variables truncated conjugate gradient (IVTCG) method for bioluminescence tomography (BLT). Considering the sparse characteristic of the light source and insufficient surface measurement in the BLT scenarios, we combine a sparseness-inducing (ℓ1 norm) regularization term with a quadratic error term in the IVTCG-based framework for solving the inverse problem. By limiting the number of variables updated at each iterative and combining a variable splitting strategy to find the search direction more efficiently, it obtains fast and stable source reconstruction, even without a priori information of the permissible source region and multispectral measurements. Numerical experiments on a mouse atlas validate the effectiveness of the method. In vivo mouse experimental results further indicate its potential for a practical BLT system.

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.

A novel aliasing-free subband information fusion approach for wideband sparse spectral estimation

NASA Astrophysics Data System (ADS)

Luo, Ji-An; Zhang, Xiao-Ping; Wang, Zhi

2017-12-01

Wideband sparse spectral estimation is generally formulated as a multi-dictionary/multi-measurement (MD/MM) problem which can be solved by using group sparsity techniques. In this paper, the MD/MM problem is reformulated as a single sparse indicative vector (SIV) recovery problem at the cost of introducing an additional system error. Thus, the number of unknowns is reduced greatly. We show that the system error can be neglected under certain conditions. We then present a new subband information fusion (SIF) method to estimate the SIV by jointly utilizing all the frequency bins. With orthogonal matching pursuit (OMP) leveraging the binary property of SIV's components, we develop a SIF-OMP algorithm to reconstruct the SIV. The numerical simulations demonstrate the performance of the proposed method.

Many-core graph analytics using accelerated sparse linear algebra routines

NASA Astrophysics Data System (ADS)

Kozacik, Stephen; Paolini, Aaron L.; Fox, Paul; Kelmelis, Eric

2016-05-01

Graph analytics is a key component in identifying emerging trends and threats in many real-world applications. Largescale graph analytics frameworks provide a convenient and highly-scalable platform for developing algorithms to analyze large datasets. Although conceptually scalable, these techniques exhibit poor performance on modern computational hardware. Another model of graph computation has emerged that promises improved performance and scalability by using abstract linear algebra operations as the basis for graph analysis as laid out by the GraphBLAS standard. By using sparse linear algebra as the basis, existing highly efficient algorithms can be adapted to perform computations on the graph. This approach, however, is often less intuitive to graph analytics experts, who are accustomed to vertex-centric APIs such as Giraph, GraphX, and Tinkerpop. We are developing an implementation of the high-level operations supported by these APIs in terms of linear algebra operations. This implementation is be backed by many-core implementations of the fundamental GraphBLAS operations required, and offers the advantages of both the intuitive programming model of a vertex-centric API and the performance of a sparse linear algebra implementation. This technology can reduce the number of nodes required, as well as the run-time for a graph analysis problem, enabling customers to perform more complex analysis with less hardware at lower cost. All of this can be accomplished without the requirement for the customer to make any changes to their analytics code, thanks to the compatibility with existing graph APIs.

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.

The construction of sparse models of Mars' crustal magnetic field

NASA Astrophysics Data System (ADS)

Moore, Kimberly; Bloxham, Jeremy

2017-04-01

The crustal magnetic field of Mars is a key constraint on Martian geophysical history, especially the timing of the dynamo shutoff. Maps of the crustal magnetic field of Mars show wide variations in the intensity of magnetization, with most of the Northern hemisphere only weakly magnetized. Previous methods of analysis tend to favor smooth solutions for the crustal magnetic field of Mars, making use of techniques such as L2 norms. Here we utilize inversion methods designed for sparse models, to see how much of the surface area of Mars must be magnetized in order to fit available spacecraft magnetic field data. We solve for the crustal magnetic field at 10,000 individual magnetic pixels on the surface of Mars. We employ an L1 regularization, and solve for models where each magnetic pixel is identically zero, unless required otherwise by the data. We find solutions with an adequate fit to the data with over 90% sparsity (90% of magnetic pixels having a field value of exactly 0). We contrast these solutions with L2-based solutions, as well as an elastic net model (combination of L1 and L2). We find our sparse solutions look dramatically different from previous models in the literature, but still give a physically reasonable history of the dynamo (shutting off around 4.1 Ga).

Multi-Source Multi-Target Dictionary Learning for Prediction of Cognitive Decline

PubMed Central

Zhang, Jie; Li, Qingyang; Caselli, Richard J.; Thompson, Paul M.; Ye, Jieping; Wang, Yalin

2017-01-01

Alzheimer’s Disease (AD) is the most common type of dementia. Identifying correct biomarkers may determine pre-symptomatic AD subjects and enable early intervention. Recently, Multi-task sparse feature learning has been successfully applied to many computer vision and biomedical informatics researches. It aims to improve the generalization performance by exploiting the shared features among different tasks. However, most of the existing algorithms are formulated as a supervised learning scheme. Its drawback is with either insufficient feature numbers or missing label information. To address these challenges, we formulate an unsupervised framework for multi-task sparse feature learning based on a novel dictionary learning algorithm. To solve the unsupervised learning problem, we propose a two-stage Multi-Source Multi-Target Dictionary Learning (MMDL) algorithm. In stage 1, we propose a multi-source dictionary learning method to utilize the common and individual sparse features in different time slots. In stage 2, supported by a rigorous theoretical analysis, we develop a multi-task learning method to solve the missing label problem. Empirical studies on an N = 3970 longitudinal brain image data set, which involves 2 sources and 5 targets, demonstrate the improved prediction accuracy and speed efficiency of MMDL in comparison with other state-of-the-art algorithms. PMID:28943731

Nonconvex Sparse Logistic Regression With Weakly Convex Regularization

NASA Astrophysics Data System (ADS)

Shen, Xinyue; Gu, Yuantao

2018-06-01

In this work we propose to fit a sparse logistic regression model by a weakly convex regularized nonconvex optimization problem. The idea is based on the finding that a weakly convex function as an approximation of the $\\ell_0$ pseudo norm is able to better induce sparsity than the commonly used $\\ell_1$ norm. For a class of weakly convex sparsity inducing functions, we prove the nonconvexity of the corresponding sparse logistic regression problem, and study its local optimality conditions and the choice of the regularization parameter to exclude trivial solutions. Despite the nonconvexity, a method based on proximal gradient descent is used to solve the general weakly convex sparse logistic regression, and its convergence behavior is studied theoretically. Then the general framework is applied to a specific weakly convex function, and a necessary and sufficient local optimality condition is provided. The solution method is instantiated in this case as an iterative firm-shrinkage algorithm, and its effectiveness is demonstrated in numerical experiments by both randomly generated and real datasets.

Highly parallel sparse Cholesky factorization

NASA Technical Reports Server (NTRS)

Gilbert, John R.; Schreiber, Robert

1990-01-01

Several fine grained parallel algorithms were developed and compared to compute the Cholesky factorization of a sparse matrix. The experimental implementations are on the Connection Machine, a distributed memory SIMD machine whose programming model conceptually supplies one processor per data element. In contrast to special purpose algorithms in which the matrix structure conforms to the connection structure of the machine, the focus is on matrices with arbitrary sparsity structure. The most promising algorithm is one whose inner loop performs several dense factorizations simultaneously on a 2-D grid of processors. Virtually any massively parallel dense factorization algorithm can be used as the key subroutine. The sparse code attains execution rates comparable to those of the dense subroutine. Although at present architectural limitations prevent the dense factorization from realizing its potential efficiency, it is concluded that a regular data parallel architecture can be used efficiently to solve arbitrarily structured sparse problems. A performance model is also presented and it is used to analyze the algorithms.

A joint sparse representation-based method for double-trial evoked potentials estimation.

PubMed

Yu, Nannan; Liu, Haikuan; Wang, Xiaoyan; Lu, Hanbing

2013-12-01

In this paper, we present a novel approach to solving an evoked potentials estimating problem. Generally, the evoked potentials in two consecutive trials obtained by repeated identical stimuli of the nerves are extremely similar. In order to trace evoked potentials, we propose a joint sparse representation-based double-trial evoked potentials estimation method, taking full advantage of this similarity. The estimation process is performed in three stages: first, according to the similarity of evoked potentials and the randomness of a spontaneous electroencephalogram, the two consecutive observations of evoked potentials are considered as superpositions of the common component and the unique components; second, making use of their characteristics, the two sparse dictionaries are constructed; and finally, we apply the joint sparse representation method in order to extract the common component of double-trial observations, instead of the evoked potential in each trial. A series of experiments carried out on simulated and human test responses confirmed the superior performance of our method. © 2013 Elsevier Ltd. Published by Elsevier Ltd. All rights reserved.

A Hyperspherical Adaptive Sparse-Grid Method for High-Dimensional Discontinuity Detection

DOE PAGES

Zhang, Guannan; Webster, Clayton G.; Gunzburger, Max D.; ...

2015-06-24

This study proposes and analyzes a hyperspherical adaptive hierarchical sparse-grid method for detecting jump discontinuities of functions in high-dimensional spaces. The method is motivated by the theoretical and computational inefficiencies of well-known adaptive sparse-grid methods for discontinuity detection. Our novel approach constructs a function representation of the discontinuity hypersurface of an N-dimensional discontinuous quantity of interest, by virtue of a hyperspherical transformation. Then, a sparse-grid approximation of the transformed function is built in the hyperspherical coordinate system, whose value at each point is estimated by solving a one-dimensional discontinuity detection problem. Due to the smoothness of the hypersurface, the newmore » technique can identify jump discontinuities with significantly reduced computational cost, compared to existing methods. In addition, hierarchical acceleration techniques are also incorporated to further reduce the overall complexity. Rigorous complexity analyses of the new method are provided as are several numerical examples that illustrate the effectiveness of the approach.« less

Robust Joint Graph Sparse Coding for Unsupervised Spectral Feature Selection.

PubMed

Zhu, Xiaofeng; Li, Xuelong; Zhang, Shichao; Ju, Chunhua; Wu, Xindong

2017-06-01

In this paper, we propose a new unsupervised spectral feature selection model by embedding a graph regularizer into the framework of joint sparse regression for preserving the local structures of data. To do this, we first extract the bases of training data by previous dictionary learning methods and, then, map original data into the basis space to generate their new representations, by proposing a novel joint graph sparse coding (JGSC) model. In JGSC, we first formulate its objective function by simultaneously taking subspace learning and joint sparse regression into account, then, design a new optimization solution to solve the resulting objective function, and further prove the convergence of the proposed solution. Furthermore, we extend JGSC to a robust JGSC (RJGSC) via replacing the least square loss function with a robust loss function, for achieving the same goals and also avoiding the impact of outliers. Finally, experimental results on real data sets showed that both JGSC and RJGSC outperformed the state-of-the-art algorithms in terms of k -nearest neighbor classification performance.

A hyper-spherical adaptive sparse-grid method for high-dimensional discontinuity detection

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

Zhang, Guannan; Webster, Clayton G.; Gunzburger, Max D.

This work proposes and analyzes a hyper-spherical adaptive hierarchical sparse-grid method for detecting jump discontinuities of functions in high-dimensional spaces is proposed. The method is motivated by the theoretical and computational inefficiencies of well-known adaptive sparse-grid methods for discontinuity detection. Our novel approach constructs a function representation of the discontinuity hyper-surface of an N-dimensional dis- continuous quantity of interest, by virtue of a hyper-spherical transformation. Then, a sparse-grid approximation of the transformed function is built in the hyper-spherical coordinate system, whose value at each point is estimated by solving a one-dimensional discontinuity detection problem. Due to the smoothness of themore » hyper-surface, the new technique can identify jump discontinuities with significantly reduced computational cost, compared to existing methods. Moreover, hierarchical acceleration techniques are also incorporated to further reduce the overall complexity. Rigorous error estimates and complexity analyses of the new method are provided as are several numerical examples that illustrate the effectiveness of the approach.« less

Cross-domain expression recognition based on sparse coding and transfer learning

NASA Astrophysics Data System (ADS)

Yang, Yong; Zhang, Weiyi; Huang, Yong

2017-05-01

Traditional facial expression recognition methods usually assume that the training set and the test set are independent and identically distributed. However, in actual expression recognition applications, the conditions of independent and identical distribution are hardly satisfied for the training set and test set because of the difference of light, shade, race and so on. In order to solve this problem and improve the performance of expression recognition in the actual applications, a novel method based on transfer learning and sparse coding is applied to facial expression recognition. First of all, a common primitive model, that is, the dictionary is learnt. Then, based on the idea of transfer learning, the learned primitive pattern is transferred to facial expression and the corresponding feature representation is obtained by sparse coding. The experimental results in CK +, JAFFE and NVIE database shows that the transfer learning based on sparse coding method can effectively improve the expression recognition rate in the cross-domain expression recognition task and is suitable for the practical facial expression recognition applications.

Multi-sparse dictionary colorization algorithm based on the feature classification and detail enhancement

NASA Astrophysics Data System (ADS)

Yan, Dan; Bai, Lianfa; Zhang, Yi; Han, Jing

2018-02-01

For the problems of missing details and performance of the colorization based on sparse representation, we propose a conceptual model framework for colorizing gray-scale images, and then a multi-sparse dictionary colorization algorithm based on the feature classification and detail enhancement (CEMDC) is proposed based on this framework. The algorithm can achieve a natural colorized effect for a gray-scale image, and it is consistent with the human vision. First, the algorithm establishes a multi-sparse dictionary classification colorization model. Then, to improve the accuracy rate of the classification, the corresponding local constraint algorithm is proposed. Finally, we propose a detail enhancement based on Laplacian Pyramid, which is effective in solving the problem of missing details and improving the speed of image colorization. In addition, the algorithm not only realizes the colorization of the visual gray-scale image, but also can be applied to the other areas, such as color transfer between color images, colorizing gray fusion images, and infrared images.

Two conditions for equivalence of 0-norm solution and 1-norm solution in sparse representation.

PubMed

Li, Yuanqing; Amari, Shun-Ichi

2010-07-01

In sparse representation, two important sparse solutions, the 0-norm and 1-norm solutions, have been receiving much of attention. The 0-norm solution is the sparsest, however it is not easy to obtain. Although the 1-norm solution may not be the sparsest, it can be easily obtained by the linear programming method. In many cases, the 0-norm solution can be obtained through finding the 1-norm solution. Many discussions exist on the equivalence of the two sparse solutions. This paper analyzes two conditions for the equivalence of the two sparse solutions. The first condition is necessary and sufficient, however, difficult to verify. Although the second is necessary but is not sufficient, it is easy to verify. In this paper, we analyze the second condition within the stochastic framework and propose a variant. We then prove that the equivalence of the two sparse solutions holds with high probability under the variant of the second condition. Furthermore, in the limit case where the 0-norm solution is extremely sparse, the second condition is also a sufficient condition with probability 1.

On the scalability of the Albany/FELIX first-order Stokes approximation ice sheet solver for large-scale simulations of the Greenland and Antarctic ice sheets

DOE PAGES

Tezaur, Irina K.; Tuminaro, Raymond S.; Perego, Mauro; ...

2015-01-01

We examine the scalability of the recently developed Albany/FELIX finite-element based code for the first-order Stokes momentum balance equations for ice flow. We focus our analysis on the performance of two possible preconditioners for the iterative solution of the sparse linear systems that arise from the discretization of the governing equations: (1) a preconditioner based on the incomplete LU (ILU) factorization, and (2) a recently-developed algebraic multigrid (AMG) preconditioner, constructed using the idea of semi-coarsening. A strong scalability study on a realistic, high resolution Greenland ice sheet problem reveals that, for a given number of processor cores, the AMG preconditionermore » results in faster linear solve times but the ILU preconditioner exhibits better scalability. In addition, a weak scalability study is performed on a realistic, moderate resolution Antarctic ice sheet problem, a substantial fraction of which contains floating ice shelves, making it fundamentally different from the Greenland ice sheet problem. We show that as the problem size increases, the performance of the ILU preconditioner deteriorates whereas the AMG preconditioner maintains scalability. This is because the linear systems are extremely ill-conditioned in the presence of floating ice shelves, and the ill-conditioning has a greater negative effect on the ILU preconditioner than on the AMG preconditioner.« less

On supporting students' understanding of solving linear equation by using flowchart

NASA Astrophysics Data System (ADS)

Toyib, Muhamad; Kusmayadi, Tri Atmojo; Riyadi

2017-05-01

The aim of this study was to support 7th graders to gradually understand the concepts and procedures of solving linear equation. Thirty-two 7th graders of a Junior High School in Surakarta, Indonesia were involved in this study. Design research was used as the research approach to achieve the aim. A set of learning activities in solving linear equation with one unknown were designed based on Realistic Mathematics Education (RME) approach. The activities were started by playing LEGO to find a linear equation then solve the equation by using flowchart. The results indicate that using the realistic problems, playing LEGO could stimulate students to construct linear equation. Furthermore, Flowchart used to encourage students' reasoning and understanding on the concepts and procedures of solving linear equation with one unknown.

Time-domain finite elements in optimal control with application to launch-vehicle guidance. PhD. Thesis

NASA Technical Reports Server (NTRS)

Bless, Robert R.

1991-01-01

A time-domain finite element method is developed for optimal control problems. The theory derived is general enough to handle a large class of problems including optimal control problems that are continuous in the states and controls, problems with discontinuities in the states and/or system equations, problems with control inequality constraints, problems with state inequality constraints, or problems involving any combination of the above. The theory is developed in such a way that no numerical quadrature is necessary regardless of the degree of nonlinearity in the equations. Also, the same shape functions may be employed for every problem because all strong boundary conditions are transformed into natural or weak boundary conditions. In addition, the resulting nonlinear algebraic equations are very sparse. Use of sparse matrix solvers allows for the rapid and accurate solution of very difficult optimization problems. The formulation is applied to launch-vehicle trajectory optimization problems, and results show that real-time optimal guidance is realizable with this method. Finally, a general problem solving environment is created for solving a large class of optimal control problems. The algorithm uses both FORTRAN and a symbolic computation program to solve problems with a minimum of user interaction. The use of symbolic computation eliminates the need for user-written subroutines which greatly reduces the setup time for solving problems.

Split Bregman's optimization method for image construction in compressive sensing

NASA Astrophysics Data System (ADS)

Skinner, D.; Foo, S.; Meyer-Bäse, A.

2014-05-01

The theory of compressive sampling (CS) was reintroduced by Candes, Romberg and Tao, and D. Donoho in 2006. Using a priori knowledge that a signal is sparse, it has been mathematically proven that CS can defY Nyquist sampling theorem. Theoretically, reconstruction of a CS image relies on the minimization and optimization techniques to solve this complex almost NP-complete problem. There are many paths to consider when compressing and reconstructing an image but these methods have remained untested and unclear on natural images, such as underwater sonar images. The goal of this research is to perfectly reconstruct the original sonar image from a sparse signal while maintaining pertinent information, such as mine-like object, in Side-scan sonar (SSS) images. Goldstein and Osher have shown how to use an iterative method to reconstruct the original image through a method called Split Bregman's iteration. This method "decouples" the energies using portions of the energy from both the !1 and !2 norm. Once the energies are split, Bregman iteration is used to solve the unconstrained optimization problem by recursively solving the problems simultaneously. The faster these two steps or energies can be solved then the faster the overall method becomes. While the majority of CS research is still focused on the medical field, this paper will demonstrate the effectiveness of the Split Bregman's methods on sonar images.

Efficient dense blur map estimation for automatic 2D-to-3D conversion

NASA Astrophysics Data System (ADS)

Vosters, L. P. J.; de Haan, G.

2012-03-01

Focus is an important depth cue for 2D-to-3D conversion of low depth-of-field images and video. However, focus can be only reliably estimated on edges. Therefore, Bea et al. [1] first proposed an optimization based approach to propagate focus to non-edge image portions, for single image focus editing. While their approach produces accurate dense blur maps, the computational complexity and memory requirements for solving the resulting sparse linear system with standard multigrid or (multilevel) preconditioning techniques, are infeasible within the stringent requirements of the consumer electronics and broadcast industry. In this paper we propose fast, efficient, low latency, line scanning based focus propagation, which mitigates the need for complex multigrid or (multilevel) preconditioning techniques. In addition we propose facial blur compensation to compensate for false shading edges that cause incorrect blur estimates in people's faces. In general shading leads to incorrect focus estimates, which may lead to unnatural 3D and visual discomfort. Since visual attention mostly tends to faces, our solution solves the most distracting errors. A subjective assessment by paired comparison on a set of challenging low-depth-of-field images shows that the proposed approach achieves equal 3D image quality as optimization based approaches, and that facial blur compensation results in a significant improvement.

Modelling and Computation in the Valuation of Carbon Derivatives with Stochastic Convenience Yields

PubMed Central

Chang, Shuhua; Wang, Xinyu

2015-01-01

The anthropogenic greenhouse gas (GHG) emission has risen dramatically during the last few decades, which mainstream researchers believe to be the main cause of climate change, especially the global warming. The mechanism of market-based carbon emission trading is regarded as a policy instrument to deal with global climate change. Although several empirical researches about the carbon allowance and its derivatives price have been made, theoretical results seem to be sparse. In this paper, we theoretically develop a mathematical model to price the CO2 emission allowance derivatives with stochastic convenience yields by the principle of absence of arbitrage opportunities. In the case of American options, we formulate the pricing problem to a linear parabolic variational inequality (VI) in two spatial dimensions and develop a power penalty method to solve it. Then, a fitted finite volume method is designed to solve the nonlinear partial differential equation (PDE) resulting from the power penalty method and governing the futures, European and American option valuation. Moreover, some numerical results are performed to illustrate the efficiency and usefulness of this method. We find that the stochastic convenience yield does effect the valuation of carbon emission derivatives. In addition, some sensitivity analyses are also made to examine the effects of some parameters on the valuation results. PMID:26010900

Data Structures for Extreme Scale Computing

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

Kahan, Simon

As computing problems of national importance grow, the government meets the increased demand by funding the development of ever larger systems. The overarching goal of the work supported in part by this grant is to increase efficiency of programming and performing computations on these large computing systems. In past work, we have demonstrated that some of these computations once thought to require expensive hardware designs and/or complex, special-purpose programming may be executed efficiently on low-cost commodity cluster computing systems using a general-purpose “latency-tolerant” programming framework. One important developed application of the ideas underlying this framework is graph database technology supportingmore » social network pattern matching used by US intelligence agencies to more quickly identify potential terrorist threats. This database application has been spun out by the Pacific Northwest National Laboratory, a Department of Energy Laboratory, into a commercial start-up, Trovares Inc. We explore an alternative application of the same underlying ideas to a well-studied challenge arising in engineering: solving unstructured sparse linear equations. Solving these equations is key to predicting the behavior of large electronic circuits before they are fabricated. Predicting that behavior ahead of fabrication means that designs can optimized and errors corrected ahead of the expense of manufacture.« less

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.

Modelling and computation in the valuation of carbon derivatives with stochastic convenience yields.

PubMed

Chang, Shuhua; Wang, Xinyu

2015-01-01

The anthropogenic greenhouse gas (GHG) emission has risen dramatically during the last few decades, which mainstream researchers believe to be the main cause of climate change, especially the global warming. The mechanism of market-based carbon emission trading is regarded as a policy instrument to deal with global climate change. Although several empirical researches about the carbon allowance and its derivatives price have been made, theoretical results seem to be sparse. In this paper, we theoretically develop a mathematical model to price the CO2 emission allowance derivatives with stochastic convenience yields by the principle of absence of arbitrage opportunities. In the case of American options, we formulate the pricing problem to a linear parabolic variational inequality (VI) in two spatial dimensions and develop a power penalty method to solve it. Then, a fitted finite volume method is designed to solve the nonlinear partial differential equation (PDE) resulting from the power penalty method and governing the futures, European and American option valuation. Moreover, some numerical results are performed to illustrate the efficiency and usefulness of this method. We find that the stochastic convenience yield does effect the valuation of carbon emission derivatives. In addition, some sensitivity analyses are also made to examine the effects of some parameters on the valuation results.

Elastic-Waveform Inversion with Compressive Sensing for Sparse Seismic Data

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

Lin, Youzuo; Huang, Lianjie

2015-01-28

Accurate velocity models of compressional- and shear-waves are essential for geothermal reservoir characterization and microseismic imaging. Elastic-waveform inversion of multi-component seismic data can provide high-resolution inversion results of subsurface geophysical properties. However, the method requires seismic data acquired using dense source and receiver arrays. In practice, seismic sources and/or geophones are often sparsely distributed on the surface and/or in a borehole, such as 3D vertical seismic profiling (VSP) surveys. We develop a novel elastic-waveform inversion method with compressive sensing for inversion of sparse seismic data. We employ an alternating-minimization algorithm to solve the optimization problem of our new waveform inversionmore » method. We validate our new method using synthetic VSP data for a geophysical model built using geologic features found at the Raft River enhanced-geothermal-system (EGS) field. We apply our method to synthetic VSP data with a sparse source array and compare the results with those obtained with a dense source array. Our numerical results demonstrate that the velocity models produced with our new method using a sparse source array are almost as accurate as those obtained using a dense source array.« less

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.

Cerebellar Functional Parcellation Using Sparse Dictionary Learning Clustering.

PubMed

Wang, Changqing; Kipping, Judy; Bao, Chenglong; Ji, Hui; Qiu, Anqi

2016-01-01

The human cerebellum has recently been discovered to contribute to cognition and emotion beyond the planning and execution of movement, suggesting its functional heterogeneity. We aimed to identify the functional parcellation of the cerebellum using information from resting-state functional magnetic resonance imaging (rs-fMRI). For this, we introduced a new data-driven decomposition-based functional parcellation algorithm, called Sparse Dictionary Learning Clustering (SDLC). SDLC integrates dictionary learning, sparse representation of rs-fMRI, and k-means clustering into one optimization problem. The dictionary is comprised of an over-complete set of time course signals, with which a sparse representation of rs-fMRI signals can be constructed. Cerebellar functional regions were then identified using k-means clustering based on the sparse representation of rs-fMRI signals. We solved SDLC using a multi-block hybrid proximal alternating method that guarantees strong convergence. We evaluated the reliability of SDLC and benchmarked its classification accuracy against other clustering techniques using simulated data. We then demonstrated that SDLC can identify biologically reasonable functional regions of the cerebellum as estimated by their cerebello-cortical functional connectivity. We further provided new insights into the cerebello-cortical functional organization in children.

Medical image classification based on multi-scale non-negative sparse coding.

PubMed

Zhang, Ruijie; Shen, Jian; Wei, Fushan; Li, Xiong; Sangaiah, Arun Kumar

2017-11-01

With the rapid development of modern medical imaging technology, medical image classification has become more and more important in medical diagnosis and clinical practice. Conventional medical image classification algorithms usually neglect the semantic gap problem between low-level features and high-level image semantic, which will largely degrade the classification performance. To solve this problem, we propose a multi-scale non-negative sparse coding based medical image classification algorithm. Firstly, Medical images are decomposed into multiple scale layers, thus diverse visual details can be extracted from different scale layers. Secondly, for each scale layer, the non-negative sparse coding model with fisher discriminative analysis is constructed to obtain the discriminative sparse representation of medical images. Then, the obtained multi-scale non-negative sparse coding features are combined to form a multi-scale feature histogram as the final representation for a medical image. Finally, SVM classifier is combined to conduct medical image classification. The experimental results demonstrate that our proposed algorithm can effectively utilize multi-scale and contextual spatial information of medical images, reduce the semantic gap in a large degree and improve medical image classification performance. Copyright © 2017 Elsevier B.V. All rights reserved.

LDRD final report on massively-parallel linear programming : the parPCx system.

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

Parekh, Ojas; Phillips, Cynthia Ann; Boman, Erik Gunnar

2005-02-01

This report summarizes the research and development performed from October 2002 to September 2004 at Sandia National Laboratories under the Laboratory-Directed Research and Development (LDRD) project ''Massively-Parallel Linear Programming''. We developed a linear programming (LP) solver designed to use a large number of processors. LP is the optimization of a linear objective function subject to linear constraints. Companies and universities have expended huge efforts over decades to produce fast, stable serial LP solvers. Previous parallel codes run on shared-memory systems and have little or no distribution of the constraint matrix. We have seen no reports of general LP solver runsmore » on large numbers of processors. Our parallel LP code is based on an efficient serial implementation of Mehrotra's interior-point predictor-corrector algorithm (PCx). The computational core of this algorithm is the assembly and solution of a sparse linear system. We have substantially rewritten the PCx code and based it on Trilinos, the parallel linear algebra library developed at Sandia. Our interior-point method can use either direct or iterative solvers for the linear system. To achieve a good parallel data distribution of the constraint matrix, we use a (pre-release) version of a hypergraph partitioner from the Zoltan partitioning library. We describe the design and implementation of our new LP solver called parPCx and give preliminary computational results. We summarize a number of issues related to efficient parallel solution of LPs with interior-point methods including data distribution, numerical stability, and solving the core linear system using both direct and iterative methods. We describe a number of applications of LP specific to US Department of Energy mission areas and we summarize our efforts to integrate parPCx (and parallel LP solvers in general) into Sandia's massively-parallel integer programming solver PICO (Parallel Interger and Combinatorial Optimizer). We conclude with directions for long-term future algorithmic research and for near-term development that could improve the performance of parPCx.« less

Protein crystal structure from non-oriented, single-axis sparse X-ray data

DOE PAGES

Wierman, Jennifer L.; Lan, Ti-Yen; Tate, Mark W.; ...

2016-01-01

X-ray free-electron lasers (XFELs) have inspired the development of serial femtosecond crystallography (SFX) as a method to solve the structure of proteins. SFX datasets are collected from a sequence of protein microcrystals injected across ultrashort X-ray pulses. The idea behind SFX is that diffraction from the intense, ultrashort X-ray pulses leaves the crystal before the crystal is obliterated by the effects of the X-ray pulse. The success of SFX at XFELs has catalyzed interest in analogous experiments at synchrotron-radiation (SR) sources, where data are collected from many small crystals and the ultrashort pulses are replaced by exposure times that aremore » kept short enough to avoid significant crystal damage. The diffraction signal from each short exposure is so `sparse' in recorded photons that the process of recording the crystal intensity is itself a reconstruction problem. Using theEMCalgorithm, a successful reconstruction is demonstrated here in a sparsity regime where there are no Bragg peaks that conventionally would serve to determine the orientation of the crystal in each exposure. In this proof-of-principle experiment, a hen egg-white lysozyme (HEWL) crystal rotating about a single axis was illuminated by an X-ray beam from an X-ray generator to simulate the diffraction patterns of microcrystals from synchrotron radiation. Millions of these sparse frames, typically containing only ~200 photons per frame, were recorded using a fast-framing detector. It is shown that reconstruction of three-dimensional diffraction intensity is possible using theEMCalgorithm, even with these extremely sparse frames and without knowledge of the rotation angle. Further, the reconstructed intensity can be phased and refined to solve the protein structure using traditional crystallographic software. In conclusion, this suggests that synchrotron-based serial crystallography of micrometre-sized crystals can be practical with the aid of theEMCalgorithm even in cases where the data are sparse.« less

Protein crystal structure from non-oriented, single-axis sparse X-ray data

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

Wierman, Jennifer L.; Lan, Ti-Yen; Tate, Mark W.

X-ray free-electron lasers (XFELs) have inspired the development of serial femtosecond crystallography (SFX) as a method to solve the structure of proteins. SFX datasets are collected from a sequence of protein microcrystals injected across ultrashort X-ray pulses. The idea behind SFX is that diffraction from the intense, ultrashort X-ray pulses leaves the crystal before the crystal is obliterated by the effects of the X-ray pulse. The success of SFX at XFELs has catalyzed interest in analogous experiments at synchrotron-radiation (SR) sources, where data are collected from many small crystals and the ultrashort pulses are replaced by exposure times that aremore » kept short enough to avoid significant crystal damage. The diffraction signal from each short exposure is so `sparse' in recorded photons that the process of recording the crystal intensity is itself a reconstruction problem. Using theEMCalgorithm, a successful reconstruction is demonstrated here in a sparsity regime where there are no Bragg peaks that conventionally would serve to determine the orientation of the crystal in each exposure. In this proof-of-principle experiment, a hen egg-white lysozyme (HEWL) crystal rotating about a single axis was illuminated by an X-ray beam from an X-ray generator to simulate the diffraction patterns of microcrystals from synchrotron radiation. Millions of these sparse frames, typically containing only ~200 photons per frame, were recorded using a fast-framing detector. It is shown that reconstruction of three-dimensional diffraction intensity is possible using theEMCalgorithm, even with these extremely sparse frames and without knowledge of the rotation angle. Further, the reconstructed intensity can be phased and refined to solve the protein structure using traditional crystallographic software. In conclusion, this suggests that synchrotron-based serial crystallography of micrometre-sized crystals can be practical with the aid of theEMCalgorithm even in cases where the data are sparse.« less

New Parallel Algorithms for Structural Analysis and Design of Aerospace Structures

NASA Technical Reports Server (NTRS)

Nguyen, Duc T.

1998-01-01

Subspace and Lanczos iterations have been developed, well documented, and widely accepted as efficient methods for obtaining p-lowest eigen-pair solutions of large-scale, practical engineering problems. The focus of this paper is to incorporate recent developments in vectorized sparse technologies in conjunction with Subspace and Lanczos iterative algorithms for computational enhancements. Numerical performance, in terms of accuracy and efficiency of the proposed sparse strategies for Subspace and Lanczos algorithm, is demonstrated by solving for the lowest frequencies and mode shapes of structural problems on the IBM-R6000/590 and SunSparc 20 workstations.

Distributed memory compiler design for sparse problems

NASA Technical Reports Server (NTRS)

Wu, Janet; Saltz, Joel; Berryman, Harry; Hiranandani, Seema

1991-01-01

A compiler and runtime support mechanism is described and demonstrated. The methods presented are capable of solving a wide range of sparse and unstructured problems in scientific computing. The compiler takes as input a FORTRAN 77 program enhanced with specifications for distributing data, and the compiler outputs a message passing program that runs on a distributed memory computer. The runtime support for this compiler is a library of primitives designed to efficiently support irregular patterns of distributed array accesses and irregular distributed array partitions. A variety of Intel iPSC/860 performance results obtained through the use of this compiler are presented.

Parallel solution of sparse one-dimensional dynamic programming problems

NASA Technical Reports Server (NTRS)

Nicol, David M.

1989-01-01

Parallel computation offers the potential for quickly solving large computational problems. However, it is often a non-trivial task to effectively use parallel computers. Solution methods must sometimes be reformulated to exploit parallelism; the reformulations are often more complex than their slower serial counterparts. We illustrate these points by studying the parallelization of sparse one-dimensional dynamic programming problems, those which do not obviously admit substantial parallelization. We propose a new method for parallelizing such problems, develop analytic models which help us to identify problems which parallelize well, and compare the performance of our algorithm with existing algorithms on a multiprocessor.

Sparse learning of stochastic dynamical equations

NASA Astrophysics Data System (ADS)

Boninsegna, Lorenzo; Nüske, Feliks; Clementi, Cecilia

2018-06-01

With the rapid increase of available data for complex systems, there is great interest in the extraction of physically relevant information from massive datasets. Recently, a framework called Sparse Identification of Nonlinear Dynamics (SINDy) has been introduced to identify the governing equations of dynamical systems from simulation data. In this study, we extend SINDy to stochastic dynamical systems which are frequently used to model biophysical processes. We prove the asymptotic correctness of stochastic SINDy in the infinite data limit, both in the original and projected variables. We discuss algorithms to solve the sparse regression problem arising from the practical implementation of SINDy and show that cross validation is an essential tool to determine the right level of sparsity. We demonstrate the proposed methodology on two test systems, namely, the diffusion in a one-dimensional potential and the projected dynamics of a two-dimensional diffusion process.

Sparse regularization for force identification using dictionaries

NASA Astrophysics Data System (ADS)

Qiao, Baijie; Zhang, Xingwu; Wang, Chenxi; Zhang, Hang; Chen, Xuefeng

2016-04-01

The classical function expansion method based on minimizing l2-norm of the response residual employs various basis functions to represent the unknown force. Its difficulty lies in determining the optimum number of basis functions. Considering the sparsity of force in the time domain or in other basis space, we develop a general sparse regularization method based on minimizing l1-norm of the coefficient vector of basis functions. The number of basis functions is adaptively determined by minimizing the number of nonzero components in the coefficient vector during the sparse regularization process. First, according to the profile of the unknown force, the dictionary composed of basis functions is determined. Second, a sparsity convex optimization model for force identification is constructed. Third, given the transfer function and the operational response, Sparse reconstruction by separable approximation (SpaRSA) is developed to solve the sparse regularization problem of force identification. Finally, experiments including identification of impact and harmonic forces are conducted on a cantilever thin plate structure to illustrate the effectiveness and applicability of SpaRSA. Besides the Dirac dictionary, other three sparse dictionaries including Db6 wavelets, Sym4 wavelets and cubic B-spline functions can also accurately identify both the single and double impact forces from highly noisy responses in a sparse representation frame. The discrete cosine functions can also successfully reconstruct the harmonic forces including the sinusoidal, square and triangular forces. Conversely, the traditional Tikhonov regularization method with the L-curve criterion fails to identify both the impact and harmonic forces in these cases.

Multivariate quadrature for representing cloud condensation nuclei activity of aerosol populations

DOE PAGES

Fierce, Laura; McGraw, Robert L.

2017-07-26

Here, sparse representations of atmospheric aerosols are needed for efficient regional- and global-scale chemical transport models. Here we introduce a new framework for representing aerosol distributions, based on the quadrature method of moments. Given a set of moment constraints, we show how linear programming, combined with an entropy-inspired cost function, can be used to construct optimized quadrature representations of aerosol distributions. The sparse representations derived from this approach accurately reproduce cloud condensation nuclei (CCN) activity for realistically complex distributions simulated by a particleresolved model. Additionally, the linear programming techniques described in this study can be used to bound key aerosolmore » properties, such as the number concentration of CCN. Unlike the commonly used sparse representations, such as modal and sectional schemes, the maximum-entropy approach described here is not constrained to pre-determined size bins or assumed distribution shapes. This study is a first step toward a particle-based aerosol scheme that will track multivariate aerosol distributions with sufficient computational efficiency for large-scale simulations.« less

Multivariate quadrature for representing cloud condensation nuclei activity of aerosol populations

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

Fierce, Laura; McGraw, Robert L.

Here, sparse representations of atmospheric aerosols are needed for efficient regional- and global-scale chemical transport models. Here we introduce a new framework for representing aerosol distributions, based on the quadrature method of moments. Given a set of moment constraints, we show how linear programming, combined with an entropy-inspired cost function, can be used to construct optimized quadrature representations of aerosol distributions. The sparse representations derived from this approach accurately reproduce cloud condensation nuclei (CCN) activity for realistically complex distributions simulated by a particleresolved model. Additionally, the linear programming techniques described in this study can be used to bound key aerosolmore » properties, such as the number concentration of CCN. Unlike the commonly used sparse representations, such as modal and sectional schemes, the maximum-entropy approach described here is not constrained to pre-determined size bins or assumed distribution shapes. This study is a first step toward a particle-based aerosol scheme that will track multivariate aerosol distributions with sufficient computational efficiency for large-scale simulations.« less

A linear recurrent kernel online learning algorithm with sparse updates.

PubMed

Fan, Haijin; Song, Qing

2014-02-01

In this paper, we propose a recurrent kernel algorithm with selectively sparse updates for online learning. The algorithm introduces a linear recurrent term in the estimation of the current output. This makes the past information reusable for updating of the algorithm in the form of a recurrent gradient term. To ensure that the reuse of this recurrent gradient indeed accelerates the convergence speed, a novel hybrid recurrent training is proposed to switch on or off learning the recurrent information according to the magnitude of the current training error. Furthermore, the algorithm includes a data-dependent adaptive learning rate which can provide guaranteed system weight convergence at each training iteration. The learning rate is set as zero when the training violates the derived convergence conditions, which makes the algorithm updating process sparse. Theoretical analyses of the weight convergence are presented and experimental results show the good performance of the proposed algorithm in terms of convergence speed and estimation accuracy. Copyright © 2013 Elsevier Ltd. All rights reserved.

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...

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.

Single image super-resolution based on compressive sensing and improved TV minimization sparse recovery

NASA Astrophysics Data System (ADS)

Vishnukumar, S.; Wilscy, M.

2017-12-01

In this paper, we propose a single image Super-Resolution (SR) method based on Compressive Sensing (CS) and Improved Total Variation (TV) Minimization Sparse Recovery. In the CS framework, low-resolution (LR) image is treated as the compressed version of high-resolution (HR) image. Dictionary Training and Sparse Recovery are the two phases of the method. K-Singular Value Decomposition (K-SVD) method is used for dictionary training and the dictionary represents HR image patches in a sparse manner. Here, only the interpolated version of the LR image is used for training purpose and thereby the structural self similarity inherent in the LR image is exploited. In the sparse recovery phase the sparse representation coefficients with respect to the trained dictionary for LR image patches are derived using Improved TV Minimization method. HR image can be reconstructed by the linear combination of the dictionary and the sparse coefficients. The experimental results show that the proposed method gives better results quantitatively as well as qualitatively on both natural and remote sensing images. The reconstructed images have better visual quality since edges and other sharp details are preserved.

The Linearized Bregman Method for Frugal Full-waveform Inversion with Compressive Sensing and Sparsity-promoting

NASA Astrophysics Data System (ADS)

Chai, Xintao; Tang, Genyang; Peng, Ronghua; Liu, Shaoyong

2018-03-01

Full-waveform inversion (FWI) reconstructs the subsurface properties from acquired seismic data via minimization of the misfit between observed and simulated data. However, FWI suffers from considerable computational costs resulting from the numerical solution of the wave equation for each source at each iteration. To reduce the computational burden, constructing supershots by combining several sources (aka source encoding) allows mitigation of the number of simulations at each iteration, but it gives rise to crosstalk artifacts because of interference between the individual sources of the supershot. A modified Gauss-Newton FWI (MGNFWI) approach showed that as long as the difference between the initial and true models permits a sparse representation, the ℓ _1-norm constrained model updates suppress subsampling-related artifacts. However, the spectral-projected gradient ℓ _1 (SPGℓ _1) algorithm employed by MGNFWI is rather complicated that makes its implementation difficult. To facilitate realistic applications, we adapt a linearized Bregman (LB) method to sparsity-promoting FWI (SPFWI) because of the efficiency and simplicity of LB in the framework of ℓ _1-norm constrained optimization problem and compressive sensing. Numerical experiments performed with the BP Salt model, the Marmousi model and the BG Compass model verify the following points. The FWI result with LB solving ℓ _1-norm sparsity-promoting problem for the model update outperforms that generated by solving ℓ _2-norm problem in terms of crosstalk elimination and high-fidelity results. The simpler LB method performs comparably and even superiorly to the complicated SPGℓ _1 method in terms of computational efficiency and model quality, making the LB method a viable alternative for realistic implementations of SPFWI.

Sparse Regression as a Sparse Eigenvalue Problem

NASA Technical Reports Server (NTRS)

Moghaddam, Baback; Gruber, Amit; Weiss, Yair; Avidan, Shai

2008-01-01

We extend the l0-norm "subspectral" algorithms for sparse-LDA [5] and sparse-PCA [6] to general quadratic costs such as MSE in linear (kernel) regression. The resulting "Sparse Least Squares" (SLS) problem is also NP-hard, by way of its equivalence to a rank-1 sparse eigenvalue problem (e.g., binary sparse-LDA [7]). Specifically, for a general quadratic cost we use a highly-efficient technique for direct eigenvalue computation using partitioned matrix inverses which leads to dramatic x103 speed-ups over standard eigenvalue decomposition. This increased efficiency mitigates the O(n4) scaling behaviour that up to now has limited the previous algorithms' utility for high-dimensional learning problems. Moreover, the new computation prioritizes the role of the less-myopic backward elimination stage which becomes more efficient than forward selection. Similarly, branch-and-bound search for Exact Sparse Least Squares (ESLS) also benefits from partitioned matrix inverse techniques. Our Greedy Sparse Least Squares (GSLS) generalizes Natarajan's algorithm [9] also known as Order-Recursive Matching Pursuit (ORMP). Specifically, the forward half of GSLS is exactly equivalent to ORMP but more efficient. By including the backward pass, which only doubles the computation, we can achieve lower MSE than ORMP. Experimental comparisons to the state-of-the-art LARS algorithm [3] show forward-GSLS is faster, more accurate and more flexible in terms of choice of regularization

Sparse Modeling of Human Actions from Motion Imagery

DTIC Science & Technology

2011-09-02

is here developed. Spatio-temporal features that char- acterize local changes in the image are rst extracted. This is followed by the learning of a...video comes from the optimal sparse linear com- bination of the learned basis vectors (action primitives) representing the actions. A low...computational cost deep-layer model learning the inter- class correlations of the data is added for increasing discriminative power. In spite of its simplicity

CPDES3: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in three dimensions

NASA Astrophysics Data System (ADS)

Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

1988-11-01

Many physical problems require the solution of coupled partial differential equations on three-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES3 allows each spatial operator to have 7, 15, 19, or 27 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect induces which is vectorizable on some of the newer scientific computers.

CPDES2: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in two dimensions

NASA Astrophysics Data System (ADS)

Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

1988-11-01

Many physical problems require the solution of coupled partial differential equations on two-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES2 allows each spatial operator to have 5 or 9 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect indices which is vectorizable on some of the newer scientific computers.

Automated problem scheduling and reduction of synchronization delay effects

NASA Technical Reports Server (NTRS)

Saltz, Joel H.

1987-01-01

It is anticipated that in order to make effective use of many future high performance architectures, programs will have to exhibit at least a medium grained parallelism. A framework is presented for partitioning very sparse triangular systems of linear equations that is designed to produce favorable preformance results in a wide variety of parallel architectures. Efficient methods for solving these systems are of interest because: (1) they provide a useful model problem for use in exploring heuristics for the aggregation, mapping and scheduling of relatively fine grained computations whose data dependencies are specified by directed acrylic graphs, and (2) because such efficient methods can find direct application in the development of parallel algorithms for scientific computation. Simple expressions are derived that describe how to schedule computational work with varying degrees of granularity. The Encore Multimax was used as a hardware simulator to investigate the performance effects of using the partitioning techniques presented in shared memory architectures with varying relative synchronization costs.

Using absolute gravimeter data to determine vertical gravity gradients

USGS Publications Warehouse

Robertson, D.S.

2001-01-01

The position versus time data from a free-fall absolute gravimeter can be used to estimate the vertical gravity gradient in addition to the gravity value itself. Hipkin has reported success in estimating the vertical gradient value using a data set of unusually good quality. This paper explores techniques that may be applicable to a broader class of data that may be contaminated with "system response" errors of larger magnitude than were evident in the data used by Hipkin. This system response function is usually modelled as a sum of exponentially decaying sinusoidal components. The technique employed here involves combining the x0, v0 and g parameters from all the drops made during a site occupation into a single least-squares solution, and including the value of the vertical gradient and the coefficients of system response function in the same solution. The resulting non-linear equations must be solved iteratively and convergence presents some difficulties. Sparse matrix techniques are used to make the least-squares problem computationally tractable.

Fiber Orientation Estimation Guided by a Deep Network.

PubMed

Ye, Chuyang; Prince, Jerry L

2017-09-01

Diffusion magnetic resonance imaging (dMRI) is currently the only tool for noninvasively imaging the brain's white matter tracts. The fiber orientation (FO) is a key feature computed from dMRI for tract reconstruction. Because the number of FOs in a voxel is usually small, dictionary-based sparse reconstruction has been used to estimate FOs. However, accurate estimation of complex FO configurations in the presence of noise can still be challenging. In this work we explore the use of a deep network for FO estimation in a dictionary-based framework and propose an algorithm named Fiber Orientation Reconstruction guided by a Deep Network (FORDN). FORDN consists of two steps. First, we use a smaller dictionary encoding coarse basis FOs to represent diffusion signals. To estimate the mixture fractions of the dictionary atoms, a deep network is designed to solve the sparse reconstruction problem. Second, the coarse FOs inform the final FO estimation, where a larger dictionary encoding a dense basis of FOs is used and a weighted ℓ 1 -norm regularized least squares problem is solved to encourage FOs that are consistent with the network output. FORDN was evaluated and compared with state-of-the-art algorithms that estimate FOs using sparse reconstruction on simulated and typical clinical dMRI data. The results demonstrate the benefit of using a deep network for FO estimation.

EIT Imaging Regularization Based on Spectral Graph Wavelets.

PubMed

Gong, Bo; Schullcke, Benjamin; Krueger-Ziolek, Sabine; Vauhkonen, Marko; Wolf, Gerhard; Mueller-Lisse, Ullrich; Moeller, Knut

2017-09-01

The objective of electrical impedance tomographic reconstruction is to identify the distribution of tissue conductivity from electrical boundary conditions. This is an ill-posed inverse problem usually solved under the finite-element method framework. In previous studies, standard sparse regularization was used for difference electrical impedance tomography to achieve a sparse solution. However, regarding elementwise sparsity, standard sparse regularization interferes with the smoothness of conductivity distribution between neighboring elements and is sensitive to noise. As an effect, the reconstructed images are spiky and depict a lack of smoothness. Such unexpected artifacts are not realistic and may lead to misinterpretation in clinical applications. To eliminate such artifacts, we present a novel sparse regularization method that uses spectral graph wavelet transforms. Single-scale or multiscale graph wavelet transforms are employed to introduce local smoothness on different scales into the reconstructed images. The proposed approach relies on viewing finite-element meshes as undirected graphs and applying wavelet transforms derived from spectral graph theory. Reconstruction results from simulations, a phantom experiment, and patient data suggest that our algorithm is more robust to noise and produces more reliable images.

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.

Seeking Space Aliens and the Strong Approximation Property: A (disjoint) Study in Dust Plumes on Planetary Satellites and Nonsymmetric Algebraic Multigrid

NASA Astrophysics Data System (ADS)

Southworth, Benjamin Scott

PART I: One of the most fascinating questions to humans has long been whether life exists outside of our planet. To our knowledge, water is a fundamental building block of life, which makes liquid water on other bodies in the universe a topic of great interest. In fact, there are large bodies of water right here in our solar system, underneath the icy crust of moons around Saturn and Jupiter. The NASA-ESA Cassini Mission spent two decades studying the Saturnian system. One of the many exciting discoveries was a "plume" on the south pole of Enceladus, emitting hundreds of kg/s of water vapor and frozen water-ice particles from Enceladus' subsurface ocean. It has since been determined that Enceladus likely has a global liquid water ocean separating its rocky core from icy surface, with conditions that are relatively favorable to support life. The plume is of particular interest because it gives direct access to ocean particles from space, by flying through the plume. Recently, evidence has been found for similar geological activity occurring on Jupiter's moon Europa, long considered one of the most likely candidate bodies to support life in our solar system. Here, a model for plume-particle dynamics is developed based on studies of the Enceladus plume and data from the Cassini Cosmic Dust Analyzer. A C++, OpenMP/MPI parallel software package is then built to run large scale simulations of dust plumes on planetary satellites. In the case of Enceladus, data from simulations and the Cassini mission provide insight into the structure of emissions on the surface, the total mass production of the plume, and the distribution of particles being emitted. Each of these are fundamental to understanding the plume and, for Europa and Enceladus, simulation data provide important results for the planning of future missions to these icy moons. In particular, this work has contributed to the Europa Clipper mission and proposed Enceladus Life Finder. PART II: Solving large, sparse linear systems arises often in the modeling of biological and physical phenomenon, data analysis through graphs and networks, and other scientific applications. This work focuses primarily on linear systems resulting from the discretization of partial differential equations (PDEs). Because solving linear systems is the bottleneck of many large simulation codes, there is a rich field of research in developing "fast" solvers, with the ultimate goal being a method that solves an n x n linear system in O(n) operations. One of the most effective classes of solvers is algebraic multigrid (AMG), which is a multilevel iterative method based on projecting the problem into progressively smaller spaces, and scales like O(n) or O(nlog n) for certain classes of problems. The field of AMG is well-developed for symmetric positive definite matrices, and is typically most effective on linear systems resulting from the discretization of scalar elliptic PDEs, such as the heat equation. Systems of PDEs can add additional difficulties, but the underlying linear algebraic theory is consistent and, in many cases, an elliptic system of PDEs can be handled well by AMG with appropriate modifications of the solver. Solving general, nonsymmetric linear systems remains the wild west of AMG (and other fast solvers), lacking significant results in convergence theory as well as robust methods. Here, we develop new theoretical motivation and practical variations of AMG to solve nonsymmetric linear systems, often resulting from the discretization of hyperbolic PDEs. In particular, multilevel convergence of AMG for nonsymmetric systems is proven for the first time. A new nonsymmetric AMG solver is also developed based on an approximate ideal restriction, referred to as AIR, which is able to solve advection-dominated, hyperbolic-type problems that are outside the scope of existing AMG solvers and other fast iterative methods. AIR demonstrates scalable convergence on unstructured meshes, in multiple dimensions, and with high-order finite elements, expanding the applicability of AMG to a new class of problems.

Dose-shaping using targeted sparse optimization

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

Sayre, George A.; Ruan, Dan

2013-07-15

Purpose: Dose volume histograms (DVHs) are common tools in radiation therapy treatment planning to characterize plan quality. As statistical metrics, DVHs provide a compact summary of the underlying plan at the cost of losing spatial information: the same or similar dose-volume histograms can arise from substantially different spatial dose maps. This is exactly the reason why physicians and physicists scrutinize dose maps even after they satisfy all DVH endpoints numerically. However, up to this point, little has been done to control spatial phenomena, such as the spatial distribution of hot spots, which has significant clinical implications. To this end, themore » authors propose a novel objective function that enables a more direct tradeoff between target coverage, organ-sparing, and planning target volume (PTV) homogeneity, and presents our findings from four prostate cases, a pancreas case, and a head-and-neck case to illustrate the advantages and general applicability of our method.Methods: In designing the energy minimization objective (E{sub tot}{sup sparse}), the authors utilized the following robust cost functions: (1) an asymmetric linear well function to allow differential penalties for underdose, relaxation of prescription dose, and overdose in the PTV; (2) a two-piece linear function to heavily penalize high dose and mildly penalize low and intermediate dose in organs-at risk (OARs); and (3) a total variation energy, i.e., the L{sub 1} norm applied to the first-order approximation of the dose gradient in the PTV. By minimizing a weighted sum of these robust costs, general conformity to dose prescription and dose-gradient prescription is achieved while encouraging prescription violations to follow a Laplace distribution. In contrast, conventional quadratic objectives are associated with a Gaussian distribution of violations, which is less forgiving to large violations of prescription than the Laplace distribution. As a result, the proposed objective E{sub tot}{sup sparse} improves tradeoff between planning goals by 'sacrificing' voxels that have already been violated to improve PTV coverage, PTV homogeneity, and/or OAR-sparing. In doing so, overall plan quality is increased since these large violations only arise if a net reduction in E{sub tot}{sup sparse} occurs as a result. For example, large violations to dose prescription in the PTV in E{sub tot}{sup sparse}-optimized plans will naturally localize to voxels in and around PTV-OAR overlaps where OAR-sparing may be increased without compromising target coverage. The authors compared the results of our method and the corresponding clinical plans using analyses of DVH plots, dose maps, and two quantitative metrics that quantify PTV homogeneity and overdose. These metrics do not penalize underdose since E{sub tot}{sup sparse}-optimized plans were planned such that their target coverage was similar or better than that of the clinical plans. Finally, plan deliverability was assessed with the 2D modulation index.Results: The proposed method was implemented using IBM's CPLEX optimization package (ILOG CPLEX, Sunnyvale, CA) and required 1-4 min to solve with a 12-core Intel i7 processor. In the testing procedure, the authors optimized for several points on the Pareto surface of four 7-field 6MV prostate cases that were optimized for different levels of PTV homogeneity and OAR-sparing. The generated results were compared against each other and the clinical plan by analyzing their DVH plots and dose maps. After developing intuition by planning the four prostate cases, which had relatively few tradeoffs, the authors applied our method to a 7-field 6 MV pancreas case and a 9-field 6MV head-and-neck case to test the potential impact of our method on more challenging cases. The authors found that our formulation: (1) provided excellent flexibility for balancing OAR-sparing with PTV homogeneity; and (2) permitted the dose planner more control over the evolution of the PTV's spatial dose distribution than conventional objective functions. In particular, E{sub tot}{sup sparse}-optimized plans for the pancreas case and head-and-neck case exhibited substantially improved sparing of the spinal cord and parotid glands, respectively, while maintaining or improving sparing for other OARs and markedly improving PTV homogeneity. Plan deliverability for E{sub tot}{sup sparse}-optimized plans was shown to be better than their associated clinical plans, according to the two-dimensional modulation index.Conclusions: These results suggest that our formulation may be used to improve dose-shaping and OAR-sparing for complicated disease sites, such as the pancreas or head and neck. Furthermore, our objective function and constraints are linear and constitute a linear program, which converges to the global minimum quickly, and can be easily implemented in treatment planning software. Thus, the authors expect fast translation of our method to the clinic where it may have a positive impact on plan quality for challenging disease sites.« less

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.

An adaptive image sparse reconstruction method combined with nonlocal similarity and cosparsity for mixed Gaussian-Poisson noise removal

NASA Astrophysics Data System (ADS)

Chen, Yong-fei; Gao, Hong-xia; Wu, Zi-ling; Kang, Hui

2018-01-01

Compressed sensing (CS) has achieved great success in single noise removal. However, it cannot restore the images contaminated with mixed noise efficiently. This paper introduces nonlocal similarity and cosparsity inspired by compressed sensing to overcome the difficulties in mixed noise removal, in which nonlocal similarity explores the signal sparsity from similar patches, and cosparsity assumes that the signal is sparse after a possibly redundant transform. Meanwhile, an adaptive scheme is designed to keep the balance between mixed noise removal and detail preservation based on local variance. Finally, IRLSM and RACoSaMP are adopted to solve the objective function. Experimental results demonstrate that the proposed method is superior to conventional CS methods, like K-SVD and state-of-art method nonlocally centralized sparse representation (NCSR), in terms of both visual results and quantitative measures.

Incoherent dictionary learning for reducing crosstalk noise in least-squares reverse time migration

NASA Astrophysics Data System (ADS)

Wu, Juan; Bai, Min

2018-05-01

We propose to apply a novel incoherent dictionary learning (IDL) algorithm for regularizing the least-squares inversion in seismic imaging. The IDL is proposed to overcome the drawback of traditional dictionary learning algorithm in losing partial texture information. Firstly, the noisy image is divided into overlapped image patches, and some random patches are extracted for dictionary learning. Then, we apply the IDL technology to minimize the coherency between atoms during dictionary learning. Finally, the sparse representation problem is solved by a sparse coding algorithm, and image is restored by those sparse coefficients. By reducing the correlation among atoms, it is possible to preserve most of the small-scale features in the image while removing much of the long-wavelength noise. The application of the IDL method to regularization of seismic images from least-squares reverse time migration shows successful performance.

QUADRO: A SUPERVISED DIMENSION REDUCTION METHOD VIA RAYLEIGH QUOTIENT OPTIMIZATION.

PubMed

Fan, Jianqing; Ke, Zheng Tracy; Liu, Han; Xia, Lucy

We propose a novel Rayleigh quotient based sparse quadratic dimension reduction method-named QUADRO (Quadratic Dimension Reduction via Rayleigh Optimization)-for analyzing high-dimensional data. Unlike in the linear setting where Rayleigh quotient optimization coincides with classification, these two problems are very different under nonlinear settings. In this paper, we clarify this difference and show that Rayleigh quotient optimization may be of independent scientific interests. One major challenge of Rayleigh quotient optimization is that the variance of quadratic statistics involves all fourth cross-moments of predictors, which are infeasible to compute for high-dimensional applications and may accumulate too many stochastic errors. This issue is resolved by considering a family of elliptical models. Moreover, for heavy-tail distributions, robust estimates of mean vectors and covariance matrices are employed to guarantee uniform convergence in estimating non-polynomially many parameters, even though only the fourth moments are assumed. Methodologically, QUADRO is based on elliptical models which allow us to formulate the Rayleigh quotient maximization as a convex optimization problem. Computationally, we propose an efficient linearized augmented Lagrangian method to solve the constrained optimization problem. Theoretically, we provide explicit rates of convergence in terms of Rayleigh quotient under both Gaussian and general elliptical models. Thorough numerical results on both synthetic and real datasets are also provided to back up our theoretical results.

Optimal pre-scheduling of problem remappings

NASA Technical Reports Server (NTRS)

Nicol, David M.; Saltz, Joel H.

1987-01-01

A large class of scientific computational problems can be characterized as a sequence of steps where a significant amount of computation occurs each step, but the work performed at each step is not necessarily identical. Two good examples of this type of computation are: (1) regridding methods which change the problem discretization during the course of the computation, and (2) methods for solving sparse triangular systems of linear equations. Recent work has investigated a means of mapping such computations onto parallel processors; the method defines a family of static mappings with differing degrees of importance placed on the conflicting goals of good load balance and low communication/synchronization overhead. The performance tradeoffs are controllable by adjusting the parameters of the mapping method. To achieve good performance it may be necessary to dynamically change these parameters at run-time, but such changes can impose additional costs. If the computation's behavior can be determined prior to its execution, it can be possible to construct an optimal parameter schedule using a low-order-polynomial-time dynamic programming algorithm. Since the latter can be expensive, the performance is studied of the effect of a linear-time scheduling heuristic on one of the model problems, and it is shown to be effective and nearly optimal.

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.

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

The intelligence of dual simplex method to solve linear fractional fuzzy transportation problem.

PubMed

Narayanamoorthy, S; Kalyani, S

2015-01-01

An approach is presented to solve a fuzzy transportation problem with linear fractional fuzzy objective function. In this proposed approach the fractional fuzzy transportation problem is decomposed into two linear fuzzy transportation problems. The optimal solution of the two linear fuzzy transportations is solved by dual simplex method and the optimal solution of the fractional fuzzy transportation problem is obtained. The proposed method is explained in detail with an example.

Joint fMRI analysis and subject clustering using sparse dictionary learning

NASA Astrophysics Data System (ADS)

Kim, Seung-Jun; Dontaraju, Krishna K.

2017-08-01

Multi-subject fMRI data analysis methods based on sparse dictionary learning are proposed. In addition to identifying the component spatial maps by exploiting the sparsity of the maps, clusters of the subjects are learned by postulating that the fMRI volumes admit a subspace clustering structure. Furthermore, in order to tune the associated hyper-parameters systematically, a cross-validation strategy is developed based on entry-wise sampling of the fMRI dataset. Efficient algorithms for solving the proposed constrained dictionary learning formulations are developed. Numerical tests performed on synthetic fMRI data show promising results and provides insights into the proposed technique.

Fast Boundary Element Method for acoustics with the Sparse Cardinal Sine Decomposition

NASA Astrophysics Data System (ADS)

Alouges, François; Aussal, Matthieu; Parolin, Emile

2017-07-01

This paper presents the newly proposed method Sparse Cardinal Sine Decomposition that allows fast convolution on unstructured grids. We focus on its use when coupled with finite element techniques to solve acoustic problems with the (compressed) Boundary Element Method. In addition, we also compare the computational performances of two equivalent Matlab® and Python implementations of the method. We show validation test cases in order to assess the precision of the approach. Eventually, the performance of the method is illustrated by the computation of the acoustic target strength of a realistic submarine from the Benchmark Target Strength Simulation international workshop.

New shape models of asteroids reconstructed from sparse-in-time photometry

NASA Astrophysics Data System (ADS)

Durech, Josef; Hanus, Josef; Vanco, Radim; Oszkiewicz, Dagmara Anna

2015-08-01

Asteroid physical parameters - the shape, the sidereal rotation period, and the spin axis orientation - can be reconstructed from the disk-integrated photometry either dense (classical lightcurves) or sparse in time by the lightcurve inversion method. We will review our recent progress in asteroid shape reconstruction from sparse photometry. The problem of finding a unique solution of the inverse problem is time consuming because the sidereal rotation period has to be found by scanning a wide interval of possible periods. This can be efficiently solved by splitting the period parameter space into small parts that are sent to computers of volunteers and processed in parallel. We will show how this approach of distributed computing works with currently available sparse photometry processed in the framework of project Asteroids@home. In particular, we will show the results based on the Lowell Photometric Database. The method produce reliable asteroid models with very low rate of false solutions and the pipelines and codes can be directly used also to other sources of sparse photometry - Gaia data, for example. We will present the distribution of spin axis of hundreds of asteroids, discuss the dependence of the spin obliquity on the size of an asteroid,and show examples of spin-axis distribution in asteroid families that confirm the Yarkovsky/YORP evolution scenario.

ℓ0 -based sparse hyperspectral unmixing using spectral information and a multi-objectives formulation

NASA Astrophysics Data System (ADS)

Xu, Xia; Shi, Zhenwei; Pan, Bin

2018-07-01

Sparse unmixing aims at recovering pure materials from hyperpspectral images and estimating their abundance fractions. Sparse unmixing is actually ℓ0 problem which is NP-h ard, and a relaxation is often used. In this paper, we attempt to deal with ℓ0 problem directly via a multi-objective based method, which is a non-convex manner. The characteristics of hyperspectral images are integrated into the proposed method, which leads to a new spectra and multi-objective based sparse unmixing method (SMoSU). In order to solve the ℓ0 norm optimization problem, the spectral library is encoded in a binary vector, and a bit-wise flipping strategy is used to generate new individuals in the evolution process. However, a multi-objective method usually produces a number of non-dominated solutions, while sparse unmixing requires a single solution. How to make the final decision for sparse unmixing is challenging. To handle this problem, we integrate the spectral characteristic of hyperspectral images into SMoSU. By considering the spectral correlation in hyperspectral data, we improve the Tchebycheff decomposition function in SMoSU via a new regularization item. This regularization item is able to enforce the individual divergence in the evolution process of SMoSU. In this way, the diversity and convergence of population is further balanced, which is beneficial to the concentration of individuals. In the experiments part, three synthetic datasets and one real-world data are used to analyse the effectiveness of SMoSU, and several state-of-art sparse unmixing algorithms are compared.

Solving Boltzmann and Fokker-Planck Equations Using Sparse Representation

DTIC Science & Technology

2011-05-31

material science. We have com- puted the electronic structure of 2D quantum dot system, and compared the efficiency with the benchmark software OCTOPUS . For...one self-consistent iteration step with 512 electrons, OCTOPUS costs 1091 sec, and selected inversion costs 9.76 sec. The algorithm exhibits

Multigrid approaches to non-linear diffusion problems on unstructured meshes

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.; Bushnell, Dennis M. (Technical Monitor)

2001-01-01

The efficiency of three multigrid methods for solving highly non-linear diffusion problems on two-dimensional unstructured meshes is examined. The three multigrid methods differ mainly in the manner in which the nonlinearities of the governing equations are handled. These comprise a non-linear full approximation storage (FAS) multigrid method which is used to solve the non-linear equations directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the non-linear system, and a hybrid scheme which is based on a non-linear FAS multigrid scheme, but employs a linear solver on each level as a smoother. Results indicate that all methods are equally effective at converging the non-linear residual in a given number of grid sweeps, but that the linear solver is more efficient in cpu time due to the lower cost of linear versus non-linear grid sweeps.

Chosen interval methods for solving linear interval systems with special type of matrix

NASA Astrophysics Data System (ADS)

Szyszka, Barbara

2013-10-01

The paper is devoted to chosen direct interval methods for solving linear interval systems with special type of matrix. This kind of matrix: band matrix with a parameter, from finite difference problem is obtained. Such linear systems occur while solving one dimensional wave equation (Partial Differential Equations of hyperbolic type) by using the central difference interval method of the second order. Interval methods are constructed so as the errors of method are enclosed in obtained results, therefore presented linear interval systems contain elements that determining the errors of difference method. The chosen direct algorithms have been applied for solving linear systems because they have no errors of method. All calculations were performed in floating-point interval arithmetic.

The Intelligence of Dual Simplex Method to Solve Linear Fractional Fuzzy Transportation Problem

PubMed Central

Narayanamoorthy, S.; Kalyani, S.

2015-01-01

An approach is presented to solve a fuzzy transportation problem with linear fractional fuzzy objective function. In this proposed approach the fractional fuzzy transportation problem is decomposed into two linear fuzzy transportation problems. The optimal solution of the two linear fuzzy transportations is solved by dual simplex method and the optimal solution of the fractional fuzzy transportation problem is obtained. The proposed method is explained in detail with an example. PMID:25810713

Computing Gröbner Bases within Linear Algebra

NASA Astrophysics Data System (ADS)

Suzuki, Akira

In this paper, we present an alternative algorithm to compute Gröbner bases, which is based on computations on sparse linear algebra. Both of S-polynomial computations and monomial reductions are computed in linear algebra simultaneously in this algorithm. So it can be implemented to any computational system which can handle linear algebra. For a given ideal in a polynomial ring, it calculates a Gröbner basis along with the corresponding term order appropriately.

Nonlocal sparse model with adaptive structural clustering for feature extraction of aero-engine bearings

NASA Astrophysics Data System (ADS)

Zhang, Han; Chen, Xuefeng; Du, Zhaohui; Li, Xiang; Yan, Ruqiang

2016-04-01

Fault information of aero-engine bearings presents two particular phenomena, i.e., waveform distortion and impulsive feature frequency band dispersion, which leads to a challenging problem for current techniques of bearing fault diagnosis. Moreover, although many progresses of sparse representation theory have been made in feature extraction of fault information, the theory also confronts inevitable performance degradation due to the fact that relatively weak fault information has not sufficiently prominent and sparse representations. Therefore, a novel nonlocal sparse model (coined NLSM) and its algorithm framework has been proposed in this paper, which goes beyond simple sparsity by introducing more intrinsic structures of feature information. This work adequately exploits the underlying prior information that feature information exhibits nonlocal self-similarity through clustering similar signal fragments and stacking them together into groups. Within this framework, the prior information is transformed into a regularization term and a sparse optimization problem, which could be solved through block coordinate descent method (BCD), is formulated. Additionally, the adaptive structural clustering sparse dictionary learning technique, which utilizes k-Nearest-Neighbor (kNN) clustering and principal component analysis (PCA) learning, is adopted to further enable sufficient sparsity of feature information. Moreover, the selection rule of regularization parameter and computational complexity are described in detail. The performance of the proposed framework is evaluated through numerical experiment and its superiority with respect to the state-of-the-art method in the field is demonstrated through the vibration signals of experimental rig of aircraft engine bearings.

Adaptive low-rank subspace learning with online optimization for robust visual tracking.

PubMed

Liu, Risheng; Wang, Di; Han, Yuzhuo; Fan, Xin; Luo, Zhongxuan

2017-04-01

In recent years, sparse and low-rank models have been widely used to formulate appearance subspace for visual tracking. However, most existing methods only consider the sparsity or low-rankness of the coefficients, which is not sufficient enough for appearance subspace learning on complex video sequences. Moreover, as both the low-rank and the column sparse measures are tightly related to all the samples in the sequences, it is challenging to incrementally solve optimization problems with both nuclear norm and column sparse norm on sequentially obtained video data. To address above limitations, this paper develops a novel low-rank subspace learning with adaptive penalization (LSAP) framework for subspace based robust visual tracking. Different from previous work, which often simply decomposes observations as low-rank features and sparse errors, LSAP simultaneously learns the subspace basis, low-rank coefficients and column sparse errors to formulate appearance subspace. Within LSAP framework, we introduce a Hadamard production based regularization to incorporate rich generative/discriminative structure constraints to adaptively penalize the coefficients for subspace learning. It is shown that such adaptive penalization can significantly improve the robustness of LSAP on severely corrupted dataset. To utilize LSAP for online visual tracking, we also develop an efficient incremental optimization scheme for nuclear norm and column sparse norm minimizations. Experiments on 50 challenging video sequences demonstrate that our tracker outperforms other state-of-the-art methods. Copyright © 2017 Elsevier Ltd. All rights reserved.

Multi-color incomplete Cholesky conjugate gradient methods for vector computers. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Poole, E. L.

1986-01-01

In this research, we are concerned with the solution on vector computers of linear systems of equations, Ax = b, where A is a larger, sparse symmetric positive definite matrix. We solve the system using an iterative method, the incomplete Cholesky conjugate gradient method (ICCG). We apply a multi-color strategy to obtain p-color matrices for which a block-oriented ICCG method is implemented on the CYBER 205. (A p-colored matrix is a matrix which can be partitioned into a pXp block matrix where the diagonal blocks are diagonal matrices). This algorithm, which is based on a no-fill strategy, achieves O(N/p) length vector operations in both the decomposition of A and in the forward and back solves necessary at each iteration of the method. We discuss the natural ordering of the unknowns as an ordering that minimizes the number of diagonals in the matrix and define multi-color orderings in terms of disjoint sets of the unknowns. We give necessary and sufficient conditions to determine which multi-color orderings of the unknowns correpond to p-color matrices. A performance model is given which is used both to predict execution time for ICCG methods and also to compare an ICCG method to conjugate gradient without preconditioning or another ICCG method. Results are given from runs on the CYBER 205 at NASA's Langley Research Center for four model problems.

Design of Linear Quadratic Regulators and Kalman Filters

NASA Technical Reports Server (NTRS)

Lehtinen, B.; Geyser, L.

1986-01-01

AESOP solves problems associated with design of controls and state estimators for linear time-invariant systems. Systems considered are modeled in state-variable form by set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are linear quadratic regulator (LQR) design problem and steady-state Kalman filter design problem. AESOP is interactive. User solves design problems and analyzes solutions in single interactive session. Both numerical and graphical information available to user during the session.

Solving a mixture of many random linear equations by tensor decomposition and alternating minimization.

DOT National Transportation Integrated Search

2016-09-01

We consider the problem of solving mixed random linear equations with k components. This is the noiseless setting of mixed linear regression. The goal is to estimate multiple linear models from mixed samples in the case where the labels (which sample...

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.

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.

ADM For Solving Linear Second-Order Fredholm Integro-Differential Equations

NASA Astrophysics Data System (ADS)

Karim, Mohd F.; Mohamad, Mahathir; Saifullah Rusiman, Mohd; Che-Him, Norziha; Roslan, Rozaini; Khalid, Kamil

2018-04-01

In this paper, we apply Adomian Decomposition Method (ADM) as numerically analyse linear second-order Fredholm Integro-differential Equations. The approximate solutions of the problems are calculated by Maple package. Some numerical examples have been considered to illustrate the ADM for solving this equation. The results are compared with the existing exact solution. Thus, the Adomian decomposition method can be the best alternative method for solving linear second-order Fredholm Integro-Differential equation. It converges to the exact solution quickly and in the same time reduces computational work for solving the equation. The result obtained by ADM shows the ability and efficiency for solving these equations.

Discrete-time neural network for fast solving large linear L1 estimation problems and its application to image restoration.

PubMed

Xia, Youshen; Sun, Changyin; Zheng, Wei Xing

2012-05-01

There is growing interest in solving linear L1 estimation problems for sparsity of the solution and robustness against non-Gaussian noise. This paper proposes a discrete-time neural network which can calculate large linear L1 estimation problems fast. The proposed neural network has a fixed computational step length and is proved to be globally convergent to an optimal solution. Then, the proposed neural network is efficiently applied to image restoration. Numerical results show that the proposed neural network is not only efficient in solving degenerate problems resulting from the nonunique solutions of the linear L1 estimation problems but also needs much less computational time than the related algorithms in solving both linear L1 estimation and image restoration problems.

Encouraging Students to Think Strategically when Learning to Solve Linear Equations

ERIC Educational Resources Information Center

Robson, Daphne; Abell, Walt; Boustead, Therese

2012-01-01

Students who are preparing to study science and engineering need to understand equation solving but adult students returning to study can find this difficult. In this paper, the design of an online resource, Equations2go, for helping students learn to solve linear equations is investigated. Students learning to solve equations need to consider…

Mind Wandering and the Incubation Effect in Insight Problem Solving

ERIC Educational Resources Information Center

Tan, Tengteng; Zou, Hong; Chen, Chuansheng; Luo, Jin

2015-01-01

Although many anecdotes suggest that creative insights often arise during mind wandering, empirical research is still sparse. In this study, the number reduction task (NRT) was used to assess whether insightful solutions were related to mind wandering during the incubation stage of the creative process. An experience sampling paradigm was used to…

Optimal parallel solution of sparse triangular systems

NASA Technical Reports Server (NTRS)

Alvarado, Fernando L.; Schreiber, Robert

1990-01-01

A method for the parallel solution of triangular sets of equations is described that is appropriate when there are many right-handed sides. By preprocessing, the method can reduce the number of parallel steps required to solve Lx = b compared to parallel forward or backsolve. Applications are to iterative solvers with triangular preconditioners, to structural analysis, or to power systems applications, where there may be many right-handed sides (not all available a priori). The inverse of L is represented as a product of sparse triangular factors. The problem is to find a factored representation of this inverse of L with the smallest number of factors (or partitions), subject to the requirement that no new nonzero elements be created in the formation of these inverse factors. A method from an earlier reference is shown to solve this problem. This method is improved upon by constructing a permutation of the rows and columns of L that preserves triangularity and allow for the best possible such partition. A number of practical examples and algorithmic details are presented. The parallelism attainable is illustrated by means of elimination trees and clique trees.

Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. II. Linear scaling domain based pair natural orbital coupled cluster theory

NASA Astrophysics Data System (ADS)

Riplinger, Christoph; Pinski, Peter; Becker, Ute; Valeev, Edward F.; Neese, Frank

2016-01-01

Domain based local pair natural orbital coupled cluster theory with single-, double-, and perturbative triple excitations (DLPNO-CCSD(T)) is a highly efficient local correlation method. It is known to be accurate and robust and can be used in a black box fashion in order to obtain coupled cluster quality total energies for large molecules with several hundred atoms. While previous implementations showed near linear scaling up to a few hundred atoms, several nonlinear scaling steps limited the applicability of the method for very large systems. In this work, these limitations are overcome and a linear scaling DLPNO-CCSD(T) method for closed shell systems is reported. The new implementation is based on the concept of sparse maps that was introduced in Part I of this series [P. Pinski, C. Riplinger, E. F. Valeev, and F. Neese, J. Chem. Phys. 143, 034108 (2015)]. Using the sparse map infrastructure, all essential computational steps (integral transformation and storage, initial guess, pair natural orbital construction, amplitude iterations, triples correction) are achieved in a linear scaling fashion. In addition, a number of additional algorithmic improvements are reported that lead to significant speedups of the method. The new, linear-scaling DLPNO-CCSD(T) implementation typically is 7 times faster than the previous implementation and consumes 4 times less disk space for large three-dimensional systems. For linear systems, the performance gains and memory savings are substantially larger. Calculations with more than 20 000 basis functions and 1000 atoms are reported in this work. In all cases, the time required for the coupled cluster step is comparable to or lower than for the preceding Hartree-Fock calculation, even if this is carried out with the efficient resolution-of-the-identity and chain-of-spheres approximations. The new implementation even reduces the error in absolute correlation energies by about a factor of two, compared to the already accurate previous implementation.

Experimental quantum computing to solve systems of linear equations.

PubMed

Cai, X-D; Weedbrook, C; Su, Z-E; Chen, M-C; Gu, Mile; Zhu, M-J; Li, Li; Liu, Nai-Le; Lu, Chao-Yang; Pan, Jian-Wei

2013-06-07

Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time proportional to the number of variables N. A recently proposed quantum algorithm shows that quantum computers could solve linear systems in a time scale of order log(N), giving an exponential speedup over classical computers. Here we realize the simplest instance of this algorithm, solving 2×2 linear equations for various input vectors on a quantum computer. We use four quantum bits and four controlled logic gates to implement every subroutine required, demonstrating the working principle of this algorithm.

Students’ difficulties in solving linear equation problems

NASA Astrophysics Data System (ADS)

Wati, S.; Fitriana, L.; Mardiyana

2018-03-01

A linear equation is an algebra material that exists in junior high school to university. It is a very important material for students in order to learn more advanced mathematics topics. Therefore, linear equation material is essential to be mastered. However, the result of 2016 national examination in Indonesia showed that students’ achievement in solving linear equation problem was low. This fact became a background to investigate students’ difficulties in solving linear equation problems. This study used qualitative descriptive method. An individual written test on linear equation tasks was administered, followed by interviews. Twenty-one sample students of grade VIII of SMPIT Insan Kamil Karanganyar did the written test, and 6 of them were interviewed afterward. The result showed that students with high mathematics achievement donot have difficulties, students with medium mathematics achievement have factual difficulties, and students with low mathematics achievement have factual, conceptual, operational, and principle difficulties. Based on the result there is a need of meaningfulness teaching strategy to help students to overcome difficulties in solving linear equation problems.

Semilinear programming: applications and implementation

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

Mohan, S.

Semilinear programming is a method of solving optimization problems with linear constraints where the non-negativity restrictions on the variables are dropped and the objective function coefficients can take on different values depending on whether the variable is positive or negative. The simplex method for linear programming is modified in this thesis to solve general semilinear and piecewise linear programs efficiently without having to transform them into equivalent standard linear programs. Several models in widely different areas of optimization such as production smoothing, facility locations, goal programming and L/sub 1/ estimation are presented first to demonstrate the compact formulation that arisesmore » when such problems are formulated as semilinear programs. A code SLP is constructed using the semilinear programming techniques. Problems in aggregate planning and L/sub 1/ estimation are solved using SLP and equivalent linear programs using a linear programming simplex code. Comparisons of CPU times and number iterations indicate SLP to be far superior. The semilinear programming techniques are extended to piecewise linear programming in the implementation of the code PLP. Piecewise linear models in aggregate planning are solved using PLP and equivalent standard linear programs using a simple upper bounded linear programming code SUBLP.« less

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).

In vivo quantitative evaluation of vascular parameters for angiogenesis based on sparse principal component analysis and aggregated boosted trees

NASA Astrophysics Data System (ADS)

Zhao, Fengjun; Liu, Junting; Qu, Xiaochao; Xu, Xianhui; Chen, Xueli; Yang, Xiang; Cao, Feng; Liang, Jimin; Tian, Jie

2014-12-01

To solve the multicollinearity issue and unequal contribution of vascular parameters for the quantification of angiogenesis, we developed a quantification evaluation method of vascular parameters for angiogenesis based on in vivo micro-CT imaging of hindlimb ischemic model mice. Taking vascular volume as the ground truth parameter, nine vascular parameters were first assembled into sparse principal components (PCs) to reduce the multicolinearity issue. Aggregated boosted trees (ABTs) were then employed to analyze the importance of vascular parameters for the quantification of angiogenesis via the loadings of sparse PCs. The results demonstrated that vascular volume was mainly characterized by vascular area, vascular junction, connectivity density, segment number and vascular length, which indicated they were the key vascular parameters for the quantification of angiogenesis. The proposed quantitative evaluation method was compared with both the ABTs directly using the nine vascular parameters and Pearson correlation, which were consistent. In contrast to the ABTs directly using the vascular parameters, the proposed method can select all the key vascular parameters simultaneously, because all the key vascular parameters were assembled into the sparse PCs with the highest relative importance.

Sparse Additive Ordinary Differential Equations for Dynamic Gene Regulatory Network Modeling.

PubMed

Wu, Hulin; Lu, Tao; Xue, Hongqi; Liang, Hua

2014-04-02

The gene regulation network (GRN) is a high-dimensional complex system, which can be represented by various mathematical or statistical models. The ordinary differential equation (ODE) model is one of the popular dynamic GRN models. High-dimensional linear ODE models have been proposed to identify GRNs, but with a limitation of the linear regulation effect assumption. In this article, we propose a sparse additive ODE (SA-ODE) model, coupled with ODE estimation methods and adaptive group LASSO techniques, to model dynamic GRNs that could flexibly deal with nonlinear regulation effects. The asymptotic properties of the proposed method are established and simulation studies are performed to validate the proposed approach. An application example for identifying the nonlinear dynamic GRN of T-cell activation is used to illustrate the usefulness of the proposed method.

Reconstructing Interlaced High-Dynamic-Range Video Using Joint Learning.

PubMed

Inchang Choi; Seung-Hwan Baek; Kim, Min H

2017-11-01

For extending the dynamic range of video, it is a common practice to capture multiple frames sequentially with different exposures and combine them to extend the dynamic range of each video frame. However, this approach results in typical ghosting artifacts due to fast and complex motion in nature. As an alternative, video imaging with interlaced exposures has been introduced to extend the dynamic range. However, the interlaced approach has been hindered by jaggy artifacts and sensor noise, leading to concerns over image quality. In this paper, we propose a data-driven approach for jointly solving two specific problems of deinterlacing and denoising that arise in interlaced video imaging with different exposures. First, we solve the deinterlacing problem using joint dictionary learning via sparse coding. Since partial information of detail in differently exposed rows is often available via interlacing, we make use of the information to reconstruct details of the extended dynamic range from the interlaced video input. Second, we jointly solve the denoising problem by tailoring sparse coding to better handle additive noise in low-/high-exposure rows, and also adopt multiscale homography flow to temporal sequences for denoising. We anticipate that the proposed method will allow for concurrent capture of higher dynamic range video frames without suffering from ghosting artifacts. We demonstrate the advantages of our interlaced video imaging compared with the state-of-the-art high-dynamic-range video methods.

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.

Hierarchical Bayesian sparse image reconstruction with application to MRFM.

PubMed

Dobigeon, Nicolas; Hero, Alfred O; Tourneret, Jean-Yves

2009-09-01

This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is well suited to such naturally sparse image applications as it seamlessly accounts for properties such as sparsity and positivity of the image via appropriate Bayes priors. We propose a prior that is based on a weighted mixture of a positive exponential distribution and a mass at zero. The prior has hyperparameters that are tuned automatically by marginalization over the hierarchical Bayesian model. To overcome the complexity of the posterior distribution, a Gibbs sampling strategy is proposed. The Gibbs samples can be used to estimate the image to be recovered, e.g., by maximizing the estimated posterior distribution. In our fully Bayesian approach, the posteriors of all the parameters are available. Thus, our algorithm provides more information than other previously proposed sparse reconstruction methods that only give a point estimate. The performance of the proposed hierarchical Bayesian sparse reconstruction method is illustrated on synthetic data and real data collected from a tobacco virus sample using a prototype MRFM instrument.

Folded concave penalized learning in identifying multimodal MRI marker for Parkinson’s disease

PubMed Central

Liu, Hongcheng; Du, Guangwei; Zhang, Lijun; Lewis, Mechelle M.; Wang, Xue; Yao, Tao; Li, Runze; Huang, Xuemei

2016-01-01

Background Brain MRI holds promise to gauge different aspects of Parkinson’s disease (PD)-related pathological changes. Its analysis, however, is hindered by the high-dimensional nature of the data. New method This study introduces folded concave penalized (FCP) sparse logistic regression to identify biomarkers for PD from a large number of potential factors. The proposed statistical procedures target the challenges of high-dimensionality with limited data samples acquired. The maximization problem associated with the sparse logistic regression model is solved by local linear approximation. The proposed procedures then are applied to the empirical analysis of multimodal MRI data. Results From 45 features, the proposed approach identified 15 MRI markers and the UPSIT, which are known to be clinically relevant to PD. By combining the MRI and clinical markers, we can enhance substantially the specificity and sensitivity of the model, as indicated by the ROC curves. Comparison to existing methods We compare the folded concave penalized learning scheme with both the Lasso penalized scheme and the principle component analysis-based feature selection (PCA) in the Parkinson’s biomarker identification problem that takes into account both the clinical features and MRI markers. The folded concave penalty method demonstrates a substantially better clinical potential than both the Lasso and PCA in terms of specificity and sensitivity. Conclusions For the first time, we applied the FCP learning method to MRI biomarker discovery in PD. The proposed approach successfully identified MRI markers that are clinically relevant. Combining these biomarkers with clinical features can substantially enhance performance. PMID:27102045

Sparse and Adaptive Diffusion Dictionary (SADD) for recovering intra-voxel white matter structure.

PubMed

Aranda, Ramon; Ramirez-Manzanares, Alonso; Rivera, Mariano

2015-12-01

On the analysis of the Diffusion-Weighted Magnetic Resonance Images, multi-compartment models overcome the limitations of the well-known Diffusion Tensor model for fitting in vivo brain axonal orientations at voxels with fiber crossings, branching, kissing or bifurcations. Some successful multi-compartment methods are based on diffusion dictionaries. The diffusion dictionary-based methods assume that the observed Magnetic Resonance signal at each voxel is a linear combination of the fixed dictionary elements (dictionary atoms). The atoms are fixed along different orientations and diffusivity profiles. In this work, we present a sparse and adaptive diffusion dictionary method based on the Diffusion Basis Functions Model to estimate in vivo brain axonal fiber populations. Our proposal overcomes the following limitations of the diffusion dictionary-based methods: the limited angular resolution and the fixed shapes for the atom set. We propose to iteratively re-estimate the orientations and the diffusivity profile of the atoms independently at each voxel by using a simplified and easier-to-solve mathematical approach. As a result, we improve the fitting of the Diffusion-Weighted Magnetic Resonance signal. The advantages with respect to the former Diffusion Basis Functions method are demonstrated on the synthetic data-set used on the 2012 HARDI Reconstruction Challenge and in vivo human data. We demonstrate that improvements obtained in the intra-voxel fiber structure estimations benefit brain research allowing to obtain better tractography estimations. Hence, these improvements result in an accurate computation of the brain connectivity patterns. Copyright © 2015 Elsevier B.V. All rights reserved.

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.

An efficient method for generalized linear multiplicative programming problem with multiplicative constraints.

PubMed

Zhao, Yingfeng; Liu, Sanyang

2016-01-01

We present a practical branch and bound algorithm for globally solving generalized linear multiplicative programming problem with multiplicative constraints. To solve the problem, a relaxation programming problem which is equivalent to a linear programming is proposed by utilizing a new two-phase relaxation technique. In the algorithm, lower and upper bounds are simultaneously obtained by solving some linear relaxation programming problems. Global convergence has been proved and results of some sample examples and a small random experiment show that the proposed algorithm is feasible and efficient.

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.

Performance bounds for modal analysis using sparse linear arrays

NASA Astrophysics Data System (ADS)

Li, Yuanxin; Pezeshki, Ali; Scharf, Louis L.; Chi, Yuejie

2017-05-01

We study the performance of modal analysis using sparse linear arrays (SLAs) such as nested and co-prime arrays, in both first-order and second-order measurement models. We treat SLAs as constructed from a subset of sensors in a dense uniform linear array (ULA), and characterize the performance loss of SLAs with respect to the ULA due to using much fewer sensors. In particular, we claim that, provided the same aperture, in order to achieve comparable performance in terms of Cramér-Rao bound (CRB) for modal analysis, SLAs require more snapshots, of which the number is about the number of snapshots used by ULA times the compression ratio in the number of sensors. This is shown analytically for the case with one undamped mode, as well as empirically via extensive numerical experiments for more complex scenarios. Moreover, the misspecified CRB proposed by Richmond and Horowitz is also studied, where SLAs suffer more performance loss than their ULA counterpart.

Augmented l1 and Nuclear-Norm Models with a Globally Linearly Convergent Algorithm. Revision 1

DTIC Science & Technology

2012-10-17

nonzero and sampled from the standard Gaussian distribution (for Figure 2) or the Bernoulli distribution (for Figure 3). Both tests had the same sensing...dual variable y(k) Figure 3: Convergence of primal and dual variables of three algorithms on Bernoulli sparse x0 was the slowest. Besides the obvious...slower convergence than the final stage. Comparing the results of two tests, the convergence was faster on the Bernoulli sparse signal than the

Solving the Problem of Linear Viscoelasticity for Piecewise-Homogeneous Anisotropic Plates

NASA Astrophysics Data System (ADS)

Kaloerov, S. A.; Koshkin, A. A.

2017-11-01

An approximate method for solving the problem of linear viscoelasticity for thin anisotropic plates subject to transverse bending is proposed. The method of small parameter is used to reduce the problem to a sequence of boundary problems of applied theory of bending of plates solved using complex potentials. The general form of complex potentials in approximations and the boundary conditions for determining them are obtained. Problems for a plate with elliptic elastic inclusions are solved as an example. The numerical results for a plate with one, two elliptical (circular), and linear inclusions are analyzed.

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

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).

From 2D to 3D modelling in long term tectonics: Modelling challenges and HPC solutions (Invited)

NASA Astrophysics Data System (ADS)

Le Pourhiet, L.; May, D.

2013-12-01

Over the last decades, 3D thermo-mechanical codes have been made available to the long term tectonics community either as open source (Underworld, Gale) or more limited access (Fantom, Elvis3D, Douar, LaMem etc ...). However, to date, few published results using these methods have included the coupling between crustal and lithospheric dynamics at large strain. The fact that these computations are computational expensive is not the primary reason for the relatively slow development of 3D modeling in the long term tectonics community, as compare to the rapid development observed within the mantle dynamic community, or in the short-term tectonics field. Long term tectonics problems have specific issues not found in either of these two field, including; large strain (not an issue for short-term), the inclusion of free surface and the occurence of large viscosity contrasts. The first issue is typically eliminated using a combined marker-ALE method instead of fully lagrangian method, however, the marker-ALE approach can pose some algorithmic challenges in a massively parallel environment. The two last issues are more problematic because they affect the convergence of the linear/non-linear solver and the memory cost. Two options have been tested so far, using low order element and solving with a sparse direct solver, or using higher order stable elements together with a multi-grid solver. The first options, is simpler to code and to use but reaches its limit at around 80^3 low order elements. The second option requires more operations but allows using iterative solver on extremely large computers. In this presentation, I will describe the design philosophy and highlight results obtained using a code from the second-class method. The presentation will be oriented from an end-user point of view, using an application from 3D continental break up to illustrate key concepts. The description will proceed point by point from implementing physics into the code, to dealing with specific issues related to solving the discrete system of non linear equations.

Parameter Estimation and Model Selection for Indoor Environments Based on Sparse Observations

NASA Astrophysics Data System (ADS)

Dehbi, Y.; Loch-Dehbi, S.; Plümer, L.

2017-09-01

This paper presents a novel method for the parameter estimation and model selection for the reconstruction of indoor environments based on sparse observations. While most approaches for the reconstruction of indoor models rely on dense observations, we predict scenes of the interior with high accuracy in the absence of indoor measurements. We use a model-based top-down approach and incorporate strong but profound prior knowledge. The latter includes probability density functions for model parameters and sparse observations such as room areas and the building footprint. The floorplan model is characterized by linear and bi-linear relations with discrete and continuous parameters. We focus on the stochastic estimation of model parameters based on a topological model derived by combinatorial reasoning in a first step. A Gauss-Markov model is applied for estimation and simulation of the model parameters. Symmetries are represented and exploited during the estimation process. Background knowledge as well as observations are incorporated in a maximum likelihood estimation and model selection is performed with AIC/BIC. The likelihood is also used for the detection and correction of potential errors in the topological model. Estimation results are presented and discussed.

Optimal image alignment with random projections of manifolds: algorithm and geometric analysis.

PubMed

Kokiopoulou, Effrosyni; Kressner, Daniel; Frossard, Pascal

2011-06-01

This paper addresses the problem of image alignment based on random measurements. Image alignment consists of estimating the relative transformation between a query image and a reference image. We consider the specific problem where the query image is provided in compressed form in terms of linear measurements captured by a vision sensor. We cast the alignment problem as a manifold distance minimization problem in the linear subspace defined by the measurements. The transformation manifold that represents synthesis of shift, rotation, and isotropic scaling of the reference image can be given in closed form when the reference pattern is sparsely represented over a parametric dictionary. We show that the objective function can then be decomposed as the difference of two convex functions (DC) in the particular case where the dictionary is built on Gaussian functions. Thus, the optimization problem becomes a DC program, which in turn can be solved globally by a cutting plane method. The quality of the solution is typically affected by the number of random measurements and the condition number of the manifold that describes the transformations of the reference image. We show that the curvature, which is closely related to the condition number, remains bounded in our image alignment problem, which means that the relative transformation between two images can be determined optimally in a reduced subspace.

QUADRO: A SUPERVISED DIMENSION REDUCTION METHOD VIA RAYLEIGH QUOTIENT OPTIMIZATION

PubMed Central

Fan, Jianqing; Ke, Zheng Tracy; Liu, Han; Xia, Lucy

2016-01-01

We propose a novel Rayleigh quotient based sparse quadratic dimension reduction method—named QUADRO (Quadratic Dimension Reduction via Rayleigh Optimization)—for analyzing high-dimensional data. Unlike in the linear setting where Rayleigh quotient optimization coincides with classification, these two problems are very different under nonlinear settings. In this paper, we clarify this difference and show that Rayleigh quotient optimization may be of independent scientific interests. One major challenge of Rayleigh quotient optimization is that the variance of quadratic statistics involves all fourth cross-moments of predictors, which are infeasible to compute for high-dimensional applications and may accumulate too many stochastic errors. This issue is resolved by considering a family of elliptical models. Moreover, for heavy-tail distributions, robust estimates of mean vectors and covariance matrices are employed to guarantee uniform convergence in estimating non-polynomially many parameters, even though only the fourth moments are assumed. Methodologically, QUADRO is based on elliptical models which allow us to formulate the Rayleigh quotient maximization as a convex optimization problem. Computationally, we propose an efficient linearized augmented Lagrangian method to solve the constrained optimization problem. Theoretically, we provide explicit rates of convergence in terms of Rayleigh quotient under both Gaussian and general elliptical models. Thorough numerical results on both synthetic and real datasets are also provided to back up our theoretical results. PMID:26778864

Porting AMG2013 to Heterogeneous CPU+GPU Nodes

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

Samfass, Philipp

LLNL's future advanced technology system SIERRA will feature heterogeneous compute nodes that consist of IBM PowerV9 CPUs and NVIDIA Volta GPUs. Conceptually, the motivation for such an architecture is quite straightforward: While GPUs are optimized for throughput on massively parallel workloads, CPUs strive to minimize latency for rather sequential operations. Yet, making optimal use of heterogeneous architectures raises new challenges for the development of scalable parallel software, e.g., with respect to work distribution. Porting LLNL's parallel numerical libraries to upcoming heterogeneous CPU+GPU architectures is therefore a critical factor for ensuring LLNL's future success in ful lling its national mission. Onemore » of these libraries, called HYPRE, provides parallel solvers and precondi- tioners for large, sparse linear systems of equations. In the context of this intern- ship project, I consider AMG2013 which is a proxy application for major parts of HYPRE that implements a benchmark for setting up and solving di erent systems of linear equations. In the following, I describe in detail how I ported multiple parts of AMG2013 to the GPU (Section 2) and present results for di erent experiments that demonstrate a successful parallel implementation on the heterogeneous ma- chines surface and ray (Section 3). In Section 4, I give guidelines on how my code should be used. Finally, I conclude and give an outlook for future work (Section 5).« less

Dimension Reduction With Extreme Learning Machine.

PubMed

Kasun, Liyanaarachchi Lekamalage Chamara; Yang, Yan; Huang, Guang-Bin; Zhang, Zhengyou

2016-08-01

Data may often contain noise or irrelevant information, which negatively affect the generalization capability of machine learning algorithms. The objective of dimension reduction algorithms, such as principal component analysis (PCA), non-negative matrix factorization (NMF), random projection (RP), and auto-encoder (AE), is to reduce the noise or irrelevant information of the data. The features of PCA (eigenvectors) and linear AE are not able to represent data as parts (e.g. nose in a face image). On the other hand, NMF and non-linear AE are maimed by slow learning speed and RP only represents a subspace of original data. This paper introduces a dimension reduction framework which to some extend represents data as parts, has fast learning speed, and learns the between-class scatter subspace. To this end, this paper investigates a linear and non-linear dimension reduction framework referred to as extreme learning machine AE (ELM-AE) and sparse ELM-AE (SELM-AE). In contrast to tied weight AE, the hidden neurons in ELM-AE and SELM-AE need not be tuned, and their parameters (e.g, input weights in additive neurons) are initialized using orthogonal and sparse random weights, respectively. Experimental results on USPS handwritten digit recognition data set, CIFAR-10 object recognition, and NORB object recognition data set show the efficacy of linear and non-linear ELM-AE and SELM-AE in terms of discriminative capability, sparsity, training time, and normalized mean square error.

Fast online deconvolution of calcium imaging data

PubMed Central

Zhou, Pengcheng; Paninski, Liam

2017-01-01

Fluorescent calcium indicators are a popular means for observing the spiking activity of large neuronal populations, but extracting the activity of each neuron from raw fluorescence calcium imaging data is a nontrivial problem. We present a fast online active set method to solve this sparse non-negative deconvolution problem. Importantly, the algorithm 3progresses through each time series sequentially from beginning to end, thus enabling real-time online estimation of neural activity during the imaging session. Our algorithm is a generalization of the pool adjacent violators algorithm (PAVA) for isotonic regression and inherits its linear-time computational complexity. We gain remarkable increases in processing speed: more than one order of magnitude compared to currently employed state of the art convex solvers relying on interior point methods. Unlike these approaches, our method can exploit warm starts; therefore optimizing model hyperparameters only requires a handful of passes through the data. A minor modification can further improve the quality of activity inference by imposing a constraint on the minimum spike size. The algorithm enables real-time simultaneous deconvolution of O(105) traces of whole-brain larval zebrafish imaging data on a laptop. PMID:28291787

A Novel Centrality Measure for Network-wide Cyber Vulnerability Assessment

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

Sathanur, Arun V.; Haglin, David J.

In this work we propose a novel formulation that models the attack and compromise on a cyber network as a combination of two parts - direct compromise of a host and the compromise occurring through the spread of the attack on the network from a compromised host. The model parameters for the nodes are a concise representation of the host profiles that can include the risky behaviors of the associated human users while the model parameters for the edges are based on the existence of vulnerabilities between each pair of connected hosts. The edge models relate to the summary representationsmore » of the corresponding attack-graphs. This results in a formulation based on Random Walk with Restart (RWR) and the resulting centrality metric can be solved for in an efficient manner through the use of sparse linear solvers. Thus the formulation goes beyond mere topological considerations in centrality computations by summarizing the host profiles and the attack graphs into the model parameters. The computational efficiency of the method also allows us to also quantify the uncertainty in the centrality measure through Monte Carlo analysis.« less

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.

Solution of the three-dimensional Helmholtz equation with nonlocal boundary conditions

NASA Technical Reports Server (NTRS)

Hodge, Steve L.; Zorumski, William E.; Watson, Willie R.

1995-01-01

The Helmholtz equation is solved within a three-dimensional rectangular duct with a nonlocal radiation boundary condition at the duct exit plane. This condition accurately models the acoustic admittance at an arbitrarily-located computational boundary plane. A linear system of equations is constructed with second-order central differences for the Helmholtz operator and second-order backward differences for both local admittance conditions and the gradient term in the nonlocal radiation boundary condition. The resulting matrix equation is large, sparse, and non-Hermitian. The size and structure of the matrix makes direct solution techniques impractical; as a result, a nonstationary iterative technique is used for its solution. The theory behind the nonstationary technique is reviewed, and numerical results are presented for radiation from both a point source and a planar acoustic source. The solutions with the nonlocal boundary conditions are invariant to the location of the computational boundary, and the same nonlocal conditions are valid for all solutions. The nonlocal conditions thus provide a means of minimizing the size of three-dimensional computational domains.

Linear System of Equations, Matrix Inversion, and Linear Programming Using MS Excel

ERIC Educational Resources Information Center

El-Gebeily, M.; Yushau, B.

2008-01-01

In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…

Image super-resolution via sparse representation.

PubMed

Yang, Jianchao; Wright, John; Huang, Thomas S; Ma, Yi

2010-11-01

This paper presents a new approach to single-image super-resolution, based on sparse signal representation. Research on image statistics suggests that image patches can be well-represented as a sparse linear combination of elements from an appropriately chosen over-complete dictionary. Inspired by this observation, we seek a sparse representation for each patch of the low-resolution input, and then use the coefficients of this representation to generate the high-resolution output. Theoretical results from compressed sensing suggest that under mild conditions, the sparse representation can be correctly recovered from the downsampled signals. By jointly training two dictionaries for the low- and high-resolution image patches, we can enforce the similarity of sparse representations between the low resolution and high resolution image patch pair with respect to their own dictionaries. Therefore, the sparse representation of a low resolution image patch can be applied with the high resolution image patch dictionary to generate a high resolution image patch. The learned dictionary pair is a more compact representation of the patch pairs, compared to previous approaches, which simply sample a large amount of image patch pairs, reducing the computational cost substantially. The effectiveness of such a sparsity prior is demonstrated for both general image super-resolution and the special case of face hallucination. In both cases, our algorithm generates high-resolution images that are competitive or even superior in quality to images produced by other similar SR methods. In addition, the local sparse modeling of our approach is naturally robust to noise, and therefore the proposed algorithm can handle super-resolution with noisy inputs in a more unified framework.

Decreasing the temporal complexity for nonlinear, implicit reduced-order models by forecasting

DOE PAGES

Carlberg, Kevin; Ray, Jaideep; van Bloemen Waanders, Bart

2015-02-14

Implicit numerical integration of nonlinear ODEs requires solving a system of nonlinear algebraic equations at each time step. Each of these systems is often solved by a Newton-like method, which incurs a sequence of linear-system solves. Most model-reduction techniques for nonlinear ODEs exploit knowledge of system's spatial behavior to reduce the computational complexity of each linear-system solve. However, the number of linear-system solves for the reduced-order simulation often remains roughly the same as that for the full-order simulation. We propose exploiting knowledge of the model's temporal behavior to (1) forecast the unknown variable of the reduced-order system of nonlinear equationsmore » at future time steps, and (2) use this forecast as an initial guess for the Newton-like solver during the reduced-order-model simulation. To compute the forecast, we propose using the Gappy POD technique. As a result, the goal is to generate an accurate initial guess so that the Newton solver requires many fewer iterations to converge, thereby decreasing the number of linear-system solves in the reduced-order-model simulation.« less

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

Systematic sparse matrix error control for linear scaling electronic structure calculations.

PubMed

Rubensson, Emanuel H; Sałek, Paweł

2005-11-30

Efficient truncation criteria used in multiatom blocked sparse matrix operations for ab initio calculations are proposed. As system size increases, so does the need to stay on top of errors and still achieve high performance. A variant of a blocked sparse matrix algebra to achieve strict error control with good performance is proposed. The presented idea is that the condition to drop a certain submatrix should depend not only on the magnitude of that particular submatrix, but also on which other submatrices that are dropped. The decision to remove a certain submatrix is based on the contribution the removal would cause to the error in the chosen norm. We study the effect of an accumulated truncation error in iterative algorithms like trace correcting density matrix purification. One way to reduce the initial exponential growth of this error is presented. The presented error control for a sparse blocked matrix toolbox allows for achieving optimal performance by performing only necessary operations needed to maintain the requested level of accuracy. Copyright 2005 Wiley Periodicals, Inc.

Thin-film sparse boundary array design for passive acoustic mapping during ultrasound therapy.

PubMed

Coviello, Christian M; Kozick, Richard J; Hurrell, Andrew; Smith, Penny Probert; Coussios, Constantin-C

2012-10-01

A new 2-D hydrophone array for ultrasound therapy monitoring is presented, along with a novel algorithm for passive acoustic mapping using a sparse weighted aperture. The array is constructed using existing polyvinylidene fluoride (PVDF) ultrasound sensor technology, and is utilized for its broadband characteristics and its high receive sensitivity. For most 2-D arrays, high-resolution imagery is desired, which requires a large aperture at the cost of a large number of elements. The proposed array's geometry is sparse, with elements only on the boundary of the rectangular aperture. The missing information from the interior is filled in using linear imaging techniques. After receiving acoustic emissions during ultrasound therapy, this algorithm applies an apodization to the sparse aperture to limit side lobes and then reconstructs acoustic activity with high spatiotemporal resolution. Experiments show verification of the theoretical point spread function, and cavitation maps in agar phantoms correspond closely to predicted areas, showing the validity of the array and methodology.

Insights from Classifying Visual Concepts with Multiple Kernel Learning

PubMed Central

Binder, Alexander; Nakajima, Shinichi; Kloft, Marius; Müller, Christina; Samek, Wojciech; Brefeld, Ulf; Müller, Klaus-Robert; Kawanabe, Motoaki

2012-01-01

Combining information from various image features has become a standard technique in concept recognition tasks. However, the optimal way of fusing the resulting kernel functions is usually unknown in practical applications. Multiple kernel learning (MKL) techniques allow to determine an optimal linear combination of such similarity matrices. Classical approaches to MKL promote sparse mixtures. Unfortunately, 1-norm regularized MKL variants are often observed to be outperformed by an unweighted sum kernel. The main contributions of this paper are the following: we apply a recently developed non-sparse MKL variant to state-of-the-art concept recognition tasks from the application domain of computer vision. We provide insights on benefits and limits of non-sparse MKL and compare it against its direct competitors, the sum-kernel SVM and sparse MKL. We report empirical results for the PASCAL VOC 2009 Classification and ImageCLEF2010 Photo Annotation challenge data sets. Data sets (kernel matrices) as well as further information are available at http://doc.ml.tu-berlin.de/image_mkl/(Accessed 2012 Jun 25). PMID:22936970

Computing row and column counts for sparse QR and LU factorization

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

Gilbert, John R.; Li, Xiaoye S.; Ng, Esmond G.

2001-01-01

We present algorithms to determine the number of nonzeros in each row and column of the factors of a sparse matrix, for both the QR factorization and the LU factorization with partial pivoting. The algorithms use only the nonzero structure of the input matrix, and run in time nearly linear in the number of nonzeros in that matrix. They may be used to set up data structures or schedule parallel operations in advance of the numerical factorization. The row and column counts we compute are upper bounds on the actual counts. If the input matrix is strong Hall and theremore » is no coincidental numerical cancellation, the counts are exact for QR factorization and are the tightest bounds possible for LU factorization. These algorithms are based on our earlier work on computing row and column counts for sparse Cholesky factorization, plus an efficient method to compute the column elimination tree of a sparse matrix without explicitly forming the product of the matrix and its transpose.« less

A new sparse optimization scheme for simultaneous beam angle and fluence map optimization in radiotherapy planning

NASA Astrophysics Data System (ADS)

Liu, Hongcheng; Dong, Peng; Xing, Lei

2017-08-01

{{\\ell }2,1} -minimization-based sparse optimization was employed to solve the beam angle optimization (BAO) in intensity-modulated radiation therapy (IMRT) planning. The technique approximates the exact BAO formulation with efficiently computable convex surrogates, leading to plans that are inferior to those attainable with recently proposed gradient-based greedy schemes. In this paper, we alleviate/reduce the nontrivial inconsistencies between the {{\\ell }2,1} -based formulations and the exact BAO model by proposing a new sparse optimization framework based on the most recent developments in group variable selection. We propose the incorporation of the group-folded concave penalty (gFCP) as a substitution to the {{\\ell }2,1} -minimization framework. The new formulation is then solved by a variation of an existing gradient method. The performance of the proposed scheme is evaluated by both plan quality and the computational efficiency using three IMRT cases: a coplanar prostate case, a coplanar head-and-neck case, and a noncoplanar liver case. Involved in the evaluation are two alternative schemes: the {{\\ell }2,1} -minimization approach and the gradient norm method (GNM). The gFCP-based scheme outperforms both counterpart approaches. In particular, gFCP generates better plans than those obtained using the {{\\ell }2,1} -minimization for all three cases with a comparable computation time. As compared to the GNM, the gFCP improves both the plan quality and computational efficiency. The proposed gFCP-based scheme provides a promising framework for BAO and promises to improve both planning time and plan quality.

Limited angle CT reconstruction by simultaneous spatial and Radon domain regularization based on TV and data-driven tight frame

NASA Astrophysics Data System (ADS)

Zhang, Wenkun; Zhang, Hanming; Wang, Linyuan; Cai, Ailong; Li, Lei; Yan, Bin

2018-02-01

Limited angle computed tomography (CT) reconstruction is widely performed in medical diagnosis and industrial testing because of the size of objects, engine/armor inspection requirements, and limited scan flexibility. Limited angle reconstruction necessitates usage of optimization-based methods that utilize additional sparse priors. However, most of conventional methods solely exploit sparsity priors of spatial domains. When CT projection suffers from serious data deficiency or various noises, obtaining reconstruction images that meet the requirement of quality becomes difficult and challenging. To solve this problem, this paper developed an adaptive reconstruction method for limited angle CT problem. The proposed method simultaneously uses spatial and Radon domain regularization model based on total variation (TV) and data-driven tight frame. Data-driven tight frame being derived from wavelet transformation aims at exploiting sparsity priors of sinogram in Radon domain. Unlike existing works that utilize pre-constructed sparse transformation, the framelets of the data-driven regularization model can be adaptively learned from the latest projection data in the process of iterative reconstruction to provide optimal sparse approximations for given sinogram. At the same time, an effective alternating direction method is designed to solve the simultaneous spatial and Radon domain regularization model. The experiments for both simulation and real data demonstrate that the proposed algorithm shows better performance in artifacts depression and details preservation than the algorithms solely using regularization model of spatial domain. Quantitative evaluations for the results also indicate that the proposed algorithm applying learning strategy performs better than the dual domains algorithms without learning regularization model

A new sparse optimization scheme for simultaneous beam angle and fluence map optimization in radiotherapy planning.

PubMed

Liu, Hongcheng; Dong, Peng; Xing, Lei

2017-07-20

[Formula: see text]-minimization-based sparse optimization was employed to solve the beam angle optimization (BAO) in intensity-modulated radiation therapy (IMRT) planning. The technique approximates the exact BAO formulation with efficiently computable convex surrogates, leading to plans that are inferior to those attainable with recently proposed gradient-based greedy schemes. In this paper, we alleviate/reduce the nontrivial inconsistencies between the [Formula: see text]-based formulations and the exact BAO model by proposing a new sparse optimization framework based on the most recent developments in group variable selection. We propose the incorporation of the group-folded concave penalty (gFCP) as a substitution to the [Formula: see text]-minimization framework. The new formulation is then solved by a variation of an existing gradient method. The performance of the proposed scheme is evaluated by both plan quality and the computational efficiency using three IMRT cases: a coplanar prostate case, a coplanar head-and-neck case, and a noncoplanar liver case. Involved in the evaluation are two alternative schemes: the [Formula: see text]-minimization approach and the gradient norm method (GNM). The gFCP-based scheme outperforms both counterpart approaches. In particular, gFCP generates better plans than those obtained using the [Formula: see text]-minimization for all three cases with a comparable computation time. As compared to the GNM, the gFCP improves both the plan quality and computational efficiency. The proposed gFCP-based scheme provides a promising framework for BAO and promises to improve both planning time and plan quality.

A Sparse Bayesian Learning Algorithm for White Matter Parameter Estimation from Compressed Multi-shell Diffusion MRI.

PubMed

Pisharady, Pramod Kumar; Sotiropoulos, Stamatios N; Sapiro, Guillermo; Lenglet, Christophe

2017-09-01

We propose a sparse Bayesian learning algorithm for improved estimation of white matter fiber parameters from compressed (under-sampled q-space) multi-shell diffusion MRI data. The multi-shell data is represented in a dictionary form using a non-monoexponential decay model of diffusion, based on continuous gamma distribution of diffusivities. The fiber volume fractions with predefined orientations, which are the unknown parameters, form the dictionary weights. These unknown parameters are estimated with a linear un-mixing framework, using a sparse Bayesian learning algorithm. A localized learning of hyperparameters at each voxel and for each possible fiber orientations improves the parameter estimation. Our experiments using synthetic data from the ISBI 2012 HARDI reconstruction challenge and in-vivo data from the Human Connectome Project demonstrate the improvements.

A novel structured dictionary for fast processing of 3D medical images, with application to computed tomography restoration and denoising

NASA Astrophysics Data System (ADS)

Karimi, Davood; Ward, Rabab K.

2016-03-01

Sparse representation of signals in learned overcomplete dictionaries has proven to be a powerful tool with applications in denoising, restoration, compression, reconstruction, and more. Recent research has shown that learned overcomplete dictionaries can lead to better results than analytical dictionaries such as wavelets in almost all image processing applications. However, a major disadvantage of these dictionaries is that their learning and usage is very computationally intensive. In particular, finding the sparse representation of a signal in these dictionaries requires solving an optimization problem that leads to very long computational times, especially in 3D image processing. Moreover, the sparse representation found by greedy algorithms is usually sub-optimal. In this paper, we propose a novel two-level dictionary structure that improves the performance and the speed of standard greedy sparse coding methods. The first (i.e., the top) level in our dictionary is a fixed orthonormal basis, whereas the second level includes the atoms that are learned from the training data. We explain how such a dictionary can be learned from the training data and how the sparse representation of a new signal in this dictionary can be computed. As an application, we use the proposed dictionary structure for removing the noise and artifacts in 3D computed tomography (CT) images. Our experiments with real CT images show that the proposed method achieves results that are comparable with standard dictionary-based methods while substantially reducing the computational time.

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.

Students' Emotions in the High School Mathematical Class: Appraisals in Terms of a Structure of Goals

ERIC Educational Resources Information Center

Martínez-Sierra, Gustavo; García-González, María del Socorro

2017-01-01

Little research in the field of Mathematics Education is directed towards emotions of students beyond their emotions in problem-solving. In particular, the daily emotions of students in a mathematics class have been sparsely studied in the field of mathematics education. In order to fill this gap, this qualitative research aims to identify high…

Joint image restoration and location in visual navigation system

NASA Astrophysics Data System (ADS)

Wu, Yuefeng; Sang, Nong; Lin, Wei; Shao, Yuanjie

2018-02-01

Image location methods are the key technologies of visual navigation, most previous image location methods simply assume the ideal inputs without taking into account the real-world degradations (e.g. low resolution and blur). In view of such degradations, the conventional image location methods first perform image restoration and then match the restored image on the reference image. However, the defective output of the image restoration can affect the result of localization, by dealing with the restoration and location separately. In this paper, we present a joint image restoration and location (JRL) method, which utilizes the sparse representation prior to handle the challenging problem of low-quality image location. The sparse representation prior states that the degraded input image, if correctly restored, will have a good sparse representation in terms of the dictionary constructed from the reference image. By iteratively solving the image restoration in pursuit of the sparest representation, our method can achieve simultaneous restoration and location. Based on such a sparse representation prior, we demonstrate that the image restoration task and the location task can benefit greatly from each other. Extensive experiments on real scene images with Gaussian blur are carried out and our joint model outperforms the conventional methods of treating the two tasks independently.

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.

New Galerkin operational matrices for solving Lane-Emden type equations

NASA Astrophysics Data System (ADS)

Abd-Elhameed, W. M.; Doha, E. H.; Saad, A. S.; Bassuony, M. A.

2016-04-01

Lane-Emden type equations model many phenomena in mathematical physics and astrophysics, such as thermal explosions. This paper is concerned with introducing third and fourth kind Chebyshev-Galerkin operational matrices in order to solve such problems. The principal idea behind the suggested algorithms is based on converting the linear or nonlinear Lane-Emden problem, through the application of suitable spectral methods, into a system of linear or nonlinear equations in the expansion coefficients, which can be efficiently solved. The main advantage of the proposed algorithm in the linear case is that the resulting linear systems are specially structured, and this of course reduces the computational effort required to solve such systems. As an application, we consider the solar model polytrope with n=3 to show that the suggested solutions in this paper are in good agreement with the numerical results.

Low-rank structure learning via nonconvex heuristic recovery.

PubMed

Deng, Yue; Dai, Qionghai; Liu, Risheng; Zhang, Zengke; Hu, Sanqing

2013-03-01

In this paper, we propose a nonconvex framework to learn the essential low-rank structure from corrupted data. Different from traditional approaches, which directly utilizes convex norms to measure the sparseness, our method introduces more reasonable nonconvex measurements to enhance the sparsity in both the intrinsic low-rank structure and the sparse corruptions. We will, respectively, introduce how to combine the widely used ℓp norm (0 < p < 1) and log-sum term into the framework of low-rank structure learning. Although the proposed optimization is no longer convex, it still can be effectively solved by a majorization-minimization (MM)-type algorithm, with which the nonconvex objective function is iteratively replaced by its convex surrogate and the nonconvex problem finally falls into the general framework of reweighed approaches. We prove that the MM-type algorithm can converge to a stationary point after successive iterations. The proposed model is applied to solve two typical problems: robust principal component analysis and low-rank representation. Experimental results on low-rank structure learning demonstrate that our nonconvex heuristic methods, especially the log-sum heuristic recovery algorithm, generally perform much better than the convex-norm-based method (0 < p < 1) for both data with higher rank and with denser corruptions.

Bilevel Model-Based Discriminative Dictionary Learning for Recognition.

PubMed

Zhou, Pan; Zhang, Chao; Lin, Zhouchen

2017-03-01

Most supervised dictionary learning methods optimize the combinations of reconstruction error, sparsity prior, and discriminative terms. Thus, the learnt dictionaries may not be optimal for recognition tasks. Also, the sparse codes learning models in the training and the testing phases are inconsistent. Besides, without utilizing the intrinsic data structure, many dictionary learning methods only employ the l 0 or l 1 norm to encode each datum independently, limiting the performance of the learnt dictionaries. We present a novel bilevel model-based discriminative dictionary learning method for recognition tasks. The upper level directly minimizes the classification error, while the lower level uses the sparsity term and the Laplacian term to characterize the intrinsic data structure. The lower level is subordinate to the upper level. Therefore, our model achieves an overall optimality for recognition in that the learnt dictionary is directly tailored for recognition. Moreover, the sparse codes learning models in the training and the testing phases can be the same. We further propose a novel method to solve our bilevel optimization problem. It first replaces the lower level with its Karush-Kuhn-Tucker conditions and then applies the alternating direction method of multipliers to solve the equivalent problem. Extensive experiments demonstrate the effectiveness and robustness of our method.

MODFLOW–USG version 1: An unstructured grid version of MODFLOW for simulating groundwater flow and tightly coupled processes using a control volume finite-difference formulation

USGS Publications Warehouse

Panday, Sorab; Langevin, Christian D.; Niswonger, Richard G.; Ibaraki, Motomu; Hughes, Joseph D.

2013-01-01

A new version of MODFLOW, called MODFLOW–USG (for UnStructured Grid), was developed to support a wide variety of structured and unstructured grid types, including nested grids and grids based on prismatic triangles, rectangles, hexagons, and other cell shapes. Flexibility in grid design can be used to focus resolution along rivers and around wells, for example, or to subdiscretize individual layers to better represent hydrostratigraphic units. MODFLOW–USG is based on an underlying control volume finite difference (CVFD) formulation in which a cell can be connected to an arbitrary number of adjacent cells. To improve accuracy of the CVFD formulation for irregular grid-cell geometries or nested grids, a generalized Ghost Node Correction (GNC) Package was developed, which uses interpolated heads in the flow calculation between adjacent connected cells. MODFLOW–USG includes a Groundwater Flow (GWF) Process, based on the GWF Process in MODFLOW–2005, as well as a new Connected Linear Network (CLN) Process to simulate the effects of multi-node wells, karst conduits, and tile drains, for example. The CLN Process is tightly coupled with the GWF Process in that the equations from both processes are formulated into one matrix equation and solved simultaneously. This robustness results from using an unstructured grid with unstructured matrix storage and solution schemes. MODFLOW–USG also contains an optional Newton-Raphson formulation, based on the formulation in MODFLOW–NWT, for improving solution convergence and avoiding problems with the drying and rewetting of cells. Because the existing MODFLOW solvers were developed for structured and symmetric matrices, they were replaced with a new Sparse Matrix Solver (SMS) Package developed specifically for MODFLOW–USG. The SMS Package provides several methods for resolving nonlinearities and multiple symmetric and asymmetric linear solution schemes to solve the matrix arising from the flow equations and the Newton-Raphson formulation, respectively.

Sparse SPM: Group Sparse-dictionary learning in SPM framework for resting-state functional connectivity MRI analysis.

PubMed

Lee, Young-Beom; Lee, Jeonghyeon; Tak, Sungho; Lee, Kangjoo; Na, Duk L; Seo, Sang Won; Jeong, Yong; Ye, Jong Chul

2016-01-15

Recent studies of functional connectivity MR imaging have revealed that the default-mode network activity is disrupted in diseases such as Alzheimer's disease (AD). However, there is not yet a consensus on the preferred method for resting-state analysis. Because the brain is reported to have complex interconnected networks according to graph theoretical analysis, the independency assumption, as in the popular independent component analysis (ICA) approach, often does not hold. Here, rather than using the independency assumption, we present a new statistical parameter mapping (SPM)-type analysis method based on a sparse graph model where temporal dynamics at each voxel position are described as a sparse combination of global brain dynamics. In particular, a new concept of a spatially adaptive design matrix has been proposed to represent local connectivity that shares the same temporal dynamics. If we further assume that local network structures within a group are similar, the estimation problem of global and local dynamics can be solved using sparse dictionary learning for the concatenated temporal data across subjects. Moreover, under the homoscedasticity variance assumption across subjects and groups that is often used in SPM analysis, the aforementioned individual and group analyses using sparse dictionary learning can be accurately modeled by a mixed-effect model, which also facilitates a standard SPM-type group-level inference using summary statistics. Using an extensive resting fMRI data set obtained from normal, mild cognitive impairment (MCI), and Alzheimer's disease patient groups, we demonstrated that the changes in the default mode network extracted by the proposed method are more closely correlated with the progression of Alzheimer's disease. Copyright © 2015 Elsevier Inc. All rights reserved.

Anderson acceleration of the Jacobi iterative method: An efficient alternative to Krylov methods for large, sparse linear systems

DOE PAGES

Pratapa, Phanisri P.; Suryanarayana, Phanish; Pask, John E.

2015-12-01

We employ Anderson extrapolation to accelerate the classical Jacobi iterative method for large, sparse linear systems. Specifically, we utilize extrapolation at periodic intervals within the Jacobi iteration to develop the Alternating Anderson–Jacobi (AAJ) method. We verify the accuracy and efficacy of AAJ in a range of test cases, including nonsymmetric systems of equations. We demonstrate that AAJ possesses a favorable scaling with system size that is accompanied by a small prefactor, even in the absence of a preconditioner. In particular, we show that AAJ is able to accelerate the classical Jacobi iteration by over four orders of magnitude, with speed-upsmore » that increase as the system gets larger. Moreover, we find that AAJ significantly outperforms the Generalized Minimal Residual (GMRES) method in the range of problems considered here, with the relative performance again improving with size of the system. As a result, the proposed method represents a simple yet efficient technique that is particularly attractive for large-scale parallel solutions of linear systems of equations.« less

Anderson acceleration of the Jacobi iterative method: An efficient alternative to Krylov methods for large, sparse linear systems

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

Pratapa, Phanisri P.; Suryanarayana, Phanish; Pask, John E.

We employ Anderson extrapolation to accelerate the classical Jacobi iterative method for large, sparse linear systems. Specifically, we utilize extrapolation at periodic intervals within the Jacobi iteration to develop the Alternating Anderson–Jacobi (AAJ) method. We verify the accuracy and efficacy of AAJ in a range of test cases, including nonsymmetric systems of equations. We demonstrate that AAJ possesses a favorable scaling with system size that is accompanied by a small prefactor, even in the absence of a preconditioner. In particular, we show that AAJ is able to accelerate the classical Jacobi iteration by over four orders of magnitude, with speed-upsmore » that increase as the system gets larger. Moreover, we find that AAJ significantly outperforms the Generalized Minimal Residual (GMRES) method in the range of problems considered here, with the relative performance again improving with size of the system. As a result, the proposed method represents a simple yet efficient technique that is particularly attractive for large-scale parallel solutions of linear systems of equations.« less

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.

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

Gearhart, Jared Lee; Adair, Kristin Lynn; Durfee, Justin David.

When developing linear programming models, issues such as budget limitations, customer requirements, or licensing may preclude the use of commercial linear programming solvers. In such cases, one option is to use an open-source linear programming solver. A survey of linear programming tools was conducted to identify potential open-source solvers. From this survey, four open-source solvers were tested using a collection of linear programming test problems and the results were compared to IBM ILOG CPLEX Optimizer (CPLEX) [1], an industry standard. The solvers considered were: COIN-OR Linear Programming (CLP) [2], [3], GNU Linear Programming Kit (GLPK) [4], lp_solve [5] and Modularmore » In-core Nonlinear Optimization System (MINOS) [6]. As no open-source solver outperforms CPLEX, this study demonstrates the power of commercial linear programming software. CLP was found to be the top performing open-source solver considered in terms of capability and speed. GLPK also performed well but cannot match the speed of CLP or CPLEX. lp_solve and MINOS were considerably slower and encountered issues when solving several test problems.« less

Signal processing using sparse derivatives with applications to chromatograms and ECG

NASA Astrophysics Data System (ADS)

Ning, Xiaoran

In this thesis, we investigate the sparsity exist in the derivative domain. Particularly, we focus on the type of signals which posses up to Mth (M > 0) order sparse derivatives. Efforts are put on formulating proper penalty functions and optimization problems to capture properties related to sparse derivatives, searching for fast, computationally efficient solvers. Also the effectiveness of these algorithms are applied to two real world applications. In the first application, we provide an algorithm which jointly addresses the problems of chromatogram baseline correction and noise reduction. The series of chromatogram peaks are modeled as sparse with sparse derivatives, and the baseline is modeled as a low-pass signal. A convex optimization problem is formulated so as to encapsulate these non-parametric models. To account for the positivity of chromatogram peaks, an asymmetric penalty function is also utilized with symmetric penalty functions. A robust, computationally efficient, iterative algorithm is developed that is guaranteed to converge to the unique optimal solution. The approach, termed Baseline Estimation And Denoising with Sparsity (BEADS), is evaluated and compared with two state-of-the-art methods using both simulated and real chromatogram data. Promising result is obtained. In the second application, a novel Electrocardiography (ECG) enhancement algorithm is designed also based on sparse derivatives. In the real medical environment, ECG signals are often contaminated by various kinds of noise or artifacts, for example, morphological changes due to motion artifact, non-stationary noise due to muscular contraction (EMG), etc. Some of these contaminations severely affect the usefulness of ECG signals, especially when computer aided algorithms are utilized. By solving the proposed convex l1 optimization problem, artifacts are reduced by modeling the clean ECG signal as a sum of two signals whose second and third-order derivatives (differences) are sparse respectively. At the end, the algorithm is applied to a QRS detection system and validated using the MIT-BIH Arrhythmia database (109452 anotations), resulting a sensitivity of Se = 99.87%$ and a positive prediction of +P = 99.88%.

Information-optimal genome assembly via sparse read-overlap graphs.

PubMed

Shomorony, Ilan; Kim, Samuel H; Courtade, Thomas A; Tse, David N C

2016-09-01

In the context of third-generation long-read sequencing technologies, read-overlap-based approaches are expected to play a central role in the assembly step. A fundamental challenge in assembling from a read-overlap graph is that the true sequence corresponds to a Hamiltonian path on the graph, and, under most formulations, the assembly problem becomes NP-hard, restricting practical approaches to heuristics. In this work, we avoid this seemingly fundamental barrier by first setting the computational complexity issue aside, and seeking an algorithm that targets information limits In particular, we consider a basic feasibility question: when does the set of reads contain enough information to allow unambiguous reconstruction of the true sequence? Based on insights from this information feasibility question, we present an algorithm-the Not-So-Greedy algorithm-to construct a sparse read-overlap graph. Unlike most other assembly algorithms, Not-So-Greedy comes with a performance guarantee: whenever information feasibility conditions are satisfied, the algorithm reduces the assembly problem to an Eulerian path problem on the resulting graph, and can thus be solved in linear time. In practice, this theoretical guarantee translates into assemblies of higher quality. Evaluations on both simulated reads from real genomes and a PacBio Escherichia coli K12 dataset demonstrate that Not-So-Greedy compares favorably with standard string graph approaches in terms of accuracy of the resulting read-overlap graph and contig N50. Available at github.com/samhykim/nsg courtade@eecs.berkeley.edu or dntse@stanford.edu Supplementary data are available at Bioinformatics online. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Hierarchical Bayesian modelling of mobility metrics for hazard model input calibration

NASA Astrophysics Data System (ADS)

Calder, Eliza; Ogburn, Sarah; Spiller, Elaine; Rutarindwa, Regis; Berger, Jim

2015-04-01

In this work we present a method to constrain flow mobility input parameters for pyroclastic flow models using hierarchical Bayes modeling of standard mobility metrics such as H/L and flow volume etc. The advantage of hierarchical modeling is that it can leverage the information in global dataset for a particular mobility metric in order to reduce the uncertainty in modeling of an individual volcano, especially important where individual volcanoes have only sparse datasets. We use compiled pyroclastic flow runout data from Colima, Merapi, Soufriere Hills, Unzen and Semeru volcanoes, presented in an open-source database FlowDat (https://vhub.org/groups/massflowdatabase). While the exact relationship between flow volume and friction varies somewhat between volcanoes, dome collapse flows originating from the same volcano exhibit similar mobility relationships. Instead of fitting separate regression models for each volcano dataset, we use a variation of the hierarchical linear model (Kass and Steffey, 1989). The model presents a hierarchical structure with two levels; all dome collapse flows and dome collapse flows at specific volcanoes. The hierarchical model allows us to assume that the flows at specific volcanoes share a common distribution of regression slopes, then solves for that distribution. We present comparisons of the 95% confidence intervals on the individual regression lines for the data set from each volcano as well as those obtained from the hierarchical model. The results clearly demonstrate the advantage of considering global datasets using this technique. The technique developed is demonstrated here for mobility metrics, but can be applied to many other global datasets of volcanic parameters. In particular, such methods can provide a means to better contain parameters for volcanoes for which we only have sparse data, a ubiquitous problem in volcanology.

The Joker: A Custom Monte Carlo Sampler for Binary-star and Exoplanet Radial Velocity Data

NASA Astrophysics Data System (ADS)

Price-Whelan, Adrian M.; Hogg, David W.; Foreman-Mackey, Daniel; Rix, Hans-Walter

2017-03-01

Given sparse or low-quality radial velocity measurements of a star, there are often many qualitatively different stellar or exoplanet companion orbit models that are consistent with the data. The consequent multimodality of the likelihood function leads to extremely challenging search, optimization, and Markov chain Monte Carlo (MCMC) posterior sampling over the orbital parameters. Here we create a custom Monte Carlo sampler for sparse or noisy radial velocity measurements of two-body systems that can produce posterior samples for orbital parameters even when the likelihood function is poorly behaved. The six standard orbital parameters for a binary system can be split into four nonlinear parameters (period, eccentricity, argument of pericenter, phase) and two linear parameters (velocity amplitude, barycenter velocity). We capitalize on this by building a sampling method in which we densely sample the prior probability density function (pdf) in the nonlinear parameters and perform rejection sampling using a likelihood function marginalized over the linear parameters. With sparse or uninformative data, the sampling obtained by this rejection sampling is generally multimodal and dense. With informative data, the sampling becomes effectively unimodal but too sparse: in these cases we follow the rejection sampling with standard MCMC. The method produces correct samplings in orbital parameters for data that include as few as three epochs. The Joker can therefore be used to produce proper samplings of multimodal pdfs, which are still informative and can be used in hierarchical (population) modeling. We give some examples that show how the posterior pdf depends sensitively on the number and time coverage of the observations and their uncertainties.

A sparse reconstruction method for the estimation of multiresolution emission fields via atmospheric inversion

DOE PAGES

Ray, J.; Lee, J.; Yadav, V.; ...

2014-08-20

We present a sparse reconstruction scheme that can also be used to ensure non-negativity when fitting wavelet-based random field models to limited observations in non-rectangular geometries. The method is relevant when multiresolution fields are estimated using linear inverse problems. Examples include the estimation of emission fields for many anthropogenic pollutants using atmospheric inversion or hydraulic conductivity in aquifers from flow measurements. The scheme is based on three new developments. Firstly, we extend an existing sparse reconstruction method, Stagewise Orthogonal Matching Pursuit (StOMP), to incorporate prior information on the target field. Secondly, we develop an iterative method that uses StOMP tomore » impose non-negativity on the estimated field. Finally, we devise a method, based on compressive sensing, to limit the estimated field within an irregularly shaped domain. We demonstrate the method on the estimation of fossil-fuel CO 2 (ffCO 2) emissions in the lower 48 states of the US. The application uses a recently developed multiresolution random field model and synthetic observations of ffCO 2 concentrations from a limited set of measurement sites. We find that our method for limiting the estimated field within an irregularly shaped region is about a factor of 10 faster than conventional approaches. It also reduces the overall computational cost by a factor of two. Further, the sparse reconstruction scheme imposes non-negativity without introducing strong nonlinearities, such as those introduced by employing log-transformed fields, and thus reaps the benefits of simplicity and computational speed that are characteristic of linear inverse problems.« less

Controls/CFD Interdisciplinary Research Software Generates Low-Order Linear Models for Control Design From Steady-State CFD Results

NASA Technical Reports Server (NTRS)

Melcher, Kevin J.

1997-01-01

The NASA Lewis Research Center is developing analytical methods and software tools to create a bridge between the controls and computational fluid dynamics (CFD) disciplines. Traditionally, control design engineers have used coarse nonlinear simulations to generate information for the design of new propulsion system controls. However, such traditional methods are not adequate for modeling the propulsion systems of complex, high-speed vehicles like the High Speed Civil Transport. To properly model the relevant flow physics of high-speed propulsion systems, one must use simulations based on CFD methods. Such CFD simulations have become useful tools for engineers that are designing propulsion system components. The analysis techniques and software being developed as part of this effort are an attempt to evolve CFD into a useful tool for control design as well. One major aspect of this research is the generation of linear models from steady-state CFD results. CFD simulations, often used during the design of high-speed inlets, yield high resolution operating point data. Under a NASA grant, the University of Akron has developed analytical techniques and software tools that use these data to generate linear models for control design. The resulting linear models have the same number of states as the original CFD simulation, so they are still very large and computationally cumbersome. Model reduction techniques have been successfully applied to reduce these large linear models by several orders of magnitude without significantly changing the dynamic response. The result is an accurate, easy to use, low-order linear model that takes less time to generate than those generated by traditional means. The development of methods for generating low-order linear models from steady-state CFD is most complete at the one-dimensional level, where software is available to generate models with different kinds of input and output variables. One-dimensional methods have been extended somewhat so that linear models can also be generated from two- and three-dimensional steady-state results. Standard techniques are adequate for reducing the order of one-dimensional CFD-based linear models. However, reduction of linear models based on two- and three-dimensional CFD results is complicated by very sparse, ill-conditioned matrices. Some novel approaches are being investigated to solve this problem.

EZLP: An Interactive Computer Program for Solving Linear Programming Problems. Final Report.

ERIC Educational Resources Information Center

Jarvis, John J.; And Others

Designed for student use in solving linear programming problems, the interactive computer program described (EZLP) permits the student to input the linear programming model in exactly the same manner in which it would be written on paper. This report includes a brief review of the development of EZLP; narrative descriptions of program features,…

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.

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.

Compressive Sensing with Cross-Validation and Stop-Sampling for Sparse Polynomial Chaos Expansions

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

Huan, Xun; Safta, Cosmin; Sargsyan, Khachik

Compressive sensing is a powerful technique for recovering sparse solutions of underdetermined linear systems, which is often encountered in uncertainty quanti cation analysis of expensive and high-dimensional physical models. We perform numerical investigations employing several com- pressive sensing solvers that target the unconstrained LASSO formulation, with a focus on linear systems that arise in the construction of polynomial chaos expansions. With core solvers of l1 ls, SpaRSA, CGIST, FPC AS, and ADMM, we develop techniques to mitigate over tting through an automated selection of regularization constant based on cross-validation, and a heuristic strategy to guide the stop-sampling decision. Practical recommendationsmore » on parameter settings for these tech- niques are provided and discussed. The overall method is applied to a series of numerical examples of increasing complexity, including large eddy simulations of supersonic turbulent jet-in-cross flow involving a 24-dimensional input. Through empirical phase-transition diagrams and convergence plots, we illustrate sparse recovery performance under structures induced by polynomial chaos, accuracy and computational tradeoffs between polynomial bases of different degrees, and practi- cability of conducting compressive sensing for a realistic, high-dimensional physical application. Across test cases studied in this paper, we find ADMM to have demonstrated empirical advantages through consistent lower errors and faster computational times.« less

Sparse modeling applied to patient identification for safety in medical physics applications

NASA Astrophysics Data System (ADS)

Lewkowitz, Stephanie

Every scheduled treatment at a radiation therapy clinic involves a series of safety protocol to ensure the utmost patient care. Despite safety protocol, on a rare occasion an entirely preventable medical event, an accident, may occur. Delivering a treatment plan to the wrong patient is preventable, yet still is a clinically documented error. This research describes a computational method to identify patients with a novel machine learning technique to combat misadministration. The patient identification program stores face and fingerprint data for each patient. New, unlabeled data from those patients are categorized according to the library. The categorization of data by this face-fingerprint detector is accomplished with new machine learning algorithms based on Sparse Modeling that have already begun transforming the foundation of Computer Vision. Previous patient recognition software required special subroutines for faces and different tailored subroutines for fingerprints. In this research, the same exact model is used for both fingerprints and faces, without any additional subroutines and even without adjusting the two hyperparameters. Sparse modeling is a powerful tool, already shown utility in the areas of super-resolution, denoising, inpainting, demosaicing, and sub-nyquist sampling, i.e. compressed sensing. Sparse Modeling is possible because natural images are inherently sparse in some bases, due to their inherent structure. This research chooses datasets of face and fingerprint images to test the patient identification model. The model stores the images of each dataset as a basis (library). One image at a time is removed from the library, and is classified by a sparse code in terms of the remaining library. The Locally Competitive Algorithm, a truly neural inspired Artificial Neural Network, solves the computationally difficult task of finding the sparse code for the test image. The components of the sparse representation vector are summed by ℓ1 pooling, and correct patient identification is consistently achieved 100% over 1000 trials, when either the face data or fingerprint data are implemented as a classification basis. The algorithm gets 100% classification when faces and fingerprints are concatenated into multimodal datasets. This suggests that 100% patient identification will be achievable in the clinal setting.

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.

Fast RBF OGr for solving PDEs on arbitrary surfaces

NASA Astrophysics Data System (ADS)

Piret, Cécile; Dunn, Jarrett

2016-10-01

The Radial Basis Functions Orthogonal Gradients method (RBF-OGr) was introduced in [1] to discretize differential operators defined on arbitrary manifolds defined only by a point cloud. We take advantage of the meshfree character of RBFs, which give us a high accuracy and the flexibility to represent complex geometries in any spatial dimension. A large limitation of the RBF-OGr method was its large computational complexity, which greatly restricted the size of the point cloud. In this paper, we apply the RBF-Finite Difference (RBF-FD) technique to the RBF-OGr method for building sparse differentiation matrices discretizing continuous differential operators such as the Laplace-Beltrami operator. This method can be applied to solving PDEs on arbitrary surfaces embedded in ℛ3. We illustrate the accuracy of our new method by solving the heat equation on the unit sphere.

Can Linear Superiorization Be Useful for Linear Optimization Problems?

PubMed Central

Censor, Yair

2017-01-01

Linear superiorization considers linear programming problems but instead of attempting to solve them with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward reduced (not necessarily minimal) target function values. The two questions that we set out to explore experimentally are (i) Does linear superiorization provide a feasible point whose linear target function value is lower than that obtained by running the same feasibility-seeking algorithm without superiorization under identical conditions? and (ii) How does linear superiorization fare in comparison with the Simplex method for solving linear programming problems? Based on our computational experiments presented here, the answers to these two questions are: “yes” and “very well”, respectively. PMID:29335660

Krylov subspace methods - Theory, algorithms, and applications

NASA Technical Reports Server (NTRS)

Sad, Youcef

1990-01-01

Projection methods based on Krylov subspaces for solving various types of scientific problems are reviewed. The main idea of this class of methods when applied to a linear system Ax = b, is to generate in some manner an approximate solution to the original problem from the so-called Krylov subspace span. Thus, the original problem of size N is approximated by one of dimension m, typically much smaller than N. Krylov subspace methods have been very successful in solving linear systems and eigenvalue problems and are now becoming popular for solving nonlinear equations. The main ideas in Krylov subspace methods are shown and their use in solving linear systems, eigenvalue problems, parabolic partial differential equations, Liapunov matrix equations, and nonlinear system of equations are discussed.

Bypassing the Limits of Ll Regularization: Convex Sparse Signal Processing Using Non-Convex Regularization

NASA Astrophysics Data System (ADS)

Parekh, Ankit

Sparsity has become the basis of some important signal processing methods over the last ten years. Many signal processing problems (e.g., denoising, deconvolution, non-linear component analysis) can be expressed as inverse problems. Sparsity is invoked through the formulation of an inverse problem with suitably designed regularization terms. The regularization terms alone encode sparsity into the problem formulation. Often, the ℓ1 norm is used to induce sparsity, so much so that ℓ1 regularization is considered to be `modern least-squares'. The use of ℓ1 norm, as a sparsity-inducing regularizer, leads to a convex optimization problem, which has several benefits: the absence of extraneous local minima, well developed theory of globally convergent algorithms, even for large-scale problems. Convex regularization via the ℓ1 norm, however, tends to under-estimate the non-zero values of sparse signals. In order to estimate the non-zero values more accurately, non-convex regularization is often favored over convex regularization. However, non-convex regularization generally leads to non-convex optimization, which suffers from numerous issues: convergence may be guaranteed to only a stationary point, problem specific parameters may be difficult to set, and the solution is sensitive to the initialization of the algorithm. The first part of this thesis is aimed toward combining the benefits of non-convex regularization and convex optimization to estimate sparse signals more effectively. To this end, we propose to use parameterized non-convex regularizers with designated non-convexity and provide a range for the non-convex parameter so as to ensure that the objective function is strictly convex. By ensuring convexity of the objective function (sum of data-fidelity and non-convex regularizer), we can make use of a wide variety of convex optimization algorithms to obtain the unique global minimum reliably. The second part of this thesis proposes a non-linear signal decomposition technique for an important biomedical signal processing problem: the detection of sleep spindles and K-complexes in human sleep electroencephalography (EEG). We propose a non-linear model for the EEG consisting of three components: (1) a transient (sparse piecewise constant) component, (2) a low-frequency component, and (3) an oscillatory component. The oscillatory component admits a sparse time-frequency representation. Using a convex objective function, we propose a fast non-linear optimization algorithm to estimate the three components in the proposed signal model. The low-frequency and oscillatory components are then used to estimate the K-complexes and sleep spindles respectively. The proposed detection method is shown to outperform several state-of-the-art automated sleep spindles detection methods.

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.

Compressive sensing-based electrostatic sensor array signal processing and exhausted abnormal debris detecting

NASA Astrophysics Data System (ADS)

Tang, Xin; Chen, Zhongsheng; Li, Yue; Yang, Yongmin

2018-05-01

When faults happen at gas path components of gas turbines, some sparsely-distributed and charged debris will be generated and released into the exhaust gas. The debris is called abnormal debris. Electrostatic sensors can detect the debris online and further indicate the faults. It is generally considered that, under a specific working condition, a more serious fault generates more and larger debris, and a piece of larger debris carries more charge. Therefore, the amount and charge of the abnormal debris are important indicators of the fault severity. However, because an electrostatic sensor can only detect the superposed effect on the electrostatic field of all the debris, it can hardly identify the amount and position of the debris. Moreover, because signals of electrostatic sensors depend on not only charge but also position of debris, and the position information is difficult to acquire, measuring debris charge accurately using the electrostatic detecting method is still a technical difficulty. To solve these problems, a hemisphere-shaped electrostatic sensors' circular array (HSESCA) is used, and an array signal processing method based on compressive sensing (CS) is proposed in this paper. To research in a theoretical framework of CS, the measurement model of the HSESCA is discretized into a sparse representation form by meshing. In this way, the amount and charge of the abnormal debris are described as a sparse vector. It is further reconstructed by constraining l1-norm when solving an underdetermined equation. In addition, a pre-processing method based on singular value decomposition and a result calibration method based on weighted-centroid algorithm are applied to ensure the accuracy of the reconstruction. The proposed method is validated by both numerical simulations and experiments. Reconstruction errors, characteristics of the results and some related factors are discussed.

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.

Optshrink LR + S: accelerated fMRI reconstruction using non-convex optimal singular value shrinkage.

PubMed

Aggarwal, Priya; Shrivastava, Parth; Kabra, Tanay; Gupta, Anubha

2017-03-01

This paper presents a new accelerated fMRI reconstruction method, namely, OptShrink LR + S method that reconstructs undersampled fMRI data using a linear combination of low-rank and sparse components. The low-rank component has been estimated using non-convex optimal singular value shrinkage algorithm, while the sparse component has been estimated using convex l 1 minimization. The performance of the proposed method is compared with the existing state-of-the-art algorithms on real fMRI dataset. The proposed OptShrink LR + S method yields good qualitative and quantitative results.

On A Nonlinear Generalization of Sparse Coding and Dictionary Learning.

PubMed

Xie, Yuchen; Ho, Jeffrey; Vemuri, Baba

2013-01-01

Existing dictionary learning algorithms are based on the assumption that the data are vectors in an Euclidean vector space ℝ d , and the dictionary is learned from the training data using the vector space structure of ℝ d and its Euclidean L 2 -metric. However, in many applications, features and data often originated from a Riemannian manifold that does not support a global linear (vector space) structure. Furthermore, the extrinsic viewpoint of existing dictionary learning algorithms becomes inappropriate for modeling and incorporating the intrinsic geometry of the manifold that is potentially important and critical to the application. This paper proposes a novel framework for sparse coding and dictionary learning for data on a Riemannian manifold, and it shows that the existing sparse coding and dictionary learning methods can be considered as special (Euclidean) cases of the more general framework proposed here. We show that both the dictionary and sparse coding can be effectively computed for several important classes of Riemannian manifolds, and we validate the proposed method using two well-known classification problems in computer vision and medical imaging analysis.

On A Nonlinear Generalization of Sparse Coding and Dictionary Learning

PubMed Central

Xie, Yuchen; Ho, Jeffrey; Vemuri, Baba

2013-01-01

Existing dictionary learning algorithms are based on the assumption that the data are vectors in an Euclidean vector space ℝd, and the dictionary is learned from the training data using the vector space structure of ℝd and its Euclidean L2-metric. However, in many applications, features and data often originated from a Riemannian manifold that does not support a global linear (vector space) structure. Furthermore, the extrinsic viewpoint of existing dictionary learning algorithms becomes inappropriate for modeling and incorporating the intrinsic geometry of the manifold that is potentially important and critical to the application. This paper proposes a novel framework for sparse coding and dictionary learning for data on a Riemannian manifold, and it shows that the existing sparse coding and dictionary learning methods can be considered as special (Euclidean) cases of the more general framework proposed here. We show that both the dictionary and sparse coding can be effectively computed for several important classes of Riemannian manifolds, and we validate the proposed method using two well-known classification problems in computer vision and medical imaging analysis. PMID:24129583

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.

SPReM: Sparse Projection Regression Model For High-dimensional Linear Regression *

PubMed Central

Sun, Qiang; Zhu, Hongtu; Liu, Yufeng; Ibrahim, Joseph G.

2014-01-01

The aim of this paper is to develop a sparse projection regression modeling (SPReM) framework to perform multivariate regression modeling with a large number of responses and a multivariate covariate of interest. We propose two novel heritability ratios to simultaneously perform dimension reduction, response selection, estimation, and testing, while explicitly accounting for correlations among multivariate responses. Our SPReM is devised to specifically address the low statistical power issue of many standard statistical approaches, such as the Hotelling’s T2 test statistic or a mass univariate analysis, for high-dimensional data. We formulate the estimation problem of SPREM as a novel sparse unit rank projection (SURP) problem and propose a fast optimization algorithm for SURP. Furthermore, we extend SURP to the sparse multi-rank projection (SMURP) by adopting a sequential SURP approximation. Theoretically, we have systematically investigated the convergence properties of SURP and the convergence rate of SURP estimates. Our simulation results and real data analysis have shown that SPReM out-performs other state-of-the-art methods. PMID:26527844

Sparse Logistic Regression for Diagnosis of Liver Fibrosis in Rat by Using SCAD-Penalized Likelihood

PubMed Central

Yan, Fang-Rong; Lin, Jin-Guan; Liu, Yu

2011-01-01

The objective of the present study is to find out the quantitative relationship between progression of liver fibrosis and the levels of certain serum markers using mathematic model. We provide the sparse logistic regression by using smoothly clipped absolute deviation (SCAD) penalized function to diagnose the liver fibrosis in rats. Not only does it give a sparse solution with high accuracy, it also provides the users with the precise probabilities of classification with the class information. In the simulative case and the experiment case, the proposed method is comparable to the stepwise linear discriminant analysis (SLDA) and the sparse logistic regression with least absolute shrinkage and selection operator (LASSO) penalty, by using receiver operating characteristic (ROC) with bayesian bootstrap estimating area under the curve (AUC) diagnostic sensitivity for selected variable. Results show that the new approach provides a good correlation between the serum marker levels and the liver fibrosis induced by thioacetamide (TAA) in rats. Meanwhile, this approach might also be used in predicting the development of liver cirrhosis. PMID:21716672

Sparseness- and continuity-constrained seismic imaging

NASA Astrophysics Data System (ADS)

Herrmann, Felix J.

2005-04-01

Non-linear solution strategies to the least-squares seismic inverse-scattering problem with sparseness and continuity constraints are proposed. Our approach is designed to (i) deal with substantial amounts of additive noise (SNR < 0 dB); (ii) use the sparseness and locality (both in position and angle) of directional basis functions (such as curvelets and contourlets) on the model: the reflectivity; and (iii) exploit the near invariance of these basis functions under the normal operator, i.e., the scattering-followed-by-imaging operator. Signal-to-noise ratio and the continuity along the imaged reflectors are significantly enhanced by formulating the solution of the seismic inverse problem in terms of an optimization problem. During the optimization, sparseness on the basis and continuity along the reflectors are imposed by jointly minimizing the l1- and anisotropic diffusion/total-variation norms on the coefficients and reflectivity, respectively. [Joint work with Peyman P. Moghaddam was carried out as part of the SINBAD project, with financial support secured through ITF (the Industry Technology Facilitator) from the following organizations: BG Group, BP, ExxonMobil, and SHELL. Additional funding came from the NSERC Discovery Grants 22R81254.

Optical fringe-reflection deflectometry with sparse representation

NASA Astrophysics Data System (ADS)

Xiao, Yong-Liang; Li, Sikun; Zhang, Qican; Zhong, Jianxin; Su, Xianyu; You, Zhisheng

2018-05-01

Optical fringe-reflection deflectometry is a surprisingly attractive scratch detection technique for specular surfaces owing to its unparalleled local sensibility. Full-field surface topography is obtained from a measured normal field using gradient integration. However, there may not be an ideal measured gradient field for deflectometry reconstruction in practice. Both the non-integrability condition and various kinds of image noise distributions, which are present in the indirect measured gradient field, may lead to ambiguity about the scratches on specular surfaces. In order to reduce misjudgment of scratches, sparse representation is introduced into the Southwell curl equation for deflectometry. The curl can be represented as a linear combination of the given redundant dictionary for curl and the sparsest solution for gradient refinement. The non-integrability condition and noise permutation can be overcome with sparse representation for gradient refinement. Numerical simulations demonstrate that the accuracy rate of judgment of scratches can be enhanced with sparse representation compared to the standard least-squares integration. Preliminary experiments are performed with the application of practical measured deflectometric data to verify the validity of the algorithm.

Joint sparse coding based spatial pyramid matching for classification of color medical image.

PubMed

Shi, Jun; Li, Yi; Zhu, Jie; Sun, Haojie; Cai, Yin

2015-04-01

Although color medical images are important in clinical practice, they are usually converted to grayscale for further processing in pattern recognition, resulting in loss of rich color information. The sparse coding based linear spatial pyramid matching (ScSPM) and its variants are popular for grayscale image classification, but cannot extract color information. In this paper, we propose a joint sparse coding based SPM (JScSPM) method for the classification of color medical images. A joint dictionary can represent both the color information in each color channel and the correlation between channels. Consequently, the joint sparse codes calculated from a joint dictionary can carry color information, and therefore this method can easily transform a feature descriptor originally designed for grayscale images to a color descriptor. A color hepatocellular carcinoma histological image dataset was used to evaluate the performance of the proposed JScSPM algorithm. Experimental results show that JScSPM provides significant improvements as compared with the majority voting based ScSPM and the original ScSPM for color medical image classification. Copyright © 2014 Elsevier Ltd. All rights reserved.

Application of a sparse representation method using K-SVD to data compression of experimental ambient vibration data for SHM

NASA Astrophysics Data System (ADS)

Noh, Hae Young; Kiremidjian, Anne S.

2011-04-01

This paper introduces a data compression method using the K-SVD algorithm and its application to experimental ambient vibration data for structural health monitoring purposes. Because many damage diagnosis algorithms that use system identification require vibration measurements of multiple locations, it is necessary to transmit long threads of data. In wireless sensor networks for structural health monitoring, however, data transmission is often a major source of battery consumption. Therefore, reducing the amount of data to transmit can significantly lengthen the battery life and reduce maintenance cost. The K-SVD algorithm was originally developed in information theory for sparse signal representation. This algorithm creates an optimal over-complete set of bases, referred to as a dictionary, using singular value decomposition (SVD) and represents the data as sparse linear combinations of these bases using the orthogonal matching pursuit (OMP) algorithm. Since ambient vibration data are stationary, we can segment them and represent each segment sparsely. Then only the dictionary and the sparse vectors of the coefficients need to be transmitted wirelessly for restoration of the original data. We applied this method to ambient vibration data measured from a four-story steel moment resisting frame. The results show that the method can compress the data efficiently and restore the data with very little error.

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 application of low-rank and sparse decomposition method in the field of climatology

NASA Astrophysics Data System (ADS)

Gupta, Nitika; Bhaskaran, Prasad K.

2018-04-01

The present study reports a low-rank and sparse decomposition method that separates the mean and the variability of a climate data field. Until now, the application of this technique was limited only in areas such as image processing, web data ranking, and bioinformatics data analysis. In climate science, this method exactly separates the original data into a set of low-rank and sparse components, wherein the low-rank components depict the linearly correlated dataset (expected or mean behavior), and the sparse component represents the variation or perturbation in the dataset from its mean behavior. The study attempts to verify the efficacy of this proposed technique in the field of climatology with two examples of real world. The first example attempts this technique on the maximum wind-speed (MWS) data for the Indian Ocean (IO) region. The study brings to light a decadal reversal pattern in the MWS for the North Indian Ocean (NIO) during the months of June, July, and August (JJA). The second example deals with the sea surface temperature (SST) data for the Bay of Bengal region that exhibits a distinct pattern in the sparse component. The study highlights the importance of the proposed technique used for interpretation and visualization of climate data.

On the sparseness of 1-norm support vector machines.

PubMed

Zhang, Li; Zhou, Weida

2010-04-01

There is some empirical evidence available showing that 1-norm Support Vector Machines (1-norm SVMs) have good sparseness; however, both how good sparseness 1-norm SVMs can reach and whether they have a sparser representation than that of standard SVMs are not clear. In this paper we take into account the sparseness of 1-norm SVMs. Two upper bounds on the number of nonzero coefficients in the decision function of 1-norm SVMs are presented. First, the number of nonzero coefficients in 1-norm SVMs is at most equal to the number of only the exact support vectors lying on the +1 and -1 discriminating surfaces, while that in standard SVMs is equal to the number of support vectors, which implies that 1-norm SVMs have better sparseness than that of standard SVMs. Second, the number of nonzero coefficients is at most equal to the rank of the sample matrix. A brief review of the geometry of linear programming and the primal steepest edge pricing simplex method are given, which allows us to provide the proof of the two upper bounds and evaluate their tightness by experiments. Experimental results on toy data sets and the UCI data sets illustrate our analysis. Copyright 2009 Elsevier Ltd. All rights reserved.

Orthogonal Procrustes Analysis for Dictionary Learning in Sparse Linear Representation.

PubMed

Grossi, Giuliano; Lanzarotti, Raffaella; Lin, Jianyi

2017-01-01

In the sparse representation model, the design of overcomplete dictionaries plays a key role for the effectiveness and applicability in different domains. Recent research has produced several dictionary learning approaches, being proven that dictionaries learnt by data examples significantly outperform structured ones, e.g. wavelet transforms. In this context, learning consists in adapting the dictionary atoms to a set of training signals in order to promote a sparse representation that minimizes the reconstruction error. Finding the best fitting dictionary remains a very difficult task, leaving the question still open. A well-established heuristic method for tackling this problem is an iterative alternating scheme, adopted for instance in the well-known K-SVD algorithm. Essentially, it consists in repeating two stages; the former promotes sparse coding of the training set and the latter adapts the dictionary to reduce the error. In this paper we present R-SVD, a new method that, while maintaining the alternating scheme, adopts the Orthogonal Procrustes analysis to update the dictionary atoms suitably arranged into groups. Comparative experiments on synthetic data prove the effectiveness of R-SVD with respect to well known dictionary learning algorithms such as K-SVD, ILS-DLA and the online method OSDL. Moreover, experiments on natural data such as ECG compression, EEG sparse representation, and image modeling confirm R-SVD's robustness and wide applicability.

Linear: A Novel Algorithm for Reconstructing Slitless Spectroscopy from HST/WFC3

NASA Astrophysics Data System (ADS)

Ryan, R. E., Jr.; Casertano, S.; Pirzkal, N.

2018-03-01

We present a grism extraction package (LINEAR) designed to reconstruct 1D spectra from a collection of slitless spectroscopic images, ideally taken at a variety of orientations, dispersion directions, and/or dither positions. Our approach is to enumerate every transformation between all direct image positions (i.e., a potential source) and the collection of grism images at all relevant wavelengths. This leads to solving a large, sparse system of linear equations, which we invert using the standard LSQR algorithm. We implement a number of color and geometric corrections (such as flat field, pixel-area map, source morphology, and spectral bandwidth), but assume many effects have been calibrated out (such as basic reductions, background subtraction, and astrometric refinement). We demonstrate the power of our approach with several Monte Carlo simulations and the analysis of archival data. The simulations include astrometric and photometric uncertainties, sky-background estimation, and signal-to-noise calculations. The data are G141 observations obtained with the Wide-Field Camera 3 of the Hubble Ultra-Deep Field, and show the power of our formalism by improving the spectral resolution without sacrificing the signal-to-noise (a tradeoff that is often made by current approaches). Additionally, our approach naturally accounts for source contamination, which is only handled heuristically by present softwares. We conclude with a discussion of various observations where our approach will provide much improved spectral 1D spectra, such as crowded fields (star or galaxy clusters), spatially resolved spectroscopy, or surveys with strict completeness requirements. At present our software is heavily geared for Wide-Field Camera 3 IR, however we plan extend the codebase for additional instruments.

Covariance Matrix Estimation for the Cryo-EM Heterogeneity Problem*

PubMed Central

Katsevich, E.; Katsevich, A.; Singer, A.

2015-01-01

In cryo-electron microscopy (cryo-EM), a microscope generates a top view of a sample of randomly oriented copies of a molecule. The problem of single particle reconstruction (SPR) from cryo-EM is to use the resulting set of noisy two-dimensional projection images taken at unknown directions to reconstruct the three-dimensional (3D) structure of the molecule. In some situations, the molecule under examination exhibits structural variability, which poses a fundamental challenge in SPR. The heterogeneity problem is the task of mapping the space of conformational states of a molecule. It has been previously suggested that the leading eigenvectors of the covariance matrix of the 3D molecules can be used to solve the heterogeneity problem. Estimating the covariance matrix is challenging, since only projections of the molecules are observed, but not the molecules themselves. In this paper, we formulate a general problem of covariance estimation from noisy projections of samples. This problem has intimate connections with matrix completion problems and high-dimensional principal component analysis. We propose an estimator and prove its consistency. When there are finitely many heterogeneity classes, the spectrum of the estimated covariance matrix reveals the number of classes. The estimator can be found as the solution to a certain linear system. In the cryo-EM case, the linear operator to be inverted, which we term the projection covariance transform, is an important object in covariance estimation for tomographic problems involving structural variation. Inverting it involves applying a filter akin to the ramp filter in tomography. We design a basis in which this linear operator is sparse and thus can be tractably inverted despite its large size. We demonstrate via numerical experiments on synthetic datasets the robustness of our algorithm to high levels of noise. PMID:25699132

A duality approach for solving bounded linear programming problems with fuzzy variables based on ranking functions and its application in bounded transportation problems

NASA Astrophysics Data System (ADS)

Ebrahimnejad, Ali

2015-08-01

There are several methods, in the literature, for solving fuzzy variable linear programming problems (fuzzy linear programming in which the right-hand-side vectors and decision variables are represented by trapezoidal fuzzy numbers). In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings a new method based on the bounded dual simplex method is proposed to determine the fuzzy optimal solution of that kind of fuzzy variable linear programming problems in which some or all variables are restricted to lie within lower and upper bounds. To illustrate the proposed method, an application example is solved and the obtained results are given. The advantages of the proposed method over existing methods are discussed. Also, one application of this algorithm in solving bounded transportation problems with fuzzy supplies and demands is dealt with. The proposed method is easy to understand and to apply for determining the fuzzy optimal solution of bounded fuzzy variable linear programming problems occurring in real-life situations.

Chemical Equation Balancing.

ERIC Educational Resources Information Center

Blakley, G. R.

1982-01-01

Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)

Symbolic Solution of Linear Differential Equations

NASA Technical Reports Server (NTRS)

Feinberg, R. B.; Grooms, R. G.

1981-01-01

An algorithm for solving linear constant-coefficient ordinary differential equations is presented. The computational complexity of the algorithm is discussed and its implementation in the FORMAC system is described. A comparison is made between the algorithm and some classical algorithms for solving differential equations.

On Solving Linear Recurrences

ERIC Educational Resources Information Center

Dobbs, David E.

2013-01-01

A direct method is given for solving first-order linear recurrences with constant coefficients. The limiting value of that solution is studied as "n to infinity." This classroom note could serve as enrichment material for the typical introductory course on discrete mathematics that follows a calculus course.

Infrared moving small target detection based on saliency extraction and image sparse representation

NASA Astrophysics Data System (ADS)

Zhang, Xiaomin; Ren, Kan; Gao, Jin; Li, Chaowei; Gu, Guohua; Wan, Minjie

2016-10-01

Moving small target detection in infrared image is a crucial technique of infrared search and tracking system. This paper present a novel small target detection technique based on frequency-domain saliency extraction and image sparse representation. First, we exploit the features of Fourier spectrum image and magnitude spectrum of Fourier transform to make a rough extract of saliency regions and use a threshold segmentation system to classify the regions which look salient from the background, which gives us a binary image as result. Second, a new patch-image model and over-complete dictionary were introduced to the detection system, then the infrared small target detection was converted into a problem solving and optimization process of patch-image information reconstruction based on sparse representation. More specifically, the test image and binary image can be decomposed into some image patches follow certain rules. We select the target potential area according to the binary patch-image which contains salient region information, then exploit the over-complete infrared small target dictionary to reconstruct the test image blocks which may contain targets. The coefficients of target image patch satisfy sparse features. Finally, for image sequence, Euclidean distance was used to reduce false alarm ratio and increase the detection accuracy of moving small targets in infrared images due to the target position correlation between frames.

Feature learning and change feature classification based on deep learning for ternary change detection in SAR images

NASA Astrophysics Data System (ADS)

Gong, Maoguo; Yang, Hailun; Zhang, Puzhao

2017-07-01

Ternary change detection aims to detect changes and group the changes into positive change and negative change. It is of great significance in the joint interpretation of spatial-temporal synthetic aperture radar images. In this study, sparse autoencoder, convolutional neural networks (CNN) and unsupervised clustering are combined to solve ternary change detection problem without any supervison. Firstly, sparse autoencoder is used to transform log-ratio difference image into a suitable feature space for extracting key changes and suppressing outliers and noise. And then the learned features are clustered into three classes, which are taken as the pseudo labels for training a CNN model as change feature classifier. The reliable training samples for CNN are selected from the feature maps learned by sparse autoencoder with certain selection rules. Having training samples and the corresponding pseudo labels, the CNN model can be trained by using back propagation with stochastic gradient descent. During its training procedure, CNN is driven to learn the concept of change, and more powerful model is established to distinguish different types of changes. Unlike the traditional methods, the proposed framework integrates the merits of sparse autoencoder and CNN to learn more robust difference representations and the concept of change for ternary change detection. Experimental results on real datasets validate the effectiveness and superiority of the proposed framework.

Large-scale linear rankSVM.

PubMed

Lee, Ching-Pei; Lin, Chih-Jen

2014-04-01

Linear rankSVM is one of the widely used methods for learning to rank. Although its performance may be inferior to nonlinear methods such as kernel rankSVM and gradient boosting decision trees, linear rankSVM is useful to quickly produce a baseline model. Furthermore, following its recent development for classification, linear rankSVM may give competitive performance for large and sparse data. A great deal of works have studied linear rankSVM. The focus is on the computational efficiency when the number of preference pairs is large. In this letter, we systematically study existing works, discuss their advantages and disadvantages, and propose an efficient algorithm. We discuss different implementation issues and extensions with detailed experiments. Finally, we develop a robust linear rankSVM tool for public use.

FPGA implementation of sparse matrix algorithm for information retrieval

NASA Astrophysics Data System (ADS)

Bojanic, Slobodan; Jevtic, Ruzica; Nieto-Taladriz, Octavio

2005-06-01

Information text data retrieval requires a tremendous amount of processing time because of the size of the data and the complexity of information retrieval algorithms. In this paper the solution to this problem is proposed via hardware supported information retrieval algorithms. Reconfigurable computing may adopt frequent hardware modifications through its tailorable hardware and exploits parallelism for a given application through reconfigurable and flexible hardware units. The degree of the parallelism can be tuned for data. In this work we implemented standard BLAS (basic linear algebra subprogram) sparse matrix algorithm named Compressed Sparse Row (CSR) that is showed to be more efficient in terms of storage space requirement and query-processing timing over the other sparse matrix algorithms for information retrieval application. Although inverted index algorithm is treated as the de facto standard for information retrieval for years, an alternative approach to store the index of text collection in a sparse matrix structure gains more attention. This approach performs query processing using sparse matrix-vector multiplication and due to parallelization achieves a substantial efficiency over the sequential inverted index. The parallel implementations of information retrieval kernel are presented in this work targeting the Virtex II Field Programmable Gate Arrays (FPGAs) board from Xilinx. A recent development in scientific applications is the use of FPGA to achieve high performance results. Computational results are compared to implementations on other platforms. The design achieves a high level of parallelism for the overall function while retaining highly optimised hardware within processing unit.

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.

DOLPHIn—Dictionary Learning for Phase Retrieval

NASA Astrophysics Data System (ADS)

Tillmann, Andreas M.; Eldar, Yonina C.; Mairal, Julien

2016-12-01

We propose a new algorithm to learn a dictionary for reconstructing and sparsely encoding signals from measurements without phase. Specifically, we consider the task of estimating a two-dimensional image from squared-magnitude measurements of a complex-valued linear transformation of the original image. Several recent phase retrieval algorithms exploit underlying sparsity of the unknown signal in order to improve recovery performance. In this work, we consider such a sparse signal prior in the context of phase retrieval, when the sparsifying dictionary is not known in advance. Our algorithm jointly reconstructs the unknown signal - possibly corrupted by noise - and learns a dictionary such that each patch of the estimated image can be sparsely represented. Numerical experiments demonstrate that our approach can obtain significantly better reconstructions for phase retrieval problems with noise than methods that cannot exploit such "hidden" sparsity. Moreover, on the theoretical side, we provide a convergence result for our method.

A review on classification methods for solving fully fuzzy linear systems

NASA Astrophysics Data System (ADS)

Daud, Wan Suhana Wan; Ahmad, Nazihah; Aziz, Khairu Azlan Abd

2015-12-01

Fully Fuzzy Linear System (FFLS) exists when there are fuzzy numbers on both sides of the linear systems. This system is quite significant today since most of the linear systems play with uncertainties of parameters especially in mathematics, engineering and finance. Many researchers and practitioners used the FFLS to model their problem and they apply various methods to solve it. In this paper, we present the outcome of a comprehensive review that we have done on various methods used for solving the FFLS. We classify our findings based on parameters' type used for the FFLS either restricted or unrestricted. We also discuss some of the methods by illustrating numerical examples and identify the differences between the methods. Ultimately, we summarize all findings in a table. We hope this study will encourage researchers to appreciate the use of this method and with that it will be easier for them to choose the right method or to propose any new method for solving the FFLS.

Discrete-state phasor neural networks

NASA Astrophysics Data System (ADS)

Noest, André J.

1988-08-01

An associative memory network with local variables assuming one of q equidistant positions on the unit circle (q-state phasors) is introduced, and its recall behavior is solved exactly for any q when the interactions are sparse and asymmetric. Such models can describe natural or artifical networks of (neuro-)biological, chemical, or electronic limit-cycle oscillators with q-fold instead of circular symmetry, or similar optical computing devices using a phase-encoded data representation.

Sparsity and Nullity: Paradigm for Analysis Dictionary Learning

DTIC Science & Technology

2016-08-09

16. SECURITY CLASSIFICATION OF: Sparse models in dictionary learning have been successfully applied in a wide variety of machine learning and...we investigate the relation between the SNS problem and the analysis dictionary learning problem, and show that the SNS problem plays a central role...and may be utilized to solve dictionary learning problems. 1. REPORT DATE (DD-MM-YYYY) 4. TITLE AND SUBTITLE 13. SUPPLEMENTARY NOTES 12

Robust Group Sparse Beamforming for Multicast Green Cloud-RAN With Imperfect CSI

NASA Astrophysics Data System (ADS)

Shi, Yuanming; Zhang, Jun; Letaief, Khaled B.

2015-09-01

In this paper, we investigate the network power minimization problem for the multicast cloud radio access network (Cloud-RAN) with imperfect channel state information (CSI). The key observation is that network power minimization can be achieved by adaptively selecting active remote radio heads (RRHs) via controlling the group-sparsity structure of the beamforming vector. However, this yields a non-convex combinatorial optimization problem, for which we propose a three-stage robust group sparse beamforming algorithm. In the first stage, a quadratic variational formulation of the weighted mixed l1/l2-norm is proposed to induce the group-sparsity structure in the aggregated beamforming vector, which indicates those RRHs that can be switched off. A perturbed alternating optimization algorithm is then proposed to solve the resultant non-convex group-sparsity inducing optimization problem by exploiting its convex substructures. In the second stage, we propose a PhaseLift technique based algorithm to solve the feasibility problem with a given active RRH set, which helps determine the active RRHs. Finally, the semidefinite relaxation (SDR) technique is adopted to determine the robust multicast beamformers. Simulation results will demonstrate the convergence of the perturbed alternating optimization algorithm, as well as, the effectiveness of the proposed algorithm to minimize the network power consumption for multicast Cloud-RAN.

Can linear superiorization be useful for linear optimization problems?

NASA Astrophysics Data System (ADS)

Censor, Yair

2017-04-01

Linear superiorization (LinSup) considers linear programming problems but instead of attempting to solve them with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward reduced (not necessarily minimal) target function values. The two questions that we set out to explore experimentally are: (i) does LinSup provide a feasible point whose linear target function value is lower than that obtained by running the same feasibility-seeking algorithm without superiorization under identical conditions? (ii) How does LinSup fare in comparison with the Simplex method for solving linear programming problems? Based on our computational experiments presented here, the answers to these two questions are: ‘yes’ and ‘very well’, respectively.

Multiple Sparse Representations Classification

PubMed Central

Plenge, Esben; Klein, Stefan S.; Niessen, Wiro J.; Meijering, Erik

2015-01-01

Sparse representations classification (SRC) is a powerful technique for pixelwise classification of images and it is increasingly being used for a wide variety of image analysis tasks. The method uses sparse representation and learned redundant dictionaries to classify image pixels. In this empirical study we propose to further leverage the redundancy of the learned dictionaries to achieve a more accurate classifier. In conventional SRC, each image pixel is associated with a small patch surrounding it. Using these patches, a dictionary is trained for each class in a supervised fashion. Commonly, redundant/overcomplete dictionaries are trained and image patches are sparsely represented by a linear combination of only a few of the dictionary elements. Given a set of trained dictionaries, a new patch is sparse coded using each of them, and subsequently assigned to the class whose dictionary yields the minimum residual energy. We propose a generalization of this scheme. The method, which we call multiple sparse representations classification (mSRC), is based on the observation that an overcomplete, class specific dictionary is capable of generating multiple accurate and independent estimates of a patch belonging to the class. So instead of finding a single sparse representation of a patch for each dictionary, we find multiple, and the corresponding residual energies provides an enhanced statistic which is used to improve classification. We demonstrate the efficacy of mSRC for three example applications: pixelwise classification of texture images, lumen segmentation in carotid artery magnetic resonance imaging (MRI), and bifurcation point detection in carotid artery MRI. We compare our method with conventional SRC, K-nearest neighbor, and support vector machine classifiers. The results show that mSRC outperforms SRC and the other reference methods. In addition, we present an extensive evaluation of the effect of the main mSRC parameters: patch size, dictionary size, and sparsity level. PMID:26177106

Using the Multiplicative Schwarz Alternating Algorithm (MSAA) for Solving the Large Linear System of Equations Related to Global Gravity Field Recovery up to Degree and Order 120

NASA Astrophysics Data System (ADS)

Safari, A.; Sharifi, M. A.; Amjadiparvar, B.

2010-05-01

The GRACE mission has substantiated the low-low satellite-to-satellite tracking (LL-SST) concept. The LL-SST configuration can be combined with the previously realized high-low SST concept in the CHAMP mission to provide a much higher accuracy. The line of sight (LOS) acceleration difference between the GRACE satellite pair is the mostly used observable for mapping the global gravity field of the Earth in terms of spherical harmonic coefficients. In this paper, mathematical formulae for LOS acceleration difference observations have been derived and the corresponding linear system of equations has been set up for spherical harmonic up to degree and order 120. The total number of unknowns is 14641. Such a linear equation system can be solved with iterative solvers or direct solvers. However, the runtime of direct methods or that of iterative solvers without a suitable preconditioner increases tremendously. This is the reason why we need a more sophisticated method to solve the linear system of problems with a large number of unknowns. Multiplicative variant of the Schwarz alternating algorithm is a domain decomposition method, which allows it to split the normal matrix of the system into several smaller overlaped submatrices. In each iteration step the multiplicative variant of the Schwarz alternating algorithm solves linear systems with the matrices obtained from the splitting successively. It reduces both runtime and memory requirements drastically. In this paper we propose the Multiplicative Schwarz Alternating Algorithm (MSAA) for solving the large linear system of gravity field recovery. The proposed algorithm has been tested on the International Association of Geodesy (IAG)-simulated data of the GRACE mission. The achieved results indicate the validity and efficiency of the proposed algorithm in solving the linear system of equations from accuracy and runtime points of view. Keywords: Gravity field recovery, Multiplicative Schwarz Alternating Algorithm, Low-Low Satellite-to-Satellite Tracking

Broadband implementation of coprime linear microphone arrays for direction of arrival estimation.

PubMed

Bush, Dane; Xiang, Ning

2015-07-01

Coprime arrays represent a form of sparse sensing which can achieve narrow beams using relatively few elements, exceeding the spatial Nyquist sampling limit. The purpose of this paper is to expand on and experimentally validate coprime array theory in an acoustic implementation. Two nested sparse uniform linear subarrays with coprime number of elements ( M and N) each produce grating lobes that overlap with one another completely in just one direction. When the subarray outputs are combined it is possible to retain the shared beam while mostly canceling the other superfluous grating lobes. In this way a small number of microphones ( N+M-1) creates a narrow beam at higher frequencies, comparable to a densely populated uniform linear array of MN microphones. In this work beampatterns are simulated for a range of single frequencies, as well as bands of frequencies. Narrowband experimental beampatterns are shown to correspond with simulated results even at frequencies other than the arrays design frequency. Narrowband side lobe locations are shown to correspond to the theoretical values. Side lobes in the directional pattern are mitigated by increasing bandwidth of analyzed signals. Direction of arrival estimation is also implemented for two simultaneous noise sources in a free field condition.

On Facilitating the use of HARDI in population studies by creating Rotation-Invariant Markers

PubMed Central

Caruyer, Emmanuel; Verma, Ragini

2014-01-01

We design and evaluate a novel method to compute rotationally invariant features using High Angular Resolution Diffusion Imaging (HARDI) data. These measures quantify the complexity of the angular diffusion profile modeled using a higher order model, thereby giving more information than classical diffusion tensor-derived parameters. The method is based on the spherical harmonic (SH) representation of the angular diffusion information, and is generalizable to a range of HARDI reconstruction models. These scalars are obtained as homogeneous polynomials of the SH representation of a HARDI reconstruction model. We show that finding such polynomials is equivalent to solving a large linear system of equations, and present a numerical method based on sparse matrices to efficiently solve this system. Among the solutions, we only keep a subset of algebraically independent polynomials, using an algorithm based on a numerical implementation of the Jacobian criterion. We compute a set of 12 or 25 rotationally invariant measures representative of the underlying white matter for the rank-4 or rank-6 spherical harmonics (SH) representation of the apparent diffusion coefficient (ADC) profile, respectively. Synthetic data was used to investigate and quantify the difference in contrast. Real data acquired with multiple repetitions showed that within subject variation in the invariants was less than the difference across subjects - facilitating their use to study population differences. These results demonstrate that our measures are able to characterize white matter, especially complex white matter found in regions of fiber crossings and hence can be used to derive new biomarkers for HARDI and can be used for HARDI-based population analysis. PMID:25465846

Novel methods for Solving Economic Dispatch of Security-Constrained Unit Commitment Based on Linear Programming

NASA Astrophysics Data System (ADS)

Guo, Sangang

2017-09-01

There are two stages in solving security-constrained unit commitment problems (SCUC) within Lagrangian framework: one is to obtain feasible units’ states (UC), the other is power economic dispatch (ED) for each unit. The accurate solution of ED is more important for enhancing the efficiency of the solution to SCUC for the fixed feasible units’ statues. Two novel methods named after Convex Combinatorial Coefficient Method and Power Increment Method respectively based on linear programming problem for solving ED are proposed by the piecewise linear approximation to the nonlinear convex fuel cost functions. Numerical testing results show that the methods are effective and efficient.

On a new iterative method for solving linear systems and comparison results

NASA Astrophysics Data System (ADS)

Jing, Yan-Fei; Huang, Ting-Zhu

2008-10-01

In Ujevic [A new iterative method for solving linear systems, Appl. Math. Comput. 179 (2006) 725-730], the author obtained a new iterative method for solving linear systems, which can be considered as a modification of the Gauss-Seidel method. In this paper, we show that this is a special case from a point of view of projection techniques. And a different approach is established, which is both theoretically and numerically proven to be better than (at least the same as) Ujevic's. As the presented numerical examples show, in most cases, the convergence rate is more than one and a half that of Ujevic.

A Dictionary Learning Method with Total Generalized Variation for MRI Reconstruction

PubMed Central

Lu, Hongyang; Wei, Jingbo; Wang, Yuhao; Deng, Xiaohua

2016-01-01

Reconstructing images from their noisy and incomplete measurements is always a challenge especially for medical MR image with important details and features. This work proposes a novel dictionary learning model that integrates two sparse regularization methods: the total generalized variation (TGV) approach and adaptive dictionary learning (DL). In the proposed method, the TGV selectively regularizes different image regions at different levels to avoid oil painting artifacts largely. At the same time, the dictionary learning adaptively represents the image features sparsely and effectively recovers details of images. The proposed model is solved by variable splitting technique and the alternating direction method of multiplier. Extensive simulation experimental results demonstrate that the proposed method consistently recovers MR images efficiently and outperforms the current state-of-the-art approaches in terms of higher PSNR and lower HFEN values. PMID:27110235

A Dictionary Learning Method with Total Generalized Variation for MRI Reconstruction.

PubMed

Lu, Hongyang; Wei, Jingbo; Liu, Qiegen; Wang, Yuhao; Deng, Xiaohua

2016-01-01

Reconstructing images from their noisy and incomplete measurements is always a challenge especially for medical MR image with important details and features. This work proposes a novel dictionary learning model that integrates two sparse regularization methods: the total generalized variation (TGV) approach and adaptive dictionary learning (DL). In the proposed method, the TGV selectively regularizes different image regions at different levels to avoid oil painting artifacts largely. At the same time, the dictionary learning adaptively represents the image features sparsely and effectively recovers details of images. The proposed model is solved by variable splitting technique and the alternating direction method of multiplier. Extensive simulation experimental results demonstrate that the proposed method consistently recovers MR images efficiently and outperforms the current state-of-the-art approaches in terms of higher PSNR and lower HFEN values.

A dictionary learning approach for Poisson image deblurring.

PubMed

Ma, Liyan; Moisan, Lionel; Yu, Jian; Zeng, Tieyong

2013-07-01

The restoration of images corrupted by blur and Poisson noise is a key issue in medical and biological image processing. While most existing methods are based on variational models, generally derived from a maximum a posteriori (MAP) formulation, recently sparse representations of images have shown to be efficient approaches for image recovery. Following this idea, we propose in this paper a model containing three terms: a patch-based sparse representation prior over a learned dictionary, the pixel-based total variation regularization term and a data-fidelity term capturing the statistics of Poisson noise. The resulting optimization problem can be solved by an alternating minimization technique combined with variable splitting. Extensive experimental results suggest that in terms of visual quality, peak signal-to-noise ratio value and the method noise, the proposed algorithm outperforms state-of-the-art methods.

Generalised Assignment Matrix Methodology in Linear Programming

ERIC Educational Resources Information Center

Jerome, Lawrence

2012-01-01

Discrete Mathematics instructors and students have long been struggling with various labelling and scanning algorithms for solving many important problems. This paper shows how to solve a wide variety of Discrete Mathematics and OR problems using assignment matrices and linear programming, specifically using Excel Solvers although the same…

Solving the linear inviscid shallow water equations in one dimension, with variable depth, using a recursion formula

NASA Astrophysics Data System (ADS)

Hernandez-Walls, R.; Martín-Atienza, B.; Salinas-Matus, M.; Castillo, J.

2017-11-01

When solving the linear inviscid shallow water equations with variable depth in one dimension using finite differences, a tridiagonal system of equations must be solved. Here we present an approach, which is more efficient than the commonly used numerical method, to solve this tridiagonal system of equations using a recursion formula. We illustrate this approach with an example in which we solve for a rectangular channel to find the resonance modes. Our numerical solution agrees very well with the analytical solution. This new method is easy to use and understand by undergraduate students, so it can be implemented in undergraduate courses such as Numerical Methods, Lineal Algebra or Differential Equations.

Transient dynamics in trial-offer markets with social influence: Trade-offs between appeal and quality

PubMed Central

Altszyler, Edgar; Berbeglia, Franco; Van Hentenryck, Pascal

2017-01-01

We study a trial-offer market where consumers may purchase one of two competing products. Consumer preferences are affected by the products quality, their appeal, and their popularity. While the asymptotic convergence or stationary states of these, and related dynamical systems, has been vastly studied, the literature regarding the transitory dynamics remains surprisingly sparse. To fill this gap, we derive a system of Ordinary Differential Equations, which is solved exactly to gain insight into the roles played by product qualities and appeals in the market behavior. We observe a logarithmic tradeoff between quality and appeal for medium and long-term marketing strategies: The expected market shares remain constant if a decrease in quality is followed by an exponential increase in the product appeal. However, for short time horizons, the trade-off is linear. Finally, we study the variability of the dynamics through Monte Carlo simulations and discover that low appeals may result in high levels of variability. The model results suggest effective marketing strategies for short and long time horizons and emphasize the significance of advertising early in the market life to increase sales and predictability. PMID:28746334

Bas-Relief Modeling from Normal Images with Intuitive Styles.

PubMed

Ji, Zhongping; Ma, Weiyin; Sun, Xianfang

2014-05-01

Traditional 3D model-based bas-relief modeling methods are often limited to model-dependent and monotonic relief styles. This paper presents a novel method for digital bas-relief modeling with intuitive style control. Given a composite normal image, the problem discussed in this paper involves generating a discontinuity-free depth field with high compression of depth data while preserving or even enhancing fine details. In our framework, several layers of normal images are composed into a single normal image. The original normal image on each layer is usually generated from 3D models or through other techniques as described in this paper. The bas-relief style is controlled by choosing a parameter and setting a targeted height for them. Bas-relief modeling and stylization are achieved simultaneously by solving a sparse linear system. Different from previous work, our method can be used to freely design bas-reliefs in normal image space instead of in object space, which makes it possible to use any popular image editing tools for bas-relief modeling. Experiments with a wide range of 3D models and scenes show that our method can effectively generate digital bas-reliefs.

Transient dynamics in trial-offer markets with social influence: Trade-offs between appeal and quality.

PubMed

Altszyler, Edgar; Berbeglia, Franco; Berbeglia, Gerardo; Van Hentenryck, Pascal

2017-01-01

We study a trial-offer market where consumers may purchase one of two competing products. Consumer preferences are affected by the products quality, their appeal, and their popularity. While the asymptotic convergence or stationary states of these, and related dynamical systems, has been vastly studied, the literature regarding the transitory dynamics remains surprisingly sparse. To fill this gap, we derive a system of Ordinary Differential Equations, which is solved exactly to gain insight into the roles played by product qualities and appeals in the market behavior. We observe a logarithmic tradeoff between quality and appeal for medium and long-term marketing strategies: The expected market shares remain constant if a decrease in quality is followed by an exponential increase in the product appeal. However, for short time horizons, the trade-off is linear. Finally, we study the variability of the dynamics through Monte Carlo simulations and discover that low appeals may result in high levels of variability. The model results suggest effective marketing strategies for short and long time horizons and emphasize the significance of advertising early in the market life to increase sales and predictability.

A scalable nonlinear fluid-structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D

NASA Astrophysics Data System (ADS)

Kong, Fande; Cai, Xiao-Chuan

2017-07-01

Nonlinear fluid-structure interaction (FSI) problems on unstructured meshes in 3D appear in many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexact Newton-Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here "geometry" includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.

Efficient algorithm for locating and sizing series compensation devices in large power transmission grids: II. Solutions and applications

DOE PAGES

Frolov, Vladimir; Backhaus, Scott; Chertkov, Misha

2014-10-01

In a companion manuscript, we developed a novel optimization method for placement, sizing, and operation of Flexible Alternating Current Transmission System (FACTS) devices to relieve transmission network congestion. Specifically, we addressed FACTS that provide Series Compensation (SC) via modification of line inductance. In this manuscript, this heuristic algorithm and its solutions are explored on a number of test cases: a 30-bus test network and a realistically-sized model of the Polish grid (~ 2700 nodes and ~ 3300 lines). The results on the 30-bus network are used to study the general properties of the solutions including non-locality and sparsity. The Polishmore » grid is used as a demonstration of the computational efficiency of the heuristics that leverages sequential linearization of power flow constraints and cutting plane methods that take advantage of the sparse nature of the SC placement solutions. Using these approaches, the algorithm is able to solve an instance of Polish grid in tens of seconds. We explore the utility of the algorithm by analyzing transmission networks congested by (a) uniform load growth, (b) multiple overloaded configurations, and (c) sequential generator retirements.« less

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.

A scalable nonlinear fluid–structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D

DOE PAGES

Kong, Fande; Cai, Xiao-Chuan

2017-03-24

Nonlinear fluid-structure interaction (FSI) problems on unstructured meshes in 3D appear many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexactmore » Newton-Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here ''geometry'' includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.« less

PsiQuaSP-A library for efficient computation of symmetric open quantum systems.

PubMed

Gegg, Michael; Richter, Marten

2017-11-24

In a recent publication we showed that permutation symmetry reduces the numerical complexity of Lindblad quantum master equations for identical multi-level systems from exponential to polynomial scaling. This is important for open system dynamics including realistic system bath interactions and dephasing in, for instance, the Dicke model, multi-Λ system setups etc. Here we present an object-oriented C++ library that allows to setup and solve arbitrary quantum optical Lindblad master equations, especially those that are permutationally symmetric in the multi-level systems. PsiQuaSP (Permutation symmetry for identical Quantum Systems Package) uses the PETSc package for sparse linear algebra methods and differential equations as basis. The aim of PsiQuaSP is to provide flexible, storage efficient and scalable code while being as user friendly as possible. It is easily applied to many quantum optical or quantum information systems with more than one multi-level system. We first review the basics of the permutation symmetry for multi-level systems in quantum master equations. The application of PsiQuaSP to quantum dynamical problems is illustrated with several typical, simple examples of open quantum optical systems.

Efficient Algorithm for Locating and Sizing Series Compensation Devices in Large Transmission Grids: Solutions and Applications (PART II)

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

Frolov, Vladimir; Backhaus, Scott N.; Chertkov, Michael

2014-01-14

In a companion manuscript, we developed a novel optimization method for placement, sizing, and operation of Flexible Alternating Current Transmission System (FACTS) devices to relieve transmission network congestion. Specifically, we addressed FACTS that provide Series Compensation (SC) via modification of line inductance. In this manuscript, this heuristic algorithm and its solutions are explored on a number of test cases: a 30-bus test network and a realistically-sized model of the Polish grid (~2700 nodes and ~3300 lines). The results on the 30-bus network are used to study the general properties of the solutions including non-locality and sparsity. The Polish grid ismore » used as a demonstration of the computational efficiency of the heuristics that leverages sequential linearization of power flow constraints and cutting plane methods that take advantage of the sparse nature of the SC placement solutions. Using these approaches, the algorithm is able to solve an instance of Polish grid in tens of seconds. We explore the utility of the algorithm by analyzing transmission networks congested by (a) uniform load growth, (b) multiple overloaded configurations, and (c) sequential generator retirements« less

Object matching using a locally affine invariant and linear programming techniques.

PubMed

Li, Hongsheng; Huang, Xiaolei; He, Lei

2013-02-01

In this paper, we introduce a new matching method based on a novel locally affine-invariant geometric constraint and linear programming techniques. To model and solve the matching problem in a linear programming formulation, all geometric constraints should be able to be exactly or approximately reformulated into a linear form. This is a major difficulty for this kind of matching algorithm. We propose a novel locally affine-invariant constraint which can be exactly linearized and requires a lot fewer auxiliary variables than other linear programming-based methods do. The key idea behind it is that each point in the template point set can be exactly represented by an affine combination of its neighboring points, whose weights can be solved easily by least squares. Errors of reconstructing each matched point using such weights are used to penalize the disagreement of geometric relationships between the template points and the matched points. The resulting overall objective function can be solved efficiently by linear programming techniques. Our experimental results on both rigid and nonrigid object matching show the effectiveness of the proposed algorithm.

Technology, Linear Equations, and Buying a Car.

ERIC Educational Resources Information Center

Sandefur, James T.

1992-01-01

Discusses the use of technology in solving compound interest-rate problems that can be modeled by linear relationships. Uses a graphing calculator to solve the specific problem of determining the amount of money that can be borrowed to buy a car for a given monthly payment and interest rate. (MDH)

Model's sparse representation based on reduced mixed GMsFE basis methods

NASA Astrophysics Data System (ADS)

Jiang, Lijian; Li, Qiuqi

2017-06-01

In this paper, we propose a model's sparse representation based on reduced mixed generalized multiscale finite element (GMsFE) basis methods for elliptic PDEs with random inputs. A typical application for the elliptic PDEs is the flow in heterogeneous random porous media. Mixed generalized multiscale finite element method (GMsFEM) is one of the accurate and efficient approaches to solve the flow problem in a coarse grid and obtain the velocity with local mass conservation. When the inputs of the PDEs are parameterized by the random variables, the GMsFE basis functions usually depend on the random parameters. This leads to a large number degree of freedoms for the mixed GMsFEM and substantially impacts on the computation efficiency. In order to overcome the difficulty, we develop reduced mixed GMsFE basis methods such that the multiscale basis functions are independent of the random parameters and span a low-dimensional space. To this end, a greedy algorithm is used to find a set of optimal samples from a training set scattered in the parameter space. Reduced mixed GMsFE basis functions are constructed based on the optimal samples using two optimal sampling strategies: basis-oriented cross-validation and proper orthogonal decomposition. Although the dimension of the space spanned by the reduced mixed GMsFE basis functions is much smaller than the dimension of the original full order model, the online computation still depends on the number of coarse degree of freedoms. To significantly improve the online computation, we integrate the reduced mixed GMsFE basis methods with sparse tensor approximation and obtain a sparse representation for the model's outputs. The sparse representation is very efficient for evaluating the model's outputs for many instances of parameters. To illustrate the efficacy of the proposed methods, we present a few numerical examples for elliptic PDEs with multiscale and random inputs. In particular, a two-phase flow model in random porous media is simulated by the proposed sparse representation method.

Model's sparse representation based on reduced mixed GMsFE basis methods

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

Jiang, Lijian, E-mail: ljjiang@hnu.edu.cn; Li, Qiuqi, E-mail: qiuqili@hnu.edu.cn

2017-06-01

In this paper, we propose a model's sparse representation based on reduced mixed generalized multiscale finite element (GMsFE) basis methods for elliptic PDEs with random inputs. A typical application for the elliptic PDEs is the flow in heterogeneous random porous media. Mixed generalized multiscale finite element method (GMsFEM) is one of the accurate and efficient approaches to solve the flow problem in a coarse grid and obtain the velocity with local mass conservation. When the inputs of the PDEs are parameterized by the random variables, the GMsFE basis functions usually depend on the random parameters. This leads to a largemore » number degree of freedoms for the mixed GMsFEM and substantially impacts on the computation efficiency. In order to overcome the difficulty, we develop reduced mixed GMsFE basis methods such that the multiscale basis functions are independent of the random parameters and span a low-dimensional space. To this end, a greedy algorithm is used to find a set of optimal samples from a training set scattered in the parameter space. Reduced mixed GMsFE basis functions are constructed based on the optimal samples using two optimal sampling strategies: basis-oriented cross-validation and proper orthogonal decomposition. Although the dimension of the space spanned by the reduced mixed GMsFE basis functions is much smaller than the dimension of the original full order model, the online computation still depends on the number of coarse degree of freedoms. To significantly improve the online computation, we integrate the reduced mixed GMsFE basis methods with sparse tensor approximation and obtain a sparse representation for the model's outputs. The sparse representation is very efficient for evaluating the model's outputs for many instances of parameters. To illustrate the efficacy of the proposed methods, we present a few numerical examples for elliptic PDEs with multiscale and random inputs. In particular, a two-phase flow model in random porous media is simulated by the proposed sparse representation method.« less

An algebraic equation solution process formulated in anticipation of banded linear equations.

DOT National Transportation Integrated Search

1971-01-01

A general method for the solution of large, sparsely banded, positive-definite, coefficient matrices is presented. The goal in developing the method was to produce an efficient and reliable solution process and to provide the user-programmer with a p...

Multistatic Array Sampling Scheme for Fast Near-Field Image Reconstruction

DTIC Science & Technology

2016-01-01

reconstruction. The array topology samples the scene on a regular grid of phase centers, using a tiling of Boundary Arrays (BAs). Following a simple correction...hardware. Fig. 1 depicts the multistatic array topology. As seen, the topology is a tiled arrangement of Boundary Arrays (BAs). The BA is a well-known...sparse array layout comprised of two linear transmit arrays, and two linear receive arrays [6]. A slightly different tiled arrangement of BAs was used

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.

A Block-LU Update for Large-Scale Linear Programming

DTIC Science & Technology

1990-01-01

linear programming problems. Results are given from runs on the Cray Y -MP. 1. Introduction We wish to use the simplex method [Dan63] to solve the...standard linear program, minimize cTx subject to Ax = b 1< x <U, where A is an m by n matrix and c, x, 1, u, and b are of appropriate dimension. The simplex...the identity matrix. The basis is used to solve for the search direction y and the dual variables 7r in the following linear systems: Bky = aq (1.2) and

A comparison of Heuristic method and Llewellyn’s rules for identification of redundant constraints

NASA Astrophysics Data System (ADS)

Estiningsih, Y.; Farikhin; Tjahjana, R. H.

2018-03-01

Important techniques in linear programming is modelling and solving practical optimization. Redundant constraints are consider for their effects on general linear programming problems. Identification and reduce redundant constraints are for avoidance of all the calculations associated when solving an associated linear programming problems. Many researchers have been proposed for identification redundant constraints. This paper a compararison of Heuristic method and Llewellyn’s rules for identification of redundant constraints.

Discrete integration of continuous Kalman filtering equations for time invariant second-order structural systems

NASA Technical Reports Server (NTRS)

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

1990-01-01

A general form for the first-order representation of the continuous second-order linear structural-dynamics equations is introduced to derive a corresponding form of first-order continuous Kalman filtering equations. Time integration of the resulting equations is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete Kalman filtering equations involving only symmetric sparse N x N solution matrices.

Orthogonal Procrustes Analysis for Dictionary Learning in Sparse Linear Representation

PubMed Central

Grossi, Giuliano; Lin, Jianyi

2017-01-01

In the sparse representation model, the design of overcomplete dictionaries plays a key role for the effectiveness and applicability in different domains. Recent research has produced several dictionary learning approaches, being proven that dictionaries learnt by data examples significantly outperform structured ones, e.g. wavelet transforms. In this context, learning consists in adapting the dictionary atoms to a set of training signals in order to promote a sparse representation that minimizes the reconstruction error. Finding the best fitting dictionary remains a very difficult task, leaving the question still open. A well-established heuristic method for tackling this problem is an iterative alternating scheme, adopted for instance in the well-known K-SVD algorithm. Essentially, it consists in repeating two stages; the former promotes sparse coding of the training set and the latter adapts the dictionary to reduce the error. In this paper we present R-SVD, a new method that, while maintaining the alternating scheme, adopts the Orthogonal Procrustes analysis to update the dictionary atoms suitably arranged into groups. Comparative experiments on synthetic data prove the effectiveness of R-SVD with respect to well known dictionary learning algorithms such as K-SVD, ILS-DLA and the online method OSDL. Moreover, experiments on natural data such as ECG compression, EEG sparse representation, and image modeling confirm R-SVD’s robustness and wide applicability. PMID:28103283

An Improved Sparse Representation over Learned Dictionary Method for Seizure Detection.

PubMed

Li, Junhui; Zhou, Weidong; Yuan, Shasha; Zhang, Yanli; Li, Chengcheng; Wu, Qi

2016-02-01

Automatic seizure detection has played an important role in the monitoring, diagnosis and treatment of epilepsy. In this paper, a patient specific method is proposed for seizure detection in the long-term intracranial electroencephalogram (EEG) recordings. This seizure detection method is based on sparse representation with online dictionary learning and elastic net constraint. The online learned dictionary could sparsely represent the testing samples more accurately, and the elastic net constraint which combines the 11-norm and 12-norm not only makes the coefficients sparse but also avoids over-fitting problem. First, the EEG signals are preprocessed using wavelet filtering and differential filtering, and the kernel function is applied to make the samples closer to linearly separable. Then the dictionaries of seizure and nonseizure are respectively learned from original ictal and interictal training samples with online dictionary optimization algorithm to compose the training dictionary. After that, the test samples are sparsely coded over the learned dictionary and the residuals associated with ictal and interictal sub-dictionary are calculated, respectively. Eventually, the test samples are classified as two distinct categories, seizure or nonseizure, by comparing the reconstructed residuals. The average segment-based sensitivity of 95.45%, specificity of 99.08%, and event-based sensitivity of 94.44% with false detection rate of 0.23/h and average latency of -5.14 s have been achieved with our proposed method.