SLAP, Large Sparse Linear System Solution Package

International Nuclear Information System (INIS)

Greenbaum, A.

1987-01-01

1 - Description of program or function: SLAP is a set of routines for solving large sparse systems of linear equations. One need not store the entire matrix - only the nonzero elements and their row and column numbers. Any nonzero structure is acceptable, so the linear system solver need not be modified when the structure of the matrix changes. Auxiliary storage space is acquired and released within the routines themselves by use of the LRLTRAN POINTER statement. 2 - Method of solution: SLAP contains one direct solver, a band matrix factorization and solution routine, BAND, and several interactive solvers. The iterative routines are as follows: JACOBI, Jacobi iteration; GS, Gauss-Seidel Iteration; ILUIR, incomplete LU decomposition with iterative refinement; DSCG and ICCG, diagonal scaling and incomplete Cholesky decomposition with conjugate gradient iteration (for symmetric positive definite matrices only); DSCGN and ILUGGN, diagonal scaling and incomplete LU decomposition with conjugate gradient interaction on the normal equations; DSBCG and ILUBCG, diagonal scaling and incomplete LU decomposition with bi-conjugate gradient iteration; and DSOMN and ILUOMN, diagonal scaling and incomplete LU decomposition with ORTHOMIN iteration

Structure and stability of genetic variance-covariance matrices: A Bayesian sparse factor analysis of transcriptional variation in the three-spined stickleback.

Science.gov (United States)

Siren, J; Ovaskainen, O; Merilä, J

2017-10-01

The genetic variance-covariance matrix (G) is a quantity of central importance in evolutionary biology due to its influence on the rate and direction of multivariate evolution. However, the predictive power of empirically estimated G-matrices is limited for two reasons. First, phenotypes are high-dimensional, whereas traditional statistical methods are tuned to estimate and analyse low-dimensional matrices. Second, the stability of G to environmental effects and over time remains poorly understood. Using Bayesian sparse factor analysis (BSFG) designed to estimate high-dimensional G-matrices, we analysed levels variation and covariation in 10,527 expressed genes in a large (n = 563) half-sib breeding design of three-spined sticklebacks subject to two temperature treatments. We found significant differences in the structure of G between the treatments: heritabilities and evolvabilities were higher in the warm than in the low-temperature treatment, suggesting more and faster opportunity to evolve in warm (stressful) conditions. Furthermore, comparison of G and its phenotypic equivalent P revealed the latter is a poor substitute of the former. Most strikingly, the results suggest that the expected impact of G on evolvability-as well as the similarity among G-matrices-may depend strongly on the number of traits included into analyses. In our results, the inclusion of only few traits in the analyses leads to underestimation in the differences between the G-matrices and their predicted impacts on evolution. While the results highlight the challenges involved in estimating G, they also illustrate that by enabling the estimation of large G-matrices, the BSFG method can improve predicted evolutionary responses to selection. © 2017 John Wiley & Sons Ltd.

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

Science.gov (United States)

Zubair, M.; Ghose, M.

1992-01-01

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

Technique detection software for Sparse Matrices

Directory of Open Access Journals (Sweden)

KHAN Muhammad Taimoor

2009-12-01

Full Text Available Sparse storage formats are techniques for storing and processing the sparse matrix data efficiently. The performance of these storage formats depend upon the distribution of non-zeros, within the matrix in different dimensions. In order to have better results we need a technique that suits best the organization of data in a particular matrix. So the decision of selecting a better technique is the main step towards improving the system's results otherwise the efficiency can be decreased. The purpose of this research is to help identify the best storage format in case of reduced storage size and high processing efficiency for a sparse matrix.

Performance optimization of Sparse Matrix-Vector Multiplication for multi-component PDE-based applications using GPUs

KAUST Repository

Abdelfattah, Ahmad

2016-05-23

Simulations of many multi-component PDE-based applications, such as petroleum reservoirs or reacting flows, are dominated by the solution, on each time step and within each Newton step, of large sparse linear systems. The standard solver is a preconditioned Krylov method. Along with application of the preconditioner, memory-bound Sparse Matrix-Vector Multiplication (SpMV) is the most time-consuming operation in such solvers. Multi-species models produce Jacobians with a dense block structure, where the block size can be as large as a few dozen. Failing to exploit this dense block structure vastly underutilizes hardware capable of delivering high performance on dense BLAS operations. This paper presents a GPU-accelerated SpMV kernel for block-sparse matrices. Dense matrix-vector multiplications within the sparse-block structure leverage optimization techniques from the KBLAS library, a high performance library for dense BLAS kernels. The design ideas of KBLAS can be applied to block-sparse matrices. Furthermore, a technique is proposed to balance the workload among thread blocks when there are large variations in the lengths of nonzero rows. Multi-GPU performance is highlighted. The proposed SpMV kernel outperforms existing state-of-the-art implementations using matrices with real structures from different applications. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Performance optimization of Sparse Matrix-Vector Multiplication for multi-component PDE-based applications using GPUs

KAUST Repository

Abdelfattah, Ahmad; Ltaief, Hatem; Keyes, David E.; Dongarra, Jack

2016-01-01

Simulations of many multi-component PDE-based applications, such as petroleum reservoirs or reacting flows, are dominated by the solution, on each time step and within each Newton step, of large sparse linear systems. The standard solver is a preconditioned Krylov method. Along with application of the preconditioner, memory-bound Sparse Matrix-Vector Multiplication (SpMV) is the most time-consuming operation in such solvers. Multi-species models produce Jacobians with a dense block structure, where the block size can be as large as a few dozen. Failing to exploit this dense block structure vastly underutilizes hardware capable of delivering high performance on dense BLAS operations. This paper presents a GPU-accelerated SpMV kernel for block-sparse matrices. Dense matrix-vector multiplications within the sparse-block structure leverage optimization techniques from the KBLAS library, a high performance library for dense BLAS kernels. The design ideas of KBLAS can be applied to block-sparse matrices. Furthermore, a technique is proposed to balance the workload among thread blocks when there are large variations in the lengths of nonzero rows. Multi-GPU performance is highlighted. The proposed SpMV kernel outperforms existing state-of-the-art implementations using matrices with real structures from different applications. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Dissecting high-dimensional phenotypes with bayesian sparse factor analysis of genetic covariance matrices.

Science.gov (United States)

Runcie, Daniel E; Mukherjee, Sayan

2013-07-01

Quantitative genetic studies that model complex, multivariate phenotypes are important for both evolutionary prediction and artificial selection. For example, changes in gene expression can provide insight into developmental and physiological mechanisms that link genotype and phenotype. However, classical analytical techniques are poorly suited to quantitative genetic studies of gene expression where the number of traits assayed per individual can reach many thousand. Here, we derive a Bayesian genetic sparse factor model for estimating the genetic covariance matrix (G-matrix) of high-dimensional traits, such as gene expression, in a mixed-effects model. The key idea of our model is that we need consider only G-matrices that are biologically plausible. An organism's entire phenotype is the result of processes that are modular and have limited complexity. This implies that the G-matrix will be highly structured. In particular, we assume that a limited number of intermediate traits (or factors, e.g., variations in development or physiology) control the variation in the high-dimensional phenotype, and that each of these intermediate traits is sparse - affecting only a few observed traits. The advantages of this approach are twofold. First, sparse factors are interpretable and provide biological insight into mechanisms underlying the genetic architecture. Second, enforcing sparsity helps prevent sampling errors from swamping out the true signal in high-dimensional data. We demonstrate the advantages of our model on simulated data and in an analysis of a published Drosophila melanogaster gene expression data set.

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

Science.gov (United States)

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.

Numerical solution of large sparse linear systems

International Nuclear Information System (INIS)

Meurant, Gerard; Golub, Gene.

1982-02-01

This note is based on one of the lectures given at the 1980 CEA-EDF-INRIA Numerical Analysis Summer School whose aim is the study of large sparse linear systems. The main topics are solving least squares problems by orthogonal transformation, fast Poisson solvers and solution of sparse linear system by iterative methods with a special emphasis on preconditioned conjuguate gradient method [fr

Likelihood Approximation With Hierarchical Matrices For Large Spatial Datasets

KAUST Repository

Litvinenko, Alexander

2017-09-03

We use available measurements to estimate the unknown parameters (variance, smoothness parameter, and covariance length) of a covariance function by maximizing the joint Gaussian log-likelihood function. To overcome cubic complexity in the linear algebra, we approximate the discretized covariance function in the hierarchical (H-) matrix format. The H-matrix format has a log-linear computational cost and storage O(kn log n), where the rank k is a small integer and n is the number of locations. The H-matrix technique allows us to work with general covariance matrices in an efficient way, since H-matrices can approximate inhomogeneous covariance functions, with a fairly general mesh that is not necessarily axes-parallel, and neither the covariance matrix itself nor its inverse have to be sparse. We demonstrate our method with Monte Carlo simulations and an application to soil moisture data. The C, C++ codes and data are freely available.

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

Science.gov (United States)

Reddy, C. J.

2000-01-01

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

Inference for High-dimensional Differential Correlation Matrices.

Science.gov (United States)

Cai, T Tony; Zhang, Anru

2016-01-01

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

Ordering sparse matrices for cache-based systems

International Nuclear Information System (INIS)

Biswas, Rupak; Oliker, Leonid

2001-01-01

The Conjugate Gradient (CG) algorithm is the oldest and best-known Krylov subspace method used to solve sparse linear systems. Most of the coating-point operations within each CG iteration is spent performing sparse matrix-vector multiplication (SPMV). We examine how various ordering and partitioning strategies affect the performance of CG and SPMV when different programming paradigms are used on current commercial cache-based computers. However, a multithreaded implementation on the cacheless Cray MTA demonstrates high efficiency and scalability without any special ordering or partitioning

Deterministic matrices matching the compressed sensing phase transitions of Gaussian random matrices

Science.gov (United States)

Monajemi, Hatef; Jafarpour, Sina; Gavish, Matan; Donoho, David L.; Ambikasaran, Sivaram; Bacallado, Sergio; Bharadia, Dinesh; Chen, Yuxin; Choi, Young; Chowdhury, Mainak; Chowdhury, Soham; Damle, Anil; Fithian, Will; Goetz, Georges; Grosenick, Logan; Gross, Sam; Hills, Gage; Hornstein, Michael; Lakkam, Milinda; Lee, Jason; Li, Jian; Liu, Linxi; Sing-Long, Carlos; Marx, Mike; Mittal, Akshay; Monajemi, Hatef; No, Albert; Omrani, Reza; Pekelis, Leonid; Qin, Junjie; Raines, Kevin; Ryu, Ernest; Saxe, Andrew; Shi, Dai; Siilats, Keith; Strauss, David; Tang, Gary; Wang, Chaojun; Zhou, Zoey; Zhu, Zhen

2013-01-01

In compressed sensing, one takes samples of an N-dimensional vector using an matrix A, obtaining undersampled measurements . For random matrices with independent standard Gaussian entries, it is known that, when is k-sparse, there is a precisely determined phase transition: for a certain region in the (,)-phase diagram, convex optimization typically finds the sparsest solution, whereas outside that region, it typically fails. It has been shown empirically that the same property—with the same phase transition location—holds for a wide range of non-Gaussian random matrix ensembles. We report extensive experiments showing that the Gaussian phase transition also describes numerous deterministic matrices, including Spikes and Sines, Spikes and Noiselets, Paley Frames, Delsarte-Goethals Frames, Chirp Sensing Matrices, and Grassmannian Frames. Namely, for each of these deterministic matrices in turn, for a typical k-sparse object, we observe that convex optimization is successful over a region of the phase diagram that coincides with the region known for Gaussian random matrices. Our experiments considered coefficients constrained to for four different sets , and the results establish our finding for each of the four associated phase transitions. PMID:23277588

Biclustering via Sparse Singular Value Decomposition

KAUST Repository

Lee, Mihee

2010-02-16

Sparse singular value decomposition (SSVD) is proposed as a new exploratory analysis tool for biclustering or identifying interpretable row-column associations within high-dimensional data matrices. SSVD seeks a low-rank, checkerboard structured matrix approximation to data matrices. The desired checkerboard structure is achieved by forcing both the left- and right-singular vectors to be sparse, that is, having many zero entries. By interpreting singular vectors as regression coefficient vectors for certain linear regressions, sparsity-inducing regularization penalties are imposed to the least squares regression to produce sparse singular vectors. An efficient iterative algorithm is proposed for computing the sparse singular vectors, along with some discussion of penalty parameter selection. A lung cancer microarray dataset and a food nutrition dataset are used to illustrate SSVD as a biclustering method. SSVD is also compared with some existing biclustering methods using simulated datasets. © 2010, The International Biometric Society.

The application of sparse estimation of covariance matrix to quadratic discriminant analysis

OpenAIRE

Sun, Jiehuan; Zhao, Hongyu

2015-01-01

Background Although Linear Discriminant Analysis (LDA) is commonly used for classification, it may not be directly applied in genomics studies due to the large p, small n problem in these studies. Different versions of sparse LDA have been proposed to address this significant challenge. One implicit assumption of various LDA-based methods is that the covariance matrices are the same across different classes. However, rewiring of genetic networks (therefore different covariance matrices) acros...

Rotational image deblurring with sparse matrices

DEFF Research Database (Denmark)

Hansen, Per Christian; Nagy, James G.; Tigkos, Konstantinos

2014-01-01

We describe iterative deblurring algorithms that can handle blur caused by a rotation along an arbitrary axis (including the common case of pure rotation). Our algorithms use a sparse-matrix representation of the blurring operation, which allows us to easily handle several different boundary...

Using sparse LU factorisation to precondition GMRES for a family of similarly structured matrices arising from process modelling

Energy Technology Data Exchange (ETDEWEB)

Brooking, C. [Univ. of Bath (United Kingdom)

1996-12-31

Process engineering software is used to simulate the operation of large chemical plants. Such simulations are used for a variety of tasks, including operator training. For the software to be of practical use for this, dynamic simulations need to run in real-time. The models that the simulation is based upon are written in terms of Differential Algebraic Equations (DAE`s). In the numerical time-integration of systems of DAE`s using an implicit method such as backward Euler, the solution of nonlinear systems is required at each integration point. When solved using Newton`s method, this leads to the repeated solution of nonsymmetric sparse linear systems. These systems range in size from 500 to 20,000 variables. A typical integration may require around 3000 timesteps, and if 4 Newton iterates were needed on each time step, then this means approximately 12,000 linear systems must be solved. The matrices produced by the simulations have a similar sparsity pattern throughout the integration. They are also severely ill-conditioned, and have widely-scattered spectra.

Accelerating Matrix-Vector Multiplication on Hierarchical Matrices Using Graphical Processing Units

KAUST Repository

Boukaram, W.

2015-03-25

Large dense matrices arise from the discretization of many physical phenomena in computational sciences. In statistics very large dense covariance matrices are used for describing random fields and processes. One can, for instance, describe distribution of dust particles in the atmosphere, concentration of mineral resources in the earth\\'s crust or uncertain permeability coefficient in reservoir modeling. When the problem size grows, storing and computing with the full dense matrix becomes prohibitively expensive both in terms of computational complexity and physical memory requirements. Fortunately, these matrices can often be approximated by a class of data sparse matrices called hierarchical matrices (H-matrices) where various sub-blocks of the matrix are approximated by low rank matrices. These matrices can be stored in memory that grows linearly with the problem size. In addition, arithmetic operations on these H-matrices, such as matrix-vector multiplication, can be completed in almost linear time. Originally the H-matrix technique was developed for the approximation of stiffness matrices coming from partial differential and integral equations. Parallelizing these arithmetic operations on the GPU has been the focus of this work and we will present work done on the matrix vector operation on the GPU using the KSPARSE library.

Fast wavelet based sparse approximate inverse preconditioner

Energy Technology Data Exchange (ETDEWEB)

Wan, W.L. [Univ. of California, Los Angeles, CA (United States)

1996-12-31

Incomplete LU factorization is a robust preconditioner for both general and PDE problems but unfortunately not easy to parallelize. Recent study of Huckle and Grote and Chow and Saad showed that sparse approximate inverse could be a potential alternative while readily parallelizable. However, for special class of matrix A that comes from elliptic PDE problems, their preconditioners are not optimal in the sense that independent of mesh size. A reason may be that no good sparse approximate inverse exists for the dense inverse matrix. Our observation is that for this kind of matrices, its inverse entries typically have piecewise smooth changes. We can take advantage of this fact and use wavelet compression techniques to construct a better sparse approximate inverse preconditioner. We shall show numerically that our approach is effective for this kind of matrices.

Matrices over runtime systems at exascale

KAUST Repository

Agullo, Emmanuel

2012-11-01

The goal of Matrices Over Runtime Systems at Exascale (MORSE) project is to design dense and sparse linear algebra methods that achieve the fastest possible time to an accurate solution on large-scale multicore systems with GPU accelerators, using all the processing power that future high end systems can make available. In this poster, we propose a framework for describing linear algebra algorithms at a high level of abstraction and delegating the actual execution to a runtime system in order to design software whose performance is portable accross architectures. We illustrate our methodology on three classes of problems: dense linear algebra, sparse direct methods and fast multipole methods. The resulting codes have been incorporated into Magma, Pastix and ScalFMM solvers, respectively. © 2012 IEEE.

Tensor Dictionary Learning for Positive Definite Matrices.

Science.gov (United States)

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

2015-11-01

Sparse models have proven to be extremely successful in image processing and computer vision. However, a majority of the effort has been focused on sparse representation of vectors and low-rank models for general matrices. The success of sparse modeling, along with popularity of region covariances, has inspired the development of sparse coding approaches for these positive definite descriptors. While in earlier work, the dictionary was formed from all, or a random subset of, the training signals, it is clearly advantageous to learn a concise dictionary from the entire training set. In this paper, we propose a novel approach for dictionary learning over positive definite matrices. The dictionary is learned by alternating minimization between sparse coding and dictionary update stages, and different atom update methods are described. A discriminative version of the dictionary learning approach is also proposed, which simultaneously learns dictionaries for different classes in classification or clustering. Experimental results demonstrate the advantage of learning dictionaries from data both from reconstruction and classification viewpoints. Finally, a software library is presented comprising C++ binaries for all the positive definite sparse coding and dictionary learning approaches presented here.

Massively parallel sparse matrix function calculations with NTPoly

Science.gov (United States)

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.

P-SPARSLIB: A parallel sparse iterative solution package

Energy Technology Data Exchange (ETDEWEB)

Saad, Y. [Univ. of Minnesota, Minneapolis, MN (United States)

1994-12-31

Iterative methods are gaining popularity in engineering and sciences at a time where the computational environment is changing rapidly. P-SPARSLIB is a project to build a software library for sparse matrix computations on parallel computers. The emphasis is on iterative methods and the use of distributed sparse matrices, an extension of the domain decomposition approach to general sparse matrices. One of the goals of this project is to develop a software package geared towards specific applications. For example, the author will test the performance and usefulness of P-SPARSLIB modules on linear systems arising from CFD applications. Equally important is the goal of portability. In the long run, the author wishes to ensure that this package is portable on a variety of platforms, including SIMD environments and shared memory environments.

The Roles of Sparse Direct Methods in Large-scale Simulations

Energy Technology Data Exchange (ETDEWEB)

Li, Xiaoye S.; Gao, Weiguo; Husbands, Parry J.R.; Yang, Chao; Ng, Esmond G.

2005-06-27

Sparse systems of linear equations and eigen-equations arise at the heart of many large-scale, vital simulations in DOE. Examples include the Accelerator Science and Technology SciDAC (Omega3P code, electromagnetic problem), the Center for Extended Magnetohydrodynamic Modeling SciDAC(NIMROD and M3D-C1 codes, fusion plasma simulation). The Terascale Optimal PDE Simulations (TOPS)is providing high-performance sparse direct solvers, which have had significant impacts on these applications. Over the past several years, we have been working closely with the other SciDAC teams to solve their large, sparse matrix problems arising from discretization of the partial differential equations. Most of these systems are very ill-conditioned, resulting in extremely poor convergence deployed our direct methods techniques in these applications, which achieved significant scientific results as well as performance gains. These successes were made possible through the SciDAC model of computer scientists and application scientists working together to take full advantage of terascale computing systems and new algorithms research.

The Roles of Sparse Direct Methods in Large-scale Simulations

International Nuclear Information System (INIS)

Li, Xiaoye S.; Gao, Weiguo; Husbands, Parry J.R.; Yang, Chao; Ng, Esmond G.

2005-01-01

Sparse systems of linear equations and eigen-equations arise at the heart of many large-scale, vital simulations in DOE. Examples include the Accelerator Science and Technology SciDAC (Omega3P code, electromagnetic problem), the Center for Extended Magnetohydrodynamic Modeling SciDAC(NIMROD and M3D-C1 codes, fusion plasma simulation). The Terascale Optimal PDE Simulations (TOPS)is providing high-performance sparse direct solvers, which have had significant impacts on these applications. Over the past several years, we have been working closely with the other SciDAC teams to solve their large, sparse matrix problems arising from discretization of the partial differential equations. Most of these systems are very ill-conditioned, resulting in extremely poor convergence deployed our direct methods techniques in these applications, which achieved significant scientific results as well as performance gains. These successes were made possible through the SciDAC model of computer scientists and application scientists working together to take full advantage of terascale computing systems and new algorithms research

Design Patterns for Sparse-Matrix Computations on Hybrid CPU/GPU Platforms

Directory of Open Access Journals (Sweden)

Valeria Cardellini

2014-01-01

Full Text Available We apply object-oriented software design patterns to develop code for scientific software involving sparse matrices. Design patterns arise when multiple independent developments produce similar designs which converge onto a generic solution. We demonstrate how to use design patterns to implement an interface for sparse matrix computations on NVIDIA GPUs starting from PSBLAS, an existing sparse matrix library, and from existing sets of GPU kernels for sparse matrices. We also compare the throughput of the PSBLAS sparse matrix–vector multiplication on two platforms exploiting the GPU with that obtained by a CPU-only PSBLAS implementation. Our experiments exhibit encouraging results regarding the comparison between CPU and GPU executions in double precision, obtaining a speedup of up to 35.35 on NVIDIA GTX 285 with respect to AMD Athlon 7750, and up to 10.15 on NVIDIA Tesla C2050 with respect to Intel Xeon X5650.

Optimizing Sparse Matrix-Multiple Vectors Multiplication for Nuclear Configuration Interaction Calculations

Energy Technology Data Exchange (ETDEWEB)

Aktulga, Hasan Metin [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Buluc, Aydin [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Williams, Samuel [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Yang, Chao [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

2014-08-14

Obtaining highly accurate predictions on the properties of light atomic nuclei using the configuration interaction (CI) approach requires computing a few extremal Eigen pairs of the many-body nuclear Hamiltonian matrix. In the Many-body Fermion Dynamics for nuclei (MFDn) code, a block Eigen solver is used for this purpose. Due to the large size of the sparse matrices involved, a significant fraction of the time spent on the Eigen value computations is associated with the multiplication of a sparse matrix (and the transpose of that matrix) with multiple vectors (SpMM and SpMM-T). Existing implementations of SpMM and SpMM-T significantly underperform expectations. Thus, in this paper, we present and analyze optimized implementations of SpMM and SpMM-T. We base our implementation on the compressed sparse blocks (CSB) matrix format and target systems with multi-core architectures. We develop a performance model that allows us to understand and estimate the performance characteristics of our SpMM kernel implementations, and demonstrate the efficiency of our implementation on a series of real-world matrices extracted from MFDn. In particular, we obtain 3-4 speedup on the requisite operations over good implementations based on the commonly used compressed sparse row (CSR) matrix format. The improvements in the SpMM kernel suggest we may attain roughly a 40% speed up in the overall execution time of the block Eigen solver used in MFDn.

Hierarchical matrix approximation of large covariance matrices

KAUST Repository

Litvinenko, Alexander; Genton, Marc G.; Sun, Ying

2015-01-01

We approximate large non-structured Matérn covariance matrices of size n×n in the H-matrix format with a log-linear computational cost and storage O(kn log n), where rank k ≪ n is a small integer. Applications are: spatial statistics, machine learning and image analysis, kriging and optimal design.

Hierarchical matrix approximation of large covariance matrices

KAUST Repository

Litvinenko, Alexander

2015-11-30

We approximate large non-structured Matérn covariance matrices of size n×n in the H-matrix format with a log-linear computational cost and storage O(kn log n), where rank k ≪ n is a small integer. Applications are: spatial statistics, machine learning and image analysis, kriging and optimal design.

Large deviations of the maximum eigenvalue in Wishart random matrices

International Nuclear Information System (INIS)

Vivo, Pierpaolo; Majumdar, Satya N; Bohigas, Oriol

2007-01-01

We analytically compute the probability of large fluctuations to the left of the mean of the largest eigenvalue in the Wishart (Laguerre) ensemble of positive definite random matrices. We show that the probability that all the eigenvalues of a (N x N) Wishart matrix W = X T X (where X is a rectangular M x N matrix with independent Gaussian entries) are smaller than the mean value (λ) = N/c decreases for large N as ∼exp[-β/2 N 2 Φ - (2√c + 1: c)], where β = 1, 2 corresponds respectively to real and complex Wishart matrices, c = N/M ≤ 1 and Φ - (x; c) is a rate (sometimes also called large deviation) function that we compute explicitly. The result for the anti-Wishart case (M < N) simply follows by exchanging M and N. We also analytically determine the average spectral density of an ensemble of Wishart matrices whose eigenvalues are constrained to be smaller than a fixed barrier. Numerical simulations are in excellent agreement with the analytical predictions

Large deviations of the maximum eigenvalue in Wishart random matrices

Energy Technology Data Exchange (ETDEWEB)

Vivo, Pierpaolo [School of Information Systems, Computing and Mathematics, Brunel University, Uxbridge, Middlesex, UB8 3PH (United Kingdom) ; Majumdar, Satya N [Laboratoire de Physique Theorique et Modeles Statistiques (UMR 8626 du CNRS), Universite Paris-Sud, Batiment 100, 91405 Orsay Cedex (France); Bohigas, Oriol [Laboratoire de Physique Theorique et Modeles Statistiques (UMR 8626 du CNRS), Universite Paris-Sud, Batiment 100, 91405 Orsay Cedex (France)

2007-04-20

We analytically compute the probability of large fluctuations to the left of the mean of the largest eigenvalue in the Wishart (Laguerre) ensemble of positive definite random matrices. We show that the probability that all the eigenvalues of a (N x N) Wishart matrix W = X{sup T}X (where X is a rectangular M x N matrix with independent Gaussian entries) are smaller than the mean value ({lambda}) = N/c decreases for large N as {approx}exp[-{beta}/2 N{sup 2}{phi}{sub -} (2{radical}c + 1: c)], where {beta} = 1, 2 corresponds respectively to real and complex Wishart matrices, c = N/M {<=} 1 and {phi}{sub -}(x; c) is a rate (sometimes also called large deviation) function that we compute explicitly. The result for the anti-Wishart case (M < N) simply follows by exchanging M and N. We also analytically determine the average spectral density of an ensemble of Wishart matrices whose eigenvalues are constrained to be smaller than a fixed barrier. Numerical simulations are in excellent agreement with the analytical predictions.

Fast multipole preconditioners for sparse matrices arising from elliptic equations

KAUST Repository

Ibeid, Huda

2017-11-09

Among optimal hierarchical algorithms for the computational solution of elliptic problems, the fast multipole method (FMM) stands out for its adaptability to emerging architectures, having high arithmetic intensity, tunable accuracy, and relaxable global synchronization requirements. We demonstrate that, beyond its traditional use as a solver in problems for which explicit free-space kernel representations are available, the FMM has applicability as a preconditioner in finite domain elliptic boundary value problems, by equipping it with boundary integral capability for satisfying conditions at finite boundaries and by wrapping it in a Krylov method for extensibility to more general operators. Here, we do not discuss the well developed applications of FMM to implement matrix-vector multiplications within Krylov solvers of boundary element methods. Instead, we propose using FMM for the volume-to-volume contribution of inhomogeneous Poisson-like problems, where the boundary integral is a small part of the overall computation. Our method may be used to precondition sparse matrices arising from finite difference/element discretizations, and can handle a broader range of scientific applications. It is capable of algebraic convergence rates down to the truncation error of the discretized PDE comparable to those of multigrid methods, and it offers potentially superior multicore and distributed memory scalability properties on commodity architecture supercomputers. Compared with other methods exploiting the low-rank character of off-diagonal blocks of the dense resolvent operator, FMM-preconditioned Krylov iteration may reduce the amount of communication because it is matrix-free and exploits the tree structure of FMM. We describe our tests in reproducible detail with freely available codes and outline directions for further extensibility.

Fast multipole preconditioners for sparse matrices arising from elliptic equations

KAUST Repository

Ibeid, Huda; Yokota, Rio; Pestana, Jennifer; Keyes, David E.

2017-01-01

Among optimal hierarchical algorithms for the computational solution of elliptic problems, the fast multipole method (FMM) stands out for its adaptability to emerging architectures, having high arithmetic intensity, tunable accuracy, and relaxable global synchronization requirements. We demonstrate that, beyond its traditional use as a solver in problems for which explicit free-space kernel representations are available, the FMM has applicability as a preconditioner in finite domain elliptic boundary value problems, by equipping it with boundary integral capability for satisfying conditions at finite boundaries and by wrapping it in a Krylov method for extensibility to more general operators. Here, we do not discuss the well developed applications of FMM to implement matrix-vector multiplications within Krylov solvers of boundary element methods. Instead, we propose using FMM for the volume-to-volume contribution of inhomogeneous Poisson-like problems, where the boundary integral is a small part of the overall computation. Our method may be used to precondition sparse matrices arising from finite difference/element discretizations, and can handle a broader range of scientific applications. It is capable of algebraic convergence rates down to the truncation error of the discretized PDE comparable to those of multigrid methods, and it offers potentially superior multicore and distributed memory scalability properties on commodity architecture supercomputers. Compared with other methods exploiting the low-rank character of off-diagonal blocks of the dense resolvent operator, FMM-preconditioned Krylov iteration may reduce the amount of communication because it is matrix-free and exploits the tree structure of FMM. We describe our tests in reproducible detail with freely available codes and outline directions for further extensibility.

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

Science.gov (United States)

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

2018-05-01

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

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

Science.gov (United States)

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

2018-04-01

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

Hierarchical matrix approximation of large covariance matrices

KAUST Repository

Litvinenko, Alexander

2015-01-05

We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(nlogn). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and op- timal design.

Hierarchical matrix approximation of large covariance matrices

KAUST Repository

Litvinenko, Alexander; Genton, Marc G.; Sun, Ying; Tempone, Raul

2015-01-01

We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(nlogn). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and op- timal design.

Hierarchical matrix approximation of large covariance matrices

KAUST Repository

Litvinenko, Alexander

2015-01-07

We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(n log n). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and optimal design

Hierarchical matrix approximation of large covariance matrices

KAUST Repository

Litvinenko, Alexander; Genton, Marc G.; Sun, Ying; Tempone, Raul

2015-01-01

We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(n log n). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and optimal design

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

Science.gov (United States)

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.

SparseLeap: Efficient Empty Space Skipping for Large-Scale Volume Rendering

KAUST Repository

Hadwiger, Markus; Al-Awami, Ali K.; Beyer, Johanna; Agus, Marco; Pfister, Hanspeter

2017-01-01

Recent advances in data acquisition produce volume data of very high resolution and large size, such as terabyte-sized microscopy volumes. These data often contain many fine and intricate structures, which pose huge challenges for volume rendering, and make it particularly important to efficiently skip empty space. This paper addresses two major challenges: (1) The complexity of large volumes containing fine structures often leads to highly fragmented space subdivisions that make empty regions hard to skip efficiently. (2) The classification of space into empty and non-empty regions changes frequently, because the user or the evaluation of an interactive query activate a different set of objects, which makes it unfeasible to pre-compute a well-adapted space subdivision. We describe the novel SparseLeap method for efficient empty space skipping in very large volumes, even around fine structures. The main performance characteristic of SparseLeap is that it moves the major cost of empty space skipping out of the ray-casting stage. We achieve this via a hybrid strategy that balances the computational load between determining empty ray segments in a rasterization (object-order) stage, and sampling non-empty volume data in the ray-casting (image-order) stage. Before ray-casting, we exploit the fast hardware rasterization of GPUs to create a ray segment list for each pixel, which identifies non-empty regions along the ray. The ray-casting stage then leaps over empty space without hierarchy traversal. Ray segment lists are created by rasterizing a set of fine-grained, view-independent bounding boxes. Frame coherence is exploited by re-using the same bounding boxes unless the set of active objects changes. We show that SparseLeap scales better to large, sparse data than standard octree empty space skipping.

SparseLeap: Efficient Empty Space Skipping for Large-Scale Volume Rendering

KAUST Repository

Hadwiger, Markus

2017-08-28

Recent advances in data acquisition produce volume data of very high resolution and large size, such as terabyte-sized microscopy volumes. These data often contain many fine and intricate structures, which pose huge challenges for volume rendering, and make it particularly important to efficiently skip empty space. This paper addresses two major challenges: (1) The complexity of large volumes containing fine structures often leads to highly fragmented space subdivisions that make empty regions hard to skip efficiently. (2) The classification of space into empty and non-empty regions changes frequently, because the user or the evaluation of an interactive query activate a different set of objects, which makes it unfeasible to pre-compute a well-adapted space subdivision. We describe the novel SparseLeap method for efficient empty space skipping in very large volumes, even around fine structures. The main performance characteristic of SparseLeap is that it moves the major cost of empty space skipping out of the ray-casting stage. We achieve this via a hybrid strategy that balances the computational load between determining empty ray segments in a rasterization (object-order) stage, and sampling non-empty volume data in the ray-casting (image-order) stage. Before ray-casting, we exploit the fast hardware rasterization of GPUs to create a ray segment list for each pixel, which identifies non-empty regions along the ray. The ray-casting stage then leaps over empty space without hierarchy traversal. Ray segment lists are created by rasterizing a set of fine-grained, view-independent bounding boxes. Frame coherence is exploited by re-using the same bounding boxes unless the set of active objects changes. We show that SparseLeap scales better to large, sparse data than standard octree empty space skipping.

Tunable Sparse Network Coding for Multicast Networks

DEFF Research Database (Denmark)

Feizi, Soheil; Roetter, Daniel Enrique Lucani; Sørensen, Chres Wiant

2014-01-01

This paper shows the potential and key enabling mechanisms for tunable sparse network coding, a scheme in which the density of network coded packets varies during a transmission session. At the beginning of a transmission session, sparsely coded packets are transmitted, which benefits decoding...... complexity. At the end of a transmission, when receivers have accumulated degrees of freedom, coding density is increased. We propose a family of tunable sparse network codes (TSNCs) for multicast erasure networks with a controllable trade-off between completion time performance to decoding complexity...... a mechanism to perform efficient Gaussian elimination over sparse matrices going beyond belief propagation but maintaining low decoding complexity. Supporting simulation results are provided showing the trade-off between decoding complexity and completion time....

Parallel preconditioning techniques for sparse CG solvers

Energy Technology Data Exchange (ETDEWEB)

Basermann, A.; Reichel, B.; Schelthoff, C. [Central Institute for Applied Mathematics, Juelich (Germany)

1996-12-31

Conjugate gradient (CG) methods to solve sparse systems of linear equations play an important role in numerical methods for solving discretized partial differential equations. The large size and the condition of many technical or physical applications in this area result in the need for efficient parallelization and preconditioning techniques of the CG method. In particular for very ill-conditioned matrices, sophisticated preconditioner are necessary to obtain both acceptable convergence and accuracy of CG. Here, we investigate variants of polynomial and incomplete Cholesky preconditioners that markedly reduce the iterations of the simply diagonally scaled CG and are shown to be well suited for massively parallel machines.

SAR matrices: automated extraction of information-rich SAR tables from large compound data sets.

Science.gov (United States)

Wassermann, Anne Mai; Haebel, Peter; Weskamp, Nils; Bajorath, Jürgen

2012-07-23

We introduce the SAR matrix data structure that is designed to elucidate SAR patterns produced by groups of structurally related active compounds, which are extracted from large data sets. SAR matrices are systematically generated and sorted on the basis of SAR information content. Matrix generation is computationally efficient and enables processing of large compound sets. The matrix format is reminiscent of SAR tables, and SAR patterns revealed by different categories of matrices are easily interpretable. The structural organization underlying matrix formation is more flexible than standard R-group decomposition schemes. Hence, the resulting matrices capture SAR information in a comprehensive manner.

The application of sparse estimation of covariance matrix to quadratic discriminant analysis.

Science.gov (United States)

Sun, Jiehuan; Zhao, Hongyu

2015-02-18

Although Linear Discriminant Analysis (LDA) is commonly used for classification, it may not be directly applied in genomics studies due to the large p, small n problem in these studies. Different versions of sparse LDA have been proposed to address this significant challenge. One implicit assumption of various LDA-based methods is that the covariance matrices are the same across different classes. However, rewiring of genetic networks (therefore different covariance matrices) across different diseases has been observed in many genomics studies, which suggests that LDA and its variations may be suboptimal for disease classifications. However, it is not clear whether considering differing genetic networks across diseases can improve classification in genomics studies. We propose a sparse version of Quadratic Discriminant Analysis (SQDA) to explicitly consider the differences of the genetic networks across diseases. Both simulation and real data analysis are performed to compare the performance of SQDA with six commonly used classification methods. SQDA provides more accurate classification results than other methods for both simulated and real data. Our method should prove useful for classification in genomics studies and other research settings, where covariances differ among classes.

Aliasing-free wideband beamforming using sparse signal representation

NARCIS (Netherlands)

Tang, Z.; Blacquière, G.; Leus, G.

2011-01-01

Sparse signal representation (SSR) is considered to be an appealing alternative to classical beamforming for direction-of-arrival (DOA) estimation. For wideband signals, the SSR-based approach constructs steering matrices, referred to as dictionaries in this paper, corresponding to different

Algorithms for sparse, symmetric, definite quadratic lambda-matrix eigenproblems

International Nuclear Information System (INIS)

Scott, D.S.; Ward, R.C.

1981-01-01

Methods are presented for computing eigenpairs of the quadratic lambda-matrix, M lambda 2 + C lambda + K, where M, C, and K are large and sparse, and have special symmetry-type properties. These properties are sufficient to insure that all the eigenvalues are real and that theory analogous to the standard symmetric eigenproblem exists. The methods employ some standard techniques such as partial tri-diagonalization via the Lanczos Method and subsequent eigenpair calculation, shift-and- invert strategy and subspace iteration. The methods also employ some new techniques such as Rayleigh-Ritz quadratic roots and the inertia of symmetric, definite, quadratic lambda-matrices

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

Science.gov (United States)

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.

Likelihood Approximation With Parallel Hierarchical Matrices For Large Spatial Datasets

KAUST Repository

Litvinenko, Alexander; Sun, Ying; Genton, Marc G.; Keyes, David E.

2017-01-01

The main goal of this article is to introduce the parallel hierarchical matrix library HLIBpro to the statistical community. We describe the HLIBCov package, which is an extension of the HLIBpro library for approximating large covariance matrices and maximizing likelihood functions. We show that an approximate Cholesky factorization of a dense matrix of size $2M\\times 2M$ can be computed on a modern multi-core desktop in few minutes. Further, HLIBCov is used for estimating the unknown parameters such as the covariance length, variance and smoothness parameter of a Matérn covariance function by maximizing the joint Gaussian log-likelihood function. The computational bottleneck here is expensive linear algebra arithmetics due to large and dense covariance matrices. Therefore covariance matrices are approximated in the hierarchical ($\\H$-) matrix format with computational cost $\\mathcal{O}(k^2n \\log^2 n/p)$ and storage $\\mathcal{O}(kn \\log n)$, where the rank $k$ is a small integer (typically $k<25$), $p$ the number of cores and $n$ the number of locations on a fairly general mesh. We demonstrate a synthetic example, where the true values of known parameters are known. For reproducibility we provide the C++ code, the documentation, and the synthetic data.

Likelihood Approximation With Parallel Hierarchical Matrices For Large Spatial Datasets

KAUST Repository

Litvinenko, Alexander

2017-11-01

The main goal of this article is to introduce the parallel hierarchical matrix library HLIBpro to the statistical community. We describe the HLIBCov package, which is an extension of the HLIBpro library for approximating large covariance matrices and maximizing likelihood functions. We show that an approximate Cholesky factorization of a dense matrix of size $2M\\\\times 2M$ can be computed on a modern multi-core desktop in few minutes. Further, HLIBCov is used for estimating the unknown parameters such as the covariance length, variance and smoothness parameter of a Matérn covariance function by maximizing the joint Gaussian log-likelihood function. The computational bottleneck here is expensive linear algebra arithmetics due to large and dense covariance matrices. Therefore covariance matrices are approximated in the hierarchical ($\\\\H$-) matrix format with computational cost $\\\\mathcal{O}(k^2n \\\\log^2 n/p)$ and storage $\\\\mathcal{O}(kn \\\\log n)$, where the rank $k$ is a small integer (typically $k<25$), $p$ the number of cores and $n$ the number of locations on a fairly general mesh. We demonstrate a synthetic example, where the true values of known parameters are known. For reproducibility we provide the C++ code, the documentation, and the synthetic data.

Sparse matrix test collections

Energy Technology Data Exchange (ETDEWEB)

Duff, I.

1996-12-31

This workshop will discuss plans for coordinating and developing sets of test matrices for the comparison and testing of sparse linear algebra software. We will talk of plans for the next release (Release 2) of the Harwell-Boeing Collection and recent work on improving the accessibility of this Collection and others through the World Wide Web. There will only be three talks of about 15 to 20 minutes followed by a discussion from the floor.

Modeling and Forecasting Large Realized Covariance Matrices and Portfolio Choice

NARCIS (Netherlands)

Callot, Laurent A.F.; Kock, Anders B.; Medeiros, Marcelo C.

2017-01-01

We consider modeling and forecasting large realized covariance matrices by penalized vector autoregressive models. We consider Lasso-type estimators to reduce the dimensionality and provide strong theoretical guarantees on the forecast capability of our procedure. We show that we can forecast

Ab initio nuclear structure - the large sparse matrix eigenvalue problem

Energy Technology Data Exchange (ETDEWEB)

Vary, James P; Maris, Pieter [Department of Physics, Iowa State University, Ames, IA, 50011 (United States); Ng, Esmond; Yang, Chao [Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Sosonkina, Masha, E-mail: jvary@iastate.ed [Scalable Computing Laboratory, Ames Laboratory, Iowa State University, Ames, IA, 50011 (United States)

2009-07-01

The structure and reactions of light nuclei represent fundamental and formidable challenges for microscopic theory based on realistic strong interaction potentials. Several ab initio methods have now emerged that provide nearly exact solutions for some nuclear properties. The ab initio no core shell model (NCSM) and the no core full configuration (NCFC) method, frame this quantum many-particle problem as a large sparse matrix eigenvalue problem where one evaluates the Hamiltonian matrix in a basis space consisting of many-fermion Slater determinants and then solves for a set of the lowest eigenvalues and their associated eigenvectors. The resulting eigenvectors are employed to evaluate a set of experimental quantities to test the underlying potential. For fundamental problems of interest, the matrix dimension often exceeds 10{sup 10} and the number of nonzero matrix elements may saturate available storage on present-day leadership class facilities. We survey recent results and advances in solving this large sparse matrix eigenvalue problem. We also outline the challenges that lie ahead for achieving further breakthroughs in fundamental nuclear theory using these ab initio approaches.

Ab initio nuclear structure - the large sparse matrix eigenvalue problem

International Nuclear Information System (INIS)

Vary, James P; Maris, Pieter; Ng, Esmond; Yang, Chao; Sosonkina, Masha

2009-01-01

The structure and reactions of light nuclei represent fundamental and formidable challenges for microscopic theory based on realistic strong interaction potentials. Several ab initio methods have now emerged that provide nearly exact solutions for some nuclear properties. The ab initio no core shell model (NCSM) and the no core full configuration (NCFC) method, frame this quantum many-particle problem as a large sparse matrix eigenvalue problem where one evaluates the Hamiltonian matrix in a basis space consisting of many-fermion Slater determinants and then solves for a set of the lowest eigenvalues and their associated eigenvectors. The resulting eigenvectors are employed to evaluate a set of experimental quantities to test the underlying potential. For fundamental problems of interest, the matrix dimension often exceeds 10 10 and the number of nonzero matrix elements may saturate available storage on present-day leadership class facilities. We survey recent results and advances in solving this large sparse matrix eigenvalue problem. We also outline the challenges that lie ahead for achieving further breakthroughs in fundamental nuclear theory using these ab initio approaches.

Porting of the DBCSR library for Sparse Matrix-Matrix Multiplications to Intel Xeon Phi systems

OpenAIRE

Bethune, Iain; Gloess, Andeas; Hutter, Juerg; Lazzaro, Alfio; Pabst, Hans; Reid, Fiona

2017-01-01

Multiplication of two sparse matrices is a key operation in the simulation of the electronic structure of systems containing thousands of atoms and electrons. The highly optimized sparse linear algebra library DBCSR (Distributed Block Compressed Sparse Row) has been specifically designed to efficiently perform such sparse matrix-matrix multiplications. This library is the basic building block for linear scaling electronic structure theory and low scaling correlated methods in CP2K. It is para...

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

Science.gov (United States)

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.

Advanced incomplete factorization algorithms for Stiltijes matrices

Energy Technology Data Exchange (ETDEWEB)

Il`in, V.P. [Siberian Division RAS, Novosibirsk (Russian Federation)

1996-12-31

The modern numerical methods for solving the linear algebraic systems Au = f with high order sparse matrices A, which arise in grid approximations of multidimensional boundary value problems, are based mainly on accelerated iterative processes with easily invertible preconditioning matrices presented in the form of approximate (incomplete) factorization of the original matrix A. We consider some recent algorithmic approaches, theoretical foundations, experimental data and open questions for incomplete factorization of Stiltijes matrices which are {open_quotes}the best{close_quotes} ones in the sense that they have the most advanced results. Special attention is given to solving the elliptic differential equations with strongly variable coefficients, singular perturbated diffusion-convection and parabolic equations.

Deterministic matrices matching the compressed sensing phase transitions of Gaussian random matrices

OpenAIRE

Monajemi, Hatef; Jafarpour, Sina; Gavish, Matan; Donoho, David L.; Ambikasaran, Sivaram; Bacallado, Sergio; Bharadia, Dinesh; Chen, Yuxin; Choi, Young; Chowdhury, Mainak; Chowdhury, Soham; Damle, Anil; Fithian, Will; Goetz, Georges; Grosenick, Logan

2012-01-01

In compressed sensing, one takes samples of an N-dimensional vector using an matrix A, obtaining undersampled measurements . For random matrices with independent standard Gaussian entries, it is known that, when is k-sparse, there is a precisely determined phase transition: for a certain region in the (,)-phase diagram, convex optimization typically finds the sparsest solution, whereas outside that region, it typically fails. It has been shown empirically that the same property—with the ...

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

Science.gov (United States)

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

2017-01-01

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

Improving the computation efficiency of COBRA-TF for LWR safety analysis of large problems

International Nuclear Information System (INIS)

Cuervo, D.; Avramova, M. N.; Ivanov, K. N.

2004-01-01

A matrix solver is implemented in COBRA-TF in order to improve the computation efficiency of both numerical solution methods existing in the code, the Gauss elimination and the Gauss-Seidel iterative technique. Both methods are used to solve the system of pressure linear equations and relay on the solution of large sparse matrices. The introduced solver accelerates the solution of these matrices in cases of large number of cells. The execution time is reduced in half as compared to the execution time without using matrix solver for the cases with large matrices. The achieved improvement and the planned future work in this direction are important for performing efficient LWR safety analyses of large problems. (authors)

Better Size Estimation for Sparse Matrix Products

DEFF Research Database (Denmark)

Amossen, Rasmus Resen; Campagna, Andrea; Pagh, Rasmus

2010-01-01

We consider the problem of doing fast and reliable estimation of the number of non-zero entries in a sparse Boolean matrix product. Let n denote the total number of non-zero entries in the input matrices. We show how to compute a 1 ± ε approximation (with small probability of error) in expected t...

Modern algorithms for large sparse eigenvalue problems

International Nuclear Information System (INIS)

Meyer, A.

1987-01-01

The volume is written for mathematicians interested in (numerical) linear algebra and in the solution of large sparse eigenvalue problems, as well as for specialists in engineering, who use the considered algorithms in the investigation of eigenoscillations of structures, in reactor physics, etc. Some variants of the algorithms based on the idea of a gradient-type direction of movement are presented and their convergence properties are discussed. From this, a general strategy for the direct use of preconditionings for the eigenvalue problem is derived. In this new approach the necessity of the solution of large linear systems is entirely avoided. Hence, these methods represent a new alternative to some other modern eigenvalue algorithms, as they show a slightly slower convergence on the one hand but essentially lower numerical and data processing problems on the other hand. A brief description and comparison of some well-known methods (i.e. simultaneous iteration, Lanczos algorithm) completes this volume. (author)

Parallel and Scalable Sparse Basic Linear Algebra Subprograms

DEFF Research Database (Denmark)

Liu, Weifeng

and heterogeneous processors. The thesis compares the proposed methods with state-of-the-art approaches on six homogeneous and five heterogeneous processors from Intel, AMD and nVidia. Using in total 38 sparse matrices as a benchmark suite, the experimental results show that the proposed methods obtain significant...

Fast Solution in Sparse LDA for Binary Classification

Science.gov (United States)

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

Sparse direct solver for large finite element problems based on the minimum degree algorithm

Czech Academy of Sciences Publication Activity Database

Pařík, Petr; Plešek, Jiří

2017-01-01

Roč. 113, November (2017), s. 2-6 ISSN 0965-9978 R&D Projects: GA ČR(CZ) GA15-20666S; GA MŠk(CZ) EF15_003/0000493 Institutional support: RVO:61388998 Keywords : sparse direct solution * finite element method * large sparse Linear systems Subject RIV: JR - Other Machinery OBOR OECD: Mechanical engineering Impact factor: 3.000, year: 2016 https://www.sciencedirect.com/science/article/pii/S0965997817302582

Designing sparse sensing matrix for compressive sensing to reconstruct high resolution medical images

Directory of Open Access Journals (Sweden)

Vibha Tiwari

2015-12-01

Full Text Available Compressive sensing theory enables faithful reconstruction of signals, sparse in domain $ \\Psi $, at sampling rate lesser than Nyquist criterion, while using sampling or sensing matrix $ \\Phi $ which satisfies restricted isometric property. The role played by sensing matrix $ \\Phi $ and sparsity matrix $ \\Psi $ is vital in faithful reconstruction. If the sensing matrix is dense then it takes large storage space and leads to high computational cost. In this paper, effort is made to design sparse sensing matrix with least incurred computational cost while maintaining quality of reconstructed image. The design approach followed is based on sparse block circulant matrix (SBCM with few modifications. The other used sparse sensing matrix consists of 15 ones in each column. The medical images used are acquired from US, MRI and CT modalities. The image quality measurement parameters are used to compare the performance of reconstructed medical images using various sensing matrices. It is observed that, since Gram matrix of dictionary matrix ($ \\Phi \\Psi \\mathrm{} $ is closed to identity matrix in case of proposed modified SBCM, therefore, it helps to reconstruct the medical images of very good quality.

Contributions to Large Covariance and Inverse Covariance Matrices Estimation

OpenAIRE

Kang, Xiaoning

2016-01-01

Estimation of covariance matrix and its inverse is of great importance in multivariate statistics with broad applications such as dimension reduction, portfolio optimization, linear discriminant analysis and gene expression analysis. However, accurate estimation of covariance or inverse covariance matrices is challenging due to the positive definiteness constraint and large number of parameters, especially in the high-dimensional cases. In this thesis, I develop several approaches for estimat...

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

Science.gov (United States)

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

2017-09-01

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

Evaluating functions of positive-definite matrices using colored-noise thermostats

Science.gov (United States)

Nava, Marco; Ceriotti, Michele; Dryzun, Chaim; Parrinello, Michele

2014-02-01

Many applications in computational science require computing the elements of a function of a large matrix. A commonly used approach is based on the the evaluation of the eigenvalue decomposition, a task that, in general, involves a computing time that scales with the cube of the size of the matrix. We present here a method that can be used to evaluate the elements of a function of a positive-definite matrix with a scaling that is linear for sparse matrices and quadratic in the general case. This methodology is based on the properties of the dynamics of a multidimensional harmonic potential coupled with colored-noise, generalized Langevin equation thermostats. This "f-thermostat" approach allows us to calculate directly elements of functions of a positive-definite matrix by carefully tailoring the properties of the stochastic dynamics. We demonstrate the scaling and the accuracy of this approach for both dense and sparse problems and compare the results with other established methodologies.

Uniform Recovery Bounds for Structured Random Matrices in Corrupted Compressed Sensing

Science.gov (United States)

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

2018-04-01

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

Sampling of finite elements for sparse recovery in large scale 3D electrical impedance tomography

International Nuclear Information System (INIS)

Javaherian, Ashkan; Moeller, Knut; Soleimani, Manuchehr

2015-01-01

This study proposes a method to improve performance of sparse recovery inverse solvers in 3D electrical impedance tomography (3D EIT), especially when the volume under study contains small-sized inclusions, e.g. 3D imaging of breast tumours. Initially, a quadratic regularized inverse solver is applied in a fast manner with a stopping threshold much greater than the optimum. Based on assuming a fixed level of sparsity for the conductivity field, finite elements are then sampled via applying a compressive sensing (CS) algorithm to the rough blurred estimation previously made by the quadratic solver. Finally, a sparse inverse solver is applied solely to the sampled finite elements, with the solution to the CS as its initial guess. The results show the great potential of the proposed CS-based sparse recovery in improving accuracy of sparse solution to the large-size 3D EIT. (paper)

An NoC Traffic Compiler for Efficient FPGA Implementation of Sparse Graph-Oriented Workloads

Directory of Open Access Journals (Sweden)

Nachiket Kapre

2011-01-01

synchronization to optimize our workloads for large networks up to 2025 parallel elements for BSP model and 25 parallel elements for Token Dataflow. This allows us to demonstrate speedups between 1.2× and 22× (3.5× mean, area reductions (number of Processing Elements between 3× and 15× (9× mean and dynamic energy savings between 2× and 3.5× (2.7× mean over a range of real-world graph applications in the BSP compute model. We deliver speedups of 0.5–13× (geomean 3.6× for Sparse Direct Matrix Solve (Token Dataflow compute model applied to a range of sparse matrices when using a high-quality placement algorithm. We expect such traffic optimization tools and techniques to become an essential part of the NoC application-mapping flow.

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

Science.gov (United States)

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.

Comparing large covariance matrices under weak conditions on the dependence structure and its application to gene clustering.

Science.gov (United States)

Chang, Jinyuan; Zhou, Wen; Zhou, Wen-Xin; Wang, Lan

2017-03-01

Comparing large covariance matrices has important applications in modern genomics, where scientists are often interested in understanding whether relationships (e.g., dependencies or co-regulations) among a large number of genes vary between different biological states. We propose a computationally fast procedure for testing the equality of two large covariance matrices when the dimensions of the covariance matrices are much larger than the sample sizes. A distinguishing feature of the new procedure is that it imposes no structural assumptions on the unknown covariance matrices. Hence, the test is robust with respect to various complex dependence structures that frequently arise in genomics. We prove that the proposed procedure is asymptotically valid under weak moment conditions. As an interesting application, we derive a new gene clustering algorithm which shares the same nice property of avoiding restrictive structural assumptions for high-dimensional genomics data. Using an asthma gene expression dataset, we illustrate how the new test helps compare the covariance matrices of the genes across different gene sets/pathways between the disease group and the control group, and how the gene clustering algorithm provides new insights on the way gene clustering patterns differ between the two groups. The proposed methods have been implemented in an R-package HDtest and are available on CRAN. © 2016, The International Biometric Society.

Speculative segmented sum for sparse matrix-vector multiplication on heterogeneous processors

DEFF Research Database (Denmark)

Liu, Weifeng; Vinter, Brian

2015-01-01

of the same chip is triggered to re-arrange the predicted partial sums for a correct resulting vector. On three heterogeneous processors from Intel, AMD and nVidia, using 20 sparse matrices as a benchmark suite, the experimental results show that our method obtains significant performance improvement over...

A Robust Incomplete Factorization Preconditioner for Positive Definite Matrices

Czech Academy of Sciences Publication Activity Database

Benzi, M.; Tůma, Miroslav

2003-01-01

Roč. 10, - (2003), s. 385-400 ISSN 1070-5325 R&D Projects: GA AV ČR IAA2030801; GA AV ČR IAA1030103 Institutional research plan: AV0Z1030915 Keywords : sparse linear systems * positive definite matrices * preconditioned conjugate gradient s * incomplete factorization * A-orthogonalization * SAINV Subject RIV: BA - General Mathematics Impact factor: 1.042, year: 2003

Large-Capacity Three-Party Quantum Digital Secret Sharing Using Three Particular Matrices Coding

International Nuclear Information System (INIS)

Lai Hong; Tao Li; Liu Zhi-Ming; Luo Ming-Xing; Pieprzyk, Josef; Orgun, Mehmet A.

2016-01-01

In this paper, we develop a large-capacity quantum digital secret sharing (QDSS) scheme, combined the Fibonacci- and Lucas-valued orbital angular momentum (OAM) entanglement with the recursive Fibonacci and Lucas matrices. To be exact, Alice prepares pairs of photons in the Fibonacci- and Lucas-valued OAM entangled states, and then allocates them to two participants, say, Bob and Charlie, to establish the secret key. Moreover, the available Fibonacci and Lucas values from the matching entangled states are used as the seed for generating the Fibonacci and Lucas matrices. This is achieved because the entries of the Fibonacci and Lucas matrices are recursive. The secret key can only be obtained jointly by Bob and Charlie, who can further recover the secret. Its security is based on the facts that nonorthogonal states are indistinguishable, and Bob or Charlie detects a Fibonacci number, there is still a twofold uncertainty for Charlie' (Bob') detected value. (paper)

A Spectral Algorithm for Envelope Reduction of Sparse Matrices

Science.gov (United States)

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.

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

International Nuclear Information System (INIS)

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

2013-01-01

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. (paper)

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

Science.gov (United States)

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 Channel Estimation Including the Impact of the Transceiver Filters with Application to OFDM

DEFF Research Database (Denmark)

Barbu, Oana-Elena; Pedersen, Niels Lovmand; Manchón, Carles Navarro

2014-01-01

Traditionally, the dictionary matrices used in sparse wireless channel estimation have been based on the discrete Fourier transform, following the assumption that the channel frequency response (CFR) can be approximated as a linear combination of a small number of multipath components, each one......) and receive (demodulation) filters. Hence, the assumption of the CFR being sparse in the canonical Fourier dictionary may no longer hold. In this work, we derive a signal model and subsequently a novel dictionary matrix for sparse estimation that account for the impact of transceiver filters. Numerical...... results obtained in an OFDM transmission scenario demonstrate the superior accuracy of a sparse estimator that uses our proposed dictionary rather than the classical Fourier dictionary, and its robustness against a mismatch in the assumed transmit filter characteristics....

Modified conjugate gradient method for diagonalizing large matrices.

Science.gov (United States)

Jie, Quanlin; Liu, Dunhuan

2003-11-01

We present an iterative method to diagonalize large matrices. The basic idea is the same as the conjugate gradient (CG) method, i.e, minimizing the Rayleigh quotient via its gradient and avoiding reintroducing errors to the directions of previous gradients. Each iteration step is to find lowest eigenvector of the matrix in a subspace spanned by the current trial vector and the corresponding gradient of the Rayleigh quotient, as well as some previous trial vectors. The gradient, together with the previous trial vectors, play a similar role as the conjugate gradient of the original CG algorithm. Our numeric tests indicate that this method converges significantly faster than the original CG method. And the computational cost of one iteration step is about the same as the original CG method. It is suitable for first principle calculations.

Sparse matrix-vector multiplication on GPGPU clusters: A new storage format and a scalable implementation

OpenAIRE

Kreutzer, Moritz; Hager, Georg; Wellein, Gerhard; Fehske, Holger; Basermann, Achim; Bishop, Alan R.

2011-01-01

Sparse matrix-vector multiplication (spMVM) is the dominant operation in many sparse solvers. We investigate performance properties of spMVM with matrices of various sparsity patterns on the nVidia “Fermi” class of GPGPUs. A new “padded jagged diagonals storage” (pJDS) format is proposed which may substantially reduce the memory overhead intrinsic to the widespread ELLPACK-R scheme while making no assumptions about the matrix structure. In our test scenarios the pJDS format cuts the ...

Introduction into Hierarchical Matrices

KAUST Repository

Litvinenko, Alexander

2013-01-01

Hierarchical matrices allow us to reduce computational storage and cost from cubic to almost linear. This technique can be applied for solving PDEs, integral equations, matrix equations and approximation of large covariance and precision matrices.

Introduction into Hierarchical Matrices

KAUST Repository

Litvinenko, Alexander

2013-12-05

Hierarchical matrices allow us to reduce computational storage and cost from cubic to almost linear. This technique can be applied for solving PDEs, integral equations, matrix equations and approximation of large covariance and precision matrices.

Sparse canonical correlation analysis: new formulation and algorithm.

Science.gov (United States)

Chu, Delin; Liao, Li-Zhi; Ng, Michael K; Zhang, Xiaowei

2013-12-01

In this paper, we study canonical correlation analysis (CCA), which is a powerful tool in multivariate data analysis for finding the correlation between two sets of multidimensional variables. The main contributions of the paper are: 1) to reveal the equivalent relationship between a recursive formula and a trace formula for the multiple CCA problem, 2) to obtain the explicit characterization for all solutions of the multiple CCA problem even when the corresponding covariance matrices are singular, 3) to develop a new sparse CCA algorithm, and 4) to establish the equivalent relationship between the uncorrelated linear discriminant analysis and the CCA problem. We test several simulated and real-world datasets in gene classification and cross-language document retrieval to demonstrate the effectiveness of the proposed algorithm. The performance of the proposed method is competitive with the state-of-the-art sparse CCA algorithms.

Hierarchical Matrices Method and Its Application in Electromagnetic Integral Equations

Directory of Open Access Journals (Sweden)

Han Guo

2012-01-01

Full Text Available Hierarchical (H- matrices method is a general mathematical framework providing a highly compact representation and efficient numerical arithmetic. When applied in integral-equation- (IE- based computational electromagnetics, H-matrices can be regarded as a fast algorithm; therefore, both the CPU time and memory requirement are reduced significantly. Its kernel independent feature also makes it suitable for any kind of integral equation. To solve H-matrices system, Krylov iteration methods can be employed with appropriate preconditioners, and direct solvers based on the hierarchical structure of H-matrices are also available along with high efficiency and accuracy, which is a unique advantage compared to other fast algorithms. In this paper, a novel sparse approximate inverse (SAI preconditioner in multilevel fashion is proposed to accelerate the convergence rate of Krylov iterations for solving H-matrices system in electromagnetic applications, and a group of parallel fast direct solvers are developed for dealing with multiple right-hand-side cases. Finally, numerical experiments are given to demonstrate the advantages of the proposed multilevel preconditioner compared to conventional “single level” preconditioners and the practicability of the fast direct solvers for arbitrary complex structures.

Non-parametric co-clustering of large scale sparse bipartite networks on the GPU

DEFF Research Database (Denmark)

Hansen, Toke Jansen; Mørup, Morten; Hansen, Lars Kai

2011-01-01

of row and column clusters from a hypothesis space of an infinite number of clusters. To reach large scale applications of co-clustering we exploit that parameter inference for co-clustering is well suited for parallel computing. We develop a generic GPU framework for efficient inference on large scale...... sparse bipartite networks and achieve a speedup of two orders of magnitude compared to estimation based on conventional CPUs. In terms of scalability we find for networks with more than 100 million links that reliable inference can be achieved in less than an hour on a single GPU. To efficiently manage...

Hierarchical matrices algorithms and analysis

CERN Document Server

Hackbusch, Wolfgang

2015-01-01

This self-contained monograph presents matrix algorithms and their analysis. The new technique enables not only the solution of linear systems but also the approximation of matrix functions, e.g., the matrix exponential. Other applications include the solution of matrix equations, e.g., the Lyapunov or Riccati equation. The required mathematical background can be found in the appendix. The numerical treatment of fully populated large-scale matrices is usually rather costly. However, the technique of hierarchical matrices makes it possible to store matrices and to perform matrix operations approximately with almost linear cost and a controllable degree of approximation error. For important classes of matrices, the computational cost increases only logarithmically with the approximation error. The operations provided include the matrix inversion and LU decomposition. Since large-scale linear algebra problems are standard in scientific computing, the subject of hierarchical matrices is of interest to scientists ...

Balanced and sparse Tamo-Barg codes

KAUST Repository

Halbawi, Wael; Duursma, Iwan; Dau, Hoang; Hassibi, Babak

2017-01-01

We construct balanced and sparse generator matrices for Tamo and Barg's Locally Recoverable Codes (LRCs). More specifically, for a cyclic Tamo-Barg code of length n, dimension k and locality r, we show how to deterministically construct a generator matrix where the number of nonzeros in any two columns differs by at most one, and where the weight of every row is d + r - 1, where d is the minimum distance of the code. Since LRCs are designed mainly for distributed storage systems, the results presented in this work provide a computationally balanced and efficient encoding scheme for these codes. The balanced property ensures that the computational effort exerted by any storage node is essentially the same, whilst the sparse property ensures that this effort is minimal. The work presented in this paper extends a similar result previously established for Reed-Solomon (RS) codes, where it is now known that any cyclic RS code possesses a generator matrix that is balanced as described, but is sparsest, meaning that each row has d nonzeros.

Balanced and sparse Tamo-Barg codes

KAUST Repository

Halbawi, Wael

2017-08-29

We construct balanced and sparse generator matrices for Tamo and Barg\\'s Locally Recoverable Codes (LRCs). More specifically, for a cyclic Tamo-Barg code of length n, dimension k and locality r, we show how to deterministically construct a generator matrix where the number of nonzeros in any two columns differs by at most one, and where the weight of every row is d + r - 1, where d is the minimum distance of the code. Since LRCs are designed mainly for distributed storage systems, the results presented in this work provide a computationally balanced and efficient encoding scheme for these codes. The balanced property ensures that the computational effort exerted by any storage node is essentially the same, whilst the sparse property ensures that this effort is minimal. The work presented in this paper extends a similar result previously established for Reed-Solomon (RS) codes, where it is now known that any cyclic RS code possesses a generator matrix that is balanced as described, but is sparsest, meaning that each row has d nonzeros.

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

Science.gov (United States)

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.

Spectral Regularization Algorithms for Learning Large Incomplete Matrices.

Science.gov (United States)

Mazumder, Rahul; Hastie, Trevor; Tibshirani, Robert

2010-03-01

We use convex relaxation techniques to provide a sequence of regularized low-rank solutions for large-scale matrix completion problems. Using the nuclear norm as a regularizer, we provide a simple and very efficient convex algorithm for minimizing the reconstruction error subject to a bound on the nuclear norm. Our algorithm Soft-Impute iteratively replaces the missing elements with those obtained from a soft-thresholded SVD. With warm starts this allows us to efficiently compute an entire regularization path of solutions on a grid of values of the regularization parameter. The computationally intensive part of our algorithm is in computing a low-rank SVD of a dense matrix. Exploiting the problem structure, we show that the task can be performed with a complexity linear in the matrix dimensions. Our semidefinite-programming algorithm is readily scalable to large matrices: for example it can obtain a rank-80 approximation of a 10(6) × 10(6) incomplete matrix with 10(5) observed entries in 2.5 hours, and can fit a rank 40 approximation to the full Netflix training set in 6.6 hours. Our methods show very good performance both in training and test error when compared to other competitive state-of-the art techniques.

Sparse Machine Learning Methods for Understanding Large Text Corpora

Data.gov (United States)

National Aeronautics and Space Administration — Sparse machine learning has recently emerged as powerful tool to obtain models of high-dimensional data with high degree of interpretability, at low computational...

Discrete Sparse Coding.

Science.gov (United States)

Exarchakis, Georgios; Lücke, Jörg

2017-11-01

Sparse coding algorithms with continuous latent variables have been the subject of a large number of studies. However, discrete latent spaces for sparse coding have been largely ignored. In this work, we study sparse coding with latents described by discrete instead of continuous prior distributions. We consider the general case in which the latents (while being sparse) can take on any value of a finite set of possible values and in which we learn the prior probability of any value from data. This approach can be applied to any data generated by discrete causes, and it can be applied as an approximation of continuous causes. As the prior probabilities are learned, the approach then allows for estimating the prior shape without assuming specific functional forms. To efficiently train the parameters of our probabilistic generative model, we apply a truncated expectation-maximization approach (expectation truncation) that we modify to work with a general discrete prior. We evaluate the performance of the algorithm by applying it to a variety of tasks: (1) we use artificial data to verify that the algorithm can recover the generating parameters from a random initialization, (2) use image patches of natural images and discuss the role of the prior for the extraction of image components, (3) use extracellular recordings of neurons to present a novel method of analysis for spiking neurons that includes an intuitive discretization strategy, and (4) apply the algorithm on the task of encoding audio waveforms of human speech. The diverse set of numerical experiments presented in this letter suggests that discrete sparse coding algorithms can scale efficiently to work with realistic data sets and provide novel statistical quantities to describe the structure of the data.

HLIBCov: Parallel Hierarchical Matrix Approximation of Large Covariance Matrices and Likelihoods with Applications in Parameter Identification

KAUST Repository

Litvinenko, Alexander

2017-09-26

The main goal of this article is to introduce the parallel hierarchical matrix library HLIBpro to the statistical community. We describe the HLIBCov package, which is an extension of the HLIBpro library for approximating large covariance matrices and maximizing likelihood functions. We show that an approximate Cholesky factorization of a dense matrix of size $2M\\\\times 2M$ can be computed on a modern multi-core desktop in few minutes. Further, HLIBCov is used for estimating the unknown parameters such as the covariance length, variance and smoothness parameter of a Mat\\\\\\'ern covariance function by maximizing the joint Gaussian log-likelihood function. The computational bottleneck here is expensive linear algebra arithmetics due to large and dense covariance matrices. Therefore covariance matrices are approximated in the hierarchical ($\\\\H$-) matrix format with computational cost $\\\\mathcal{O}(k^2n \\\\log^2 n/p)$ and storage $\\\\mathcal{O}(kn \\\\log n)$, where the rank $k$ is a small integer (typically $k<25$), $p$ the number of cores and $n$ the number of locations on a fairly general mesh. We demonstrate a synthetic example, where the true values of known parameters are known. For reproducibility we provide the C++ code, the documentation, and the synthetic data.

HLIBCov: Parallel Hierarchical Matrix Approximation of Large Covariance Matrices and Likelihoods with Applications in Parameter Identification

KAUST Repository

Litvinenko, Alexander

2017-09-24

The main goal of this article is to introduce the parallel hierarchical matrix library HLIBpro to the statistical community. We describe the HLIBCov package, which is an extension of the HLIBpro library for approximating large covariance matrices and maximizing likelihood functions. We show that an approximate Cholesky factorization of a dense matrix of size $2M\\\\times 2M$ can be computed on a modern multi-core desktop in few minutes. Further, HLIBCov is used for estimating the unknown parameters such as the covariance length, variance and smoothness parameter of a Mat\\\\\\'ern covariance function by maximizing the joint Gaussian log-likelihood function. The computational bottleneck here is expensive linear algebra arithmetics due to large and dense covariance matrices. Therefore covariance matrices are approximated in the hierarchical ($\\\\mathcal{H}$-) matrix format with computational cost $\\\\mathcal{O}(k^2n \\\\log^2 n/p)$ and storage $\\\\mathcal{O}(kn \\\\log n)$, where the rank $k$ is a small integer (typically $k<25$), $p$ the number of cores and $n$ the number of locations on a fairly general mesh. We demonstrate a synthetic example, where the true values of known parameters are known. For reproducibility we provide the C++ code, the documentation, and the synthetic data.

Algorithms for large scale singular value analysis of spatially variant tomography systems

International Nuclear Information System (INIS)

Cao-Huu, Tuan; Brownell, G.; Lachiver, G.

1996-01-01

The problem of determining the eigenvalues of large matrices occurs often in the design and analysis of modem tomography systems. As there is an interest in solving systems containing an ever-increasing number of variables, current research effort is being made to create more robust solvers which do not depend on some special feature of the matrix for convergence (e.g. block circulant), and to improve the speed of already known and understood solvers so that solving even larger systems in a reasonable time becomes viable. Our standard techniques for singular value analysis are based on sparse matrix factorization and are not applicable when the input matrices are large because the algorithms cause too much fill. Fill refers to the increase of non-zero elements in the LU decomposition of the original matrix A (the system matrix). So we have developed iterative solutions that are based on sparse direct methods. Data motion and preconditioning techniques are critical for performance. This conference paper describes our algorithmic approaches for large scale singular value analysis of spatially variant imaging systems, and in particular of PCR2, a cylindrical three-dimensional PET imager 2 built at the Massachusetts General Hospital (MGH) in Boston. We recommend the desirable features and challenges for the next generation of parallel machines for optimal performance of our solver

More on Generalizations and Modifications of Iterative Methods for Solving Large Sparse Indefinite Linear Systems

Directory of Open Access Journals (Sweden)

Jen-Yuan Chen

2014-01-01

Full Text Available Continuing from the works of Li et al. (2014, Li (2007, and Kincaid et al. (2000, we present more generalizations and modifications of iterative methods for solving large sparse symmetric and nonsymmetric indefinite systems of linear equations. We discuss a variety of iterative methods such as GMRES, MGMRES, MINRES, LQ-MINRES, QR MINRES, MMINRES, MGRES, and others.

Ordering schemes for sparse matrices using modern programming paradigms

International Nuclear Information System (INIS)

Oliker, Leonid; Li, Xiaoye; Husbands, Parry; 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. In previous work, we investigated the effects of various ordering and partitioning strategies on the performance of CG using different programming paradigms and architectures. This paper makes several extensions to our prior research. First, we present a hybrid(MPI+OpenMP) implementation of the CG algorithm on the IBM SP and show that the hybrid paradigm increases programming complexity with little performance gains compared to a pure MPI implementation. For ill-conditioned linear systems, it is often necessary to use a preconditioning technique. We present MPI results for ILU(0) preconditioned CG (PCG) using the BlockSolve95 library, and show that the initial ordering of the input matrix dramatically affect PCG's performance. Finally, a multithreaded version of the PCG is developed on the Cray (Tera) MTA. Unlike the message-passing version, this implementation did not require the complexities of special orderings or graph dependency analysis. However, only limited scalability was achieved due to the lack of available thread level parallelism

Epileptic Seizure Detection with Log-Euclidean Gaussian Kernel-Based Sparse Representation.

Science.gov (United States)

Yuan, Shasha; Zhou, Weidong; Wu, Qi; Zhang, Yanli

2016-05-01

Epileptic seizure detection plays an important role in the diagnosis of epilepsy and reducing the massive workload of reviewing electroencephalography (EEG) recordings. In this work, a novel algorithm is developed to detect seizures employing log-Euclidean Gaussian kernel-based sparse representation (SR) in long-term EEG recordings. Unlike the traditional SR for vector data in Euclidean space, the log-Euclidean Gaussian kernel-based SR framework is proposed for seizure detection in the space of the symmetric positive definite (SPD) matrices, which form a Riemannian manifold. Since the Riemannian manifold is nonlinear, the log-Euclidean Gaussian kernel function is applied to embed it into a reproducing kernel Hilbert space (RKHS) for performing SR. The EEG signals of all channels are divided into epochs and the SPD matrices representing EEG epochs are generated by covariance descriptors. Then, the testing samples are sparsely coded over the dictionary composed by training samples utilizing log-Euclidean Gaussian kernel-based SR. The classification of testing samples is achieved by computing the minimal reconstructed residuals. The proposed method is evaluated on the Freiburg EEG dataset of 21 patients and shows its notable performance on both epoch-based and event-based assessments. Moreover, this method handles multiple channels of EEG recordings synchronously which is more speedy and efficient than traditional seizure detection methods.

Statistical model for the mechanical behavior of the tissue engineering non-woven fibrous matrices under large deformation.

Science.gov (United States)

Rizvi, Mohd Suhail; Pal, Anupam

2014-09-01

The fibrous matrices are widely used as scaffolds for the regeneration of load-bearing tissues due to their structural and mechanical similarities with the fibrous components of the extracellular matrix. These scaffolds not only provide the appropriate microenvironment for the residing cells but also act as medium for the transmission of the mechanical stimuli, essential for the tissue regeneration, from macroscopic scale of the scaffolds to the microscopic scale of cells. The requirement of the mechanical loading for the tissue regeneration requires the fibrous scaffolds to be able to sustain the complex three-dimensional mechanical loading conditions. In order to gain insight into the mechanical behavior of the fibrous matrices under large amount of elongation as well as shear, a statistical model has been formulated to study the macroscopic mechanical behavior of the electrospun fibrous matrix and the transmission of the mechanical stimuli from scaffolds to the cells via the constituting fibers. The study establishes the load-deformation relationships for the fibrous matrices for different structural parameters. It also quantifies the changes in the fiber arrangement and tension generated in the fibers with the deformation of the matrix. The model reveals that the tension generated in the fibers on matrix deformation is not homogeneous and hence the cells located in different regions of the fibrous scaffold might experience different mechanical stimuli. The mechanical response of fibrous matrices was also found to be dependent on the aspect ratio of the matrix. Therefore, the model establishes a structure-mechanics interdependence of the fibrous matrices under large deformation, which can be utilized in identifying the appropriate structure and external mechanical loading conditions for the regeneration of load-bearing tissues. Copyright © 2014 Elsevier Ltd. All rights reserved.

Optimal Couple Projections for Domain Adaptive Sparse Representation-based Classification.

Science.gov (United States)

Zhang, Guoqing; Sun, Huaijiang; Porikli, Fatih; Liu, Yazhou; Sun, Quansen

2017-08-29

In recent years, sparse representation based classification (SRC) is one of the most successful methods and has been shown impressive performance in various classification tasks. However, when the training data has a different distribution than the testing data, the learned sparse representation may not be optimal, and the performance of SRC will be degraded significantly. To address this problem, in this paper, we propose an optimal couple projections for domain-adaptive sparse representation-based classification (OCPD-SRC) method, in which the discriminative features of data in the two domains are simultaneously learned with the dictionary that can succinctly represent the training and testing data in the projected space. OCPD-SRC is designed based on the decision rule of SRC, with the objective to learn coupled projection matrices and a common discriminative dictionary such that the between-class sparse reconstruction residuals of data from both domains are maximized, and the within-class sparse reconstruction residuals of data are minimized in the projected low-dimensional space. Thus, the resulting representations can well fit SRC and simultaneously have a better discriminant ability. In addition, our method can be easily extended to multiple domains and can be kernelized to deal with the nonlinear structure of data. The optimal solution for the proposed method can be efficiently obtained following the alternative optimization method. Extensive experimental results on a series of benchmark databases show that our method is better or comparable to many state-of-the-art methods.

Frequency filtering decompositions for unsymmetric matrices and matrices with strongly varying coefficients

Energy Technology Data Exchange (ETDEWEB)

Wagner, C.

1996-12-31

In 1992, Wittum introduced the frequency filtering decompositions (FFD), which yield a fast method for the iterative solution of large systems of linear equations. Based on this method, the tangential frequency filtering decompositions (TFFD) have been developed. The TFFD allow the robust and efficient treatment of matrices with strongly varying coefficients. The existence and the convergence of the TFFD can be shown for symmetric and positive definite matrices. For a large class of matrices, it is possible to prove that the convergence rate of the TFFD and of the FFD is independent of the number of unknowns. For both methods, schemes for the construction of frequency filtering decompositions for unsymmetric matrices have been developed. Since, in contrast to Wittums`s FFD, the TFFD needs only one test vector, an adaptive test vector can be used. The TFFD with respect to the adaptive test vector can be combined with other iterative methods, e.g. multi-grid methods, in order to improve the robustness of these methods. The frequency filtering decompositions have been successfully applied to the problem of the decontamination of a heterogeneous porous medium by flushing.

Computation of large covariance matrices by SAMMY on graphical processing units and multicore CPUs

International Nuclear Information System (INIS)

Arbanas, G.; Dunn, M.E.; Wiarda, D.

2011-01-01

Computational power of Graphical Processing Units and multicore CPUs was harnessed by the nuclear data evaluation code SAMMY to speed up computations of large Resonance Parameter Covariance Matrices (RPCMs). This was accomplished by linking SAMMY to vendor-optimized implementations of the matrix-matrix multiplication subroutine of the Basic Linear Algebra Library to compute the most time-consuming step. The 235 U RPCM computed previously using a triple-nested loop was re-computed using the NVIDIA implementation of the subroutine on a single Tesla Fermi Graphical Processing Unit, and also using the Intel's Math Kernel Library implementation on two different multicore CPU systems. A multiplication of two matrices of dimensions 16,000×20,000 that had previously taken days, took approximately one minute on the GPU. Comparable performance was achieved on a dual six-core CPU system. The magnitude of the speed-up suggests that these, or similar, combinations of hardware and libraries may be useful for large matrix operations in SAMMY. Uniform interfaces of standard linear algebra libraries make them a promising candidate for a programming framework of a new generation of SAMMY for the emerging heterogeneous computing platforms. (author)

Computation of large covariance matrices by SAMMY on graphical processing units and multicore CPUs

Energy Technology Data Exchange (ETDEWEB)

Arbanas, G.; Dunn, M.E.; Wiarda, D., E-mail: arbanasg@ornl.gov, E-mail: dunnme@ornl.gov, E-mail: wiardada@ornl.gov [Oak Ridge National Laboratory, Oak Ridge, TN (United States)

2011-07-01

Computational power of Graphical Processing Units and multicore CPUs was harnessed by the nuclear data evaluation code SAMMY to speed up computations of large Resonance Parameter Covariance Matrices (RPCMs). This was accomplished by linking SAMMY to vendor-optimized implementations of the matrix-matrix multiplication subroutine of the Basic Linear Algebra Library to compute the most time-consuming step. The {sup 235}U RPCM computed previously using a triple-nested loop was re-computed using the NVIDIA implementation of the subroutine on a single Tesla Fermi Graphical Processing Unit, and also using the Intel's Math Kernel Library implementation on two different multicore CPU systems. A multiplication of two matrices of dimensions 16,000×20,000 that had previously taken days, took approximately one minute on the GPU. Comparable performance was achieved on a dual six-core CPU system. The magnitude of the speed-up suggests that these, or similar, combinations of hardware and libraries may be useful for large matrix operations in SAMMY. Uniform interfaces of standard linear algebra libraries make them a promising candidate for a programming framework of a new generation of SAMMY for the emerging heterogeneous computing platforms. (author)

A Novel CSR-Based Sparse Matrix-Vector Multiplication on GPUs

Directory of Open Access Journals (Sweden)

Guixia He

2016-01-01

Full Text Available Sparse matrix-vector multiplication (SpMV is an important operation in scientific computations. Compressed sparse row (CSR is the most frequently used format to store sparse matrices. However, CSR-based SpMVs on graphic processing units (GPUs, for example, CSR-scalar and CSR-vector, usually have poor performance due to irregular memory access patterns. This motivates us to propose a perfect CSR-based SpMV on the GPU that is called PCSR. PCSR involves two kernels and accesses CSR arrays in a fully coalesced manner by introducing a middle array, which greatly alleviates the deficiencies of CSR-scalar (rare coalescing and CSR-vector (partial coalescing. Test results on a single C2050 GPU show that PCSR fully outperforms CSR-scalar, CSR-vector, and CSRMV and HYBMV in the vendor-tuned CUSPARSE library and is comparable with a most recently proposed CSR-based algorithm, CSR-Adaptive. Furthermore, we extend PCSR on a single GPU to multiple GPUs. Experimental results on four C2050 GPUs show that no matter whether the communication between GPUs is considered or not PCSR on multiple GPUs achieves good performance and has high parallel efficiency.

Enhancing Scalability of Sparse Direct Methods

International Nuclear Information System (INIS)

Li, Xiaoye S.; Demmel, James; Grigori, Laura; Gu, Ming; Xia, Jianlin; Jardin, Steve; Sovinec, Carl; Lee, Lie-Quan

2007-01-01

TOPS is providing high-performance, scalable sparse direct solvers, which have had significant impacts on the SciDAC applications, including fusion simulation (CEMM), accelerator modeling (COMPASS), as well as many other mission-critical applications in DOE and elsewhere. Our recent developments have been focusing on new techniques to overcome scalability bottleneck of direct methods, in both time and memory. These include parallelizing symbolic analysis phase and developing linear-complexity sparse factorization methods. The new techniques will make sparse direct methods more widely usable in large 3D simulations on highly-parallel petascale computers

Sparse adaptive filters for echo cancellation

CERN Document Server

Paleologu, Constantin

2011-01-01

Adaptive filters with a large number of coefficients are usually involved in both network and acoustic echo cancellation. Consequently, it is important to improve the convergence rate and tracking of the conventional algorithms used for these applications. This can be achieved by exploiting the sparseness character of the echo paths. Identification of sparse impulse responses was addressed mainly in the last decade with the development of the so-called ``proportionate''-type algorithms. The goal of this book is to present the most important sparse adaptive filters developed for echo cancellati

Sparse distributed memory overview

Science.gov (United States)

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.

Scaling Sparse Matrices for Optimization Algorithms

OpenAIRE

Gajulapalli Ravindra S; Lasdon Leon S

2006-01-01

To iteratively solve large scale optimization problems in various contexts like planning, operations, design etc., we need to generate descent directions that are based on linear system solutions. Irrespective of the optimization algorithm or the solution method employed for the linear systems, ill conditioning introduced by problem characteristics or the algorithm or both need to be addressed. In [GL01] we used an intuitive heuristic approach in scaling linear systems that improved performan...

Accelerating Scientific Applications using High Performance Dense and Sparse Linear Algebra Kernels on GPUs

KAUST Repository

Abdelfattah, Ahmad

2015-01-15

High performance computing (HPC) platforms are evolving to more heterogeneous configurations to support the workloads of various applications. The current hardware landscape is composed of traditional multicore CPUs equipped with hardware accelerators that can handle high levels of parallelism. Graphical Processing Units (GPUs) are popular high performance hardware accelerators in modern supercomputers. GPU programming has a different model than that for CPUs, which means that many numerical kernels have to be redesigned and optimized specifically for this architecture. GPUs usually outperform multicore CPUs in some compute intensive and massively parallel applications that have regular processing patterns. However, most scientific applications rely on crucial memory-bound kernels and may witness bottlenecks due to the overhead of the memory bus latency. They can still take advantage of the GPU compute power capabilities, provided that an efficient architecture-aware design is achieved. This dissertation presents a uniform design strategy for optimizing critical memory-bound kernels on GPUs. Based on hierarchical register blocking, double buffering and latency hiding techniques, this strategy leverages the performance of a wide range of standard numerical kernels found in dense and sparse linear algebra libraries. The work presented here focuses on matrix-vector multiplication kernels (MVM) as repre- sentative and most important memory-bound operations in this context. Each kernel inherits the benefits of the proposed strategies. By exposing a proper set of tuning parameters, the strategy is flexible enough to suit different types of matrices, ranging from large dense matrices, to sparse matrices with dense block structures, while high performance is maintained. Furthermore, the tuning parameters are used to maintain the relative performance across different GPU architectures. Multi-GPU acceleration is proposed to scale the performance on several devices. The

Efficient Statistical Extraction of the Per-Unit-Length Capacitance and Inductance Matrices of Cables with Random Parameters

Directory of Open Access Journals (Sweden)

P. Manfredi

2015-05-01

Full Text Available Cable bundles often exhibit random parameter variations due to uncertain or uncontrollable physical properties and wire positioning. Efficient tools, based on the so-called polynomial chaos, exist to rapidly assess the impact of such variations on the per-unit-length capacitance and inductance matrices, and on the pertinent cable response. Nevertheless, the state-of-the-art method for the statistical extraction of the per-unit-length capacitance and inductance matrices of cables suffers from several inefficiencies that hinder its applicability to large problems, in terms of number of random parameters and/or conductors. This paper presents an improved methodology that overcomes the aforementioned limitations by exploiting a recently-published, alternative approach to generate the pertinent polynomial chaos system of equations. A sparse and decoupled system is obtained that provides remarkable benefits in terms of speed, memory consumption and problem size that can be dealt with. The technique is thoroughly validated through the statistical analysis of two canonical structures, i.e. a ribbon cable and a shielded cable with random geometry and position.

Inverse m-matrices and ultrametric matrices

CERN Document Server

Dellacherie, Claude; San Martin, Jaime

2014-01-01

The study of M-matrices, their inverses and discrete potential theory is now a well-established part of linear algebra and the theory of Markov chains. The main focus of this monograph is the so-called inverse M-matrix problem, which asks for a characterization of nonnegative matrices whose inverses are M-matrices. We present an answer in terms of discrete potential theory based on the Choquet-Deny Theorem. A distinguished subclass of inverse M-matrices is ultrametric matrices, which are important in applications such as taxonomy. Ultrametricity is revealed to be a relevant concept in linear algebra and discrete potential theory because of its relation with trees in graph theory and mean expected value matrices in probability theory. Remarkable properties of Hadamard functions and products for the class of inverse M-matrices are developed and probabilistic insights are provided throughout the monograph.

Multi-Frequency Polarimetric SAR Classification Based on Riemannian Manifold and Simultaneous Sparse Representation

Directory of Open Access Journals (Sweden)

Fan Yang

2015-07-01

Full Text Available Normally, polarimetric SAR classification is a high-dimensional nonlinear mapping problem. In the realm of pattern recognition, sparse representation is a very efficacious and powerful approach. As classical descriptors of polarimetric SAR, covariance and coherency matrices are Hermitian semidefinite and form a Riemannian manifold. Conventional Euclidean metrics are not suitable for a Riemannian manifold, and hence, normal sparse representation classification cannot be applied to polarimetric SAR directly. This paper proposes a new land cover classification approach for polarimetric SAR. There are two principal novelties in this paper. First, a Stein kernel on a Riemannian manifold instead of Euclidean metrics, combined with sparse representation, is employed for polarimetric SAR land cover classification. This approach is named Stein-sparse representation-based classification (SRC. Second, using simultaneous sparse representation and reasonable assumptions of the correlation of representation among different frequency bands, Stein-SRC is generalized to simultaneous Stein-SRC for multi-frequency polarimetric SAR classification. These classifiers are assessed using polarimetric SAR images from the Airborne Synthetic Aperture Radar (AIRSAR sensor of the Jet Propulsion Laboratory (JPL and the Electromagnetics Institute Synthetic Aperture Radar (EMISAR sensor of the Technical University of Denmark (DTU. Experiments on single-band and multi-band data both show that these approaches acquire more accurate classification results in comparison to many conventional and advanced classifiers.

Massive Asynchronous Parallelization of Sparse Matrix Factorizations

Energy Technology Data Exchange (ETDEWEB)

Chow, Edmond [Georgia Inst. of Technology, Atlanta, GA (United States)

2018-01-08

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.

Free probability and random matrices

CERN Document Server

Mingo, James A

2017-01-01

This volume opens the world of free probability to a wide variety of readers. From its roots in the theory of operator algebras, free probability has intertwined with non-crossing partitions, random matrices, applications in wireless communications, representation theory of large groups, quantum groups, the invariant subspace problem, large deviations, subfactors, and beyond. This book puts a special emphasis on the relation of free probability to random matrices, but also touches upon the operator algebraic, combinatorial, and analytic aspects of the theory. The book serves as a combination textbook/research monograph, with self-contained chapters, exercises scattered throughout the text, and coverage of important ongoing progress of the theory. It will appeal to graduate students and all mathematicians interested in random matrices and free probability from the point of view of operator algebras, combinatorics, analytic functions, or applications in engineering and statistical physics.

Sample size reduction in groundwater surveys via sparse data assimilation

KAUST Repository

Hussain, Z.; Muhammad, A.

2013-01-01

In this paper, we focus on sparse signal recovery methods for data assimilation in groundwater models. The objective of this work is to exploit the commonly understood spatial sparsity in hydrodynamic models and thereby reduce the number of measurements to image a dynamic groundwater profile. To achieve this we employ a Bayesian compressive sensing framework that lets us adaptively select the next measurement to reduce the estimation error. An extension to the Bayesian compressive sensing framework is also proposed which incorporates the additional model information to estimate system states from even lesser measurements. Instead of using cumulative imaging-like measurements, such as those used in standard compressive sensing, we use sparse binary matrices. This choice of measurements can be interpreted as randomly sampling only a small subset of dug wells at each time step, instead of sampling the entire grid. Therefore, this framework offers groundwater surveyors a significant reduction in surveying effort without compromising the quality of the survey. © 2013 IEEE.

Sample size reduction in groundwater surveys via sparse data assimilation

KAUST Repository

Hussain, Z.

2013-04-01

In this paper, we focus on sparse signal recovery methods for data assimilation in groundwater models. The objective of this work is to exploit the commonly understood spatial sparsity in hydrodynamic models and thereby reduce the number of measurements to image a dynamic groundwater profile. To achieve this we employ a Bayesian compressive sensing framework that lets us adaptively select the next measurement to reduce the estimation error. An extension to the Bayesian compressive sensing framework is also proposed which incorporates the additional model information to estimate system states from even lesser measurements. Instead of using cumulative imaging-like measurements, such as those used in standard compressive sensing, we use sparse binary matrices. This choice of measurements can be interpreted as randomly sampling only a small subset of dug wells at each time step, instead of sampling the entire grid. Therefore, this framework offers groundwater surveyors a significant reduction in surveying effort without compromising the quality of the survey. © 2013 IEEE.

Tensor-GMRES method for large sparse systems of nonlinear equations

Science.gov (United States)

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.

Chequered surfaces and complex matrices

International Nuclear Information System (INIS)

Morris, T.R.; Southampton Univ.

1991-01-01

We investigate a large-N matrix model involving general complex matrices. It can be reinterpreted as a model of two hermitian matrices with specific couplings, and as a model of positive definite hermitian matrices. Large-N perturbation theory generates dynamical triangulations in which the triangles can be chequered (i.e. coloured so that neighbours are opposite colours). On a sphere there is a simple relation between such triangulations and those generated by the single hermitian matrix model. For the torus (and a quartic potential) we solve the counting problem for the number of triangulations that cannot be quechered. The critical physics of chequered triangulations is the same as that of the hermitian matrix model. We show this explicitly by solving non-perturbatively pure two-dimensional ''chequered'' gravity. The interpretative framework given here applies to a number of other generalisations of the hermitian matrix model. (orig.)

A fast algorithm for sparse matrix computations related to inversion

International Nuclear Information System (INIS)

Li, S.; Wu, W.; Darve, E.

2013-01-01

We have developed a fast algorithm for computing certain entries of the inverse of a sparse matrix. Such computations are critical to many applications, such as the calculation of non-equilibrium Green’s functions G r and G for nano-devices. The FIND (Fast Inverse using Nested Dissection) algorithm is optimal in the big-O sense. However, in practice, FIND suffers from two problems due to the width-2 separators used by its partitioning scheme. One problem is the presence of a large constant factor in the computational cost of FIND. The other problem is that the partitioning scheme used by FIND is incompatible with most existing partitioning methods and libraries for nested dissection, which all use width-1 separators. Our new algorithm resolves these problems by thoroughly decomposing the computation process such that width-1 separators can be used, resulting in a significant speedup over FIND for realistic devices — up to twelve-fold in simulation. The new algorithm also has the added advantage that desired off-diagonal entries can be computed for free. Consequently, our algorithm is faster than the current state-of-the-art recursive methods for meshes of any size. Furthermore, the framework used in the analysis of our algorithm is the first attempt to explicitly apply the widely-used relationship between mesh nodes and matrix computations to the problem of multiple eliminations with reuse of intermediate results. This framework makes our algorithm easier to generalize, and also easier to compare against other methods related to elimination trees. Finally, our accuracy analysis shows that the algorithms that require back-substitution are subject to significant extra round-off errors, which become extremely large even for some well-conditioned matrices or matrices with only moderately large condition numbers. When compared to these back-substitution algorithms, our algorithm is generally a few orders of magnitude more accurate, and our produced round-off errors

A fast algorithm for sparse matrix computations related to inversion

Energy Technology Data Exchange (ETDEWEB)

Li, S., E-mail: lisong@stanford.edu [Institute for Computational and Mathematical Engineering, Stanford University, 496 Lomita Mall, Durand Building, Stanford, CA 94305 (United States); Wu, W. [Department of Electrical Engineering, Stanford University, 350 Serra Mall, Packard Building, Room 268, Stanford, CA 94305 (United States); Darve, E. [Institute for Computational and Mathematical Engineering, Stanford University, 496 Lomita Mall, Durand Building, Stanford, CA 94305 (United States); Department of Mechanical Engineering, Stanford University, 496 Lomita Mall, Durand Building, Room 209, Stanford, CA 94305 (United States)

2013-06-01

We have developed a fast algorithm for computing certain entries of the inverse of a sparse matrix. Such computations are critical to many applications, such as the calculation of non-equilibrium Green’s functions G{sup r} and G{sup <} for nano-devices. The FIND (Fast Inverse using Nested Dissection) algorithm is optimal in the big-O sense. However, in practice, FIND suffers from two problems due to the width-2 separators used by its partitioning scheme. One problem is the presence of a large constant factor in the computational cost of FIND. The other problem is that the partitioning scheme used by FIND is incompatible with most existing partitioning methods and libraries for nested dissection, which all use width-1 separators. Our new algorithm resolves these problems by thoroughly decomposing the computation process such that width-1 separators can be used, resulting in a significant speedup over FIND for realistic devices — up to twelve-fold in simulation. The new algorithm also has the added advantage that desired off-diagonal entries can be computed for free. Consequently, our algorithm is faster than the current state-of-the-art recursive methods for meshes of any size. Furthermore, the framework used in the analysis of our algorithm is the first attempt to explicitly apply the widely-used relationship between mesh nodes and matrix computations to the problem of multiple eliminations with reuse of intermediate results. This framework makes our algorithm easier to generalize, and also easier to compare against other methods related to elimination trees. Finally, our accuracy analysis shows that the algorithms that require back-substitution are subject to significant extra round-off errors, which become extremely large even for some well-conditioned matrices or matrices with only moderately large condition numbers. When compared to these back-substitution algorithms, our algorithm is generally a few orders of magnitude more accurate, and our produced round

A new scheduling algorithm for parallel sparse LU factorization with static pivoting

Energy Technology Data Exchange (ETDEWEB)

Grigori, Laura; Li, Xiaoye S.

2002-08-20

In this paper we present a static scheduling algorithm for parallel sparse LU factorization with static pivoting. The algorithm is divided into mapping and scheduling phases, using the symmetric pruned graphs of L' and U to represent dependencies. The scheduling algorithm is designed for driving the parallel execution of the factorization on a distributed-memory architecture. Experimental results and comparisons with SuperLU{_}DIST are reported after applying this algorithm on real world application matrices on an IBM SP RS/6000 distributed memory machine.

Manifold regularization for sparse unmixing of hyperspectral images.

Science.gov (United States)

Liu, Junmin; Zhang, Chunxia; Zhang, Jiangshe; Li, Huirong; Gao, Yuelin

2016-01-01

Recently, sparse unmixing has been successfully applied to spectral mixture analysis of remotely sensed hyperspectral images. Based on the assumption that the observed image signatures can be expressed in the form of linear combinations of a number of pure spectral signatures known in advance, unmixing of each mixed pixel in the scene is to find an optimal subset of signatures in a very large spectral library, which is cast into the framework of sparse regression. However, traditional sparse regression models, such as collaborative sparse regression , ignore the intrinsic geometric structure in the hyperspectral data. In this paper, we propose a novel model, called manifold regularized collaborative sparse regression , by introducing a manifold regularization to the collaborative sparse regression model. The manifold regularization utilizes a graph Laplacian to incorporate the locally geometrical structure of the hyperspectral data. An algorithm based on alternating direction method of multipliers has been developed for the manifold regularized collaborative sparse regression model. Experimental results on both the simulated and real hyperspectral data sets have demonstrated the effectiveness of our proposed model.

Solution methods for large systems of linear equations in BACCHUS

International Nuclear Information System (INIS)

Homann, C.; Dorr, B.

1993-05-01

The computer programme BACCHUS is used to describe steady state and transient thermal-hydraulic behaviour of a coolant in a fuel element with intact geometry in a fast breeder reactor. In such computer programmes generally large systems of linear equations with sparse matrices of coefficients, resulting from discretization of coolant conservation equations, must be solved thousands of times giving rise to large demands of main storage and CPU time. Direct and iterative solution methods of the systems of linear equations, available in BACCHUS, are described, giving theoretical details and experience with their use in the programme. Besides use of a method of lines, a Runge-Kutta-method, for solution of the partial differential equation is outlined. (orig.) [de

Semiparametric estimation of covariance matrices for longitudinal data.

Science.gov (United States)

Fan, Jianqing; Wu, Yichao

2008-12-01

Estimation of longitudinal data covariance structure poses significant challenges because the data are usually collected at irregular time points. A viable semiparametric model for covariance matrices was proposed in Fan, Huang and Li (2007) that allows one to estimate the variance function nonparametrically and to estimate the correlation function parametrically via aggregating information from irregular and sparse data points within each subject. However, the asymptotic properties of their quasi-maximum likelihood estimator (QMLE) of parameters in the covariance model are largely unknown. In the current work, we address this problem in the context of more general models for the conditional mean function including parametric, nonparametric, or semi-parametric. We also consider the possibility of rough mean regression function and introduce the difference-based method to reduce biases in the context of varying-coefficient partially linear mean regression models. This provides a more robust estimator of the covariance function under a wider range of situations. Under some technical conditions, consistency and asymptotic normality are obtained for the QMLE of the parameters in the correlation function. Simulation studies and a real data example are used to illustrate the proposed approach.

Robust Face Recognition Via Gabor Feature and Sparse Representation

Directory of Open Access Journals (Sweden)

Hao Yu-Juan

2016-01-01

Full Text Available Sparse representation based on compressed sensing theory has been widely used in the field of face recognition, and has achieved good recognition results. but the face feature extraction based on sparse representation is too simple, and the sparse coefficient is not sparse. In this paper, we improve the classification algorithm based on the fusion of sparse representation and Gabor feature, and then improved algorithm for Gabor feature which overcomes the problem of large dimension of the vector dimension, reduces the computation and storage cost, and enhances the robustness of the algorithm to the changes of the environment.The classification efficiency of sparse representation is determined by the collaborative representation,we simplify the sparse constraint based on L1 norm to the least square constraint, which makes the sparse coefficients both positive and reduce the complexity of the algorithm. Experimental results show that the proposed method is robust to illumination, facial expression and pose variations of face recognition, and the recognition rate of the algorithm is improved.

Semi-supervised sparse coding

KAUST Repository

Wang, Jim Jing-Yan; Gao, Xin

2014-01-01

Sparse coding approximates the data sample as a sparse linear combination of some basic codewords and uses the sparse codes as new presentations. In this paper, we investigate learning discriminative sparse codes by sparse coding in a semi-supervised manner, where only a few training samples are labeled. By using the manifold structure spanned by the data set of both labeled and unlabeled samples and the constraints provided by the labels of the labeled samples, we learn the variable class labels for all the samples. Furthermore, to improve the discriminative ability of the learned sparse codes, we assume that the class labels could be predicted from the sparse codes directly using a linear classifier. By solving the codebook, sparse codes, class labels and classifier parameters simultaneously in a unified objective function, we develop a semi-supervised sparse coding algorithm. Experiments on two real-world pattern recognition problems demonstrate the advantage of the proposed methods over supervised sparse coding methods on partially labeled data sets.

Semi-supervised sparse coding

KAUST Repository

Wang, Jim Jing-Yan

2014-07-06

Sparse coding approximates the data sample as a sparse linear combination of some basic codewords and uses the sparse codes as new presentations. In this paper, we investigate learning discriminative sparse codes by sparse coding in a semi-supervised manner, where only a few training samples are labeled. By using the manifold structure spanned by the data set of both labeled and unlabeled samples and the constraints provided by the labels of the labeled samples, we learn the variable class labels for all the samples. Furthermore, to improve the discriminative ability of the learned sparse codes, we assume that the class labels could be predicted from the sparse codes directly using a linear classifier. By solving the codebook, sparse codes, class labels and classifier parameters simultaneously in a unified objective function, we develop a semi-supervised sparse coding algorithm. Experiments on two real-world pattern recognition problems demonstrate the advantage of the proposed methods over supervised sparse coding methods on partially labeled data sets.

Minimax Rate-optimal Estimation of High-dimensional Covariance Matrices with Incomplete Data.

Science.gov (United States)

Cai, T Tony; Zhang, Anru

2016-09-01

Missing data occur frequently in a wide range of applications. In this paper, we consider estimation of high-dimensional covariance matrices in the presence of missing observations under a general missing completely at random model in the sense that the missingness is not dependent on the values of the data. Based on incomplete data, estimators for bandable and sparse covariance matrices are proposed and their theoretical and numerical properties are investigated. Minimax rates of convergence are established under the spectral norm loss and the proposed estimators are shown to be rate-optimal under mild regularity conditions. Simulation studies demonstrate that the estimators perform well numerically. The methods are also illustrated through an application to data from four ovarian cancer studies. The key technical tools developed in this paper are of independent interest and potentially useful for a range of related problems in high-dimensional statistical inference with missing data.

Minimax Rate-optimal Estimation of High-dimensional Covariance Matrices with Incomplete Data*

Science.gov (United States)

Cai, T. Tony; Zhang, Anru

2016-01-01

Missing data occur frequently in a wide range of applications. In this paper, we consider estimation of high-dimensional covariance matrices in the presence of missing observations under a general missing completely at random model in the sense that the missingness is not dependent on the values of the data. Based on incomplete data, estimators for bandable and sparse covariance matrices are proposed and their theoretical and numerical properties are investigated. Minimax rates of convergence are established under the spectral norm loss and the proposed estimators are shown to be rate-optimal under mild regularity conditions. Simulation studies demonstrate that the estimators perform well numerically. The methods are also illustrated through an application to data from four ovarian cancer studies. The key technical tools developed in this paper are of independent interest and potentially useful for a range of related problems in high-dimensional statistical inference with missing data. PMID:27777471

In Defense of Sparse Tracking: Circulant Sparse Tracker

KAUST Repository

Zhang, Tianzhu; Bibi, Adel Aamer; Ghanem, Bernard

2016-01-01

Sparse representation has been introduced to visual tracking by finding the best target candidate with minimal reconstruction error within the particle filter framework. However, most sparse representation based trackers have high computational cost, less than promising tracking performance, and limited feature representation. To deal with the above issues, we propose a novel circulant sparse tracker (CST), which exploits circulant target templates. Because of the circulant structure property, CST has the following advantages: (1) It can refine and reduce particles using circular shifts of target templates. (2) The optimization can be efficiently solved entirely in the Fourier domain. (3) High dimensional features can be embedded into CST to significantly improve tracking performance without sacrificing much computation time. Both qualitative and quantitative evaluations on challenging benchmark sequences demonstrate that CST performs better than all other sparse trackers and favorably against state-of-the-art methods.

In Defense of Sparse Tracking: Circulant Sparse Tracker

KAUST Repository

Zhang, Tianzhu

2016-12-13

Sparse representation has been introduced to visual tracking by finding the best target candidate with minimal reconstruction error within the particle filter framework. However, most sparse representation based trackers have high computational cost, less than promising tracking performance, and limited feature representation. To deal with the above issues, we propose a novel circulant sparse tracker (CST), which exploits circulant target templates. Because of the circulant structure property, CST has the following advantages: (1) It can refine and reduce particles using circular shifts of target templates. (2) The optimization can be efficiently solved entirely in the Fourier domain. (3) High dimensional features can be embedded into CST to significantly improve tracking performance without sacrificing much computation time. Both qualitative and quantitative evaluations on challenging benchmark sequences demonstrate that CST performs better than all other sparse trackers and favorably against state-of-the-art methods.

Deformable segmentation via sparse representation and dictionary learning.

Science.gov (United States)

Zhang, Shaoting; Zhan, Yiqiang; Metaxas, Dimitris N

2012-10-01

"Shape" and "appearance", the two pillars of a deformable model, complement each other in object segmentation. In many medical imaging applications, while the low-level appearance information is weak or mis-leading, shape priors play a more important role to guide a correct segmentation, thanks to the strong shape characteristics of biological structures. Recently a novel shape prior modeling method has been proposed based on sparse learning theory. Instead of learning a generative shape model, shape priors are incorporated on-the-fly through the sparse shape composition (SSC). SSC is robust to non-Gaussian errors and still preserves individual shape characteristics even when such characteristics is not statistically significant. Although it seems straightforward to incorporate SSC into a deformable segmentation framework as shape priors, the large-scale sparse optimization of SSC has low runtime efficiency, which cannot satisfy clinical requirements. In this paper, we design two strategies to decrease the computational complexity of SSC, making a robust, accurate and efficient deformable segmentation system. (1) When the shape repository contains a large number of instances, which is often the case in 2D problems, K-SVD is used to learn a more compact but still informative shape dictionary. (2) If the derived shape instance has a large number of vertices, which often appears in 3D problems, an affinity propagation method is used to partition the surface into small sub-regions, on which the sparse shape composition is performed locally. Both strategies dramatically decrease the scale of the sparse optimization problem and hence speed up the algorithm. Our method is applied on a diverse set of biomedical image analysis problems. Compared to the original SSC, these two newly-proposed modules not only significant reduce the computational complexity, but also improve the overall accuracy. Copyright © 2012 Elsevier B.V. All rights reserved.

Exhaustive Search for Sparse Variable Selection in Linear Regression

Science.gov (United States)

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.

Formal matrices

CERN Document Server

Krylov, Piotr

2017-01-01

This monograph is a comprehensive account of formal matrices, examining homological properties of modules over formal matrix rings and summarising the interplay between Morita contexts and K theory. While various special types of formal matrix rings have been studied for a long time from several points of view and appear in various textbooks, for instance to examine equivalences of module categories and to illustrate rings with one-sided non-symmetric properties, this particular class of rings has, so far, not been treated systematically. Exploring formal matrix rings of order 2 and introducing the notion of the determinant of a formal matrix over a commutative ring, this monograph further covers the Grothendieck and Whitehead groups of rings. Graduate students and researchers interested in ring theory, module theory and operator algebras will find this book particularly valuable. Containing numerous examples, Formal Matrices is a largely self-contained and accessible introduction to the topic, assuming a sol...

Iterative algorithms for large sparse linear systems on parallel computers

Science.gov (United States)

Adams, L. M.

1982-01-01

Algorithms for assembling in parallel the sparse system of linear equations that result from finite difference or finite element discretizations of elliptic partial differential equations, such as those that arise in structural engineering are developed. Parallel linear stationary iterative algorithms and parallel preconditioned conjugate gradient algorithms are developed for solving these systems. In addition, a model for comparing parallel algorithms on array architectures is developed and results of this model for the algorithms are given.

Theoretical Properties for Neural Networks with Weight Matrices of Low Displacement Rank

OpenAIRE

Zhao, Liang; Liao, Siyu; Wang, Yanzhi; Li, Zhe; Tang, Jian; Pan, Victor; Yuan, Bo

2017-01-01

Recently low displacement rank (LDR) matrices, or so-called structured matrices, have been proposed to compress large-scale neural networks. Empirical results have shown that neural networks with weight matrices of LDR matrices, referred as LDR neural networks, can achieve significant reduction in space and computational complexity while retaining high accuracy. We formally study LDR matrices in deep learning. First, we prove the universal approximation property of LDR neural networks with a ...

Efficient coordinated recovery of sparse channels in massive MIMO

KAUST Repository

Masood, Mudassir

2015-01-01

This paper addresses the problem of estimating sparse channels in massive MIMO-OFDM systems. Most wireless channels are sparse in nature with large delay spread. In addition, these channels as observed by multiple antennas in a neighborhood have approximately common support. The sparsity and common support properties are attractive when it comes to the efficient estimation of large number of channels in massive MIMO systems. Moreover, to avoid pilot contamination and to achieve better spectral efficiency, it is important to use a small number of pilots. We present a novel channel estimation approach which utilizes the sparsity and common support properties to estimate sparse channels and requires a small number of pilots. Two algorithms based on this approach have been developed that perform Bayesian estimates of sparse channels even when the prior is non-Gaussian or unknown. Neighboring antennas share among each other their beliefs about the locations of active channel taps to perform estimation. The coordinated approach improves channel estimates and also reduces the required number of pilots. Further improvement is achieved by the data-aided version of the algorithm. Extensive simulation results are provided to demonstrate the performance of the proposed algorithms.

Object tracking by occlusion detection via structured sparse learning

KAUST Repository

Zhang, Tianzhu

2013-06-01

Sparse representation based methods have recently drawn much attention in visual tracking due to good performance against illumination variation and occlusion. They assume the errors caused by image variations can be modeled as pixel-wise sparse. However, in many practical scenarios these errors are not truly pixel-wise sparse but rather sparsely distributed in a structured way. In fact, pixels in error constitute contiguous regions within the object\\'s track. This is the case when significant occlusion occurs. To accommodate for non-sparse occlusion in a given frame, we assume that occlusion detected in previous frames can be propagated to the current one. This propagated information determines which pixels will contribute to the sparse representation of the current track. In other words, pixels that were detected as part of an occlusion in the previous frame will be removed from the target representation process. As such, this paper proposes a novel tracking algorithm that models and detects occlusion through structured sparse learning. We test our tracker on challenging benchmark sequences, such as sports videos, which involve heavy occlusion, drastic illumination changes, and large pose variations. Experimental results show that our tracker consistently outperforms the state-of-the-art. © 2013 IEEE.

In-Storage Embedded Accelerator for Sparse Pattern Processing

OpenAIRE

Jun, Sang-Woo; Nguyen, Huy T.; Gadepally, Vijay N.; Arvind

2016-01-01

We present a novel architecture for sparse pattern processing, using flash storage with embedded accelerators. Sparse pattern processing on large data sets is the essence of applications such as document search, natural language processing, bioinformatics, subgraph matching, machine learning, and graph processing. One slice of our prototype accelerator is capable of handling up to 1TB of data, and experiments show that it can outperform C/C++ software solutions on a 16-core system at a fracti...

Process Knowledge Discovery Using Sparse Principal Component Analysis

DEFF Research Database (Denmark)

Gao, Huihui; Gajjar, Shriram; Kulahci, Murat

2016-01-01

As the goals of ensuring process safety and energy efficiency become ever more challenging, engineers increasingly rely on data collected from such processes for informed decision making. During recent decades, extracting and interpreting valuable process information from large historical data sets...... SPCA approach that helps uncover the underlying process knowledge regarding variable relations. This approach systematically determines the optimal sparse loadings for each sparse PC while improving interpretability and minimizing information loss. The salient features of the proposed approach...

A sparse matrix based full-configuration interaction algorithm

International Nuclear Information System (INIS)

Rolik, Zoltan; Szabados, Agnes; Surjan, Peter R.

2008-01-01

We present an algorithm related to the full-configuration interaction (FCI) method that makes complete use of the sparse nature of the coefficient vector representing the many-electron wave function in a determinantal basis. Main achievements of the presented sparse FCI (SFCI) algorithm are (i) development of an iteration procedure that avoids the storage of FCI size vectors; (ii) development of an efficient algorithm to evaluate the effect of the Hamiltonian when both the initial and the product vectors are sparse. As a result of point (i) large disk operations can be skipped which otherwise may be a bottleneck of the procedure. At point (ii) we progress by adopting the implementation of the linear transformation by Olsen et al. [J. Chem Phys. 89, 2185 (1988)] for the sparse case, getting the algorithm applicable to larger systems and faster at the same time. The error of a SFCI calculation depends only on the dropout thresholds for the sparse vectors, and can be tuned by controlling the amount of system memory passed to the procedure. The algorithm permits to perform FCI calculations on single node workstations for systems previously accessible only by supercomputers

Fast sparsely synchronized brain rhythms in a scale-free neural network.

Science.gov (United States)

Kim, Sang-Yoon; Lim, Woochang

2015-08-01

We consider a directed version of the Barabási-Albert scale-free network model with symmetric preferential attachment with the same in- and out-degrees and study the emergence of sparsely synchronized rhythms for a fixed attachment degree in an inhibitory population of fast-spiking Izhikevich interneurons. Fast sparsely synchronized rhythms with stochastic and intermittent neuronal discharges are found to appear for large values of J (synaptic inhibition strength) and D (noise intensity). For an intensive study we fix J at a sufficiently large value and investigate the population states by increasing D. For small D, full synchronization with the same population-rhythm frequency fp and mean firing rate (MFR) fi of individual neurons occurs, while for large D partial synchronization with fp>〈fi〉 (〈fi〉: ensemble-averaged MFR) appears due to intermittent discharge of individual neurons; in particular, the case of fp>4〈fi〉 is referred to as sparse synchronization. For the case of partial and sparse synchronization, MFRs of individual neurons vary depending on their degrees. As D passes a critical value D* (which is determined by employing an order parameter), a transition to unsynchronization occurs due to the destructive role of noise to spoil the pacing between sparse spikes. For Dsparse synchronization do contributions of individual neuronal dynamics to population synchronization change depending on their degrees, unlike in the case of full synchronization. Consequently, dynamics of individual neurons reveal the inhomogeneous network structure for the case of partial and sparse synchronization, which is in contrast to the case of

Fast sparsely synchronized brain rhythms in a scale-free neural network

Science.gov (United States)

Kim, Sang-Yoon; Lim, Woochang

2015-08-01

We consider a directed version of the Barabási-Albert scale-free network model with symmetric preferential attachment with the same in- and out-degrees and study the emergence of sparsely synchronized rhythms for a fixed attachment degree in an inhibitory population of fast-spiking Izhikevich interneurons. Fast sparsely synchronized rhythms with stochastic and intermittent neuronal discharges are found to appear for large values of J (synaptic inhibition strength) and D (noise intensity). For an intensive study we fix J at a sufficiently large value and investigate the population states by increasing D . For small D , full synchronization with the same population-rhythm frequency fp and mean firing rate (MFR) fi of individual neurons occurs, while for large D partial synchronization with fp> ( : ensemble-averaged MFR) appears due to intermittent discharge of individual neurons; in particular, the case of fp>4 is referred to as sparse synchronization. For the case of partial and sparse synchronization, MFRs of individual neurons vary depending on their degrees. As D passes a critical value D* (which is determined by employing an order parameter), a transition to unsynchronization occurs due to the destructive role of noise to spoil the pacing between sparse spikes. For D sparse synchronization do contributions of individual neuronal dynamics to population synchronization change depending on their degrees, unlike in the case of full synchronization. Consequently, dynamics of individual neurons reveal the inhomogeneous network structure for the case of partial and sparse synchronization, which is in contrast to the case of statistically homogeneous

Structural Sparse Tracking

KAUST Repository

Zhang, Tianzhu

2015-06-01

Sparse representation has been applied to visual tracking by finding the best target candidate with minimal reconstruction error by use of target templates. However, most sparse representation based trackers only consider holistic or local representations and do not make full use of the intrinsic structure among and inside target candidates, thereby making the representation less effective when similar objects appear or under occlusion. In this paper, we propose a novel Structural Sparse Tracking (SST) algorithm, which not only exploits the intrinsic relationship among target candidates and their local patches to learn their sparse representations jointly, but also preserves the spatial layout structure among the local patches inside each target candidate. We show that our SST algorithm accommodates most existing sparse trackers with the respective merits. Both qualitative and quantitative evaluations on challenging benchmark image sequences demonstrate that the proposed SST algorithm performs favorably against several state-of-the-art methods.

Averaging operations on matrices

Indian Academy of Sciences (India)

2014-07-03

Jul 3, 2014 ... Role of Positive Definite Matrices. • Diffusion Tensor Imaging: 3 × 3 pd matrices model water flow at each voxel of brain scan. • Elasticity: 6 × 6 pd matrices model stress tensors. • Machine Learning: n × n pd matrices occur as kernel matrices. Tanvi Jain. Averaging operations on matrices ...

Open vessel microwave digestion of food matrices (T6)

International Nuclear Information System (INIS)

Rhodes, L.; LeBlanc, G.

2002-01-01

Full text: Advancements in the field of open vessel microwave digestion continue to provide solutions for industries requiring acid digestion of large sample sizes. Those interesting in digesting food matrices are particularly interested in working with large amounts of sample and then diluting small final volumes. This paper will show the advantages of instantaneous regent addition and post-digestion evaporation when performing an open vessel digestion and evaporation methods for various food matrices will be presented along with analyte recovery data. (author)

Wishart and anti-Wishart random matrices

International Nuclear Information System (INIS)

Janik, Romuald A; Nowak, Maciej A

2003-01-01

We provide a compact exact representation for the distribution of the matrix elements of the Wishart-type random matrices A † A, for any finite number of rows and columns of A, without any large N approximations. In particular, we treat the case when the Wishart-type random matrix contains redundant, non-random information, which is a new result. This representation is of interest for a procedure for reconstructing the redundant information hidden in Wishart matrices, with potential applications to numerous models based on biological, social and artificial intelligence networks

BICLUSTERING METHODS FOR RE-ORDERING DATA MATRICES IN SYSTEMS BIOLOGY, DRUG DISCOVERY AND TOXICOLOGY

Directory of Open Access Journals (Sweden)

Christodoulos A. Floudas

2010-12-01

Full Text Available Biclustering has emerged as an important problem in the analysis of gene expression data since genes may only jointly respond over a subset of conditions. Many of the methods for biclustering, and clustering algorithms in general, utilize simplified models or heuristic strategies for identifying the ``best'' grouping of elements according to some metric and cluster definition and thus result in suboptimal clusters. In the first part of the presentation, we present a rigorous approach to biclustering, OREO, which is based on the Optimal RE-Ordering of the rows and columns of a data matrix so as to globally minimize the dissimilarity metric [1,2]. The physical permutations of the rows and columns of the data matrix can be modeled as either a network flow problem or a traveling salesman problem. The performance of OREO is tested on several important data matrices arising in systems biology to validate the ability of the proposed method and compare it to existing biclustering and clustering methods. In the second part of the talk, we will focus on novel methods for clustering of data matrices that are very sparse [3]. These types of data matrices arise in drug discovery where the x- and y-axis of a data matrix can correspond to different functional groups for two distinct substituent sites on a molecular scaffold. Each possible x and y pair corresponds to a single molecule which can be synthesized and tested for a certain property, such as percent inhibition of a protein function. For even moderate size matrices, synthesizing and testing a small fraction of the molecules is labor intensive and not economically feasible. Thus, it is of paramount importance to have a reliable method for guiding the synthesis process to select molecules that have a high probability of success. In the second part of the presentation, we introduce a new strategy to enable efficient substituent reordering and descriptor-free property estimation. Our approach casts

A comparison of SuperLU solvers on the intel MIC architecture

Science.gov (United States)

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.

VanderLaan Circulant Type Matrices

Directory of Open Access Journals (Sweden)

Hongyan Pan

2015-01-01

Full Text Available Circulant matrices have become a satisfactory tools in control methods for modern complex systems. In the paper, VanderLaan circulant type matrices are presented, which include VanderLaan circulant, left circulant, and g-circulant matrices. The nonsingularity of these special matrices is discussed by the surprising properties of VanderLaan numbers. The exact determinants of VanderLaan circulant type matrices are given by structuring transformation matrices, determinants of well-known tridiagonal matrices, and tridiagonal-like matrices. The explicit inverse matrices of these special matrices are obtained by structuring transformation matrices, inverses of known tridiagonal matrices, and quasi-tridiagonal matrices. Three kinds of norms and lower bound for the spread of VanderLaan circulant and left circulant matrix are given separately. And we gain the spectral norm of VanderLaan g-circulant matrix.

HLIBCov: Parallel Hierarchical Matrix Approximation of Large Covariance Matrices and Likelihoods with Applications in Parameter Identification

KAUST Repository

Litvinenko, Alexander

2017-01-01

matrices. Therefore covariance matrices are approximated in the hierarchical ($\\H$-) matrix format with computational cost $\\mathcal{O}(k^2n \\log^2 n/p)$ and storage $\\mathcal{O}(kn \\log n)$, where the rank $k$ is a small integer (typically $k<25$), $p

Occlusion detection via structured sparse learning for robust object tracking

KAUST Repository

Zhang, Tianzhu

2014-01-01

Sparse representation based methods have recently drawn much attention in visual tracking due to good performance against illumination variation and occlusion. They assume the errors caused by image variations can be modeled as pixel-wise sparse. However, in many practical scenarios, these errors are not truly pixel-wise sparse but rather sparsely distributed in a structured way. In fact, pixels in error constitute contiguous regions within the object’s track. This is the case when significant occlusion occurs. To accommodate for nonsparse occlusion in a given frame, we assume that occlusion detected in previous frames can be propagated to the current one. This propagated information determines which pixels will contribute to the sparse representation of the current track. In other words, pixels that were detected as part of an occlusion in the previous frame will be removed from the target representation process. As such, this paper proposes a novel tracking algorithm that models and detects occlusion through structured sparse learning. We test our tracker on challenging benchmark sequences, such as sports videos, which involve heavy occlusion, drastic illumination changes, and large pose variations. Extensive experimental results show that our proposed tracker consistently outperforms the state-of-the-art trackers.

JiTTree: A Just-in-Time Compiled Sparse GPU Volume Data Structure

KAUST Repository

Labschutz, Matthias

2015-08-12

Sparse volume data structures enable the efficient representation of large but sparse volumes in GPU memory for computation and visualization. However, the choice of a specific data structure for a given data set depends on several factors, such as the memory budget, the sparsity of the data, and data access patterns. In general, there is no single optimal sparse data structure, but a set of several candidates with individual strengths and drawbacks. One solution to this problem are hybrid data structures which locally adapt themselves to the sparsity. However, they typically suffer from increased traversal overhead which limits their utility in many applications. This paper presents JiTTree, a novel sparse hybrid volume data structure that uses just-in-time compilation to overcome these problems. By combining multiple sparse data structures and reducing traversal overhead we leverage their individual advantages. We demonstrate that hybrid data structures adapt well to a large range of data sets. They are especially superior to other sparse data structures for data sets that locally vary in sparsity. Possible optimization criteria are memory, performance and a combination thereof. Through just-in-time (JIT) compilation, JiTTree reduces the traversal overhead of the resulting optimal data structure. As a result, our hybrid volume data structure enables efficient computations on the GPU, while being superior in terms of memory usage when compared to non-hybrid data structures.

JiTTree: A Just-in-Time Compiled Sparse GPU Volume Data Structure

KAUST Repository

Labschutz, Matthias; Bruckner, Stefan; Groller, M. Eduard; Hadwiger, Markus; Rautek, Peter

2015-01-01

Sparse volume data structures enable the efficient representation of large but sparse volumes in GPU memory for computation and visualization. However, the choice of a specific data structure for a given data set depends on several factors, such as the memory budget, the sparsity of the data, and data access patterns. In general, there is no single optimal sparse data structure, but a set of several candidates with individual strengths and drawbacks. One solution to this problem are hybrid data structures which locally adapt themselves to the sparsity. However, they typically suffer from increased traversal overhead which limits their utility in many applications. This paper presents JiTTree, a novel sparse hybrid volume data structure that uses just-in-time compilation to overcome these problems. By combining multiple sparse data structures and reducing traversal overhead we leverage their individual advantages. We demonstrate that hybrid data structures adapt well to a large range of data sets. They are especially superior to other sparse data structures for data sets that locally vary in sparsity. Possible optimization criteria are memory, performance and a combination thereof. Through just-in-time (JIT) compilation, JiTTree reduces the traversal overhead of the resulting optimal data structure. As a result, our hybrid volume data structure enables efficient computations on the GPU, while being superior in terms of memory usage when compared to non-hybrid data structures.

JiTTree: A Just-in-Time Compiled Sparse GPU Volume Data Structure.

Science.gov (United States)

Labschütz, Matthias; Bruckner, Stefan; Gröller, M Eduard; Hadwiger, Markus; Rautek, Peter

2016-01-01

Sparse volume data structures enable the efficient representation of large but sparse volumes in GPU memory for computation and visualization. However, the choice of a specific data structure for a given data set depends on several factors, such as the memory budget, the sparsity of the data, and data access patterns. In general, there is no single optimal sparse data structure, but a set of several candidates with individual strengths and drawbacks. One solution to this problem are hybrid data structures which locally adapt themselves to the sparsity. However, they typically suffer from increased traversal overhead which limits their utility in many applications. This paper presents JiTTree, a novel sparse hybrid volume data structure that uses just-in-time compilation to overcome these problems. By combining multiple sparse data structures and reducing traversal overhead we leverage their individual advantages. We demonstrate that hybrid data structures adapt well to a large range of data sets. They are especially superior to other sparse data structures for data sets that locally vary in sparsity. Possible optimization criteria are memory, performance and a combination thereof. Through just-in-time (JIT) compilation, JiTTree reduces the traversal overhead of the resulting optimal data structure. As a result, our hybrid volume data structure enables efficient computations on the GPU, while being superior in terms of memory usage when compared to non-hybrid data structures.

Sparse PDF Volumes for Consistent Multi-Resolution Volume Rendering

KAUST Repository

Sicat, Ronell Barrera

2014-12-31

This paper presents a new multi-resolution volume representation called sparse pdf volumes, which enables consistent multi-resolution volume rendering based on probability density functions (pdfs) of voxel neighborhoods. These pdfs are defined in the 4D domain jointly comprising the 3D volume and its 1D intensity range. Crucially, the computation of sparse pdf volumes exploits data coherence in 4D, resulting in a sparse representation with surprisingly low storage requirements. At run time, we dynamically apply transfer functions to the pdfs using simple and fast convolutions. Whereas standard low-pass filtering and down-sampling incur visible differences between resolution levels, the use of pdfs facilitates consistent results independent of the resolution level used. We describe the efficient out-of-core computation of large-scale sparse pdf volumes, using a novel iterative simplification procedure of a mixture of 4D Gaussians. Finally, our data structure is optimized to facilitate interactive multi-resolution volume rendering on GPUs.

A Projected Conjugate Gradient Method for Sparse Minimax Problems

DEFF Research Database (Denmark)

Madsen, Kaj; Jonasson, Kristjan

1993-01-01

A new method for nonlinear minimax problems is presented. The method is of the trust region type and based on sequential linear programming. It is a first order method that only uses first derivatives and does not approximate Hessians. The new method is well suited for large sparse problems...... as it only requires that software for sparse linear programming and a sparse symmetric positive definite equation solver are available. On each iteration a special linear/quadratic model of the function is minimized, but contrary to the usual practice in trust region methods the quadratic model is only...... with the method are presented. In fact, we find that the number of iterations required is comparable to that of state-of-the-art quasi-Newton codes....

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

Science.gov (United States)

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

2017-05-01

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

Point-source reconstruction with a sparse light-sensor array for optical TPC readout

International Nuclear Information System (INIS)

Rutter, G; Richards, M; Bennieston, A J; Ramachers, Y A

2011-01-01

A reconstruction technique for sparse array optical signal readout is introduced and applied to the generic challenge of large-area readout of a large number of point light sources. This challenge finds a prominent example in future, large volume neutrino detector studies based on liquid argon. It is concluded that the sparse array option may be ruled out for reasons of required number of channels when compared to a benchmark derived from charge readout on wire-planes. Smaller-scale detectors, however, could benefit from this technology.

Forecasting Covariance Matrices: A Mixed Frequency Approach

DEFF Research Database (Denmark)

Halbleib, Roxana; Voev, Valeri

This paper proposes a new method for forecasting covariance matrices of financial returns. The model mixes volatility forecasts from a dynamic model of daily realized volatilities estimated with high-frequency data with correlation forecasts based on daily data. This new approach allows for flexi......This paper proposes a new method for forecasting covariance matrices of financial returns. The model mixes volatility forecasts from a dynamic model of daily realized volatilities estimated with high-frequency data with correlation forecasts based on daily data. This new approach allows...... for flexible dependence patterns for volatilities and correlations, and can be applied to covariance matrices of large dimensions. The separate modeling of volatility and correlation forecasts considerably reduces the estimation and measurement error implied by the joint estimation and modeling of covariance...

Sparse-matrix factorizations for fast symmetric Fourier transforms

International Nuclear Information System (INIS)

Sequel, J.

1987-01-01

This work proposes new fast algorithms computing the discrete Fourier transform of certain families of symmetric sequences. Sequences commonly found in problems of structure determination by x-ray crystallography and in numerical solutions of boundary-value problems in partial differential equations are dealt with. In the algorithms presented, the redundancies in the input and output data, due to the presence of symmetries in the input data sequence, were eliminated. Using ring-theoretical methods a matrix representation is obtained for the remaining calculations; which factors as the product of a complex block-diagonal matrix times as integral matrix. A basic two-step algorithm scheme arises from this factorization with a first step consisting of pre-additions and a second step containing the calculations involved in computing with the blocks in the block-diagonal factor. These blocks are structured as block-Hankel matrices, and two sparse-matrix factoring formulas are developed in order to diminish their arithmetic complexity

Topological expansion of the chain of matrices

International Nuclear Information System (INIS)

Eynard, B.; Ferrer, A. Prats

2009-01-01

We solve the loop equations to all orders in 1/N 2 , for the Chain of Matrices matrix model (with possibly an external field coupled to the last matrix of the chain). We show that the topological expansion of the free energy, is, like for the 1 and 2-matrix model, given by the symplectic invariants of [19]. As a consequence, we find the double scaling limit explicitly, and we discuss modular properties, large N asymptotics. We also briefly discuss the limit of an infinite chain of matrices (matrix quantum mechanics).

Implementing the conjugate gradient algorithm on multi-core systems

NARCIS (Netherlands)

Wiggers, W.A.; Bakker, Vincent; Kokkeler, Andre B.J.; Smit, Gerardus Johannes Maria; Nurmi, J.; Takala, J.; Vainio, O.

2007-01-01

In linear solvers, like the conjugate gradient algorithm, sparse-matrix vector multiplication is an important kernel. Due to the sparseness of the matrices, the solver runs relatively slow. For digital optical tomography (DOT), a large set of linear equations have to be solved which currently takes

Sparse modeling of spatial environmental variables associated with asthma.

Science.gov (United States)

Chang, Timothy S; Gangnon, Ronald E; David Page, C; Buckingham, William R; Tandias, Aman; Cowan, Kelly J; Tomasallo, Carrie D; Arndt, Brian G; Hanrahan, Lawrence P; Guilbert, Theresa W

2015-02-01

Geographically distributed environmental factors influence the burden of diseases such as asthma. Our objective was to identify sparse environmental variables associated with asthma diagnosis gathered from a large electronic health record (EHR) dataset while controlling for spatial variation. An EHR dataset from the University of Wisconsin's Family Medicine, Internal Medicine and Pediatrics Departments was obtained for 199,220 patients aged 5-50years over a three-year period. Each patient's home address was geocoded to one of 3456 geographic census block groups. Over one thousand block group variables were obtained from a commercial database. We developed a Sparse Spatial Environmental Analysis (SASEA). Using this method, the environmental variables were first dimensionally reduced with sparse principal component analysis. Logistic thin plate regression spline modeling was then used to identify block group variables associated with asthma from sparse principal components. The addresses of patients from the EHR dataset were distributed throughout the majority of Wisconsin's geography. Logistic thin plate regression spline modeling captured spatial variation of asthma. Four sparse principal components identified via model selection consisted of food at home, dog ownership, household size, and disposable income variables. In rural areas, dog ownership and renter occupied housing units from significant sparse principal components were associated with asthma. Our main contribution is the incorporation of sparsity in spatial modeling. SASEA sequentially added sparse principal components to Logistic thin plate regression spline modeling. This method allowed association of geographically distributed environmental factors with asthma using EHR and environmental datasets. SASEA can be applied to other diseases with environmental risk factors. Copyright © 2014 Elsevier Inc. All rights reserved.

Fast Sparse Coding for Range Data Denoising with Sparse Ridges Constraint

Directory of Open Access Journals (Sweden)

Zhi Gao

2018-05-01

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

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

Science.gov (United States)

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

2018-05-06

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

Library designs for generic C++ sparse matrix computations of iterative methods

Energy Technology Data Exchange (ETDEWEB)

Pozo, R.

1996-12-31

A new library design is presented for generic sparse matrix C++ objects for use in iterative algorithms and preconditioners. This design extends previous work on C++ numerical libraries by providing a framework in which efficient algorithms can be written *independent* of the matrix layout or format. That is, rather than supporting different codes for each (element type) / (matrix format) combination, only one version of the algorithm need be maintained. This not only reduces the effort for library developers, but also simplifies the calling interface seen by library users. Furthermore, the underlying matrix library can be naturally extended to support user-defined objects, such as hierarchical block-structured matrices, or application-specific preconditioners. Utilizing optimized kernels whenever possible, the resulting performance of such framework can be shown to be competitive with optimized Fortran programs.

When sparse coding meets ranking: a joint framework for learning sparse codes and ranking scores

KAUST Repository

Wang, Jim Jing-Yan

2017-06-28

Sparse coding, which represents a data point as a sparse reconstruction code with regard to a dictionary, has been a popular data representation method. Meanwhile, in database retrieval problems, learning the ranking scores from data points plays an important role. Up to now, these two problems have always been considered separately, assuming that data coding and ranking are two independent and irrelevant problems. However, is there any internal relationship between sparse coding and ranking score learning? If yes, how to explore and make use of this internal relationship? In this paper, we try to answer these questions by developing the first joint sparse coding and ranking score learning algorithm. To explore the local distribution in the sparse code space, and also to bridge coding and ranking problems, we assume that in the neighborhood of each data point, the ranking scores can be approximated from the corresponding sparse codes by a local linear function. By considering the local approximation error of ranking scores, the reconstruction error and sparsity of sparse coding, and the query information provided by the user, we construct a unified objective function for learning of sparse codes, the dictionary and ranking scores. We further develop an iterative algorithm to solve this optimization problem.

Recursive nearest neighbor search in a sparse and multiscale domain for comparing audio signals

DEFF Research Database (Denmark)

Sturm, Bob L.; Daudet, Laurent

2011-01-01

We investigate recursive nearest neighbor search in a sparse domain at the scale of audio signals. Essentially, to approximate the cosine distance between the signals we make pairwise comparisons between the elements of localized sparse models built from large and redundant multiscale dictionaries...

Inference algorithms and learning theory for Bayesian sparse factor analysis

International Nuclear Information System (INIS)

Rattray, Magnus; Sharp, Kevin; Stegle, Oliver; Winn, John

2009-01-01

Bayesian sparse factor analysis has many applications; for example, it has been applied to the problem of inferring a sparse regulatory network from gene expression data. We describe a number of inference algorithms for Bayesian sparse factor analysis using a slab and spike mixture prior. These include well-established Markov chain Monte Carlo (MCMC) and variational Bayes (VB) algorithms as well as a novel hybrid of VB and Expectation Propagation (EP). For the case of a single latent factor we derive a theory for learning performance using the replica method. We compare the MCMC and VB/EP algorithm results with simulated data to the theoretical prediction. The results for MCMC agree closely with the theory as expected. Results for VB/EP are slightly sub-optimal but show that the new algorithm is effective for sparse inference. In large-scale problems MCMC is infeasible due to computational limitations and the VB/EP algorithm then provides a very useful computationally efficient alternative.

Inference algorithms and learning theory for Bayesian sparse factor analysis

Energy Technology Data Exchange (ETDEWEB)

Rattray, Magnus; Sharp, Kevin [School of Computer Science, University of Manchester, Manchester M13 9PL (United Kingdom); Stegle, Oliver [Max-Planck-Institute for Biological Cybernetics, Tuebingen (Germany); Winn, John, E-mail: magnus.rattray@manchester.ac.u [Microsoft Research Cambridge, Roger Needham Building, Cambridge, CB3 0FB (United Kingdom)

2009-12-01

Bayesian sparse factor analysis has many applications; for example, it has been applied to the problem of inferring a sparse regulatory network from gene expression data. We describe a number of inference algorithms for Bayesian sparse factor analysis using a slab and spike mixture prior. These include well-established Markov chain Monte Carlo (MCMC) and variational Bayes (VB) algorithms as well as a novel hybrid of VB and Expectation Propagation (EP). For the case of a single latent factor we derive a theory for learning performance using the replica method. We compare the MCMC and VB/EP algorithm results with simulated data to the theoretical prediction. The results for MCMC agree closely with the theory as expected. Results for VB/EP are slightly sub-optimal but show that the new algorithm is effective for sparse inference. In large-scale problems MCMC is infeasible due to computational limitations and the VB/EP algorithm then provides a very useful computationally efficient alternative.

Object tracking by occlusion detection via structured sparse learning

KAUST Repository

Zhang, Tianzhu; Ghanem, Bernard; Xu, Changsheng; Ahuja, Narendra

2013-01-01

occlusion through structured sparse learning. We test our tracker on challenging benchmark sequences, such as sports videos, which involve heavy occlusion, drastic illumination changes, and large pose variations. Experimental results show that our tracker

Asymptotic Distribution of Eigenvalues of Weakly Dilute Wishart Matrices

Energy Technology Data Exchange (ETDEWEB)

Khorunzhy, A. [Institute for Low Temperature Physics (Ukraine)], E-mail: khorunjy@ilt.kharkov.ua; Rodgers, G. J. [Brunel University, Uxbridge, Department of Mathematics and Statistics (United Kingdom)], E-mail: g.j.rodgers@brunel.ac.uk

2000-03-15

We study the eigenvalue distribution of large random matrices that are randomly diluted. We consider two random matrix ensembles that in the pure (nondilute) case have a limiting eigenvalue distribution with a singular component at the origin. These include the Wishart random matrix ensemble and Gaussian random matrices with correlated entries. Our results show that the singularity in the eigenvalue distribution is rather unstable under dilution and that even weak dilution destroys it.

Infinite matrices and sequence spaces

CERN Document Server

Cooke, Richard G

2014-01-01

This clear and correct summation of basic results from a specialized field focuses on the behavior of infinite matrices in general, rather than on properties of special matrices. Three introductory chapters guide students to the manipulation of infinite matrices, covering definitions and preliminary ideas, reciprocals of infinite matrices, and linear equations involving infinite matrices.From the fourth chapter onward, the author treats the application of infinite matrices to the summability of divergent sequences and series from various points of view. Topics include consistency, mutual consi

A novel method to design sparse linear arrays for ultrasonic phased array.

Science.gov (United States)

Yang, Ping; Chen, Bin; Shi, Ke-Ren

2006-12-22

In ultrasonic phased array testing, a sparse array can increase the resolution by enlarging the aperture without adding system complexity. Designing a sparse array involves choosing the best or a better configuration from a large number of candidate arrays. We firstly designed sparse arrays by using a genetic algorithm, but found that the arrays have poor performance and poor consistency. So, a method based on the Minimum Redundancy Linear Array was then adopted. Some elements are determined by the minimum-redundancy array firstly in order to ensure spatial resolution and then a genetic algorithm is used to optimize the remaining elements. Sparse arrays designed by this method have much better performance and consistency compared to the arrays designed only by a genetic algorithm. Both simulation and experiment confirm the effectiveness.

Atmospheric inverse modeling via sparse reconstruction

Science.gov (United States)

Hase, Nils; Miller, Scot M.; Maaß, Peter; Notholt, Justus; Palm, Mathias; Warneke, Thorsten

2017-10-01

Many applications in atmospheric science involve ill-posed inverse problems. A crucial component of many inverse problems is the proper formulation of a priori knowledge about the unknown parameters. In most cases, this knowledge is expressed as a Gaussian prior. This formulation often performs well at capturing smoothed, large-scale processes but is often ill equipped to capture localized structures like large point sources or localized hot spots. Over the last decade, scientists from a diverse array of applied mathematics and engineering fields have developed sparse reconstruction techniques to identify localized structures. In this study, we present a new regularization approach for ill-posed inverse problems in atmospheric science. It is based on Tikhonov regularization with sparsity constraint and allows bounds on the parameters. We enforce sparsity using a dictionary representation system. We analyze its performance in an atmospheric inverse modeling scenario by estimating anthropogenic US methane (CH4) emissions from simulated atmospheric measurements. Different measures indicate that our sparse reconstruction approach is better able to capture large point sources or localized hot spots than other methods commonly used in atmospheric inversions. It captures the overall signal equally well but adds details on the grid scale. This feature can be of value for any inverse problem with point or spatially discrete sources. We show an example for source estimation of synthetic methane emissions from the Barnett shale formation.

Complex Wedge-Shaped Matrices: A Generalization of Jacobi Matrices

Czech Academy of Sciences Publication Activity Database

Hnětynková, Iveta; Plešinger, M.

2015-01-01

Roč. 487, 15 December (2015), s. 203-219 ISSN 0024-3795 R&D Projects: GA ČR GA13-06684S Keywords : eigenvalues * eigenvector * wedge-shaped matrices * generalized Jacobi matrices * band (or block) Krylov subspace methods Subject RIV: BA - General Mathematics Impact factor: 0.965, year: 2015

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

Science.gov (United States)

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

2017-08-01

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

Sparse structure regularized ranking

KAUST Repository

Wang, Jim Jing-Yan; Sun, Yijun; Gao, Xin

2014-01-01

Learning ranking scores is critical for the multimedia database retrieval problem. In this paper, we propose a novel ranking score learning algorithm by exploring the sparse structure and using it to regularize ranking scores. To explore the sparse

Sparse structure regularized ranking

KAUST Repository

Wang, Jim Jing-Yan

2014-04-17

Learning ranking scores is critical for the multimedia database retrieval problem. In this paper, we propose a novel ranking score learning algorithm by exploring the sparse structure and using it to regularize ranking scores. To explore the sparse structure, we assume that each multimedia object could be represented as a sparse linear combination of all other objects, and combination coefficients are regarded as a similarity measure between objects and used to regularize their ranking scores. Moreover, we propose to learn the sparse combination coefficients and the ranking scores simultaneously. A unified objective function is constructed with regard to both the combination coefficients and the ranking scores, and is optimized by an iterative algorithm. Experiments on two multimedia database retrieval data sets demonstrate the significant improvements of the propose algorithm over state-of-the-art ranking score learning algorithms.

Turbulent flows over sparse canopies

Science.gov (United States)

Sharma, Akshath; García-Mayoral, Ricardo

2018-04-01

Turbulent flows over sparse and dense canopies exerting a similar drag force on the flow are investigated using Direct Numerical Simulations. The dense canopies are modelled using a homogeneous drag force, while for the sparse canopy, the geometry of the canopy elements is represented. It is found that on using the friction velocity based on the local shear at each height, the streamwise velocity fluctuations and the Reynolds stress within the sparse canopy are similar to those from a comparable smooth-wall case. In addition, when scaled with the local friction velocity, the intensity of the off-wall peak in the streamwise vorticity for sparse canopies also recovers a value similar to a smooth-wall. This indicates that the sparse canopy does not significantly disturb the near-wall turbulence cycle, but causes its rescaling to an intensity consistent with a lower friction velocity within the canopy. In comparison, the dense canopy is found to have a higher damping effect on the turbulent fluctuations. For the case of the sparse canopy, a peak in the spectral energy density of the wall-normal velocity, and Reynolds stress is observed, which may indicate the formation of Kelvin-Helmholtz-like instabilities. It is also found that a sparse canopy is better modelled by a homogeneous drag applied on the mean flow alone, and not the turbulent fluctuations.

On reflectionless equi-transmitting matrices

Directory of Open Access Journals (Sweden)

Pavel Kurasov

2014-01-01

Full Text Available Reflectionless equi-transmitting unitary matrices are studied in connection to matching conditions in quantum graphs. All possible such matrices of size 6 are described explicitly. It is shown that such matrices form 30 six-parameter families intersected along 12 five-parameter families closely connected to conference matrices.

Discriminative sparse coding on multi-manifolds

KAUST Repository

Wang, J.J.-Y.; Bensmail, H.; Yao, N.; Gao, Xin

2013-01-01

Sparse coding has been popularly used as an effective data representation method in various applications, such as computer vision, medical imaging and bioinformatics. However, the conventional sparse coding algorithms and their manifold-regularized variants (graph sparse coding and Laplacian sparse coding), learn codebooks and codes in an unsupervised manner and neglect class information that is available in the training set. To address this problem, we propose a novel discriminative sparse coding method based on multi-manifolds, that learns discriminative class-conditioned codebooks and sparse codes from both data feature spaces and class labels. First, the entire training set is partitioned into multiple manifolds according to the class labels. Then, we formulate the sparse coding as a manifold-manifold matching problem and learn class-conditioned codebooks and codes to maximize the manifold margins of different classes. Lastly, we present a data sample-manifold matching-based strategy to classify the unlabeled data samples. Experimental results on somatic mutations identification and breast tumor classification based on ultrasonic images demonstrate the efficacy of the proposed data representation and classification approach. 2013 The Authors. All rights reserved.

Discriminative sparse coding on multi-manifolds

KAUST Repository

Wang, J.J.-Y.

2013-09-26

Sparse coding has been popularly used as an effective data representation method in various applications, such as computer vision, medical imaging and bioinformatics. However, the conventional sparse coding algorithms and their manifold-regularized variants (graph sparse coding and Laplacian sparse coding), learn codebooks and codes in an unsupervised manner and neglect class information that is available in the training set. To address this problem, we propose a novel discriminative sparse coding method based on multi-manifolds, that learns discriminative class-conditioned codebooks and sparse codes from both data feature spaces and class labels. First, the entire training set is partitioned into multiple manifolds according to the class labels. Then, we formulate the sparse coding as a manifold-manifold matching problem and learn class-conditioned codebooks and codes to maximize the manifold margins of different classes. Lastly, we present a data sample-manifold matching-based strategy to classify the unlabeled data samples. Experimental results on somatic mutations identification and breast tumor classification based on ultrasonic images demonstrate the efficacy of the proposed data representation and classification approach. 2013 The Authors. All rights reserved.

Sparse Regression by Projection and Sparse Discriminant Analysis

KAUST Repository

Qi, Xin

2015-04-03

© 2015, © American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America. Recent years have seen active developments of various penalized regression methods, such as LASSO and elastic net, to analyze high-dimensional data. In these approaches, the direction and length of the regression coefficients are determined simultaneously. Due to the introduction of penalties, the length of the estimates can be far from being optimal for accurate predictions. We introduce a new framework, regression by projection, and its sparse version to analyze high-dimensional data. The unique nature of this framework is that the directions of the regression coefficients are inferred first, and the lengths and the tuning parameters are determined by a cross-validation procedure to achieve the largest prediction accuracy. We provide a theoretical result for simultaneous model selection consistency and parameter estimation consistency of our method in high dimension. This new framework is then generalized such that it can be applied to principal components analysis, partial least squares, and canonical correlation analysis. We also adapt this framework for discriminant analysis. Compared with the existing methods, where there is relatively little control of the dependency among the sparse components, our method can control the relationships among the components. We present efficient algorithms and related theory for solving the sparse regression by projection problem. Based on extensive simulations and real data analysis, we demonstrate that our method achieves good predictive performance and variable selection in the regression setting, and the ability to control relationships between the sparse components leads to more accurate classification. In supplementary materials available online, the details of the algorithms and theoretical proofs, and R codes for all simulation studies are provided.

Occlusion detection via structured sparse learning for robust object tracking

KAUST Repository

Zhang, Tianzhu; Ghanem, Bernard; Xu, Changsheng; Ahuja, Narendra

2014-01-01

occlusion through structured sparse learning. We test our tracker on challenging benchmark sequences, such as sports videos, which involve heavy occlusion, drastic illumination changes, and large pose variations. Extensive experimental results show that our

Summer Proceedings 2016: The Center for Computing Research at Sandia National Laboratories

Energy Technology Data Exchange (ETDEWEB)

Carleton, James Brian [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Parks, Michael L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2017-02-01

Solving sparse linear systems from the discretization of elliptic partial differential equations (PDEs) is an important building block in many engineering applications. Sparse direct solvers can solve general linear systems, but are usually slower and use much more memory than effective iterative solvers. To overcome these two disadvantages, a hierarchical solver (LoRaSp) based on H2-matrices was introduced in [22]. Here, we have developed a parallel version of the algorithm in LoRaSp to solve large sparse matrices on distributed memory machines. On a single processor, the factorization time of our parallel solver scales almost linearly with the problem size for three-dimensional problems, as opposed to the quadratic scalability of many existing sparse direct solvers. Moreover, our solver leads to almost constant numbers of iterations, when used as a preconditioner for Poisson problems. On more than one processor, our algorithm has significant speedups compared to sequential runs. With this parallel algorithm, we are able to solve large problems much faster than many existing packages as demonstrated by the numerical experiments.

In-place sparse suffix sorting

DEFF Research Database (Denmark)

Prezza, Nicola

2018-01-01

information regarding the lexicographical order of a size-b subset of all n text suffixes is often needed. Such information can be stored space-efficiently (in b words) in the sparse suffix array (SSA). The SSA and its relative sparse LCP array (SLCP) can be used as a space-efficient substitute of the sparse...... suffix tree. Very recently, Gawrychowski and Kociumaka [11] showed that the sparse suffix tree (and therefore SSA and SLCP) can be built in asymptotically optimal O(b) space with a Monte Carlo algorithm running in O(n) time. The main reason for using the SSA and SLCP arrays in place of the sparse suffix...... tree is, however, their reduced space of b words each. This leads naturally to the quest for in-place algorithms building these arrays. Franceschini and Muthukrishnan [8] showed that the full suffix array can be built in-place and in optimal running time. On the other hand, finding sub-quadratic in...

Dynamic Representations of Sparse Graphs

DEFF Research Database (Denmark)

Brodal, Gerth Stølting; Fagerberg, Rolf

1999-01-01

We present a linear space data structure for maintaining graphs with bounded arboricity—a large class of sparse graphs containing e.g. planar graphs and graphs of bounded treewidth—under edge insertions, edge deletions, and adjacency queries. The data structure supports adjacency queries in worst...... case O(c) time, and edge insertions and edge deletions in amortized O(1) and O(c+log n) time, respectively, where n is the number of nodes in the graph, and c is the bound on the arboricity....

A hybrid method for the parallel computation of Green's functions

International Nuclear Information System (INIS)

Petersen, Dan Erik; Li Song; Stokbro, Kurt; Sorensen, Hans Henrik B.; Hansen, Per Christian; Skelboe, Stig; Darve, Eric

2009-01-01

Quantum transport models for nanodevices using the non-equilibrium Green's function method require the repeated calculation of the block tridiagonal part of the Green's and lesser Green's function matrices. This problem is related to the calculation of the inverse of a sparse matrix. Because of the large number of times this calculation needs to be performed, this is computationally very expensive even on supercomputers. The classical approach is based on recurrence formulas which cannot be efficiently parallelized. This practically prevents the solution of large problems with hundreds of thousands of atoms. We propose new recurrences for a general class of sparse matrices to calculate Green's and lesser Green's function matrices which extend formulas derived by Takahashi and others. We show that these recurrences may lead to a dramatically reduced computational cost because they only require computing a small number of entries of the inverse matrix. Then, we propose a parallelization strategy for block tridiagonal matrices which involves a combination of Schur complement calculations and cyclic reduction. It achieves good scalability even on problems of modest size.

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

Science.gov (United States)

Moody, Daniela; Wohlberg, Brendt

2018-01-02

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

Shape prior modeling using sparse representation and online dictionary learning.

Science.gov (United States)

Zhang, Shaoting; Zhan, Yiqiang; Zhou, Yan; Uzunbas, Mustafa; Metaxas, Dimitris N

2012-01-01

The recently proposed sparse shape composition (SSC) opens a new avenue for shape prior modeling. Instead of assuming any parametric model of shape statistics, SSC incorporates shape priors on-the-fly by approximating a shape instance (usually derived from appearance cues) by a sparse combination of shapes in a training repository. Theoretically, one can increase the modeling capability of SSC by including as many training shapes in the repository. However, this strategy confronts two limitations in practice. First, since SSC involves an iterative sparse optimization at run-time, the more shape instances contained in the repository, the less run-time efficiency SSC has. Therefore, a compact and informative shape dictionary is preferred to a large shape repository. Second, in medical imaging applications, training shapes seldom come in one batch. It is very time consuming and sometimes infeasible to reconstruct the shape dictionary every time new training shapes appear. In this paper, we propose an online learning method to address these two limitations. Our method starts from constructing an initial shape dictionary using the K-SVD algorithm. When new training shapes come, instead of re-constructing the dictionary from the ground up, we update the existing one using a block-coordinates descent approach. Using the dynamically updated dictionary, sparse shape composition can be gracefully scaled up to model shape priors from a large number of training shapes without sacrificing run-time efficiency. Our method is validated on lung localization in X-Ray and cardiac segmentation in MRI time series. Compared to the original SSC, it shows comparable performance while being significantly more efficient.

Sparse linear systems: Theory of decomposition, methods, technology, applications and implementation in Wolfram Mathematica

Energy Technology Data Exchange (ETDEWEB)

Pilipchuk, L. A., E-mail: pilipchik@bsu.by [Belarussian State University, 220030 Minsk, 4, Nezavisimosti avenue, Republic of Belarus (Belarus); Pilipchuk, A. S., E-mail: an.pilipchuk@gmail.com [The Natural Resources and Environmental Protestion Ministry of the Republic of Belarus, 220004 Minsk, 10 Kollektornaya Street, Republic of Belarus (Belarus)

2015-11-30

In this paper we propose the theory of decomposition, methods, technologies, applications and implementation in Wol-fram Mathematica for the constructing the solutions of the sparse linear systems. One of the applications is the Sensor Location Problem for the symmetric graph in the case when split ratios of some arc flows can be zeros. The objective of that application is to minimize the number of sensors that are assigned to the nodes. We obtain a sparse system of linear algebraic equations and research its matrix rank. Sparse systems of these types appear in generalized network flow programming problems in the form of restrictions and can be characterized as systems with a large sparse sub-matrix representing the embedded network structure.

Sparse linear systems: Theory of decomposition, methods, technology, applications and implementation in Wolfram Mathematica

International Nuclear Information System (INIS)

Pilipchuk, L. A.; Pilipchuk, A. S.

2015-01-01

In this paper we propose the theory of decomposition, methods, technologies, applications and implementation in Wol-fram Mathematica for the constructing the solutions of the sparse linear systems. One of the applications is the Sensor Location Problem for the symmetric graph in the case when split ratios of some arc flows can be zeros. The objective of that application is to minimize the number of sensors that are assigned to the nodes. We obtain a sparse system of linear algebraic equations and research its matrix rank. Sparse systems of these types appear in generalized network flow programming problems in the form of restrictions and can be characterized as systems with a large sparse sub-matrix representing the embedded network structure

Indefinitely preconditioned inexact Newton method for large sparse equality constrained non-linear programming problems

Czech Academy of Sciences Publication Activity Database

Lukšan, Ladislav; Vlček, Jan

1998-01-01

Roč. 5, č. 3 (1998), s. 219-247 ISSN 1070-5325 R&D Projects: GA ČR GA201/96/0918 Keywords : nonlinear programming * sparse problems * equality constraints * truncated Newton method * augmented Lagrangian function * indefinite systems * indefinite preconditioners * conjugate gradient method * residual smoothing Subject RIV: BA - General Mathematics Impact factor: 0.741, year: 1998

Flexible Bayesian Dynamic Modeling of Covariance and Correlation Matrices

KAUST Repository

Lan, Shiwei

2017-11-08

Modeling covariance (and correlation) matrices is a challenging problem due to the large dimensionality and positive-definiteness constraint. In this paper, we propose a novel Bayesian framework based on decomposing the covariance matrix into variance and correlation matrices. The highlight is that the correlations are represented as products of vectors on unit spheres. We propose a variety of distributions on spheres (e.g. the squared-Dirichlet distribution) to induce flexible prior distributions for covariance matrices that go beyond the commonly used inverse-Wishart prior. To handle the intractability of the resulting posterior, we introduce the adaptive $\\\\Delta$-Spherical Hamiltonian Monte Carlo. We also extend our structured framework to dynamic cases and introduce unit-vector Gaussian process priors for modeling the evolution of correlation among multiple time series. Using an example of Normal-Inverse-Wishart problem, a simulated periodic process, and an analysis of local field potential data (collected from the hippocampus of rats performing a complex sequence memory task), we demonstrated the validity and effectiveness of our proposed framework for (dynamic) modeling covariance and correlation matrices.

SuperLU{_}DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems

Energy Technology Data Exchange (ETDEWEB)

Li, Xiaoye S.; Demmel, James W.

2002-03-27

In this paper, we present the main algorithmic features in the software package SuperLU{_}DIST, a distributed-memory sparse direct solver for large sets of linear equations. We give in detail our parallelization strategies, with focus on scalability issues, and demonstrate the parallel performance and scalability on current machines. The solver is based on sparse Gaussian elimination, with an innovative static pivoting strategy proposed earlier by the authors. The main advantage of static pivoting over classical partial pivoting is that it permits a priori determination of data structures and communication pattern for sparse Gaussian elimination, which makes it more scalable on distributed memory machines. Based on this a priori knowledge, we designed highly parallel and scalable algorithms for both LU decomposition and triangular solve and we show that they are suitable for large-scale distributed memory machines.

Flexible Bayesian Dynamic Modeling of Covariance and Correlation Matrices

KAUST Repository

Lan, Shiwei; Holbrook, Andrew; Fortin, Norbert J.; Ombao, Hernando; Shahbaba, Babak

2017-01-01

Modeling covariance (and correlation) matrices is a challenging problem due to the large dimensionality and positive-definiteness constraint. In this paper, we propose a novel Bayesian framework based on decomposing the covariance matrix

Programming for Sparse Minimax Optimization

DEFF Research Database (Denmark)

Jonasson, K.; Madsen, Kaj

1994-01-01

We present an algorithm for nonlinear minimax optimization which is well suited for large and sparse problems. The method is based on trust regions and sequential linear programming. On each iteration, a linear minimax problem is solved for a basic step. If necessary, this is followed...... by the determination of a minimum norm corrective step based on a first-order Taylor approximation. No Hessian information needs to be stored. Global convergence is proved. This new method has been extensively tested and compared with other methods, including two well known codes for nonlinear programming...

Solving Sparse Polynomial Optimization Problems with Chordal Structure Using the Sparse, Bounded-Degree Sum-of-Squares Hierarchy

NARCIS (Netherlands)

Marandi, Ahmadreza; de Klerk, Etienne; Dahl, Joachim

The sparse bounded degree sum-of-squares (sparse-BSOS) hierarchy of Weisser, Lasserre and Toh [arXiv:1607.01151,2016] constructs a sequence of lower bounds for a sparse polynomial optimization problem. Under some assumptions, it is proven by the authors that the sequence converges to the optimal

Fungible Correlation Matrices: A Method for Generating Nonsingular, Singular, and Improper Correlation Matrices for Monte Carlo Research.

Science.gov (United States)

Waller, Niels G

2016-01-01

For a fixed set of standardized regression coefficients and a fixed coefficient of determination (R-squared), an infinite number of predictor correlation matrices will satisfy the implied quadratic form. I call such matrices fungible correlation matrices. In this article, I describe an algorithm for generating positive definite (PD), positive semidefinite (PSD), or indefinite (ID) fungible correlation matrices that have a random or fixed smallest eigenvalue. The underlying equations of this algorithm are reviewed from both algebraic and geometric perspectives. Two simulation studies illustrate that fungible correlation matrices can be profitably used in Monte Carlo research. The first study uses PD fungible correlation matrices to compare penalized regression algorithms. The second study uses ID fungible correlation matrices to compare matrix-smoothing algorithms. R code for generating fungible correlation matrices is presented in the supplemental materials.

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

Science.gov (United States)

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.

A modified sparse reconstruction method for three-dimensional synthetic aperture radar image

Science.gov (United States)

Zhang, Ziqiang; Ji, Kefeng; Song, Haibo; Zou, Huanxin

2018-03-01

There is an increasing interest in three-dimensional Synthetic Aperture Radar (3-D SAR) imaging from observed sparse scattering data. However, the existing 3-D sparse imaging method requires large computing times and storage capacity. In this paper, we propose a modified method for the sparse 3-D SAR imaging. The method processes the collection of noisy SAR measurements, usually collected over nonlinear flight paths, and outputs 3-D SAR imagery. Firstly, the 3-D sparse reconstruction problem is transformed into a series of 2-D slices reconstruction problem by range compression. Then the slices are reconstructed by the modified SL0 (smoothed l0 norm) reconstruction algorithm. The improved algorithm uses hyperbolic tangent function instead of the Gaussian function to approximate the l0 norm and uses the Newton direction instead of the steepest descent direction, which can speed up the convergence rate of the SL0 algorithm. Finally, numerical simulation results are given to demonstrate the effectiveness of the proposed algorithm. It is shown that our method, compared with existing 3-D sparse imaging method, performs better in reconstruction quality and the reconstruction time.

Robust visual tracking via multiscale deep sparse networks

Science.gov (United States)

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.

Evolutionary Games with Randomly Changing Payoff Matrices

Science.gov (United States)

Yakushkina, Tatiana; Saakian, David B.; Bratus, Alexander; Hu, Chin-Kun

2015-06-01

Evolutionary games are used in various fields stretching from economics to biology. In most of these games a constant payoff matrix is assumed, although some works also consider dynamic payoff matrices. In this article we assume a possibility of switching the system between two regimes with different sets of payoff matrices. Potentially such a model can qualitatively describe the development of bacterial or cancer cells with a mutator gene present. A finite population evolutionary game is studied. The model describes the simplest version of annealed disorder in the payoff matrix and is exactly solvable at the large population limit. We analyze the dynamics of the model, and derive the equations for both the maximum and the variance of the distribution using the Hamilton-Jacobi equation formalism.

Double stochastic matrices in quantum mechanics

International Nuclear Information System (INIS)

Louck, J.D.

1997-01-01

The general set of doubly stochastic matrices of order n corresponding to ordinary nonrelativistic quantum mechanical transition probability matrices is given. Lande's discussion of the nonquantal origin of such matrices is noted. Several concrete examples are presented for elementary and composite angular momentum systems with the focus on the unitary symmetry associated with such systems in the spirit of the recent work of Bohr and Ulfbeck. Birkhoff's theorem on doubly stochastic matrices of order n is reformulated in a geometrical language suitable for application to the subset of quantum mechanical doubly stochastic matrices. Specifically, it is shown that the set of points on the unit sphere in cartesian n'-space is subjective with the set of doubly stochastic matrices of order n. The question is raised, but not answered, as to what is the subset of points of this unit sphere that correspond to the quantum mechanical transition probability matrices, and what is the symmetry group of this subset of matrices

Bayesian Inference Methods for Sparse Channel Estimation

DEFF Research Database (Denmark)

Pedersen, Niels Lovmand

2013-01-01

This thesis deals with sparse Bayesian learning (SBL) with application to radio channel estimation. As opposed to the classical approach for sparse signal representation, we focus on the problem of inferring complex signals. Our investigations within SBL constitute the basis for the development...... of Bayesian inference algorithms for sparse channel estimation. Sparse inference methods aim at finding the sparse representation of a signal given in some overcomplete dictionary of basis vectors. Within this context, one of our main contributions to the field of SBL is a hierarchical representation...... analysis of the complex prior representation, where we show that the ability to induce sparse estimates of a given prior heavily depends on the inference method used and, interestingly, whether real or complex variables are inferred. We also show that the Bayesian estimators derived from the proposed...

Multiple instance learning tracking method with local sparse representation

KAUST Repository

Xie, Chengjun

2013-10-01

When objects undergo large pose change, illumination variation or partial occlusion, most existed visual tracking algorithms tend to drift away from targets and even fail in tracking them. To address this issue, in this study, the authors propose an online algorithm by combining multiple instance learning (MIL) and local sparse representation for tracking an object in a video system. The key idea in our method is to model the appearance of an object by local sparse codes that can be formed as training data for the MIL framework. First, local image patches of a target object are represented as sparse codes with an overcomplete dictionary, where the adaptive representation can be helpful in overcoming partial occlusion in object tracking. Then MIL learns the sparse codes by a classifier to discriminate the target from the background. Finally, results from the trained classifier are input into a particle filter framework to sequentially estimate the target state over time in visual tracking. In addition, to decrease the visual drift because of the accumulative errors when updating the dictionary and classifier, a two-step object tracking method combining a static MIL classifier with a dynamical MIL classifier is proposed. Experiments on some publicly available benchmarks of video sequences show that our proposed tracker is more robust and effective than others. © The Institution of Engineering and Technology 2013.

Matrices and linear transformations

CERN Document Server

Cullen, Charles G

1990-01-01

""Comprehensive . . . an excellent introduction to the subject."" - Electronic Engineer's Design Magazine.This introductory textbook, aimed at sophomore- and junior-level undergraduates in mathematics, engineering, and the physical sciences, offers a smooth, in-depth treatment of linear algebra and matrix theory. The major objects of study are matrices over an arbitrary field. Contents include Matrices and Linear Systems; Vector Spaces; Determinants; Linear Transformations; Similarity: Part I and Part II; Polynomials and Polynomial Matrices; Matrix Analysis; and Numerical Methods. The first

When sparse coding meets ranking: a joint framework for learning sparse codes and ranking scores

KAUST Repository

Wang, Jim Jing-Yan; Cui, Xuefeng; Yu, Ge; Guo, Lili; Gao, Xin

2017-01-01

Sparse coding, which represents a data point as a sparse reconstruction code with regard to a dictionary, has been a popular data representation method. Meanwhile, in database retrieval problems, learning the ranking scores from data points plays

High-dimensional covariance estimation with high-dimensional data

CERN Document Server

Pourahmadi, Mohsen

2013-01-01

Methods for estimating sparse and large covariance matrices Covariance and correlation matrices play fundamental roles in every aspect of the analysis of multivariate data collected from a variety of fields including business and economics, health care, engineering, and environmental and physical sciences. High-Dimensional Covariance Estimation provides accessible and comprehensive coverage of the classical and modern approaches for estimating covariance matrices as well as their applications to the rapidly developing areas lying at the intersection of statistics and mac

Characteristic Polynomials of Sample Covariance Matrices: The Non-Square Case

OpenAIRE

Kösters, Holger

2009-01-01

We consider the sample covariance matrices of large data matrices which have i.i.d. complex matrix entries and which are non-square in the sense that the difference between the number of rows and the number of columns tends to infinity. We show that the second-order correlation function of the characteristic polynomial of the sample covariance matrix is asymptotically given by the sine kernel in the bulk of the spectrum and by the Airy kernel at the edge of the spectrum. Similar results are g...

Improved Sparse Channel Estimation for Cooperative Communication Systems

Directory of Open Access Journals (Sweden)

Guan Gui

2012-01-01

Full Text Available Accurate channel state information (CSI is necessary at receiver for coherent detection in amplify-and-forward (AF cooperative communication systems. To estimate the channel, traditional methods, that is, least squares (LS and least absolute shrinkage and selection operator (LASSO, are based on assumptions of either dense channel or global sparse channel. However, LS-based linear method neglects the inherent sparse structure information while LASSO-based sparse channel method cannot take full advantage of the prior information. Based on the partial sparse assumption of the cooperative channel model, we propose an improved channel estimation method with partial sparse constraint. At first, by using sparse decomposition theory, channel estimation is formulated as a compressive sensing problem. Secondly, the cooperative channel is reconstructed by LASSO with partial sparse constraint. Finally, numerical simulations are carried out to confirm the superiority of proposed methods over global sparse channel estimation methods.

Sparse Image Reconstruction in Computed Tomography

DEFF Research Database (Denmark)

Jørgensen, Jakob Sauer

In recent years, increased focus on the potentially harmful effects of x-ray computed tomography (CT) scans, such as radiation-induced cancer, has motivated research on new low-dose imaging techniques. Sparse image reconstruction methods, as studied for instance in the field of compressed sensing...... applications. This thesis takes a systematic approach toward establishing quantitative understanding of conditions for sparse reconstruction to work well in CT. A general framework for analyzing sparse reconstruction methods in CT is introduced and two sets of computational tools are proposed: 1...... contributions to a general set of computational characterization tools. Thus, the thesis contributions help advance sparse reconstruction methods toward routine use in...

Sparse Regression by Projection and Sparse Discriminant Analysis

KAUST Repository

Qi, Xin; Luo, Ruiyan; Carroll, Raymond J.; Zhao, Hongyu

2015-01-01

predictions. We introduce a new framework, regression by projection, and its sparse version to analyze high-dimensional data. The unique nature of this framework is that the directions of the regression coefficients are inferred first, and the lengths

Using a grid platform for solving large sparse linear systems over GF(2)

OpenAIRE

Kleinjung , Thorsten; Nussbaum , Lucas; Thomé , Emmanuel

2010-01-01

International audience; In Fall 2009, the final step of the factorization of rsa768 was carried out on several clusters of the Grid'5000 platform, leading to a new record in integer factorization. This step involves solving a huge sparse linear system defined over the binary field GF(2). This article aims at describing the algorithm used, the difficulties encountered, and the methodology which led to success. In particular, we illustrate how our use of the block Wiedemann algorithm led to a m...

Lambda-matrices and vibrating systems

CERN Document Server

Lancaster, Peter; Stark, M; Kahane, J P

1966-01-01

Lambda-Matrices and Vibrating Systems presents aspects and solutions to problems concerned with linear vibrating systems with a finite degrees of freedom and the theory of matrices. The book discusses some parts of the theory of matrices that will account for the solutions of the problems. The text starts with an outline of matrix theory, and some theorems are proved. The Jordan canonical form is also applied to understand the structure of square matrices. Classical theorems are discussed further by applying the Jordan canonical form, the Rayleigh quotient, and simple matrix pencils with late

Manin matrices and Talalaev's formula

International Nuclear Information System (INIS)

Chervov, A; Falqui, G

2008-01-01

In this paper we study properties of Lax and transfer matrices associated with quantum integrable systems. Our point of view stems from the fact that their elements satisfy special commutation properties, considered by Yu I Manin some 20 years ago at the beginning of quantum group theory. These are the commutation properties of matrix elements of linear homomorphisms between polynomial rings; more explicitly these read: (1) elements of the same column commute; (2) commutators of the cross terms are equal: [M ij , M kl ] [M kj , M il ] (e.g. [M 11 , M 22 ] = [M 21 , M 12 ]). The main aim of this paper is twofold: on the one hand we observe and prove that such matrices (which we call Manin matrices in short) behave almost as well as matrices with commutative elements. Namely, the theorems of linear algebra (e.g., a natural definition of the determinant, the Cayley-Hamilton theorem, the Newton identities and so on and so forth) have a straightforward counterpart in the case of Manin matrices. On the other hand, we remark that such matrices are somewhat ubiquitous in the theory of quantum integrability. For instance, Manin matrices (and their q-analogs) include matrices satisfying the Yang-Baxter relation 'RTT=TTR' and the so-called Cartier-Foata matrices. Also, they enter Talalaev's remarkable formulae: det(∂ z -L gaudin (z)), det(1-e -∂z T Yangian (z)) for the 'quantum spectral curve', and appear in the separation of variables problem and Capelli identities. We show that theorems of linear algebra, after being established for such matrices, have various applications to quantum integrable systems and Lie algebras, e.g. in the construction of new generators in Z(U crit (gl-hat n )) (and, in general, in the construction of quantum conservation laws), in the Knizhnik-Zamolodchikov equation, and in the problem of Wick ordering. We propose, in the appendix, a construction of quantum separated variables for the XXX-Heisenberg system

Model-independent analysis with BPM correlation matrices

International Nuclear Information System (INIS)

Irwin, J.; Wang, C.X.; Yan, Y.T.; Bane, K.; Cai, Y.; Decker, F.; Minty, M.; Stupakov, G.; Zimmermann, F.

1998-06-01

The authors discuss techniques for Model-Independent Analysis (MIA) of a beamline using correlation matrices of physical variables and Singular Value Decomposition (SVD) of a beamline BPM matrix. The beamline matrix is formed from BPM readings for a large number of pulses. The method has been applied to the Linear Accelerator of the SLAC Linear Collider (SLC)

Diffusion Indexes with Sparse Loadings

DEFF Research Database (Denmark)

Kristensen, Johannes Tang

The use of large-dimensional factor models in forecasting has received much attention in the literature with the consensus being that improvements on forecasts can be achieved when comparing with standard models. However, recent contributions in the literature have demonstrated that care needs...... to the problem by using the LASSO as a variable selection method to choose between the possible variables and thus obtain sparse loadings from which factors or diffusion indexes can be formed. This allows us to build a more parsimonious factor model which is better suited for forecasting compared...... it to be an important alternative to PC....

Multi scales based sparse matrix spectral clustering image segmentation

Science.gov (United States)

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.

Sparse decompositions in 'incoherent' dictionaries

DEFF Research Database (Denmark)

Gribonval, R.; Nielsen, Morten

2003-01-01

a unique sparse representation in such a dictionary. In particular, it is proved that the result of Donoho and Huo, concerning the replacement of a combinatorial optimization problem with a linear programming problem when searching for sparse representations, has an analog for dictionaries that may...

Signal Sampling for Efficient Sparse Representation of Resting State FMRI Data

Science.gov (United States)

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

2015-01-01

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

Global Convergence of Schubert’s Method for Solving Sparse Nonlinear Equations

Directory of Open Access Journals (Sweden)

Huiping Cao

2014-01-01

Full Text Available Schubert’s method is an extension of Broyden’s method for solving sparse nonlinear equations, which can preserve the zero-nonzero structure defined by the sparse Jacobian matrix and can retain many good properties of Broyden’s method. In particular, Schubert’s method has been proved to be locally and q-superlinearly convergent. In this paper, we globalize Schubert’s method by using a nonmonotone line search. Under appropriate conditions, we show that the proposed algorithm converges globally and superlinearly. Some preliminary numerical experiments are presented, which demonstrate that our algorithm is effective for large-scale problems.

MERSENNE AND HADAMARD MATRICES CALCULATION BY SCARPIS METHOD

Directory of Open Access Journals (Sweden)

N. A. Balonin

2014-05-01

Full Text Available Purpose. The paper deals with the problem of basic generalizations of Hadamard matrices associated with maximum determinant matrices or not optimal by determinant matrices with orthogonal columns (weighing matrices, Mersenne and Euler matrices, ets.; calculation methods for the quasi-orthogonal local maximum determinant Mersenne matrices are not studied enough sufficiently. The goal of this paper is to develop the theory of Mersenne and Hadamard matrices on the base of generalized Scarpis method research. Methods. Extreme solutions are found in general by minimization of maximum for absolute values of the elements of studied matrices followed by their subsequent classification according to the quantity of levels and their values depending on orders. Less universal but more effective methods are based on structural invariants of quasi-orthogonal matrices (Silvester, Paley, Scarpis methods, ets.. Results. Generalizations of Hadamard and Belevitch matrices as a family of quasi-orthogonal matrices of odd orders are observed; they include, in particular, two-level Mersenne matrices. Definitions of section and layer on the set of generalized matrices are proposed. Calculation algorithms for matrices of adjacent layers and sections by matrices of lower orders are described. Approximation examples of the Belevitch matrix structures up to 22-nd critical order by Mersenne matrix of the third order are given. New formulation of the modified Scarpis method to approximate Hadamard matrices of high orders by lower order Mersenne matrices is proposed. Williamson method is described by example of one modular level matrices approximation by matrices with a small number of levels. Practical relevance. The efficiency of developing direction for the band-pass filters creation is justified. Algorithms for Mersenne matrices design by Scarpis method are used in developing software of the research program complex. Mersenne filters are based on the suboptimal by

Data analysis in high-dimensional sparse spaces

DEFF Research Database (Denmark)

Clemmensen, Line Katrine Harder

classification techniques for high-dimensional problems are presented: Sparse discriminant analysis, sparse mixture discriminant analysis and orthogonality constrained support vector machines. The first two introduces sparseness to the well known linear and mixture discriminant analysis and thereby provide low...... are applied to classifications of fish species, ear canal impressions used in the hearing aid industry, microbiological fungi species, and various cancerous tissues and healthy tissues. In addition, novel applications of sparse regressions (also called the elastic net) to the medical, concrete, and food...

A sparse-grid isogeometric solver

KAUST Repository

Beck, Joakim; Sangalli, Giancarlo; Tamellini, Lorenzo

2018-01-01

Isogeometric Analysis (IGA) typically adopts tensor-product splines and NURBS as a basis for the approximation of the solution of PDEs. In this work, we investigate to which extent IGA solvers can benefit from the so-called sparse-grids construction in its combination technique form, which was first introduced in the early 90’s in the context of the approximation of high-dimensional PDEs.The tests that we report show that, in accordance to the literature, a sparse-grid construction can indeed be useful if the solution of the PDE at hand is sufficiently smooth. Sparse grids can also be useful in the case of non-smooth solutions when some a-priori knowledge on the location of the singularities of the solution can be exploited to devise suitable non-equispaced meshes. Finally, we remark that sparse grids can be seen as a simple way to parallelize pre-existing serial IGA solvers in a straightforward fashion, which can be beneficial in many practical situations.

A sparse-grid isogeometric solver

KAUST Repository

Beck, Joakim

2018-02-28

Isogeometric Analysis (IGA) typically adopts tensor-product splines and NURBS as a basis for the approximation of the solution of PDEs. In this work, we investigate to which extent IGA solvers can benefit from the so-called sparse-grids construction in its combination technique form, which was first introduced in the early 90’s in the context of the approximation of high-dimensional PDEs.The tests that we report show that, in accordance to the literature, a sparse-grid construction can indeed be useful if the solution of the PDE at hand is sufficiently smooth. Sparse grids can also be useful in the case of non-smooth solutions when some a-priori knowledge on the location of the singularities of the solution can be exploited to devise suitable non-equispaced meshes. Finally, we remark that sparse grids can be seen as a simple way to parallelize pre-existing serial IGA solvers in a straightforward fashion, which can be beneficial in many practical situations.

Supervised Transfer Sparse Coding

KAUST Repository

Al-Shedivat, Maruan

2014-07-27

A combination of the sparse coding and transfer learn- ing techniques was shown to be accurate and robust in classification tasks where training and testing objects have a shared feature space but are sampled from differ- ent underlying distributions, i.e., belong to different do- mains. The key assumption in such case is that in spite of the domain disparity, samples from different domains share some common hidden factors. Previous methods often assumed that all the objects in the target domain are unlabeled, and thus the training set solely comprised objects from the source domain. However, in real world applications, the target domain often has some labeled objects, or one can always manually label a small num- ber of them. In this paper, we explore such possibil- ity and show how a small number of labeled data in the target domain can significantly leverage classifica- tion accuracy of the state-of-the-art transfer sparse cod- ing methods. We further propose a unified framework named supervised transfer sparse coding (STSC) which simultaneously optimizes sparse representation, domain transfer and classification. Experimental results on three applications demonstrate that a little manual labeling and then learning the model in a supervised fashion can significantly improve classification accuracy.

Joint Group Sparse PCA for Compressed Hyperspectral Imaging.

Science.gov (United States)

Khan, Zohaib; Shafait, Faisal; Mian, Ajmal

2015-12-01

A sparse principal component analysis (PCA) seeks a sparse linear combination of input features (variables), so that the derived features still explain most of the variations in the data. A group sparse PCA introduces structural constraints on the features in seeking such a linear combination. Collectively, the derived principal components may still require measuring all the input features. We present a joint group sparse PCA (JGSPCA) algorithm, which forces the basic coefficients corresponding to a group of features to be jointly sparse. Joint sparsity ensures that the complete basis involves only a sparse set of input features, whereas the group sparsity ensures that the structural integrity of the features is maximally preserved. We evaluate the JGSPCA algorithm on the problems of compressed hyperspectral imaging and face recognition. Compressed sensing results show that the proposed method consistently outperforms sparse PCA and group sparse PCA in reconstructing the hyperspectral scenes of natural and man-made objects. The efficacy of the proposed compressed sensing method is further demonstrated in band selection for face recognition.

Completely X-symmetric S-matrices corresponding to theta functions and models of statistical mechanics

International Nuclear Information System (INIS)

Chudnovsky, D.V.; Chudnovsky, G.V.

1981-01-01

We consider general expressions of factorized S-matrices with Abelian symmetry expressed in terms of theta-functions. These expressions arise from representations of the Heisenberg group. New examples of factorized S-matrices lead to a large class of completely integrable models of statistical mechanics which generalize the XYZ-model of the eight-vertex model. (orig.)

Positive Eigenvalues of Generalized Words in Two Hermitian Positive Definite Matrices

OpenAIRE

Hillar, Christopher; Johnson, Charles R.

2005-01-01

We define a word in two positive definite (complex Hermitian) matrices $A$ and $B$ as a finite product of real powers of $A$ and $B$. The question of which words have only positive eigenvalues is addressed. This question was raised some time ago in connection with a long-standing problem in theoretical physics, and it was previously approached by the authors for words in two real positive definite matrices with positive integral exponents. A large class of words that do guarantee positive eig...

Dose-shaping using targeted sparse optimization

International Nuclear Information System (INIS)

Sayre, George A.; Ruan, Dan

2013-01-01

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, the 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 tot 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 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 tot sparse improves

Dose-shaping using targeted sparse optimization.

Science.gov (United States)

Sayre, George A; Ruan, Dan

2013-07-01

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, the 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. In designing the energy minimization objective (E tot (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 L1 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 tot (sparse) improves tradeoff between

Parallel Sparse Matrix - Vector Product

DEFF Research Database (Denmark)

Alexandersen, Joe; Lazarov, Boyan Stefanov; Dammann, Bernd

This technical report contains a case study of a sparse matrix-vector product routine, implemented for parallel execution on a compute cluster with both pure MPI and hybrid MPI-OpenMP solutions. C++ classes for sparse data types were developed and the report shows how these class can be used...

Intrinsic character of Stokes matrices

Science.gov (United States)

Gagnon, Jean-François; Rousseau, Christiane

2017-02-01

Two germs of linear analytic differential systems x k + 1Y‧ = A (x) Y with a non-resonant irregular singularity are analytically equivalent if and only if they have the same eigenvalues and equivalent collections of Stokes matrices. The Stokes matrices are the transition matrices between sectors on which the system is analytically equivalent to its formal normal form. Each sector contains exactly one separating ray for each pair of eigenvalues. A rotation in S allows supposing that R+ lies in the intersection of two sectors. Reordering of the coordinates of Y allows ordering the real parts of the eigenvalues, thus yielding triangular Stokes matrices. However, the choice of the rotation in x is not canonical. In this paper we establish how the collection of Stokes matrices depends on this rotation, and hence on a chosen order of the projection of the eigenvalues on a line through the origin.

Multi-threaded Sparse Matrix Sparse Matrix Multiplication for Many-Core and GPU Architectures.

Energy Technology Data Exchange (ETDEWEB)

Deveci, Mehmet [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Trott, Christian Robert [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Rajamanickam, Sivasankaran [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2018-01-01

Sparse Matrix-Matrix multiplication is a key kernel that has applications in several domains such as scientific computing and graph analysis. Several algorithms have been studied in the past for this foundational kernel. In this paper, we develop parallel algorithms for sparse matrix- matrix multiplication with a focus on performance portability across different high performance computing architectures. The performance of these algorithms depend on the data structures used in them. We compare different types of accumulators in these algorithms and demonstrate the performance difference between these data structures. Furthermore, we develop a meta-algorithm, kkSpGEMM, to choose the right algorithm and data structure based on the characteristics of the problem. We show performance comparisons on three architectures and demonstrate the need for the community to develop two phase sparse matrix-matrix multiplication implementations for efficient reuse of the data structures involved.

2D sparse array transducer optimization for 3D ultrasound imaging

International Nuclear Information System (INIS)

Choi, Jae Hoon; Park, Kwan Kyu

2014-01-01

A 3D ultrasound image is desired in many medical examinations. However, the implementation of a 2D array, which is needed for a 3D image, is challenging with respect to fabrication, interconnection and cabling. A 2D sparse array, which needs fewer elements than a dense array, is a realistic way to achieve 3D images. Because the number of ways the elements can be placed in an array is extremely large, a method for optimizing the array configuration is needed. Previous research placed the target point far from the transducer array, making it impossible to optimize the array in the operating range. In our study, we focused on optimizing a 2D sparse array transducer for 3D imaging by using a simulated annealing method. We compared the far-field optimization method with the near-field optimization method by analyzing a point-spread function (PSF). The resolution of the optimized sparse array is comparable to that of the dense array.

Sparse approximation with bases

CERN Document Server

2015-01-01

This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications.  The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and do...

Efficient convolutional sparse coding

Science.gov (United States)

Wohlberg, Brendt

2017-06-20

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

Hyperspectral Unmixing with Robust Collaborative Sparse Regression

Directory of Open Access Journals (Sweden)

Chang Li

2016-07-01

Full Text Available Recently, sparse unmixing (SU of hyperspectral data has received particular attention for analyzing remote sensing images. However, most SU methods are based on the commonly admitted linear mixing model (LMM, which ignores the possible nonlinear effects (i.e., nonlinearity. In this paper, we propose a new method named robust collaborative sparse regression (RCSR based on the robust LMM (rLMM for hyperspectral unmixing. The rLMM takes the nonlinearity into consideration, and the nonlinearity is merely treated as outlier, which has the underlying sparse property. The RCSR simultaneously takes the collaborative sparse property of the abundance and sparsely distributed additive property of the outlier into consideration, which can be formed as a robust joint sparse regression problem. The inexact augmented Lagrangian method (IALM is used to optimize the proposed RCSR. The qualitative and quantitative experiments on synthetic datasets and real hyperspectral images demonstrate that the proposed RCSR is efficient for solving the hyperspectral SU problem compared with the other four state-of-the-art algorithms.

Special matrices of mathematical physics stochastic, circulant and Bell matrices

CERN Document Server

Aldrovandi, R

2001-01-01

This book expounds three special kinds of matrices that are of physical interest, centering on physical examples. Stochastic matrices describe dynamical systems of many different types, involving (or not) phenomena like transience, dissipation, ergodicity, nonequilibrium, and hypersensitivity to initial conditions. The main characteristic is growth by agglomeration, as in glass formation. Circulants are the building blocks of elementary Fourier analysis and provide a natural gateway to quantum mechanics and noncommutative geometry. Bell polynomials offer closed expressions for many formulas co

Integrative analysis of multiple diverse omics datasets by sparse group multitask regression

Directory of Open Access Journals (Sweden)

Dongdong eLin

2014-10-01

Full Text Available A variety of high throughput genome-wide assays enable the exploration of genetic risk factors underlying complex traits. Although these studies have remarkable impact on identifying susceptible biomarkers, they suffer from issues such as limited sample size and low reproducibility. Combining individual studies of different genetic levels/platforms has the promise to improve the power and consistency of biomarker identification. In this paper, we propose a novel integrative method, namely sparse group multitask regression, for integrating diverse omics datasets, platforms and populations to identify risk genes/factors of complex diseases. This method combines multitask learning with sparse group regularization, which will: 1 treat the biomarker identification in each single study as a task and then combine them by multitask learning; 2 group variables from all studies for identifying significant genes; 3 enforce sparse constraint on groups of variables to overcome the ‘small sample, but large variables’ problem. We introduce two sparse group penalties: sparse group lasso and sparse group ridge in our multitask model, and provide an effective algorithm for each model. In addition, we propose a significance test for the identification of potential risk genes. Two simulation studies are performed to evaluate the performance of our integrative method by comparing it with conventional meta-analysis method. The results show that our sparse group multitask method outperforms meta-analysis method significantly. In an application to our osteoporosis studies, 7 genes are identified as significant genes by our method and are found to have significant effects in other three independent studies for validation. The most significant gene SOD2 has been identified in our previous osteoporosis study involving the same expression dataset. Several other genes such as TREML2, HTR1E and GLO1 are shown to be novel susceptible genes for osteoporosis, as confirmed

Natural image sequences constrain dynamic receptive fields and imply a sparse code.

Science.gov (United States)

Häusler, Chris; Susemihl, Alex; Nawrot, Martin P

2013-11-06

In their natural environment, animals experience a complex and dynamic visual scenery. Under such natural stimulus conditions, neurons in the visual cortex employ a spatially and temporally sparse code. For the input scenario of natural still images, previous work demonstrated that unsupervised feature learning combined with the constraint of sparse coding can predict physiologically measured receptive fields of simple cells in the primary visual cortex. This convincingly indicated that the mammalian visual system is adapted to the natural spatial input statistics. Here, we extend this approach to the time domain in order to predict dynamic receptive fields that can account for both spatial and temporal sparse activation in biological neurons. We rely on temporal restricted Boltzmann machines and suggest a novel temporal autoencoding training procedure. When tested on a dynamic multi-variate benchmark dataset this method outperformed existing models of this class. Learning features on a large dataset of natural movies allowed us to model spatio-temporal receptive fields for single neurons. They resemble temporally smooth transformations of previously obtained static receptive fields and are thus consistent with existing theories. A neuronal spike response model demonstrates how the dynamic receptive field facilitates temporal and population sparseness. We discuss the potential mechanisms and benefits of a spatially and temporally sparse representation of natural visual input. Copyright © 2013 The Authors. Published by Elsevier B.V. All rights reserved.

Image fusion using sparse overcomplete feature dictionaries

Science.gov (United States)

Brumby, Steven P.; Bettencourt, Luis; Kenyon, Garrett T.; Chartrand, Rick; Wohlberg, Brendt

2015-10-06

Approaches for deciding what individuals in a population of visual system "neurons" are looking for using sparse overcomplete feature dictionaries are provided. A sparse overcomplete feature dictionary may be learned for an image dataset and a local sparse representation of the image dataset may be built using the learned feature dictionary. A local maximum pooling operation may be applied on the local sparse representation to produce a translation-tolerant representation of the image dataset. An object may then be classified and/or clustered within the translation-tolerant representation of the image dataset using a supervised classification algorithm and/or an unsupervised clustering algorithm.

Galaxy redshift surveys with sparse sampling

International Nuclear Information System (INIS)

Chiang, Chi-Ting; Wullstein, Philipp; Komatsu, Eiichiro; Jee, Inh; Jeong, Donghui; Blanc, Guillermo A.; Ciardullo, Robin; Gronwall, Caryl; Hagen, Alex; Schneider, Donald P.; Drory, Niv; Fabricius, Maximilian; Landriau, Martin; Finkelstein, Steven; Jogee, Shardha; Cooper, Erin Mentuch; Tuttle, Sarah; Gebhardt, Karl; Hill, Gary J.

2013-01-01

Survey observations of the three-dimensional locations of galaxies are a powerful approach to measure the distribution of matter in the universe, which can be used to learn about the nature of dark energy, physics of inflation, neutrino masses, etc. A competitive survey, however, requires a large volume (e.g., V survey ∼ 10Gpc 3 ) to be covered, and thus tends to be expensive. A ''sparse sampling'' method offers a more affordable solution to this problem: within a survey footprint covering a given survey volume, V survey , we observe only a fraction of the volume. The distribution of observed regions should be chosen such that their separation is smaller than the length scale corresponding to the wavenumber of interest. Then one can recover the power spectrum of galaxies with precision expected for a survey covering a volume of V survey (rather than the volume of the sum of observed regions) with the number density of galaxies given by the total number of observed galaxies divided by V survey (rather than the number density of galaxies within an observed region). We find that regularly-spaced sampling yields an unbiased power spectrum with no window function effect, and deviations from regularly-spaced sampling, which are unavoidable in realistic surveys, introduce calculable window function effects and increase the uncertainties of the recovered power spectrum. On the other hand, we show that the two-point correlation function (pair counting) is not affected by sparse sampling. While we discuss the sparse sampling method within the context of the forthcoming Hobby-Eberly Telescope Dark Energy Experiment, the method is general and can be applied to other galaxy surveys

Studies of Catalytic Properties of Inorganic Rock Matrices in Redox Reactions

Directory of Open Access Journals (Sweden)

Nikolay M. Dobrynkin

2017-09-01

Full Text Available Intrinsic catalytic properties of mineral matrices of various kinds (basalts, clays, sandstones were studied, which are of interest for in-situ heavy oil upgrading (i.e., underground to create advanced technologies for enhanced oil recovery. The elemental, surface and phase composition and matrix particle morphology, surface and acidic properties were studied using elemental analysis, X-ray diffraction, adsorption and desorption of nitrogen and ammonia. The data on the catalytic activity of inorganic matrices in ammonium nitrate decomposition (reaction with a large gassing, oxidation of hydrocarbons and carbon monoxide, and hydrocracking of asphaltenes into maltenes (the conversion of heavy hydrocarbons into more valuable light hydrocarbons were discussed. In order to check their applicability for the asphaltenes hydrocracking catalytic systems development, basalt and clay matrices were used as supports for iron/basalt, nickel/basalt and iron/clay catalysts. The catalytic activity of the matrices in the reactions of the decomposition of ammonium nitrate, oxidation of hydrocarbons and carbon monoxide, and hydrocracking of asphaltens was observed for the first time.

Applicability of non-invasively collected matrices for human biomonitoring

Directory of Open Access Journals (Sweden)

Nickmilder Marc

2009-03-01

Full Text Available Abstract With its inclusion under Action 3 in the Environment and Health Action Plan 2004–2010 of the European Commission, human biomonitoring is currently receiving an increasing amount of attention from the scientific community as a tool to better quantify human exposure to, and health effects of, environmental stressors. Despite the policy support, however, there are still several issues that restrict the routine application of human biomonitoring data in environmental health impact assessment. One of the main issues is the obvious need to routinely collect human samples for large-scale surveys. Particularly the collection of invasive samples from susceptible populations may suffer from ethical and practical limitations. Children, pregnant women, elderly, or chronically-ill people are among those that would benefit the most from non-invasive, repeated or routine sampling. Therefore, the use of non-invasively collected matrices for human biomonitoring should be promoted as an ethically appropriate, cost-efficient and toxicologically relevant alternative for many biomarkers that are currently determined in invasively collected matrices. This review illustrates that several non-invasively collected matrices are widely used that can be an valuable addition to, or alternative for, invasively collected matrices such as peripheral blood sampling. Moreover, a well-informed choice of matrix can provide an added value for human biomonitoring, as different non-invasively collected matrices can offer opportunities to study additional aspects of exposure to and effects from environmental contaminants, such as repeated sampling, historical overview of exposure, mother-child transfer of substances, or monitoring of substances with short biological half-lives.

Sparse distributed memory

Science.gov (United States)

Denning, Peter J.

1989-01-01

Sparse distributed memory was proposed be Pentti Kanerva as a realizable architecture that could store large patterns and retrieve them based on partial matches with patterns representing current sensory inputs. This memory exhibits behaviors, both in theory and in experiment, that resemble those previously unapproached by machines - e.g., rapid recognition of faces or odors, discovery of new connections between seemingly unrelated ideas, continuation of a sequence of events when given a cue from the middle, knowing that one doesn't know, or getting stuck with an answer on the tip of one's tongue. These behaviors are now within reach of machines that can be incorporated into the computing systems of robots capable of seeing, talking, and manipulating. Kanerva's theory is a break with the Western rationalistic tradition, allowing a new interpretation of learning and cognition that respects biology and the mysteries of individual human beings.

Regression with Sparse Approximations of Data

DEFF Research Database (Denmark)

Noorzad, Pardis; Sturm, Bob L.

2012-01-01

We propose sparse approximation weighted regression (SPARROW), a method for local estimation of the regression function that uses sparse approximation with a dictionary of measurements. SPARROW estimates the regression function at a point with a linear combination of a few regressands selected...... by a sparse approximation of the point in terms of the regressors. We show SPARROW can be considered a variant of \\(k\\)-nearest neighbors regression (\\(k\\)-NNR), and more generally, local polynomial kernel regression. Unlike \\(k\\)-NNR, however, SPARROW can adapt the number of regressors to use based...

Parallel sparse direct solver for integrated circuit simulation

CERN Document Server

Chen, Xiaoming; Yang, Huazhong

2017-01-01

This book describes algorithmic methods and parallelization techniques to design a parallel sparse direct solver which is specifically targeted at integrated circuit simulation problems. The authors describe a complete flow and detailed parallel algorithms of the sparse direct solver. They also show how to improve the performance by simple but effective numerical techniques. The sparse direct solver techniques described can be applied to any SPICE-like integrated circuit simulator and have been proven to be high-performance in actual circuit simulation. Readers will benefit from the state-of-the-art parallel integrated circuit simulation techniques described in this book, especially the latest parallel sparse matrix solution techniques. · Introduces complicated algorithms of sparse linear solvers, using concise principles and simple examples, without complex theory or lengthy derivations; · Describes a parallel sparse direct solver that can be adopted to accelerate any SPICE-like integrated circuit simulato...

Introduction to matrices and vectors

CERN Document Server

Schwartz, Jacob T

2001-01-01

In this concise undergraduate text, the first three chapters present the basics of matrices - in later chapters the author shows how to use vectors and matrices to solve systems of linear equations. 1961 edition.

Abnormal Event Detection Using Local Sparse Representation

DEFF Research Database (Denmark)

Ren, Huamin; Moeslund, Thomas B.

2014-01-01

We propose to detect abnormal events via a sparse subspace clustering algorithm. Unlike most existing approaches, which search for optimized normal bases and detect abnormality based on least square error or reconstruction error from the learned normal patterns, we propose an abnormality measurem...... is found that satisfies: the distance between its local space and the normal space is large. We evaluate our method on two public benchmark datasets: UCSD and Subway Entrance datasets. The comparison to the state-of-the-art methods validate our method's effectiveness....

Sparse Learning with Stochastic Composite Optimization.

Science.gov (United States)

Zhang, Weizhong; Zhang, Lijun; Jin, Zhongming; Jin, Rong; Cai, Deng; Li, Xuelong; Liang, Ronghua; He, Xiaofei

2017-06-01

In this paper, we study Stochastic Composite Optimization (SCO) for sparse learning that aims to learn a sparse solution from a composite function. Most of the recent SCO algorithms have already reached the optimal expected convergence rate O(1/λT), but they often fail to deliver sparse solutions at the end either due to the limited sparsity regularization during stochastic optimization (SO) or due to the limitation in online-to-batch conversion. Even when the objective function is strongly convex, their high probability bounds can only attain O(√{log(1/δ)/T}) with δ is the failure probability, which is much worse than the expected convergence rate. To address these limitations, we propose a simple yet effective two-phase Stochastic Composite Optimization scheme by adding a novel powerful sparse online-to-batch conversion to the general Stochastic Optimization algorithms. We further develop three concrete algorithms, OptimalSL, LastSL and AverageSL, directly under our scheme to prove the effectiveness of the proposed scheme. Both the theoretical analysis and the experiment results show that our methods can really outperform the existing methods at the ability of sparse learning and at the meantime we can improve the high probability bound to approximately O(log(log(T)/δ)/λT).

Construction of MDS self-dual codes from orthogonal matrices

OpenAIRE

Shi, Minjia; Sok, Lin; Solé, Patrick

2016-01-01

In this paper, we give algorithms and methods of construction of self-dual codes over finite fields using orthogonal matrices. Randomization in the orthogonal group, and code extension are the main tools. Some optimal, almost MDS, and MDS self-dual codes over both small and large prime fields are constructed.

Shearlets and Optimally Sparse Approximations

DEFF Research Database (Denmark)

Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q

2012-01-01

Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient analysis is the provision of optimally sparse approximations...... optimally sparse approximations of this model class in 2D as well as 3D. Even more, in contrast to all other directional representation systems, a theory for compactly supported shearlet frames was derived which moreover also satisfy this optimality benchmark. This chapter shall serve as an introduction...... to and a survey about sparse approximations of cartoon-like images by band-limited and also compactly supported shearlet frames as well as a reference for the state-of-the-art of this research field....

Diffusion Indexes With Sparse Loadings

DEFF Research Database (Denmark)

Kristensen, Johannes Tang

2017-01-01

The use of large-dimensional factor models in forecasting has received much attention in the literature with the consensus being that improvements on forecasts can be achieved when comparing with standard models. However, recent contributions in the literature have demonstrated that care needs...... to the problem by using the least absolute shrinkage and selection operator (LASSO) as a variable selection method to choose between the possible variables and thus obtain sparse loadings from which factors or diffusion indexes can be formed. This allows us to build a more parsimonious factor model...... in forecasting accuracy and thus find it to be an important alternative to PC. Supplementary materials for this article are available online....

Neural Network for Sparse Reconstruction

Directory of Open Access Journals (Sweden)

Qingfa Li

2014-01-01

Full Text Available We construct a neural network based on smoothing approximation techniques and projected gradient method to solve a kind of sparse reconstruction problems. Neural network can be implemented by circuits and can be seen as an important method for solving optimization problems, especially large scale problems. Smoothing approximation is an efficient technique for solving nonsmooth optimization problems. We combine these two techniques to overcome the difficulties of the choices of the step size in discrete algorithms and the item in the set-valued map of differential inclusion. In theory, the proposed network can converge to the optimal solution set of the given problem. Furthermore, some numerical experiments show the effectiveness of the proposed network in this paper.

Framing U-Net via Deep Convolutional Framelets: Application to Sparse-View CT.

Science.gov (United States)

Han, Yoseob; Ye, Jong Chul

2018-06-01

X-ray computed tomography (CT) using sparse projection views is a recent approach to reduce the radiation dose. However, due to the insufficient projection views, an analytic reconstruction approach using the filtered back projection (FBP) produces severe streaking artifacts. Recently, deep learning approaches using large receptive field neural networks such as U-Net have demonstrated impressive performance for sparse-view CT reconstruction. However, theoretical justification is still lacking. Inspired by the recent theory of deep convolutional framelets, the main goal of this paper is, therefore, to reveal the limitation of U-Net and propose new multi-resolution deep learning schemes. In particular, we show that the alternative U-Net variants such as dual frame and tight frame U-Nets satisfy the so-called frame condition which makes them better for effective recovery of high frequency edges in sparse-view CT. Using extensive experiments with real patient data set, we demonstrate that the new network architectures provide better reconstruction performance.

Dose-shaping using targeted sparse optimization

Energy Technology Data Exchange (ETDEWEB)

Sayre, George A.; Ruan, Dan [Department of Radiation Oncology, University of California - Los Angeles School of Medicine, 200 Medical Plaza, Los Angeles, California 90095 (United States)

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, the 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

Pathological rate matrices: from primates to pathogens

Directory of Open Access Journals (Sweden)

Knight Rob

2008-12-01

Full Text Available Abstract Background Continuous-time Markov models allow flexible, parametrically succinct descriptions of sequence divergence. Non-reversible forms of these models are more biologically realistic but are challenging to develop. The instantaneous rate matrices defined for these models are typically transformed into substitution probability matrices using a matrix exponentiation algorithm that employs eigendecomposition, but this algorithm has characteristic vulnerabilities that lead to significant errors when a rate matrix possesses certain 'pathological' properties. Here we tested whether pathological rate matrices exist in nature, and consider the suitability of different algorithms to their computation. Results We used concatenated protein coding gene alignments from microbial genomes, primate genomes and independent intron alignments from primate genomes. The Taylor series expansion and eigendecomposition matrix exponentiation algorithms were compared to the less widely employed, but more robust, Padé with scaling and squaring algorithm for nucleotide, dinucleotide, codon and trinucleotide rate matrices. Pathological dinucleotide and trinucleotide matrices were evident in the microbial data set, affecting the eigendecomposition and Taylor algorithms respectively. Even using a conservative estimate of matrix error (occurrence of an invalid probability, both Taylor and eigendecomposition algorithms exhibited substantial error rates: ~100% of all exonic trinucleotide matrices were pathological to the Taylor algorithm while ~10% of codon positions 1 and 2 dinucleotide matrices and intronic trinucleotide matrices, and ~30% of codon matrices were pathological to eigendecomposition. The majority of Taylor algorithm errors derived from occurrence of multiple unobserved states. A small number of negative probabilities were detected from the Pad�� algorithm on trinucleotide matrices that were attributable to machine precision. Although the Pad

Multilevel sparse functional principal component analysis.

Science.gov (United States)

Di, Chongzhi; Crainiceanu, Ciprian M; Jank, Wolfgang S

2014-01-29

We consider analysis of sparsely sampled multilevel functional data, where the basic observational unit is a function and data have a natural hierarchy of basic units. An example is when functions are recorded at multiple visits for each subject. Multilevel functional principal component analysis (MFPCA; Di et al. 2009) was proposed for such data when functions are densely recorded. Here we consider the case when functions are sparsely sampled and may contain only a few observations per function. We exploit the multilevel structure of covariance operators and achieve data reduction by principal component decompositions at both between and within subject levels. We address inherent methodological differences in the sparse sampling context to: 1) estimate the covariance operators; 2) estimate the functional principal component scores; 3) predict the underlying curves. Through simulations the proposed method is able to discover dominating modes of variations and reconstruct underlying curves well even in sparse settings. Our approach is illustrated by two applications, the Sleep Heart Health Study and eBay auctions.

A sparse version of IGA solvers

KAUST Repository

Beck, Joakim; Sangalli, Giancarlo; Tamellini, Lorenzo

2017-01-01

Isogeometric Analysis (IGA) typically adopts tensor-product splines and NURBS as a basis for the approximation of the solution of PDEs. In this work, we investigate to which extent IGA solvers can benefit from the so-called sparse-grids construction in its combination technique form, which was first introduced in the early 90s in the context of the approximation of high-dimensional PDEs. The tests that we report show that, in accordance to the literature, a sparse grids construction can indeed be useful if the solution of the PDE at hand is sufficiently smooth. Sparse grids can also be useful in the case of non-smooth solutions when some a-priori knowledge on the location of the singularities of the solution can be exploited to devise suitable non-equispaced meshes. Finally, we remark that sparse grids can be seen as a simple way to parallelize pre-existing serial IGA solvers in a straightforward fashion, which can be beneficial in many practical situations.

A sparse version of IGA solvers

KAUST Repository

Beck, Joakim

2017-07-30

Isogeometric Analysis (IGA) typically adopts tensor-product splines and NURBS as a basis for the approximation of the solution of PDEs. In this work, we investigate to which extent IGA solvers can benefit from the so-called sparse-grids construction in its combination technique form, which was first introduced in the early 90s in the context of the approximation of high-dimensional PDEs. The tests that we report show that, in accordance to the literature, a sparse grids construction can indeed be useful if the solution of the PDE at hand is sufficiently smooth. Sparse grids can also be useful in the case of non-smooth solutions when some a-priori knowledge on the location of the singularities of the solution can be exploited to devise suitable non-equispaced meshes. Finally, we remark that sparse grids can be seen as a simple way to parallelize pre-existing serial IGA solvers in a straightforward fashion, which can be beneficial in many practical situations.

New sparse matrix solver in the KIKO3D 3-dimensional reactor dynamics code

International Nuclear Information System (INIS)

Panka, I.; Kereszturi, A.; Hegedus, C.

2005-01-01

The goal of this paper is to present a more effective method Bi-CGSTAB for accelerating the large sparse matrix equation solution in the KIKO3D code. This equation system is obtained by using the factorization of the improved quasi static (IQS) method for the time dependent nodal kinetic equations. In the old methodology standard large sparse matrix techniques were considered, where Gauss-Seidel preconditioning and a GMRES-type solver were applied. The validation of KIKO3D using Bi-CGSTAB has been performed by solving of a VVER-1000 kinetic benchmark problem. Additionally, the convergence characteristics were investigated in given macro time steps of Control Rod Ejection transients. The results have been obtained by the old GMRES and new Bi-CGSTAB methods are compared. (author)

Language Recognition via Sparse Coding

Science.gov (United States)

2016-09-08

explanation is that sparse coding can achieve a near-optimal approximation of much complicated nonlinear relationship through local and piecewise linear...training examples, where x(i) ∈ RN is the ith example in the batch. Optionally, X can be normalized and whitened before sparse coding for better result...normalized input vectors are then ZCA- whitened [20]. Em- pirically, we choose ZCA- whitening over PCA- whitening , and there is no dimensionality reduction

A distributed-memory hierarchical solver for general sparse linear systems

Energy Technology Data Exchange (ETDEWEB)

Chen, Chao [Stanford Univ., CA (United States). Inst. for Computational and Mathematical Engineering; Pouransari, Hadi [Stanford Univ., CA (United States). Dept. of Mechanical Engineering; Rajamanickam, Sivasankaran [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research; Boman, Erik G. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research; Darve, Eric [Stanford Univ., CA (United States). Inst. for Computational and Mathematical Engineering and Dept. of Mechanical Engineering

2017-12-20

We present a parallel hierarchical solver for general sparse linear systems on distributed-memory machines. For large-scale problems, this fully algebraic algorithm is faster and more memory-efficient than sparse direct solvers because it exploits the low-rank structure of fill-in blocks. Depending on the accuracy of low-rank approximations, the hierarchical solver can be used either as a direct solver or as a preconditioner. The parallel algorithm is based on data decomposition and requires only local communication for updating boundary data on every processor. Moreover, the computation-to-communication ratio of the parallel algorithm is approximately the volume-to-surface-area ratio of the subdomain owned by every processor. We also provide various numerical results to demonstrate the versatility and scalability of the parallel algorithm.

Sparse seismic imaging using variable projection

NARCIS (Netherlands)

Aravkin, Aleksandr Y.; Tu, Ning; van Leeuwen, Tristan

2013-01-01

We consider an important class of signal processing problems where the signal of interest is known to be sparse, and can be recovered from data given auxiliary information about how the data was generated. For example, a sparse Green's function may be recovered from seismic experimental data using

Sparse PCA with Oracle Property.

Science.gov (United States)

Gu, Quanquan; Wang, Zhaoran; Liu, Han

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

Structural Sparse Tracking

KAUST Repository

Zhang, Tianzhu; Yang, Ming-Hsuan; Ahuja, Narendra; Ghanem, Bernard; Yan, Shuicheng; Xu, Changsheng; Liu, Si

2015-01-01

candidate. We show that our SST algorithm accommodates most existing sparse trackers with the respective merits. Both qualitative and quantitative evaluations on challenging benchmark image sequences demonstrate that the proposed SST algorithm performs

Sparse Representations of Hyperspectral Images

KAUST Repository

Swanson, Robin J.

2015-11-23

Hyperspectral image data has long been an important tool for many areas of sci- ence. The addition of spectral data yields significant improvements in areas such as object and image classification, chemical and mineral composition detection, and astronomy. Traditional capture methods for hyperspectral data often require each wavelength to be captured individually, or by sacrificing spatial resolution. Recently there have been significant improvements in snapshot hyperspectral captures using, in particular, compressed sensing methods. As we move to a compressed sensing image formation model the need for strong image priors to shape our reconstruction, as well as sparse basis become more important. Here we compare several several methods for representing hyperspectral images including learned three dimensional dictionaries, sparse convolutional coding, and decomposable nonlocal tensor dictionaries. Addi- tionally, we further explore their parameter space to identify which parameters provide the most faithful and sparse representations.

Sparse Representations of Hyperspectral Images

KAUST Repository

Swanson, Robin J.

2015-01-01

Hyperspectral image data has long been an important tool for many areas of sci- ence. The addition of spectral data yields significant improvements in areas such as object and image classification, chemical and mineral composition detection, and astronomy. Traditional capture methods for hyperspectral data often require each wavelength to be captured individually, or by sacrificing spatial resolution. Recently there have been significant improvements in snapshot hyperspectral captures using, in particular, compressed sensing methods. As we move to a compressed sensing image formation model the need for strong image priors to shape our reconstruction, as well as sparse basis become more important. Here we compare several several methods for representing hyperspectral images including learned three dimensional dictionaries, sparse convolutional coding, and decomposable nonlocal tensor dictionaries. Addi- tionally, we further explore their parameter space to identify which parameters provide the most faithful and sparse representations.

Supervised Convolutional Sparse Coding

KAUST Repository

Affara, Lama Ahmed

2018-04-08

Convolutional Sparse Coding (CSC) is a well-established image representation model especially suited for image restoration tasks. In this work, we extend the applicability of this model by proposing a supervised approach to convolutional sparse coding, which aims at learning discriminative dictionaries instead of purely reconstructive ones. We incorporate a supervised regularization term into the traditional unsupervised CSC objective to encourage the final dictionary elements to be discriminative. Experimental results show that using supervised convolutional learning results in two key advantages. First, we learn more semantically relevant filters in the dictionary and second, we achieve improved image reconstruction on unseen data.

Exploiting Data Sparsity for Large-Scale Matrix Computations

KAUST Repository

Akbudak, Kadir

2018-02-24

Exploiting data sparsity in dense matrices is an algorithmic bridge between architectures that are increasingly memory-austere on a per-core basis and extreme-scale applications. The Hierarchical matrix Computations on Manycore Architectures (HiCMA) library tackles this challenging problem by achieving significant reductions in time to solution and memory footprint, while preserving a specified accuracy requirement of the application. HiCMA provides a high-performance implementation on distributed-memory systems of one of the most widely used matrix factorization in large-scale scientific applications, i.e., the Cholesky factorization. It employs the tile low-rank data format to compress the dense data-sparse off-diagonal tiles of the matrix. It then decomposes the matrix computations into interdependent tasks and relies on the dynamic runtime system StarPU for asynchronous out-of-order scheduling, while allowing high user-productivity. Performance comparisons and memory footprint on matrix dimensions up to eleven million show a performance gain and memory saving of more than an order of magnitude for both metrics on thousands of cores, against state-of-the-art open-source and vendor optimized numerical libraries. This represents an important milestone in enabling large-scale matrix computations toward solving big data problems in geospatial statistics for climate/weather forecasting applications.

Exploiting Data Sparsity for Large-Scale Matrix Computations

KAUST Repository

Akbudak, Kadir; Ltaief, Hatem; Mikhalev, Aleksandr; Charara, Ali; Keyes, David E.

2018-01-01

Exploiting data sparsity in dense matrices is an algorithmic bridge between architectures that are increasingly memory-austere on a per-core basis and extreme-scale applications. The Hierarchical matrix Computations on Manycore Architectures (HiCMA) library tackles this challenging problem by achieving significant reductions in time to solution and memory footprint, while preserving a specified accuracy requirement of the application. HiCMA provides a high-performance implementation on distributed-memory systems of one of the most widely used matrix factorization in large-scale scientific applications, i.e., the Cholesky factorization. It employs the tile low-rank data format to compress the dense data-sparse off-diagonal tiles of the matrix. It then decomposes the matrix computations into interdependent tasks and relies on the dynamic runtime system StarPU for asynchronous out-of-order scheduling, while allowing high user-productivity. Performance comparisons and memory footprint on matrix dimensions up to eleven million show a performance gain and memory saving of more than an order of magnitude for both metrics on thousands of cores, against state-of-the-art open-source and vendor optimized numerical libraries. This represents an important milestone in enabling large-scale matrix computations toward solving big data problems in geospatial statistics for climate/weather forecasting applications.

Structure-aware Local Sparse Coding for Visual Tracking

KAUST Repository

Qi, Yuankai

2018-01-24

Sparse coding has been applied to visual tracking and related vision problems with demonstrated success in recent years. Existing tracking methods based on local sparse coding sample patches from a target candidate and sparsely encode these using a dictionary consisting of patches sampled from target template images. The discriminative strength of existing methods based on local sparse coding is limited as spatial structure constraints among the template patches are not exploited. To address this problem, we propose a structure-aware local sparse coding algorithm which encodes a target candidate using templates with both global and local sparsity constraints. For robust tracking, we show local regions of a candidate region should be encoded only with the corresponding local regions of the target templates that are the most similar from the global view. Thus, a more precise and discriminative sparse representation is obtained to account for appearance changes. To alleviate the issues with tracking drifts, we design an effective template update scheme. Extensive experiments on challenging image sequences demonstrate the effectiveness of the proposed algorithm against numerous stateof- the-art methods.

Link Prediction via Convex Nonnegative Matrix Factorization on Multiscale Blocks

Directory of Open Access Journals (Sweden)

Enming Dong

2014-01-01

Full Text Available Low rank matrices approximations have been used in link prediction for networks, which are usually global optimal methods and lack of using the local information. The block structure is a significant local feature of matrices: entities in the same block have similar values, which implies that links are more likely to be found within dense blocks. We use this insight to give a probabilistic latent variable model for finding missing links by convex nonnegative matrix factorization with block detection. The experiments show that this method gives better prediction accuracy than original method alone. Different from the original low rank matrices approximations methods for link prediction, the sparseness of solutions is in accord with the sparse property for most real complex networks. Scaling to massive size network, we use the block information mapping matrices onto distributed architectures and give a divide-and-conquer prediction method. The experiments show that it gives better results than common neighbors method when the networks have a large number of missing links.

A Generalized Lanczos-QR Technique for Structural Analysis

DEFF Research Database (Denmark)

Vissing, S.

systems with very special properties. Due to the finite discretization the matrices are sparse and a relatively large number of problems also has real and symmetric matrices. The matrix equation for an undamped vibration contains two matrices describing tangent stiffness and mass distributions......Within the field of solid mechanics such as structural dynamics and linearized as well as non-linear stability, the eigenvalue problem plays an important role. In the class of finite element and finite difference discretized problems these engineering problems are characterized by large matrix....... Alternatively, in a stability analysis, tangent stiffness and geometric stiffness matrices are introduced into an eigenvalue problem used to determine possible bifurcation points. The common basis for these types of problems is that the matrix equation describing the problem contains two real, symmetric...

Basal Cell Carcinoma With Matrical Differentiation: Clinicopathologic, Immunohistochemical, and Molecular Biological Study of 22 Cases.

Science.gov (United States)

Kyrpychova, Liubov; Carr, Richard A; Martinek, Petr; Vanecek, Tomas; Perret, Raul; Chottová-Dvořáková, Magdalena; Zamecnik, Michal; Hadravsky, Ladislav; Michal, Michal; Kazakov, Dmitry V

2017-06-01

. Immunohistochemical analysis for BerEP4, EMA, and β-catenin can be helpful in limited biopsy specimens. From a molecular biological prospective, BCC and matrical components appear to share some of the gene mutations but have differences in others, but this observation must be validated in a large series.

Chemiluminescence in cryogenic matrices

Science.gov (United States)

Lotnik, S. V.; Kazakov, Valeri P.

1989-04-01

The literature data on chemiluminescence (CL) in cryogenic matrices have been classified and correlated for the first time. The role of studies on phosphorescence and CL at low temperatures in the development of cryochemistry is shown. The features of low-temperature CL in matrices of nitrogen and inert gases (fine structure of spectra, matrix effects) and the data on the mobility and reactivity of atoms and radicals at very low temperatures are examined. The trends in the development of studies on CL in cryogenic matrices, such as the search for systems involving polyatomic molecules and extending the forms of CL reactions, are followed. The reactions of active nitrogen with hydrocarbons that are accompanied by light emission and CL in the oxidation of carbenes at T >= 77 K are examined. The bibliography includes 112 references.

Sparse Frequency Waveform Design for Radar-Embedded Communication

Directory of Open Access Journals (Sweden)

Chaoyun Mai

2016-01-01

Full Text Available According to the Tag application with function of covert communication, a method for sparse frequency waveform design based on radar-embedded communication is proposed. Firstly, sparse frequency waveforms are designed based on power spectral density fitting and quasi-Newton method. Secondly, the eigenvalue decomposition of the sparse frequency waveform sequence is used to get the dominant space. Finally the communication waveforms are designed through the projection of orthogonal pseudorandom vectors in the vertical subspace. Compared with the linear frequency modulation waveform, the sparse frequency waveform can further improve the bandwidth occupation of communication signals, thus achieving higher communication rate. A certain correlation exists between the reciprocally orthogonal communication signals samples and the sparse frequency waveform, which guarantees the low SER (signal error rate and LPI (low probability of intercept. The simulation results verify the effectiveness of this method.

Noniterative MAP reconstruction using sparse matrix representations.

Science.gov (United States)

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

2009-09-01

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

Superresolving Black Hole Images with Full-Closure Sparse Modeling

Science.gov (United States)

Crowley, Chelsea; Akiyama, Kazunori; Fish, Vincent

2018-01-01

It is believed that almost all galaxies have black holes at their centers. Imaging a black hole is a primary objective to answer scientific questions relating to relativistic accretion and jet formation. The Event Horizon Telescope (EHT) is set to capture images of two nearby black holes, Sagittarius A* at the center of the Milky Way galaxy roughly 26,000 light years away and the other M87 which is in Virgo A, a large elliptical galaxy that is 50 million light years away. Sparse imaging techniques have shown great promise for reconstructing high-fidelity superresolved images of black holes from simulated data. Previous work has included the effects of atmospheric phase errors and thermal noise, but not systematic amplitude errors that arise due to miscalibration. We explore a full-closure imaging technique with sparse modeling that uses closure amplitudes and closure phases to improve the imaging process. This new technique can successfully handle data with systematic amplitude errors. Applying our technique to synthetic EHT data of M87, we find that full-closure sparse modeling can reconstruct images better than traditional methods and recover key structural information on the source, such as the shape and size of the predicted photon ring. These results suggest that our new approach will provide superior imaging performance for data from the EHT and other interferometric arrays.

Skew-adjacency matrices of graphs

NARCIS (Netherlands)

Cavers, M.; Cioaba, S.M.; Fallat, S.; Gregory, D.A.; Haemers, W.H.; Kirkland, S.J.; McDonald, J.J.; Tsatsomeros, M.

2012-01-01

The spectra of the skew-adjacency matrices of a graph are considered as a possible way to distinguish adjacency cospectral graphs. This leads to the following topics: graphs whose skew-adjacency matrices are all cospectral; relations between the matchings polynomial of a graph and the characteristic

The invariant theory of matrices

CERN Document Server

Concini, Corrado De

2017-01-01

This book gives a unified, complete, and self-contained exposition of the main algebraic theorems of invariant theory for matrices in a characteristic free approach. More precisely, it contains the description of polynomial functions in several variables on the set of m\\times m matrices with coefficients in an infinite field or even the ring of integers, invariant under simultaneous conjugation. Following Hermann Weyl's classical approach, the ring of invariants is described by formulating and proving the first fundamental theorem that describes a set of generators in the ring of invariants, and the second fundamental theorem that describes relations between these generators. The authors study both the case of matrices over a field of characteristic 0 and the case of matrices over a field of positive characteristic. While the case of characteristic 0 can be treated following a classical approach, the case of positive characteristic (developed by Donkin and Zubkov) is much harder. A presentation of this case...

Exact Inverse Matrices of Fermat and Mersenne Circulant Matrix

Directory of Open Access Journals (Sweden)

Yanpeng Zheng

2015-01-01

Full Text Available The well known circulant matrices are applied to solve networked systems. In this paper, circulant and left circulant matrices with the Fermat and Mersenne numbers are considered. The nonsingularity of these special matrices is discussed. Meanwhile, the exact determinants and inverse matrices of these special matrices are presented.

Enhancing Understanding of Transformation Matrices

Science.gov (United States)

Dick, Jonathan; Childrey, Maria

2012-01-01

With the Common Core State Standards' emphasis on transformations, teachers need a variety of approaches to increase student understanding. Teaching matrix transformations by focusing on row vectors gives students tools to create matrices to perform transformations. This empowerment opens many doors: Students are able to create the matrices for…

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

Science.gov (United States)

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.

Experiments with conjugate gradient algorithms for homotopy curve tracking

Science.gov (United States)

Irani, Kashmira M.; Ribbens, Calvin J.; Watson, Layne T.; Kamat, Manohar P.; Walker, Homer F.

1991-01-01

There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK is a mathematical software package implementing globally convergent homotopy algorithms with three different techniques for tracking a homotopy zero curve, and has separate routines for dense and sparse Jacobian matrices. The HOMPACK algorithms for sparse Jacobian matrices use a preconditioned conjugate gradient algorithm for the computation of the kernel of the homotopy Jacobian matrix, a required linear algebra step for homotopy curve tracking. Here, variants of the conjugate gradient algorithm are implemented in the context of homotopy curve tracking and compared with Craig's preconditioned conjugate gradient method used in HOMPACK. The test problems used include actual large scale, sparse structural mechanics problems.

CT Image Sequence Restoration Based on Sparse and Low-Rank Decomposition

Science.gov (United States)

Gou, Shuiping; Wang, Yueyue; Wang, Zhilong; Peng, Yong; Zhang, Xiaopeng; Jiao, Licheng; Wu, Jianshe

2013-01-01

Blurry organ boundaries and soft tissue structures present a major challenge in biomedical image restoration. In this paper, we propose a low-rank decomposition-based method for computed tomography (CT) image sequence restoration, where the CT image sequence is decomposed into a sparse component and a low-rank component. A new point spread function of Weiner filter is employed to efficiently remove blur in the sparse component; a wiener filtering with the Gaussian PSF is used to recover the average image of the low-rank component. And then we get the recovered CT image sequence by combining the recovery low-rank image with all recovery sparse image sequence. Our method achieves restoration results with higher contrast, sharper organ boundaries and richer soft tissue structure information, compared with existing CT image restoration methods. The robustness of our method was assessed with numerical experiments using three different low-rank models: Robust Principle Component Analysis (RPCA), Linearized Alternating Direction Method with Adaptive Penalty (LADMAP) and Go Decomposition (GoDec). Experimental results demonstrated that the RPCA model was the most suitable for the small noise CT images whereas the GoDec model was the best for the large noisy CT images. PMID:24023764

Group inverses of M-matrices and their applications

CERN Document Server

Kirkland, Stephen J

2013-01-01

Group inverses for singular M-matrices are useful tools not only in matrix analysis, but also in the analysis of stochastic processes, graph theory, electrical networks, and demographic models. Group Inverses of M-Matrices and Their Applications highlights the importance and utility of the group inverses of M-matrices in several application areas. After introducing sample problems associated with Leslie matrices and stochastic matrices, the authors develop the basic algebraic and spectral properties of the group inverse of a general matrix. They then derive formulas for derivatives of matrix f

Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs

KAUST Repository

Chkifa, Abdellah

2012-11-29

The numerical approximation of parametric partial differential equations is a computational challenge, in particular when the number of involved parameter is large. This paper considers a model class of second order, linear, parametric, elliptic PDEs on a bounded domain D with diffusion coefficients depending on the parameters in an affine manner. For such models, it was shown in [9, 10] that under very weak assumptions on the diffusion coefficients, the entire family of solutions to such equations can be simultaneously approximated in the Hilbert space V = H0 1(D) by multivariate sparse polynomials in the parameter vector y with a controlled number N of terms. The convergence rate in terms of N does not depend on the number of parameters in V, which may be arbitrarily large or countably infinite, thereby breaking the curse of dimensionality. However, these approximation results do not describe the concrete construction of these polynomial expansions, and should therefore rather be viewed as benchmark for the convergence analysis of numerical methods. The present paper presents an adaptive numerical algorithm for constructing a sequence of sparse polynomials that is proved to converge toward the solution with the optimal benchmark rate. Numerical experiments are presented in large parameter dimension, which confirm the effectiveness of the adaptive approach. © 2012 EDP Sciences, SMAI.

Storage of sparse files using parallel log-structured file system

Science.gov (United States)

Bent, John M.; Faibish, Sorin; Grider, Gary; Torres, Aaron

2017-11-07

A sparse file is stored without holes by storing a data portion of the sparse file using a parallel log-structured file system; and generating an index entry for the data portion, the index entry comprising a logical offset, physical offset and length of the data portion. The holes can be restored to the sparse file upon a reading of the sparse file. The data portion can be stored at a logical end of the sparse file. Additional storage efficiency can optionally be achieved by (i) detecting a write pattern for a plurality of the data portions and generating a single patterned index entry for the plurality of the patterned data portions; and/or (ii) storing the patterned index entries for a plurality of the sparse files in a single directory, wherein each entry in the single directory comprises an identifier of a corresponding sparse file.

Sparse reconstruction using distribution agnostic bayesian matching pursuit

KAUST Repository

Masood, Mudassir

2013-11-01

A fast matching pursuit method using a Bayesian approach is introduced for sparse signal recovery. This method performs Bayesian estimates of sparse signals even when the signal prior is non-Gaussian or unknown. It is agnostic on signal statistics and utilizes a priori statistics of additive noise and the sparsity rate of the signal, which are shown to be easily estimated from data if not available. The method utilizes a greedy approach and order-recursive updates of its metrics to find the most dominant sparse supports to determine the approximate minimum mean-square error (MMSE) estimate of the sparse signal. Simulation results demonstrate the power and robustness of our proposed estimator. © 2013 IEEE.

Image understanding using sparse representations

CERN Document Server

Thiagarajan, Jayaraman J; Turaga, Pavan; Spanias, Andreas

2014-01-01

Image understanding has been playing an increasingly crucial role in several inverse problems and computer vision. Sparse models form an important component in image understanding, since they emulate the activity of neural receptors in the primary visual cortex of the human brain. Sparse methods have been utilized in several learning problems because of their ability to provide parsimonious, interpretable, and efficient models. Exploiting the sparsity of natural signals has led to advances in several application areas including image compression, denoising, inpainting, compressed sensing, blin

Iterative solution of general sparse linear systems on clusters of workstations

Energy Technology Data Exchange (ETDEWEB)

Lo, Gen-Ching; Saad, Y. [Univ. of Minnesota, Minneapolis, MN (United States)

1996-12-31

Solving sparse irregularly structured linear systems on parallel platforms poses several challenges. First, sparsity makes it difficult to exploit data locality, whether in a distributed or shared memory environment. A second, perhaps more serious challenge, is to find efficient ways to precondition the system. Preconditioning techniques which have a large degree of parallelism, such as multicolor SSOR, often have a slower rate of convergence than their sequential counterparts. Finally, a number of other computational kernels such as inner products could ruin any gains gained from parallel speed-ups, and this is especially true on workstation clusters where start-up times may be high. In this paper we discuss these issues and report on our experience with PSPARSLIB, an on-going project for building a library of parallel iterative sparse matrix solvers.

Sparse regularization for force identification using dictionaries

Science.gov (United States)

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.

Sparse inpainting and isotropy

Energy Technology Data Exchange (ETDEWEB)

Feeney, Stephen M.; McEwen, Jason D.; Peiris, Hiranya V. [Department of Physics and Astronomy, University College London, Gower Street, London, WC1E 6BT (United Kingdom); Marinucci, Domenico; Cammarota, Valentina [Department of Mathematics, University of Rome Tor Vergata, via della Ricerca Scientifica 1, Roma, 00133 (Italy); Wandelt, Benjamin D., E-mail: s.feeney@imperial.ac.uk, E-mail: marinucc@axp.mat.uniroma2.it, E-mail: jason.mcewen@ucl.ac.uk, E-mail: h.peiris@ucl.ac.uk, E-mail: wandelt@iap.fr, E-mail: cammarot@axp.mat.uniroma2.it [Kavli Institute for Theoretical Physics, Kohn Hall, University of California, 552 University Road, Santa Barbara, CA, 93106 (United States)

2014-01-01

Sparse inpainting techniques are gaining in popularity as a tool for cosmological data analysis, in particular for handling data which present masked regions and missing observations. We investigate here the relationship between sparse inpainting techniques using the spherical harmonic basis as a dictionary and the isotropy properties of cosmological maps, as for instance those arising from cosmic microwave background (CMB) experiments. In particular, we investigate the possibility that inpainted maps may exhibit anisotropies in the behaviour of higher-order angular polyspectra. We provide analytic computations and simulations of inpainted maps for a Gaussian isotropic model of CMB data, suggesting that the resulting angular trispectrum may exhibit small but non-negligible deviations from isotropy.

Phenomenological mass matrices with a democratic warp

International Nuclear Information System (INIS)

Kleppe, A.

2018-01-01

Taking into account all available data on the mass sector, we obtain unitary rotation matrices that diagonalize the quark matrices by using a specific parametrization of the Cabibbo-Kobayashi-Maskawa mixing matrix. In this way, we find mass matrices for the up- and down-quark sectors of a specific, symmetric form, with traces of a democratic texture.

Sports drug testing using complementary matrices: Advantages and limitations.

Science.gov (United States)

Thevis, Mario; Geyer, Hans; Tretzel, Laura; Schänzer, Wilhelm

2016-10-25

Today, routine doping controls largely rely on testing whole blood, serum, and urine samples. These matrices allow comprehensively covering inorganic as well as low and high molecular mass organic analytes relevant to doping controls and are collecting and transferring from sampling sites to accredited anti-doping laboratories under standardized conditions. Various aspects including time and cost-effectiveness as well as intrusiveness and invasiveness of the sampling procedure but also analyte stability and breadth of the contained information have been motivation to consider and assess values potentially provided and added to modern sports drug testing programs by alternative matrices. Such alternatives could be dried blood spots (DBS), dried plasma spots (DPS), oral fluid (OF), exhaled breath (EB), and hair. In this review, recent developments and test methods concerning these alternative matrices and expected or proven contributions as well as limitations of these specimens in the context of the international anti-doping fight are presented and discussed, guided by current regulations for prohibited substances and methods of doping as established by the World Anti-Doping Agency (WADA). Focusing on literature published between 2011 and 2015, examples for doping control analytical assays concerning non-approved substances, anabolic agents, peptide hormones/growth factors/related substances and mimetics, β 2 -agonists, hormone and metabolic modulators, diuretics and masking agents, stimulants, narcotics, cannabinoids, glucocorticoids, and beta-blockers were selected to outline the advantages and limitations of the aforementioned alternative matrices as compared to conventional doping control samples (i.e. urine and blood/serum). Copyright © 2016 Elsevier B.V. All rights reserved.

Diagonalization of the mass matrices

International Nuclear Information System (INIS)

Rhee, S.S.

1984-01-01

It is possible to make 20 types of 3x3 mass matrices which are hermitian. We have obtained unitary matrices which could diagonalize each mass matrix. Since the three elements of mass matrix can be expressed in terms of the three eigenvalues, msub(i), we can also express the unitary matrix in terms of msub(i). (Author)

Sparse Vector Distributions and Recovery from Compressed Sensing

DEFF Research Database (Denmark)

Sturm, Bob L.

It is well known that the performance of sparse vector recovery algorithms from compressive measurements can depend on the distribution underlying the non-zero elements of a sparse vector. However, the extent of these effects has yet to be explored, and formally presented. In this paper, I...... empirically investigate this dependence for seven distributions and fifteen recovery algorithms. The two morals of this work are: 1) any judgement of the recovery performance of one algorithm over that of another must be prefaced by the conditions for which this is observed to be true, including sparse vector...... distributions, and the criterion for exact recovery; and 2) a recovery algorithm must be selected carefully based on what distribution one expects to underlie the sensed sparse signal....

The construction of factorized S-matrices

International Nuclear Information System (INIS)

Chudnovsky, D.V.

1981-01-01

We study the relationships between factorized S-matrices given as representations of the Zamolodchikov algebra and exactly solvable models constructed using the Baxter method. Several new examples of symmetric and non-symmetric factorized S-matrices are proposed. (orig.)

Dissimilarities of reduced density matrices and eigenstate thermalization hypothesis

Science.gov (United States)

He, Song; Lin, Feng-Li; Zhang, Jia-ju

2017-12-01

We calculate various quantities that characterize the dissimilarity of reduced density matrices for a short interval of length ℓ in a two-dimensional (2D) large central charge conformal field theory (CFT). These quantities include the Rényi entropy, entanglement entropy, relative entropy, Jensen-Shannon divergence, as well as the Schatten 2-norm and 4-norm. We adopt the method of operator product expansion of twist operators, and calculate the short interval expansion of these quantities up to order of ℓ9 for the contributions from the vacuum conformal family. The formal forms of these dissimilarity measures and the derived Fisher information metric from contributions of general operators are also given. As an application of the results, we use these dissimilarity measures to compare the excited and thermal states, and examine the eigenstate thermalization hypothesis (ETH) by showing how they behave in high temperature limit. This would help to understand how ETH in 2D CFT can be defined more precisely. We discuss the possibility that all the dissimilarity measures considered here vanish when comparing the reduced density matrices of an excited state and a generalized Gibbs ensemble thermal state. We also discuss ETH for a microcanonical ensemble thermal state in a 2D large central charge CFT, and find that it is approximately satisfied for a small subsystem and violated for a large subsystem.

Visual recognition and inference using dynamic overcomplete sparse learning.

Science.gov (United States)

Murray, Joseph F; Kreutz-Delgado, Kenneth

2007-09-01

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

Dense tissue-like collagen matrices formed in cell-free conditions.

Science.gov (United States)

Mosser, Gervaise; Anglo, Anny; Helary, Christophe; Bouligand, Yves; Giraud-Guille, Marie-Madeleine

2006-01-01

A new protocol was developed to produce dense organized collagen matrices hierarchically ordered on a large scale. It consists of a two stage process: (1) the organization of a collagen solution and (2) the stabilization of the organizations by a sol-gel transition that leads to the formation of collagen fibrils. This new protocol relies on the continuous injection of an acid-soluble collagen solution into glass microchambers. It leads to extended concentration gradients of collagen, ranging from 5 to 1000 mg/ml. The self-organization of collagen solutions into a wide array of spatial organizations was investigated. The final matrices obtained by this procedure varied in concentration, structure and density. Changes in the liquid state of the samples were followed by polarized light microscopy, and the final stabilized gel states obtained after fibrillogenesis were analyzed by both light and electron microscopy. Typical organizations extended homogeneously by up to three centimetres in one direction and several hundreds of micrometers in other directions. Fibrillogenesis of collagen solutions of high and low concentrations led to fibrils spatially arranged as has been described in bone and derm, respectively. Moreover, a relationship was revealed between the collagen concentration and the aggregation of and rotational angles between lateral fibrils. These results constitute a strong base from which to further develop highly enriched collagen matrices that could lead to substitutes that mimic connective tissues. The matrices thus obtained may also be good candidates for the study of the three-dimensional migration of cells.

Sparse approximation of multilinear problems with applications to kernel-based methods in UQ

KAUST Repository

Nobile, Fabio; Tempone, Raul; Wolfers, Sö ren

2017-01-01

We provide a framework for the sparse approximation of multilinear problems and show that several problems in uncertainty quantification fit within this framework. In these problems, the value of a multilinear map has to be approximated using approximations of different accuracy and computational work of the arguments of this map. We propose and analyze a generalized version of Smolyak’s algorithm, which provides sparse approximation formulas with convergence rates that mitigate the curse of dimension that appears in multilinear approximation problems with a large number of arguments. We apply the general framework to response surface approximation and optimization under uncertainty for parametric partial differential equations using kernel-based approximation. The theoretical results are supplemented by numerical experiments.

Sparse approximation of multilinear problems with applications to kernel-based methods in UQ

KAUST Repository

Nobile, Fabio

2017-11-16

We provide a framework for the sparse approximation of multilinear problems and show that several problems in uncertainty quantification fit within this framework. In these problems, the value of a multilinear map has to be approximated using approximations of different accuracy and computational work of the arguments of this map. We propose and analyze a generalized version of Smolyak’s algorithm, which provides sparse approximation formulas with convergence rates that mitigate the curse of dimension that appears in multilinear approximation problems with a large number of arguments. We apply the general framework to response surface approximation and optimization under uncertainty for parametric partial differential equations using kernel-based approximation. The theoretical results are supplemented by numerical experiments.

Matrices in Engineering Problems

CERN Document Server

Tobias, Marvin

2011-01-01

This book is intended as an undergraduate text introducing matrix methods as they relate to engineering problems. It begins with the fundamentals of mathematics of matrices and determinants. Matrix inversion is discussed, with an introduction of the well known reduction methods. Equation sets are viewed as vector transformations, and the conditions of their solvability are explored. Orthogonal matrices are introduced with examples showing application to many problems requiring three dimensional thinking. The angular velocity matrix is shown to emerge from the differentiation of the 3-D orthogo

A Brief Historical Introduction to Matrices and Their Applications

Science.gov (United States)

Debnath, L.

2014-01-01

This paper deals with the ancient origin of matrices, and the system of linear equations. Included are algebraic properties of matrices, determinants, linear transformations, and Cramer's Rule for solving the system of algebraic equations. Special attention is given to some special matrices, including matrices in graph theory and electrical…

Visual properties and memorising scenes: Effects of image-space sparseness and uniformity.

Science.gov (United States)

Lukavský, Jiří; Děchtěrenko, Filip

2017-10-01

Previous studies have demonstrated that humans have a remarkable capacity to memorise a large number of scenes. The research on memorability has shown that memory performance can be predicted by the content of an image. We explored how remembering an image is affected by the image properties within the context of the reference set, including the extent to which it is different from its neighbours (image-space sparseness) and if it belongs to the same category as its neighbours (uniformity). We used a reference set of 2,048 scenes (64 categories), evaluated pairwise scene similarity using deep features from a pretrained convolutional neural network (CNN), and calculated the image-space sparseness and uniformity for each image. We ran three memory experiments, varying the memory workload with experiment length and colour/greyscale presentation. We measured the sensitivity and criterion value changes as a function of image-space sparseness and uniformity. Across all three experiments, we found separate effects of 1) sparseness on memory sensitivity, and 2) uniformity on the recognition criterion. People better remembered (and correctly rejected) images that were more separated from others. People tended to make more false alarms and fewer miss errors in images from categorically uniform portions of the image-space. We propose that both image-space properties affect human decisions when recognising images. Additionally, we found that colour presentation did not yield better memory performance over grayscale images.

The chiral Gaussian two-matrix ensemble of real asymmetric matrices

International Nuclear Information System (INIS)

Akemann, G; Phillips, M J; Sommers, H-J

2010-01-01

We solve a family of Gaussian two-matrix models with rectangular N x (N + ν) matrices, having real asymmetric matrix elements and depending on a non-Hermiticity parameter μ. Our model can be thought of as the chiral extension of the real Ginibre ensemble, relevant for Dirac operators in the same symmetry class. It has the property that its eigenvalues are either real, purely imaginary or come in complex conjugate eigenvalue pairs. The eigenvalue joint probability distribution for our model is explicitly computed, leading to a non-Gaussian distribution including K-Bessel functions. All n-point density correlation functions are expressed for finite N in terms of a Pfaffian form. This contains a kernel involving Laguerre polynomials in the complex plane as a building block which was previously computed by the authors. This kernel can be expressed in terms of the kernel for complex non-Hermitian matrices, generalizing the known relation among ensembles of Hermitian random matrices. Compact expressions are given for the density at finite N as an example, as well as its microscopic large-N limits at the origin for fixed ν at strong and weak non-Hermiticity.

A fast sparse reconstruction algorithm for electrical tomography

International Nuclear Information System (INIS)

Zhao, Jia; Xu, Yanbin; Tan, Chao; Dong, Feng

2014-01-01

Electrical tomography (ET) has been widely investigated due to its advantages of being non-radiative, low-cost and high-speed. However, the image reconstruction of ET is a nonlinear and ill-posed inverse problem and the imaging results are easily affected by measurement noise. A sparse reconstruction algorithm based on L 1 regularization is robust to noise and consequently provides a high quality of reconstructed images. In this paper, a sparse reconstruction by separable approximation algorithm (SpaRSA) is extended to solve the ET inverse problem. The algorithm is competitive with the fastest state-of-the-art algorithms in solving the standard L 2 −L 1 problem. However, it is computationally expensive when the dimension of the matrix is large. To further improve the calculation speed of solving inverse problems, a projection method based on the Krylov subspace is employed and combined with the SpaRSA algorithm. The proposed algorithm is tested with image reconstruction of electrical resistance tomography (ERT). Both simulation and experimental results demonstrate that the proposed method can reduce the computational time and improve the noise robustness for the image reconstruction. (paper)

Structure-based bayesian sparse reconstruction

KAUST Repository

Quadeer, Ahmed Abdul

2012-12-01

Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical information (Gaussian or otherwise) to obtain near optimal estimates. In addition, we make use of the rich structure of the sensing matrix encountered in many signal processing applications to develop a fast sparse recovery algorithm. The computational complexity of the proposed algorithm is very low compared with the widely used convex relaxation methods as well as greedy matching pursuit techniques, especially at high sparsity. © 1991-2012 IEEE.

Sparse Power-Law Network Model for Reliable Statistical Predictions Based on Sampled Data

Directory of Open Access Journals (Sweden)

Alexander P. Kartun-Giles

2018-04-01

Full Text Available A projective network model is a model that enables predictions to be made based on a subsample of the network data, with the predictions remaining unchanged if a larger sample is taken into consideration. An exchangeable model is a model that does not depend on the order in which nodes are sampled. Despite a large variety of non-equilibrium (growing and equilibrium (static sparse complex network models that are widely used in network science, how to reconcile sparseness (constant average degree with the desired statistical properties of projectivity and exchangeability is currently an outstanding scientific problem. Here we propose a network process with hidden variables which is projective and can generate sparse power-law networks. Despite the model not being exchangeable, it can be closely related to exchangeable uncorrelated networks as indicated by its information theory characterization and its network entropy. The use of the proposed network process as a null model is here tested on real data, indicating that the model offers a promising avenue for statistical network modelling.

Hypercyclic Abelian Semigroups of Matrices on Cn

International Nuclear Information System (INIS)

Ayadi, Adlene; Marzougui, Habib

2010-07-01

We give a complete characterization of existence of dense orbit for any abelian semigroup of matrices on C n . For finitely generated semigroups, this characterization is explicit and is used to determine the minimal number of matrices in normal form over C which forms a hypercyclic abelian semigroup on C n . In particular, we show that no abelian semigroup generated by n matrices on C n can be hypercyclic. (author)

Generalized Perron--Frobenius Theorem for Nonsquare Matrices

OpenAIRE

Avin, Chen; Borokhovich, Michael; Haddad, Yoram; Kantor, Erez; Lotker, Zvi; Parter, Merav; Peleg, David

2013-01-01

The celebrated Perron--Frobenius (PF) theorem is stated for irreducible nonnegative square matrices, and provides a simple characterization of their eigenvectors and eigenvalues. The importance of this theorem stems from the fact that eigenvalue problems on such matrices arise in many fields of science and engineering, including dynamical systems theory, economics, statistics and optimization. However, many real-life scenarios give rise to nonsquare matrices. A natural question is whether the...

Robust Single Image Super-Resolution via Deep Networks With Sparse Prior.

Science.gov (United States)

Liu, Ding; Wang, Zhaowen; Wen, Bihan; Yang, Jianchao; Han, Wei; Huang, Thomas S

2016-07-01

Single image super-resolution (SR) is an ill-posed problem, which tries to recover a high-resolution image from its low-resolution observation. To regularize the solution of the problem, previous methods have focused on designing good priors for natural images, such as sparse representation, or directly learning the priors from a large data set with models, such as deep neural networks. In this paper, we argue that domain expertise from the conventional sparse coding model can be combined with the key ingredients of deep learning to achieve further improved results. We demonstrate that a sparse coding model particularly designed for SR can be incarnated as a neural network with the merit of end-to-end optimization over training data. The network has a cascaded structure, which boosts the SR performance for both fixed and incremental scaling factors. The proposed training and testing schemes can be extended for robust handling of images with additional degradation, such as noise and blurring. A subjective assessment is conducted and analyzed in order to thoroughly evaluate various SR techniques. Our proposed model is tested on a wide range of images, and it significantly outperforms the existing state-of-the-art methods for various scaling factors both quantitatively and perceptually.

Greedy vs. L1 convex optimization in sparse coding

DEFF Research Database (Denmark)

Ren, Huamin; Pan, Hong; Olsen, Søren Ingvor

2015-01-01

Sparse representation has been applied successfully in many image analysis applications, including abnormal event detection, in which a baseline is to learn a dictionary from the training data and detect anomalies from its sparse codes. During this procedure, sparse codes which can be achieved...... solutions. Considering the property of abnormal event detection, i.e., only normal videos are used as training data due to practical reasons, effective codes in classification application may not perform well in abnormality detection. Therefore, we compare the sparse codes and comprehensively evaluate...... their performance from various aspects to better understand their applicability, including computation time, reconstruction error, sparsity, detection...

An in-depth study of sparse codes on abnormality detection

DEFF Research Database (Denmark)

Ren, Huamin; Pan, Hong; Olsen, Søren Ingvor

2016-01-01

Sparse representation has been applied successfully in abnormal event detection, in which the baseline is to learn a dictionary accompanied by sparse codes. While much emphasis is put on discriminative dictionary construction, there are no comparative studies of sparse codes regarding abnormality...... are carried out from various angles to better understand the applicability of sparse codes, including computation time, reconstruction error, sparsity, detection accuracy, and their performance combining various detection methods. The experiment results show that combining OMP codes with maximum coordinate...

On the construction of quantum field theories with factorizing S-matrices

Energy Technology Data Exchange (ETDEWEB)

Lechner, G.

2006-05-24

The subject of this thesis is a novel construction method for interacting relativistic quantum field theories on two-dimensional Minkowski space. Employing the algebraic framework of quantum field theory, it is shown under which conditions an algebra of observables localized in a wedge-shaped region of spacetime can be used to construct model theories. A crucial input in this context is the modular nuclearity condition for wedge algebras, which implies the existence of local observables. As an application of the new method, a rigorous construction of a large family of models with factorizing S-matrices is obtained. In an inverse scattering approach, a given factorizing scattering operator is used to define certain semi-localized Wightman fields associated to it. With the help of these fields, a wedge algebra can be defined, which determines the local observable content of a well-defined quantum field theory. In this approach, the modular nuclearity condition translates to certain analyticity and boundedness conditions on the formfactors of wedge-local observables. These conditions are shown to hold for a large class of underlying S-matrices, including the scattering operators of the Sinh-Gordon model and the scaling Ising model as special examples. The so constructed models are investigated with respect to their scattering properties. They are shown to solve the inverse scattering problem for the underlying S-matrices, and a proof of asymptotic completeness for these models is given. (orig.)

Sparse Principal Component Analysis in Medical Shape Modeling

DEFF Research Database (Denmark)

Sjöstrand, Karl; Stegmann, Mikkel Bille; Larsen, Rasmus

2006-01-01

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...... analysis in medicine. Results for three different data sets are given in relation to standard PCA and sparse PCA by simple thresholding of sufficiently 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...

Sparse reconstruction using distribution agnostic bayesian matching pursuit

KAUST Repository

Masood, Mudassir; Al-Naffouri, Tareq Y.

2013-01-01

A fast matching pursuit method using a Bayesian approach is introduced for sparse signal recovery. This method performs Bayesian estimates of sparse signals even when the signal prior is non-Gaussian or unknown. It is agnostic on signal statistics

THE ALGORITHM AND PROGRAM OF M-MATRICES SEARCH AND STUDY

Directory of Open Access Journals (Sweden)

Y. N. Balonin

2013-05-01

Full Text Available The algorithm and software for search and study of orthogonal bases matrices – minimax matrices (M-matrix are considered. The algorithm scheme is shown, comments on calculation blocks are given, and interface of the MMatrix software system developed with participation of the authors is explained. The results of the universal algorithm work are presented as Hadamard matrices, Belevitch matrices (C-matrices, conference matrices and matrices of even and odd orders complementary and closely related to those ones by their properties, in particular, the matrix of the 22-th order for which there is no C-matrix. Examples of portraits for alternative matrices of the 255-th and the 257-th orders are given corresponding to the sequences of Mersenne and Fermat numbers. A new way to get Hadamard matrices is explained, different from the previously known procedures based on iterative processes and calculations of Lagrange symbols, with theoretical and practical meaning.

High-sensitivity direct analysis of aflatoxins in peanuts and cereal matrices by ultra-performance liquid chromatography with fluorescence detection involving a large volume flow cell.

Science.gov (United States)

Oulkar, Dasharath; Goon, Arnab; Dhanshetty, Manisha; Khan, Zareen; Satav, Sagar; Banerjee, Kaushik

2018-04-03

This paper reports a sensitive and cost effective method of analysis for aflatoxins B1, B2, G1 and G2. The sample preparation method was primarily optimised in peanuts, followed by its validation in a range of peanut-processed products and cereal (rice, corn, millets) matrices. Peanut slurry [12.5 g peanut + 12.5 mL water] was extracted with methanol: water (8:2, 100 mL), cleaned through an immunoaffinity column and thereafter measured directly by ultra-performance liquid chromatography-fluorescence (UPLC-FLD) detection, within a chromatographic runtime of 5 minutes. The use of a large volume flow cell in the FLD nullified the requirement of any post-column derivatisation and provided the lowest ever reported limits of quantification of 0.025 for B1 and G1 and 0.01 μg/kg for B2 and G2. The single laboratory validation of the method provided acceptable selectivity, linearity, recovery and precision for reliable quantifications in all the test matrices as well as demonstrated compliance with the EC 401/2006 guidelines for analytical quality control of aflatoxins in foodstuffs.

The modified Gauss diagonalization of polynomial matrices

International Nuclear Information System (INIS)

Saeed, K.

1982-10-01

The Gauss algorithm for diagonalization of constant matrices is modified for application to polynomial matrices. Due to this modification the diagonal elements become pure polynomials rather than rational functions. (author)

Quantum Hilbert matrices and orthogonal polynomials

DEFF Research Database (Denmark)

Andersen, Jørgen Ellegaard; Berg, Christian

2009-01-01

Using the notion of quantum integers associated with a complex number q≠0 , we define the quantum Hilbert matrix and various extensions. They are Hankel matrices corresponding to certain little q -Jacobi polynomials when |q|<1 , and for the special value they are closely related to Hankel matrice...

Discrete canonical transforms that are Hadamard matrices

International Nuclear Information System (INIS)

Healy, John J; Wolf, Kurt Bernardo

2011-01-01

The group Sp(2,R) of symplectic linear canonical transformations has an integral kernel which has quadratic and linear phases, and which is realized by the geometric paraxial optical model. The discrete counterpart of this model is a finite Hamiltonian system that acts on N-point signals through N x N matrices whose elements also have a constant absolute value, although they do not form a representation of that group. Those matrices that are also unitary are Hadamard matrices. We investigate the manifolds of these N x N matrices under the Sp(2,R) equivalence imposed by the model, and find them to be on two-sided cosets. By means of an algorithm we determine representatives that lead to collections of mutually unbiased bases.

Abel-grassmann's groupoids of modulo matrices

International Nuclear Information System (INIS)

Javaid, Q.; Awan, M.D.; Naqvi, S.H.A.

2016-01-01

The binary operation of usual addition is associative in all matrices over R. However, a binary operation of addition in matrices over Z/sub n/ of a nonassociative structures of AG-groupoids and AG-groups are defined and investigated here. It is shown that both these structures exist for every integer n >≥ 3. Various properties of these structures are explored like: (i) Every AG-groupoid of matrices over Z/sub n/ is transitively commutative AG-groupoid and is a cancellative AG-groupoid if n is prime. (ii) Every AG-groupoid of matrices over Z/sub n/ of Type-II is a T/sup 3/-AG-groupoid. (iii) An AG-groupoid of matrices over Z/sub n/ ; G /sub nAG/(t,u), is an AG-band, if t+u=1(mod n). (author)

Parallel transposition of sparse data structures

DEFF Research Database (Denmark)

Wang, Hao; Liu, Weifeng; Hou, Kaixi

2016-01-01

Many applications in computational sciences and social sciences exploit sparsity and connectivity of acquired data. Even though many parallel sparse primitives such as sparse matrix-vector (SpMV) multiplication have been extensively studied, some other important building blocks, e.g., parallel tr...... transposition in the latest vendor-supplied library on an Intel multicore CPU platform, and the MergeTrans approach achieves on average of 3.4-fold (up to 11.7-fold) speedup on an Intel Xeon Phi many-core processor....

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

Science.gov (United States)

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.

Random volumes from matrices

Energy Technology Data Exchange (ETDEWEB)

Fukuma, Masafumi; Sugishita, Sotaro; Umeda, Naoya [Department of Physics, Kyoto University,Kitashirakawa Oiwake-cho, Kyoto 606-8502 (Japan)

2015-07-17

We propose a class of models which generate three-dimensional random volumes, where each configuration consists of triangles glued together along multiple hinges. The models have matrices as the dynamical variables and are characterized by semisimple associative algebras A. Although most of the diagrams represent configurations which are not manifolds, we show that the set of possible diagrams can be drastically reduced such that only (and all of the) three-dimensional manifolds with tetrahedral decompositions appear, by introducing a color structure and taking an appropriate large N limit. We examine the analytic properties when A is a matrix ring or a group ring, and show that the models with matrix ring have a novel strong-weak duality which interchanges the roles of triangles and hinges. We also give a brief comment on the relationship of our models with the colored tensor models.

Determination of tributyltin in environmental water matrices using stir bar sorptive extraction with in-situ derivatisation and large volume injection-gas chromatography-mass spectrometry.

Science.gov (United States)

Neng, N R; Santalla, R P; Nogueira, J M F

2014-08-01

Stir bar sorptive extraction with in-situ derivatization using sodium tetrahydridoborate (NaBH4) followed by liquid desorption and large volume injection-gas chromatography-mass spectrometry detection under the selected ion monitoring mode (SBSE(NaBH4)in-situ-LD/LVI-GC-MS(SIM)) was successfully developed for the determination of tributyltin (TBT) in environmental water matrices. NaBH4 proved to be an effective and easy in-situ speciation agent for TBT in aqueous media, allowing the formation of adducts with enough stability and suitable polarity for SBSE analysis. Assays performed on water samples spiked at the 10.0μg/L, yielded convenient recoveries (68.2±3.0%), showed good accuracy, suitable precision (RSD<9.0%), low detection limits (23ng/L) and excellent linear dynamic range (r(2)=0.9999) from 0.1 to 170.0µg/L, under optimized experimental conditions. By using the standard addition method, the application of the present methodology to real surface water samples allowed very good performance at the trace level. The proposed methodology proved to be a feasible alternative for routine quality control analysis, easy to implement, reliable and sensitive to monitor TBT in environmental water matrices. Copyright © 2014 Elsevier B.V. All rights reserved.

Quantum matrices in two dimensions

International Nuclear Information System (INIS)

Ewen, H.; Ogievetsky, O.; Wess, J.

1991-01-01

Quantum matrices in two-dimensions, admitting left and right quantum spaces, are classified: they fall into two families, the 2-parametric family GL p,q (2) and a 1-parametric family GL α J (2). Phenomena previously found for GL p,q (2) hold in this general situation: (a) powers of quantum matrices are again quantum and (b) entries of the logarithm of a two-dimensional quantum matrix form a Lie algebra. (orig.)

Sparse Source EEG Imaging with the Variational Garrote

DEFF Research Database (Denmark)

Hansen, Sofie Therese; Stahlhut, Carsten; Hansen, Lars Kai

2013-01-01

EEG imaging, the estimation of the cortical source distribution from scalp electrode measurements, poses an extremely ill-posed inverse problem. Recent work by Delorme et al. (2012) supports the hypothesis that distributed source solutions are sparse. We show that direct search for sparse solutions...

Low-count PET image restoration using sparse representation

Science.gov (United States)

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.

X-ray computed tomography using curvelet sparse regularization.

Science.gov (United States)

Wieczorek, Matthias; Frikel, Jürgen; Vogel, Jakob; Eggl, Elena; Kopp, Felix; Noël, Peter B; Pfeiffer, Franz; Demaret, Laurent; Lasser, Tobias

2015-04-01

Reconstruction of x-ray computed tomography (CT) data remains a mathematically challenging problem in medical imaging. Complementing the standard analytical reconstruction methods, sparse regularization is growing in importance, as it allows inclusion of prior knowledge. The paper presents a method for sparse regularization based on the curvelet frame for the application to iterative reconstruction in x-ray computed tomography. In this work, the authors present an iterative reconstruction approach based on the alternating direction method of multipliers using curvelet sparse regularization. Evaluation of the method is performed on a specifically crafted numerical phantom dataset to highlight the method's strengths. Additional evaluation is performed on two real datasets from commercial scanners with different noise characteristics, a clinical bone sample acquired in a micro-CT and a human abdomen scanned in a diagnostic CT. The results clearly illustrate that curvelet sparse regularization has characteristic strengths. In particular, it improves the restoration and resolution of highly directional, high contrast features with smooth contrast variations. The authors also compare this approach to the popular technique of total variation and to traditional filtered backprojection. The authors conclude that curvelet sparse regularization is able to improve reconstruction quality by reducing noise while preserving highly directional features.

Deformable MR Prostate Segmentation via Deep Feature Learning and Sparse Patch Matching.

Science.gov (United States)

Guo, Yanrong; Gao, Yaozong; Shen, Dinggang

2016-04-01

Automatic and reliable segmentation of the prostate is an important but difficult task for various clinical applications such as prostate cancer radiotherapy. The main challenges for accurate MR prostate localization lie in two aspects: (1) inhomogeneous and inconsistent appearance around prostate boundary, and (2) the large shape variation across different patients. To tackle these two problems, we propose a new deformable MR prostate segmentation method by unifying deep feature learning with the sparse patch matching. First, instead of directly using handcrafted features, we propose to learn the latent feature representation from prostate MR images by the stacked sparse auto-encoder (SSAE). Since the deep learning algorithm learns the feature hierarchy from the data, the learned features are often more concise and effective than the handcrafted features in describing the underlying data. To improve the discriminability of learned features, we further refine the feature representation in a supervised fashion. Second, based on the learned features, a sparse patch matching method is proposed to infer a prostate likelihood map by transferring the prostate labels from multiple atlases to the new prostate MR image. Finally, a deformable segmentation is used to integrate a sparse shape model with the prostate likelihood map for achieving the final segmentation. The proposed method has been extensively evaluated on the dataset that contains 66 T2-wighted prostate MR images. Experimental results show that the deep-learned features are more effective than the handcrafted features in guiding MR prostate segmentation. Moreover, our method shows superior performance than other state-of-the-art segmentation methods.

Synchronous correlation matrices and Connes’ embedding conjecture

Energy Technology Data Exchange (ETDEWEB)

Dykema, Kenneth J., E-mail: kdykema@math.tamu.edu [Department of Mathematics, Texas A& M University, College Station, Texas 77843-3368 (United States); Paulsen, Vern, E-mail: vern@math.uh.edu [Department of Mathematics, University of Houston, Houston, Texas 77204 (United States)

2016-01-15

In the work of Paulsen et al. [J. Funct. Anal. (in press); preprint arXiv:1407.6918], the concept of synchronous quantum correlation matrices was introduced and these were shown to correspond to traces on certain C*-algebras. In particular, synchronous correlation matrices arose in their study of various versions of quantum chromatic numbers of graphs and other quantum versions of graph theoretic parameters. In this paper, we develop these ideas further, focusing on the relations between synchronous correlation matrices and microstates. We prove that Connes’ embedding conjecture is equivalent to the equality of two families of synchronous quantum correlation matrices. We prove that if Connes’ embedding conjecture has a positive answer, then the tracial rank and projective rank are equal for every graph. We then apply these results to more general non-local games.

Realm of Matrices

Indian Academy of Sciences (India)

IAS Admin

harmonic analysis and complex analysis, in ... gebra describes not only the study of linear transforma- tions and .... special case of the Jordan canonical form of matrices. ..... Richard Bronson, Schaum's Outline Series Theory And Problems Of.

A hybrid method for the parallel computation of Green's functions

DEFF Research Database (Denmark)

Petersen, Dan Erik; Li, Song; Stokbro, Kurt

2009-01-01

of the large number of times this calculation needs to be performed, this is computationally very expensive even on supercomputers. The classical approach is based on recurrence formulas which cannot be efficiently parallelized. This practically prevents the solution of large problems with hundreds...... of thousands of atoms. We propose new recurrences for a general class of sparse matrices to calculate Green's and lesser Green's function matrices which extend formulas derived by Takahashi and others. We show that these recurrences may lead to a dramatically reduced computational cost because they only...... require computing a small number of entries of the inverse matrix. Then. we propose a parallelization strategy for block tridiagonal matrices which involves a combination of Schur complement calculations and cyclic reduction. It achieves good scalability even on problems of modest size....

Virial expansion for almost diagonal random matrices

Science.gov (United States)

Yevtushenko, Oleg; Kravtsov, Vladimir E.

2003-08-01

Energy level statistics of Hermitian random matrices hat H with Gaussian independent random entries Higeqj is studied for a generic ensemble of almost diagonal random matrices with langle|Hii|2rangle ~ 1 and langle|Hi\

Computing the sparse matrix vector product using block-based kernels without zero padding on processors with AVX-512 instructions

Directory of Open Access Journals (Sweden)

Bérenger Bramas

2018-04-01

Full Text Available The sparse matrix-vector product (SpMV is a fundamental operation in many scientific applications from various fields. The High Performance Computing (HPC community has therefore continuously invested a lot of effort to provide an efficient SpMV kernel on modern CPU architectures. Although it has been shown that block-based kernels help to achieve high performance, they are difficult to use in practice because of the zero padding they require. In the current paper, we propose new kernels using the AVX-512 instruction set, which makes it possible to use a blocking scheme without any zero padding in the matrix memory storage. We describe mask-based sparse matrix formats and their corresponding SpMV kernels highly optimized in assembly language. Considering that the optimal blocking size depends on the matrix, we also provide a method to predict the best kernel to be used utilizing a simple interpolation of results from previous executions. We compare the performance of our approach to that of the Intel MKL CSR kernel and the CSR5 open-source package on a set of standard benchmark matrices. We show that we can achieve significant improvements in many cases, both for sequential and for parallel executions. Finally, we provide the corresponding code in an open source library, called SPC5.

Procedure for the analysis of americium in complex matrices

International Nuclear Information System (INIS)

Knab, D.

1978-02-01

A radioanalytical procedure for the analysis of americium in complex matrices has been developed. Clean separations of americium can be obtained from up to 100 g of sample ash, regardless of the starting material. The ability to analyze large masses of material provides the increased sensitivity necessary to detect americium in many environmental samples. The procedure adequately decontaminates from rare earth elements and natural radioactive nuclides that interfere with the alpha spectrometric measurements

Sparse dictionary for synthetic transmit aperture medical ultrasound imaging.

Science.gov (United States)

Wang, Ping; Jiang, Jin-Yang; Li, Na; Luo, Han-Wu; Li, Fang; Cui, Shi-Gang

2017-07-01

It is possible to recover a signal below the Nyquist sampling limit using a compressive sensing technique in ultrasound imaging. However, the reconstruction enabled by common sparse transform approaches does not achieve satisfactory results. Considering the ultrasound echo signal's features of attenuation, repetition, and superposition, a sparse dictionary with the emission pulse signal is proposed. Sparse coefficients in the proposed dictionary have high sparsity. Images reconstructed with this dictionary were compared with those obtained with the three other common transforms, namely, discrete Fourier transform, discrete cosine transform, and discrete wavelet transform. The performance of the proposed dictionary was analyzed via a simulation and experimental data. The mean absolute error (MAE) was used to quantify the quality of the reconstructions. Experimental results indicate that the MAE associated with the proposed dictionary was always the smallest, the reconstruction time required was the shortest, and the lateral resolution and contrast of the reconstructed images were also the closest to the original images. The proposed sparse dictionary performed better than the other three sparse transforms. With the same sampling rate, the proposed dictionary achieved excellent reconstruction quality.

A sparse electromagnetic imaging scheme using nonlinear landweber iterations

KAUST Repository

Desmal, Abdulla; Bagci, Hakan

2015-01-01

Development and use of electromagnetic inverse scattering techniques for imagining sparse domains have been on the rise following the recent advancements in solving sparse optimization problems. Existing techniques rely on iteratively converting

Scalable group level probabilistic sparse factor analysis

DEFF Research Database (Denmark)

Hinrich, Jesper Løve; Nielsen, Søren Føns Vind; Riis, Nicolai Andre Brogaard

2017-01-01

Many data-driven approaches exist to extract neural representations of functional magnetic resonance imaging (fMRI) data, but most of them lack a proper probabilistic formulation. We propose a scalable group level probabilistic sparse factor analysis (psFA) allowing spatially sparse maps, component...... pruning using automatic relevance determination (ARD) and subject specific heteroscedastic spatial noise modeling. For task-based and resting state fMRI, we show that the sparsity constraint gives rise to components similar to those obtained by group independent component analysis. The noise modeling...... shows that noise is reduced in areas typically associated with activation by the experimental design. The psFA model identifies sparse components and the probabilistic setting provides a natural way to handle parameter uncertainties. The variational Bayesian framework easily extends to more complex...

Local posterior concentration rate for multilevel sparse sequences

NARCIS (Netherlands)

Belitser, E.N.; Nurushev, N.

2017-01-01

We consider empirical Bayesian inference in the many normal means model in the situation when the high-dimensional mean vector is multilevel sparse, that is,most of the entries of the parameter vector are some fixed values. For instance, the traditional sparse signal is a particular case (with one

Functional fixedness in a technologically sparse culture.

Science.gov (United States)

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.

Sparse modeling of EELS and EDX spectral imaging data by nonnegative matrix factorization

Energy Technology Data Exchange (ETDEWEB)

Shiga, Motoki, E-mail: shiga_m@gifu-u.ac.jp [Department of Electrical, Electronic and Computer Engineering, Gifu University, 1-1, Yanagido, Gifu 501-1193 (Japan); Tatsumi, Kazuyoshi; Muto, Shunsuke [Advanced Measurement Technology Center, Institute of Materials and Systems for Sustainability, Nagoya University, Chikusa-ku, Nagoya 464-8603 (Japan); Tsuda, Koji [Graduate School of Frontier Sciences, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa 277-8561 (Japan); Center for Materials Research by Information Integration, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba 305-0047 (Japan); Biotechnology Research Institute for Drug Discovery, National Institute of Advanced Industrial Science and Technology, 2-4-7 Aomi Koto-ku, Tokyo 135-0064 (Japan); Yamamoto, Yuta [High-Voltage Electron Microscope Laboratory, Institute of Materials and Systems for Sustainability, Nagoya University, Chikusa-ku, Nagoya 464-8603 (Japan); Mori, Toshiyuki [Environment and Energy Materials Division, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044 (Japan); Tanji, Takayoshi [Division of Materials Research, Institute of Materials and Systems for Sustainability, Nagoya University, Chikusa-ku, Nagoya 464-8603 (Japan)

2016-11-15

Advances in scanning transmission electron microscopy (STEM) techniques have enabled us to automatically obtain electron energy-loss (EELS)/energy-dispersive X-ray (EDX) spectral datasets from a specified region of interest (ROI) at an arbitrary step width, called spectral imaging (SI). Instead of manually identifying the potential constituent chemical components from the ROI and determining the chemical state of each spectral component from the SI data stored in a huge three-dimensional matrix, it is more effective and efficient to use a statistical approach for the automatic resolution and extraction of the underlying chemical components. Among many different statistical approaches, we adopt a non-negative matrix factorization (NMF) technique, mainly because of the natural assumption of non-negative values in the spectra and cardinalities of chemical components, which are always positive in actual data. This paper proposes a new NMF model with two penalty terms: (i) an automatic relevance determination (ARD) prior, which optimizes the number of components, and (ii) a soft orthogonal constraint, which clearly resolves each spectrum component. For the factorization, we further propose a fast optimization algorithm based on hierarchical alternating least-squares. Numerical experiments using both phantom and real STEM-EDX/EELS SI datasets demonstrate that the ARD prior successfully identifies the correct number of physically meaningful components. The soft orthogonal constraint is also shown to be effective, particularly for STEM-EELS SI data, where neither the spatial nor spectral entries in the matrices are sparse. - Highlights: • Automatic resolution of chemical components from spectral imaging is considered. • We propose a new non-negative matrix factorization with two new penalties. • The first penalty is sparseness to choose the number of components from data. • Experimental results with real data demonstrate effectiveness of our method.

Analog system for computing sparse codes

Science.gov (United States)

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.

Intrinsic Density Matrices of the Nuclear Shell Model

International Nuclear Information System (INIS)

Deveikis, A.; Kamuntavichius, G.

1996-01-01

A new method for calculation of shell model intrinsic density matrices, defined as two-particle density matrices integrated over the centre-of-mass position vector of two last particles and complemented with isospin variables, has been developed. The intrinsic density matrices obtained are completely antisymmetric, translation-invariant, and do not employ a group-theoretical classification of antisymmetric states. They are used for exact realistic density matrix expansion within the framework of the reduced Hamiltonian method. The procedures based on precise arithmetic for calculation of the intrinsic density matrices that involve no numerical diagonalization or orthogonalization have been developed and implemented in the computer code. (author). 11 refs., 2 tabs

Efficient Pseudorecursive Evaluation Schemes for Non-adaptive Sparse Grids

KAUST Repository

Buse, Gerrit; Pflü ger, Dirk; Jacob, Riko

2014-01-01

In this work we propose novel algorithms for storing and evaluating sparse grid functions, operating on regular (not spatially adaptive), yet potentially dimensionally adaptive grid types. Besides regular sparse grids our approach includes truncated

Level density of random matrices for decaying systems

International Nuclear Information System (INIS)

Haake, F.; Izrailev, F.; Saher, D.; Sommers, H.-J.

1991-01-01

Analytical and numerical results for the level density of a certain class of random non-Hermitian matrices H=H+iΓ are presented. The conservative part H belongs to the Gaussian orthogonal ensemble while the damping piece Γ is quadratic in Gaussian random numbers and may describe the decay of resonances through various channels. In the limit of a large matrix dimension the level density assumes a surprisingly simple dependence on the relative strength of the damping and the number of channels. 18 refs.; 4 figs

Fine structure of spectral properties for random correlation matrices: an application to financial markets.

Science.gov (United States)

Livan, Giacomo; Alfarano, Simone; Scalas, Enrico

2011-07-01

We study some properties of eigenvalue spectra of financial correlation matrices. In particular, we investigate the nature of the large eigenvalue bulks which are observed empirically, and which have often been regarded as a consequence of the supposedly large amount of noise contained in financial data. We challenge this common knowledge by acting on the empirical correlation matrices of two data sets with a filtering procedure which highlights some of the cluster structure they contain, and we analyze the consequences of such filtering on eigenvalue spectra. We show that empirically observed eigenvalue bulks emerge as superpositions of smaller structures, which in turn emerge as a consequence of cross correlations between stocks. We interpret and corroborate these findings in terms of factor models, and we compare empirical spectra to those predicted by random matrix theory for such models.

Fine structure of spectral properties for random correlation matrices: An application to financial markets

Science.gov (United States)

Livan, Giacomo; Alfarano, Simone; Scalas, Enrico

2011-07-01

We study some properties of eigenvalue spectra of financial correlation matrices. In particular, we investigate the nature of the large eigenvalue bulks which are observed empirically, and which have often been regarded as a consequence of the supposedly large amount of noise contained in financial data. We challenge this common knowledge by acting on the empirical correlation matrices of two data sets with a filtering procedure which highlights some of the cluster structure they contain, and we analyze the consequences of such filtering on eigenvalue spectra. We show that empirically observed eigenvalue bulks emerge as superpositions of smaller structures, which in turn emerge as a consequence of cross correlations between stocks. We interpret and corroborate these findings in terms of factor models, and we compare empirical spectra to those predicted by random matrix theory for such models.

Miniature Laboratory for Detecting Sparse Biomolecules

Science.gov (United States)

Lin, Ying; Yu, Nan

2005-01-01

A miniature laboratory system has been proposed for use in the field to detect sparsely distributed biomolecules. By emphasizing concentration and sorting of specimens prior to detection, the underlying system concept would make it possible to attain high detection sensitivities without the need to develop ever more sensitive biosensors. The original purpose of the proposal is to aid the search for signs of life on a remote planet by enabling the detection of specimens as sparse as a few molecules or microbes in a large amount of soil, dust, rocks, water/ice, or other raw sample material. Some version of the system could prove useful on Earth for remote sensing of biological contamination, including agents of biological warfare. Processing in this system would begin with dissolution of the raw sample material in a sample-separation vessel. The solution in the vessel would contain floating microscopic magnetic beads coated with substances that could engage in chemical reactions with various target functional groups that are parts of target molecules. The chemical reactions would cause the targeted molecules to be captured on the surfaces of the beads. By use of a controlled magnetic field, the beads would be concentrated in a specified location in the vessel. Once the beads were thus concentrated, the rest of the solution would be discarded. This procedure would obviate the filtration steps and thereby also eliminate the filter-clogging difficulties of typical prior sample-concentration schemes. For ferrous dust/soil samples, the dissolution would be done first in a separate vessel before the solution is transferred to the microbead-containing vessel.

Genetically-directed, cell type-specific sparse labeling for the analysis of neuronal morphology.

Directory of Open Access Journals (Sweden)

Thomas Rotolo

Full Text Available In mammals, genetically-directed cell labeling technologies have not yet been applied to the morphologic analysis of neurons with very large and complex arbors, an application that requires extremely sparse labeling and that is only rendered practical by limiting the labeled population to one or a few predetermined neuronal subtypes.In the present study we have addressed this application by using CreER technology to non-invasively label very small numbers of neurons so that their morphologies can be fully visualized. Four lines of IRES-CreER knock-in mice were constructed to permit labeling selectively in cholinergic or catecholaminergic neurons [choline acetyltransferase (ChAT-IRES-CreER or tyrosine hydroxylase (TH-IRES-CreER], predominantly in projection neurons [neurofilament light chain (NFL-IRES-CreER], or broadly in neurons and some glia [vesicle-associated membrane protein2 (VAMP2-IRES-CreER]. When crossed to the Z/AP reporter and exposed to 4-hydroxytamoxifen in the early postnatal period, the number of neurons expressing the human placental alkaline phosphatase reporter can be reproducibly lowered to fewer than 50 per brain. Sparse Cre-mediated recombination in ChAT-IRES-CreER;Z/AP mice shows the full axonal and dendritic arbors of individual forebrain cholinergic neurons, the first time that the complete morphologies of these very large neurons have been revealed in any species.Sparse genetically-directed, cell type-specific neuronal labeling with IRES-creER lines should prove useful for studying a wide variety of questions in neuronal development and disease.

Consensus Convolutional Sparse Coding

KAUST Repository

Choudhury, Biswarup

2017-12-01

Convolutional sparse coding (CSC) is a promising direction for unsupervised learning in computer vision. In contrast to recent supervised methods, CSC allows for convolutional image representations to be learned that are equally useful for high-level vision tasks and low-level image reconstruction and can be applied to a wide range of tasks without problem-specific retraining. Due to their extreme memory requirements, however, existing CSC solvers have so far been limited to low-dimensional problems and datasets using a handful of low-resolution example images at a time. In this paper, we propose a new approach to solving CSC as a consensus optimization problem, which lifts these limitations. By learning CSC features from large-scale image datasets for the first time, we achieve significant quality improvements in a number of imaging tasks. Moreover, the proposed method enables new applications in high-dimensional feature learning that has been intractable using existing CSC methods. This is demonstrated for a variety of reconstruction problems across diverse problem domains, including 3D multispectral demosaicing and 4D light field view synthesis.

Consensus Convolutional Sparse Coding

KAUST Repository

Choudhury, Biswarup

2017-04-11

Convolutional sparse coding (CSC) is a promising direction for unsupervised learning in computer vision. In contrast to recent supervised methods, CSC allows for convolutional image representations to be learned that are equally useful for high-level vision tasks and low-level image reconstruction and can be applied to a wide range of tasks without problem-specific retraining. Due to their extreme memory requirements, however, existing CSC solvers have so far been limited to low-dimensional problems and datasets using a handful of low-resolution example images at a time. In this paper, we propose a new approach to solving CSC as a consensus optimization problem, which lifts these limitations. By learning CSC features from large-scale image datasets for the first time, we achieve significant quality improvements in a number of imaging tasks. Moreover, the proposed method enables new applications in high dimensional feature learning that has been intractable using existing CSC methods. This is demonstrated for a variety of reconstruction problems across diverse problem domains, including 3D multispectral demosaickingand 4D light field view synthesis.

Consensus Convolutional Sparse Coding

KAUST Repository

Choudhury, Biswarup; Swanson, Robin; Heide, Felix; Wetzstein, Gordon; Heidrich, Wolfgang

2017-01-01

Convolutional sparse coding (CSC) is a promising direction for unsupervised learning in computer vision. In contrast to recent supervised methods, CSC allows for convolutional image representations to be learned that are equally useful for high-level vision tasks and low-level image reconstruction and can be applied to a wide range of tasks without problem-specific retraining. Due to their extreme memory requirements, however, existing CSC solvers have so far been limited to low-dimensional problems and datasets using a handful of low-resolution example images at a time. In this paper, we propose a new approach to solving CSC as a consensus optimization problem, which lifts these limitations. By learning CSC features from large-scale image datasets for the first time, we achieve significant quality improvements in a number of imaging tasks. Moreover, the proposed method enables new applications in high-dimensional feature learning that has been intractable using existing CSC methods. This is demonstrated for a variety of reconstruction problems across diverse problem domains, including 3D multispectral demosaicing and 4D light field view synthesis.

Sparse Representation Based SAR Vehicle Recognition along with Aspect Angle

Directory of Open Access Journals (Sweden)

Xiangwei Xing

2014-01-01

Full Text Available 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.

Slowness and sparseness have diverging effects on complex cell learning.

Directory of Open Access Journals (Sweden)

Jörn-Philipp Lies

2014-03-01

Full Text Available Following earlier studies which showed that a sparse coding principle may explain the receptive field properties of complex cells in primary visual cortex, it has been concluded that the same properties may be equally derived from a slowness principle. In contrast to this claim, we here show that slowness and sparsity drive the representations towards substantially different receptive field properties. To do so, we present complete sets of basis functions learned with slow subspace analysis (SSA in case of natural movies as well as translations, rotations, and scalings of natural images. SSA directly parallels independent subspace analysis (ISA with the only difference that SSA maximizes slowness instead of sparsity. We find a large discrepancy between the filter shapes learned with SSA and ISA. We argue that SSA can be understood as a generalization of the Fourier transform where the power spectrum corresponds to the maximally slow subspace energies in SSA. Finally, we investigate the trade-off between slowness and sparseness when combined in one objective function.

Clustering by reordering of similarity and Laplacian matrices: Application to galaxy clusters

Science.gov (United States)

Mahmoud, E.; Shoukry, A.; Takey, A.

2018-04-01

Similarity metrics, kernels and similarity-based algorithms have gained much attention due to their increasing applications in information retrieval, data mining, pattern recognition and machine learning. Similarity Graphs are often adopted as the underlying representation of similarity matrices and are at the origin of known clustering algorithms such as spectral clustering. Similarity matrices offer the advantage of working in object-object (two-dimensional) space where visualization of clusters similarities is available instead of object-features (multi-dimensional) space. In this paper, sparse ɛ-similarity graphs are constructed and decomposed into strong components using appropriate methods such as Dulmage-Mendelsohn permutation (DMperm) and/or Reverse Cuthill-McKee (RCM) algorithms. The obtained strong components correspond to groups (clusters) in the input (feature) space. Parameter ɛi is estimated locally, at each data point i from a corresponding narrow range of the number of nearest neighbors. Although more advanced clustering techniques are available, our method has the advantages of simplicity, better complexity and direct visualization of the clusters similarities in a two-dimensional space. Also, no prior information about the number of clusters is needed. We conducted our experiments on two and three dimensional, low and high-sized synthetic datasets as well as on an astronomical real-dataset. The results are verified graphically and analyzed using gap statistics over a range of neighbors to verify the robustness of the algorithm and the stability of the results. Combining the proposed algorithm with gap statistics provides a promising tool for solving clustering problems. An astronomical application is conducted for confirming the existence of 45 galaxy clusters around the X-ray positions of galaxy clusters in the redshift range [0.1..0.8]. We re-estimate the photometric redshifts of the identified galaxy clusters and obtain acceptable values

Random matrices and random difference equations

International Nuclear Information System (INIS)

Uppuluri, V.R.R.

1975-01-01

Mathematical models leading to products of random matrices and random difference equations are discussed. A one-compartment model with random behavior is introduced, and it is shown how the average concentration in the discrete time model converges to the exponential function. This is of relevance to understanding how radioactivity gets trapped in bone structure in blood--bone systems. The ideas are then generalized to two-compartment models and mammillary systems, where products of random matrices appear in a natural way. The appearance of products of random matrices in applications in demography and control theory is considered. Then random sequences motivated from the following problems are studied: constant pulsing and random decay models, random pulsing and constant decay models, and random pulsing and random decay models

Quantum Entanglement and Reduced Density Matrices

Science.gov (United States)

Purwanto, Agus; Sukamto, Heru; Yuwana, Lila

2018-05-01

We investigate entanglement and separability criteria of multipartite (n-partite) state by examining ranks of its reduced density matrices. Firstly, we construct the general formula to determine the criterion. A rank of origin density matrix always equals one, meanwhile ranks of reduced matrices have various ranks. Next, separability and entanglement criterion of multipartite is determined by calculating ranks of reduced density matrices. In this article we diversify multipartite state criteria into completely entangled state, completely separable state, and compound state, i.e. sub-entangled state and sub-entangledseparable state. Furthermore, we also shorten the calculation proposed by the previous research to determine separability of multipartite state and expand the methods to be able to differ multipartite state based on criteria above.

NDMA formation kinetics from three pharmaceuticals in four water matrices.

Science.gov (United States)

Shen, Ruqiao; Andrews, Susan A

2011-11-01

N, N-nitrosodimethylamine (NDMA) is an emerging disinfection by-product (DBP) that has been widely detected in many drinking water systems and commonly associated with the chloramine disinfection process. Some amine-based pharmaceuticals have been demonstrated to form NDMA during chloramination, but studies regarding the reaction kinetics are largely lacking. This study investigates the NDMA formation kinetics from ranitidine, chlorphenamine, and doxylamine under practical chloramine disinfection conditions. The formation profile was monitored in both lab-grade water and real water matrices, and a statistical model is proposed to describe and predict the NDMA formation from selected pharmaceuticals in various water matrices. The results indicate the significant impact of water matrix components and reaction time on the NDMA formation from selected pharmaceuticals, and provide fresh insights on the estimation of ultimate NDMA formation potential from pharmaceutical precursors. Copyright © 2011 Elsevier Ltd. All rights reserved.

Learning sparse generative models of audiovisual signals

OpenAIRE

Monaci, Gianluca; Sommer, Friedrich T.; Vandergheynst, Pierre

2008-01-01

This paper presents a novel framework to learn sparse represen- tations for audiovisual signals. An audiovisual signal is modeled as a sparse sum of audiovisual kernels. The kernels are bimodal functions made of synchronous audio and video components that can be positioned independently and arbitrarily in space and time. We design an algorithm capable of learning sets of such audiovi- sual, synchronous, shift-invariant functions by alternatingly solving a coding and a learning pr...

Improving the energy efficiency of sparse linear system solvers on multicore and manycore systems.

Science.gov (United States)

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.

Support agnostic Bayesian matching pursuit for block sparse signals

KAUST Repository

Masood, Mudassir

2013-05-01

A fast matching pursuit method using a Bayesian approach is introduced for block-sparse signal recovery. This method performs Bayesian estimates of block-sparse signals even when the distribution of active blocks is non-Gaussian or unknown. It is agnostic to the distribution of active blocks in the signal and utilizes a priori statistics of additive noise and the sparsity rate of the signal, which are shown to be easily estimated from data and no user intervention is required. The method requires a priori knowledge of block partition and utilizes a greedy approach and order-recursive updates of its metrics to find the most dominant sparse supports to determine the approximate minimum mean square error (MMSE) estimate of the block-sparse signal. Simulation results demonstrate the power and robustness of our proposed estimator. © 2013 IEEE.

MIMO-OFDM Chirp Waveform Diversity Design and Implementation Based on Sparse Matrix and Correlation Optimization

Directory of Open Access Journals (Sweden)

Wang Wen-qin

2015-02-01

Full Text Available The waveforms used in Multiple-Input Multiple-Output (MIMO Synthetic Aperture Radar (SAR should have a large time-bandwidth product and good ambiguity function performance. A scheme to design multiple orthogonal MIMO SAR Orthogonal Frequency Division Multiplexing (OFDM chirp waveforms by combinational sparse matrix and correlation optimization is proposed. First, the problem of MIMO SAR waveform design amounts to the associated design of hopping frequency and amplitudes. Then a iterative exhaustive search algorithm is adopted to optimally design the code matrix with the constraints minimizing the block correlation coefficient of sparse matrix and the sum of cross-correlation peaks. And the amplitudes matrix are adaptively designed by minimizing the cross-correlation peaks with the genetic algorithm. Additionally, the impacts of waveform number, hopping frequency interval and selectable frequency index are also analyzed. The simulation results verify the proposed scheme can design multiple orthogonal large time-bandwidth product OFDM chirp waveforms with low cross-correlation peak and sidelobes and it improves ambiguity performance.

Malware analysis using visualized image matrices.

Science.gov (United States)

Han, KyoungSoo; Kang, BooJoong; Im, Eul Gyu

2014-01-01

This paper proposes a novel malware visual analysis method that contains not only a visualization method to convert binary files into images, but also a similarity calculation method between these images. The proposed method generates RGB-colored pixels on image matrices using the opcode sequences extracted from malware samples and calculates the similarities for the image matrices. Particularly, our proposed methods are available for packed malware samples by applying them to the execution traces extracted through dynamic analysis. When the images are generated, we can reduce the overheads by extracting the opcode sequences only from the blocks that include the instructions related to staple behaviors such as functions and application programming interface (API) calls. In addition, we propose a technique that generates a representative image for each malware family in order to reduce the number of comparisons for the classification of unknown samples and the colored pixel information in the image matrices is used to calculate the similarities between the images. Our experimental results show that the image matrices of malware can effectively be used to classify malware families both statically and dynamically with accuracy of 0.9896 and 0.9732, respectively.

Malware Analysis Using Visualized Image Matrices

Directory of Open Access Journals (Sweden)

KyoungSoo Han

2014-01-01

Full Text Available This paper proposes a novel malware visual analysis method that contains not only a visualization method to convert binary files into images, but also a similarity calculation method between these images. The proposed method generates RGB-colored pixels on image matrices using the opcode sequences extracted from malware samples and calculates the similarities for the image matrices. Particularly, our proposed methods are available for packed malware samples by applying them to the execution traces extracted through dynamic analysis. When the images are generated, we can reduce the overheads by extracting the opcode sequences only from the blocks that include the instructions related to staple behaviors such as functions and application programming interface (API calls. In addition, we propose a technique that generates a representative image for each malware family in order to reduce the number of comparisons for the classification of unknown samples and the colored pixel information in the image matrices is used to calculate the similarities between the images. Our experimental results show that the image matrices of malware can effectively be used to classify malware families both statically and dynamically with accuracy of 0.9896 and 0.9732, respectively.

Preconditioned Inexact Newton for Nonlinear Sparse Electromagnetic Imaging

KAUST Repository

Desmal, Abdulla

2014-05-04

Newton-type algorithms have been extensively studied in nonlinear microwave imaging due to their quadratic convergence rate and ability to recover images with high contrast values. In the past, Newton methods have been implemented in conjunction with smoothness promoting optimization/regularization schemes. However, this type of regularization schemes are known to perform poorly when applied in imagining domains with sparse content or sharp variations. In this work, an inexact Newton algorithm is formulated and implemented in conjunction with a linear sparse optimization scheme. A novel preconditioning technique is proposed to increase the convergence rate of the optimization problem. Numerical results demonstrate that the proposed framework produces sharper and more accurate images when applied in sparse/sparsified domains.

Preconditioned Inexact Newton for Nonlinear Sparse Electromagnetic Imaging

KAUST Repository

Desmal, Abdulla

2014-01-06

Newton-type algorithms have been extensively studied in nonlinear microwave imaging due to their quadratic convergence rate and ability to recover images with high contrast values. In the past, Newton methods have been implemented in conjunction with smoothness promoting optimization/regularization schemes. However, this type of regularization schemes are known to perform poorly when applied in imagining domains with sparse content or sharp variations. In this work, an inexact Newton algorithm is formulated and implemented in conjunction with a linear sparse optimization scheme. A novel preconditioning technique is proposed to increase the convergence rate of the optimization problem. Numerical results demonstrate that the proposed framework produces sharper and more accurate images when applied in sparse/sparsified domains.

Electromagnetic Formation Flight (EMFF) for Sparse Aperture Arrays

Science.gov (United States)

Kwon, Daniel W.; Miller, David W.; Sedwick, Raymond J.

2004-01-01

Traditional methods of actuating spacecraft in sparse aperture arrays use propellant as a reaction mass. For formation flying systems, propellant becomes a critical consumable which can be quickly exhausted while maintaining relative orientation. Additional problems posed by propellant include optical contamination, plume impingement, thermal emission, and vibration excitation. For these missions where control of relative degrees of freedom is important, we consider using a system of electromagnets, in concert with reaction wheels, to replace the consumables. Electromagnetic Formation Flight sparse apertures, powered by solar energy, are designed differently from traditional propulsion systems, which are based on V. This paper investigates the design of sparse apertures both inside and outside the Earth's gravity field.

Preconditioned Inexact Newton for Nonlinear Sparse Electromagnetic Imaging

KAUST Repository

Desmal, Abdulla; Bagci, Hakan

2014-01-01

Newton-type algorithms have been extensively studied in nonlinear microwave imaging due to their quadratic convergence rate and ability to recover images with high contrast values. In the past, Newton methods have been implemented in conjunction with smoothness promoting optimization/regularization schemes. However, this type of regularization schemes are known to perform poorly when applied in imagining domains with sparse content or sharp variations. In this work, an inexact Newton algorithm is formulated and implemented in conjunction with a linear sparse optimization scheme. A novel preconditioning technique is proposed to increase the convergence rate of the optimization problem. Numerical results demonstrate that the proposed framework produces sharper and more accurate images when applied in sparse/sparsified domains.

A comprehensive study of sparse codes on abnormality detection

DEFF Research Database (Denmark)

Ren, Huamin; Pan, Hong; Olsen, Søren Ingvor

2017-01-01

Sparse representation has been applied successfully in abnor-mal event detection, in which the baseline is to learn a dic-tionary accompanied by sparse codes. While much empha-sis is put on discriminative dictionary construction, there areno comparative studies of sparse codes regarding abnormal-ity...... detection. We comprehensively study two types of sparsecodes solutions - greedy algorithms and convex L1-norm so-lutions - and their impact on abnormality detection perfor-mance. We also propose our framework of combining sparsecodes with different detection methods. Our comparative ex-periments are carried...

Support agnostic Bayesian matching pursuit for block sparse signals

KAUST Repository

Masood, Mudassir; Al-Naffouri, Tareq Y.

2013-01-01

priori knowledge of block partition and utilizes a greedy approach and order-recursive updates of its metrics to find the most dominant sparse supports to determine the approximate minimum mean square error (MMSE) estimate of the block-sparse signal

Production and characterization of cornstarch/cellulose acetate/silver sulfadiazine extrudate matrices

Energy Technology Data Exchange (ETDEWEB)

Zepon, Karine Modolon [CIMJECT, Departamento de Engenharia Mecânica, Universidade Federal de Santa Catarina, 88040-900 Florianópolis, SC (Brazil); TECFARMA, Universidade do Sul de Santa Catarina, 88704-900 Tubarão, SC (Brazil); Petronilho, Fabricia [FICEXP, Universidade do Sul de Santa Catarina, 88704-900 Tubarão, SC (Brazil); Soldi, Valdir [POLIMAT, Universidade Federal de Santa Catarina, 88040-900 Florianópolis, SC (Brazil); Salmoria, Gean Vitor [CIMJECT, Departamento de Engenharia Mecânica, Universidade Federal de Santa Catarina, 88040-900 Florianópolis, SC (Brazil); Kanis, Luiz Alberto, E-mail: luiz.kanis@unisul.br [TECFARMA, Universidade do Sul de Santa Catarina, 88704-900 Tubarão, SC (Brazil)

2014-11-01

The production and evaluation of cornstarch/cellulose acetate/silver sulfadiazine extrudate matrices are reported herein. The matrices were melt extruded under nine different conditions, altering the temperature and the screw speed values. The surface morphology of the matrices was examined by scanning electron microscopy. The micrographs revealed the presence of non-melted silver sulfadiazine microparticles in the matrices extruded at lower temperature and screw speed values. The thermal properties were evaluated and the results for both the biopolymer and the drug indicated no thermal degradation during the melt extrusion process. The differential scanning analysis of the extrudate matrices showed a shift to lower temperatures for the silver sulfadiazine melting point compared with the non-extruded drug. The starch/cellulose acetate matrices containing silver sulfadiazine demonstrated significant inhibition of the growth of Pseudomonas aeruginosa and Staphylococcus aureus. In vivo inflammatory response tests showed that the extrudate matrices, with or without silver sulfadiazine, did not trigger chronic inflammatory processes. - Highlights: • Melt extruded bio-based matrices containing silver sulfadiazine was produced. • The silver sulfadiazine is stable during melt-extrusion. • The extrudate matrices shown bacterial growth inhibition. • The matrices obtained have potential to development wound healing membranes.

Topological and kinetic determinants of the modal matrices of dynamic models of metabolism.

Directory of Open Access Journals (Sweden)

Bin Du

Full Text Available Large-scale kinetic models of metabolism are becoming increasingly comprehensive and accurate. A key challenge is to understand the biochemical basis of the dynamic properties of these models. Linear analysis methods are well-established as useful tools for characterizing the dynamic response of metabolic networks. Central to linear analysis methods are two key matrices: the Jacobian matrix (J and the modal matrix (M-1 arising from its eigendecomposition. The modal matrix M-1 contains dynamically independent motions of the kinetic model near a reference state, and it is sparse in practice for metabolic networks. However, connecting the structure of M-1 to the kinetic properties of the underlying reactions is non-trivial. In this study, we analyze the relationship between J, M-1, and the kinetic properties of the underlying network for kinetic models of metabolism. Specifically, we describe the origin of mode sparsity structure based on features of the network stoichiometric matrix S and the reaction kinetic gradient matrix G. First, we show that due to the scaling of kinetic parameters in real networks, diagonal dominance occurs in a substantial fraction of the rows of J, resulting in simple modal structures with clear biological interpretations. Then, we show that more complicated modes originate from topologically-connected reactions that have similar reaction elasticities in G. These elasticities represent dynamic equilibrium balances within reactions and are key determinants of modal structure. The work presented should prove useful towards obtaining an understanding of the dynamics of kinetic models of metabolism, which are rooted in the network structure and the kinetic properties of reactions.

Polynomial sequences generated by infinite Hessenberg matrices

Directory of Open Access Journals (Sweden)

Verde-Star Luis

2017-01-01

Full Text Available We show that an infinite lower Hessenberg matrix generates polynomial sequences that correspond to the rows of infinite lower triangular invertible matrices. Orthogonal polynomial sequences are obtained when the Hessenberg matrix is tridiagonal. We study properties of the polynomial sequences and their corresponding matrices which are related to recurrence relations, companion matrices, matrix similarity, construction algorithms, and generating functions. When the Hessenberg matrix is also Toeplitz the polynomial sequences turn out to be of interpolatory type and we obtain additional results. For example, we show that every nonderogative finite square matrix is similar to a unique Toeplitz-Hessenberg matrix.

Dynamic Stochastic Superresolution of sparsely observed turbulent systems

International Nuclear Information System (INIS)

Branicki, M.; Majda, A.J.

2013-01-01

Real-time capture of the relevant features of the unresolved turbulent dynamics of complex natural systems from sparse noisy observations and imperfect models is a notoriously difficult problem. The resulting lack of observational resolution and statistical accuracy in estimating the important turbulent processes, which intermittently send significant energy to the large-scale fluctuations, hinders efficient parameterization and real-time prediction using discretized PDE models. This issue is particularly subtle and important when dealing with turbulent geophysical systems with an vast range of interacting spatio-temporal scales and rough energy spectra near the mesh scale of numerical models. Here, we introduce and study a suite of general Dynamic Stochastic Superresolution (DSS) algorithms and show that, by appropriately filtering sparse regular observations with the help of cheap stochastic exactly solvable models, one can derive stochastically ‘superresolved’ velocity fields and gain insight into the important characteristics of the unresolved dynamics, including the detection of the so-called black swans. The DSS algorithms operate in Fourier domain and exploit the fact that the coarse observation network aliases high-wavenumber information into the resolved waveband. It is shown that these cheap algorithms are robust and have significant skill on a test bed of turbulent solutions from realistic nonlinear turbulent spatially extended systems in the presence of a significant model error. In particular, the DSS algorithms are capable of successfully capturing time-localized extreme events in the unresolved modes, and they provide good and robust skill for recovery of the unresolved processes in terms of pattern correlation. Moreover, we show that DSS improves the skill for recovering the primary modes associated with the sparse observation mesh which is equally important in applications. The skill of the various DSS algorithms depends on the energy spectrum

S-matrices and integrability

International Nuclear Information System (INIS)

Bombardelli, Diego

2016-01-01

In these notes we review the S-matrix theory in (1+1)-dimensional integrable models, focusing mainly on the relativistic case. Once the main definitions and physical properties are introduced, we discuss the factorization of scattering processes due to integrability. We then focus on the analytic properties of the two-particle scattering amplitude and illustrate the derivation of the S-matrices for all the possible bound states using the so-called bootstrap principle. General algebraic structures underlying the S-matrix theory and its relation with the form factors axioms are briefly mentioned. Finally, we discuss the S-matrices of sine-Gordon and SU (2), SU (3) chiral Gross–Neveu models. (topical review)

Matrices Aléatoires Tri-diagonales et Par Blocs.

OpenAIRE

MEKKI, Slimane

2014-01-01

Dans ce mémoire l'étude porte sur la densité de matrice aléatoire, les densités des valeurs propres d'une matrice pour les trois ensembles G.O.E, G.U.E, G.S.E. Après nous avons explicité les formules des densités de valeurs propres des matrices tri-diagonales dans les cas HERMITE et LAGUERRE Des simulations sur les constantes de normalisations pour les densités des matrices aléatoires ou des valeurs propres sont présentées.

Hierarchical quark mass matrices

International Nuclear Information System (INIS)

Rasin, A.

1998-02-01

I define a set of conditions that the most general hierarchical Yukawa mass matrices have to satisfy so that the leading rotations in the diagonalization matrix are a pair of (2,3) and (1,2) rotations. In addition to Fritzsch structures, examples of such hierarchical structures include also matrices with (1,3) elements of the same order or even much larger than the (1,2) elements. Such matrices can be obtained in the framework of a flavor theory. To leading order, the values of the angle in the (2,3) plane (s 23 ) and the angle in the (1,2) plane (s 12 ) do not depend on the order in which they are taken when diagonalizing. We find that any of the Cabbibo-Kobayashi-Maskawa matrix parametrizations that consist of at least one (1,2) and one (2,3) rotation may be suitable. In the particular case when the s 13 diagonalization angles are sufficiently small compared to the product s 12 s 23 , two special CKM parametrizations emerge: the R 12 R 23 R 12 parametrization follows with s 23 taken before the s 12 rotation, and vice versa for the R 23 R 12 R 23 parametrization. (author)

Selectivity and sparseness in randomly connected balanced networks.

Directory of Open Access Journals (Sweden)

Cengiz Pehlevan

Full Text Available Neurons in sensory cortex show stimulus selectivity and sparse population response, even in cases where no strong functionally specific structure in connectivity can be detected. This raises the question whether selectivity and sparseness can be generated and maintained in randomly connected networks. We consider a recurrent network of excitatory and inhibitory spiking neurons with random connectivity, driven by random projections from an input layer of stimulus selective neurons. In this architecture, the stimulus-to-stimulus and neuron-to-neuron modulation of total synaptic input is weak compared to the mean input. Surprisingly, we show that in the balanced state the network can still support high stimulus selectivity and sparse population response. In the balanced state, strong synapses amplify the variation in synaptic input and recurrent inhibition cancels the mean. Functional specificity in connectivity emerges due to the inhomogeneity caused by the generative statistical rule used to build the network. We further elucidate the mechanism behind and evaluate the effects of model parameters on population sparseness and stimulus selectivity. Network response to mixtures of stimuli is investigated. It is shown that a balanced state with unselective inhibition can be achieved with densely connected input to inhibitory population. Balanced networks exhibit the "paradoxical" effect: an increase in excitatory drive to inhibition leads to decreased inhibitory population firing rate. We compare and contrast selectivity and sparseness generated by the balanced network to randomly connected unbalanced networks. Finally, we discuss our results in light of experiments.

Laminin active peptide/agarose matrices as multifunctional biomaterials for tissue engineering.

Science.gov (United States)

Yamada, Yuji; Hozumi, Kentaro; Aso, Akihiro; Hotta, Atsushi; Toma, Kazunori; Katagiri, Fumihiko; Kikkawa, Yamato; Nomizu, Motoyoshi

2012-06-01

Cell adhesive peptides derived from extracellular matrix components are potential candidates to afford bio-adhesiveness to cell culture scaffolds for tissue engineering. Previously, we covalently conjugated bioactive laminin peptides to polysaccharides, such as chitosan and alginate, and demonstrated their advantages as biomaterials. Here, we prepared functional polysaccharide matrices by mixing laminin active peptides and agarose gel. Several laminin peptide/agarose matrices showed cell attachment activity. In particular, peptide AG73 (RKRLQVQLSIRT)/agarose matrices promoted strong cell attachment and the cell behavior depended on the stiffness of agarose matrices. Fibroblasts formed spheroid structures on the soft AG73/agarose matrices while the cells formed a monolayer with elongated morphologies on the stiff matrices. On the stiff AG73/agarose matrices, neuronal cells extended neuritic processes and endothelial cells formed capillary-like networks. In addition, salivary gland cells formed acini-like structures on the soft matrices. These results suggest that the peptide/agarose matrices are useful for both two- and three-dimensional cell culture systems as a multifunctional biomaterial for tissue engineering. Copyright © 2012 Elsevier Ltd. All rights reserved.

SPARSE ELECTROMAGNETIC IMAGING USING NONLINEAR LANDWEBER ITERATIONS

KAUST Repository

Desmal, Abdulla

2015-07-29

A scheme for efficiently solving the nonlinear electromagnetic inverse scattering problem on sparse investigation domains is described. The proposed scheme reconstructs the (complex) dielectric permittivity of an investigation domain from fields measured away from the domain itself. Least-squares data misfit between the computed scattered fields, which are expressed as a nonlinear function of the permittivity, and the measured fields is constrained by the L0/L1-norm of the solution. The resulting minimization problem is solved using nonlinear Landweber iterations, where at each iteration a thresholding function is applied to enforce the sparseness-promoting L0/L1-norm constraint. The thresholded nonlinear Landweber iterations are applied to several two-dimensional problems, where the ``measured\\'\\' fields are synthetically generated or obtained from actual experiments. These numerical experiments demonstrate the accuracy, efficiency, and applicability of the proposed scheme in reconstructing sparse profiles with high permittivity values.

Vector sparse representation of color image using quaternion matrix analysis.

Science.gov (United States)

Xu, Yi; Yu, Licheng; Xu, Hongteng; Zhang, Hao; Nguyen, Truong

2015-04-01

Traditional sparse image models treat color image pixel as a scalar, which represents color channels separately or concatenate color channels as a monochrome image. In this paper, we propose a vector sparse representation model for color images using quaternion matrix analysis. As a new tool for color image representation, its potential applications in several image-processing tasks are presented, including color image reconstruction, denoising, inpainting, and super-resolution. The proposed model represents the color image as a quaternion matrix, where a quaternion-based dictionary learning algorithm is presented using the K-quaternion singular value decomposition (QSVD) (generalized K-means clustering for QSVD) method. It conducts the sparse basis selection in quaternion space, which uniformly transforms the channel images to an orthogonal color space. In this new color space, it is significant that the inherent color structures can be completely preserved during vector reconstruction. Moreover, the proposed sparse model is more efficient comparing with the current sparse models for image restoration tasks due to lower redundancy between the atoms of different color channels. The experimental results demonstrate that the proposed sparse image model avoids the hue bias issue successfully and shows its potential as a general and powerful tool in color image analysis and processing domain.

Recognizing the ‘sparsely settled forest’: Multi-decade socioecological change dynamics and community exemplars

Science.gov (United States)

Derek B. Van Berkel; Bronwyn Rayfield; Sebastián Martinuzzi; Martin J. Lechowicz; Eric White; Kathleen P. Bell; Chris R. Colocousis; Kent F. Kovacs; Anita T. Morzillo; Darla K. Munroe; Benoit Parmentier; Volker C. Radeloff; Brian J. McGill

2018-01-01

Sparsely settled forests (SSF) are poorly studied, coupled natural and human systems involving rural communities in forest ecosystems that are neither largely uninhabited wildland nor forests on the edges of urban areas. We developed and applied a multidisciplinary approach to define, map, and examine changes in the spatial extent and structure of both the landscapes...

Sparse calibration of subsurface flow models using nonlinear orthogonal matching pursuit and an iterative stochastic ensemble method

KAUST Repository

Elsheikh, Ahmed H.

2013-06-01

We introduce a nonlinear orthogonal matching pursuit (NOMP) for sparse calibration of subsurface flow models. Sparse calibration is a challenging problem as the unknowns are both the non-zero components of the solution and their associated weights. NOMP is a greedy algorithm that discovers at each iteration the most correlated basis function with the residual from a large pool of basis functions. The discovered basis (aka support) is augmented across the nonlinear iterations. Once a set of basis functions are selected, the solution is obtained by applying Tikhonov regularization. The proposed algorithm relies on stochastically approximated gradient using an iterative stochastic ensemble method (ISEM). In the current study, the search space is parameterized using an overcomplete dictionary of basis functions built using the K-SVD algorithm. The proposed algorithm is the first ensemble based algorithm that tackels the sparse nonlinear parameter estimation problem. © 2013 Elsevier Ltd.

Conserved G-matrices of morphological and life-history traits among continental and island blue tit populations.

Science.gov (United States)

Delahaie, B; Charmantier, A; Chantepie, S; Garant, D; Porlier, M; Teplitsky, C

2017-08-01

The genetic variance-covariance matrix (G-matrix) summarizes the genetic architecture of multiple traits. It has a central role in the understanding of phenotypic divergence and the quantification of the evolutionary potential of populations. Laboratory experiments have shown that G-matrices can vary rapidly under divergent selective pressures. However, because of the demanding nature of G-matrix estimation and comparison in wild populations, the extent of its spatial variability remains largely unknown. In this study, we investigate spatial variation in G-matrices for morphological and life-history traits using long-term data sets from one continental and three island populations of blue tit (Cyanistes caeruleus) that have experienced contrasting population history and selective environment. We found no evidence for differences in G-matrices among populations. Interestingly, the phenotypic variance-covariance matrices (P) were divergent across populations, suggesting that using P as a substitute for G may be inadequate. These analyses also provide the first evidence in wild populations for additive genetic variation in the incubation period (that is, the period between last egg laid and hatching) in all four populations. Altogether, our results suggest that G-matrices may be stable across populations inhabiting contrasted environments, therefore challenging the results of previous simulation studies and laboratory experiments.

Low Complexity Submatrix Divided MMSE Sparse-SQRD Detection for MIMO-OFDM with ESPAR Antenna Receiver

Directory of Open Access Journals (Sweden)

Diego Javier Reinoso Chisaguano

2013-01-01

Full Text Available Multiple input multiple output-orthogonal frequency division multiplexing (MIMO-OFDM with an electronically steerable passive array radiator (ESPAR antenna receiver can improve the bit error rate performance and obtains additional diversity gain without increasing the number of Radio Frequency (RF front-end circuits. However, due to the large size of the channel matrix, the computational cost required for the detection process using Vertical-Bell Laboratories Layered Space-Time (V-BLAST detection is too high to be implemented. Using the minimum mean square error sparse-sorted QR decomposition (MMSE sparse-SQRD algorithm for the detection process the average computational cost can be considerably reduced but is still higher compared with a conventional MIMOOFDM system without ESPAR antenna receiver. In this paper, we propose to use a low complexity submatrix divided MMSE sparse-SQRD algorithm for the detection process of MIMOOFDM with ESPAR antenna receiver. The computational cost analysis and simulation results show that on average the proposed scheme can further reduce the computational cost and achieve a complexity comparable to the conventional MIMO-OFDM detection schemes.

SAR and Infrared Image Fusion in Complex Contourlet Domain Based on Joint Sparse Representation

Directory of Open Access Journals (Sweden)

Wu Yiquan

2017-08-01

Full Text Available To investigate the problems of the large grayscale difference between infrared and Synthetic Aperture Radar (SAR images and their fusion image not being fit for human visual perception, we propose a fusion method for SAR and infrared images in the complex contourlet domain based on joint sparse representation. First, we perform complex contourlet decomposition of the infrared and SAR images. Then, we employ the KSingular Value Decomposition (K-SVD method to obtain an over-complete dictionary of the low-frequency components of the two source images. Using a joint sparse representation model, we then generate a joint dictionary. We obtain the sparse representation coefficients of the low-frequency components of the source images in the joint dictionary by the Orthogonal Matching Pursuit (OMP method and select them using the selection maximization strategy. We then reconstruct these components to obtain the fused low-frequency components and fuse the high-frequency components using two criteria——the coefficient of visual sensitivity and the degree of energy matching. Finally, we obtain the fusion image by the inverse complex contourlet transform. Compared with the three classical fusion methods and recently presented fusion methods, e.g., that based on the Non-Subsampled Contourlet Transform (NSCT and another based on sparse representation, the method we propose in this paper can effectively highlight the salient features of the two source images and inherit their information to the greatest extent.

Fast convolutional sparse coding using matrix inversion lemma

Czech Academy of Sciences Publication Activity Database

Šorel, Michal; Šroubek, Filip

2016-01-01

Roč. 55, č. 1 (2016), s. 44-51 ISSN 1051-2004 R&D Projects: GA ČR GA13-29225S Institutional support: RVO:67985556 Keywords : Convolutional sparse coding * Feature learning * Deconvolution networks * Shift-invariant sparse coding Subject RIV: JD - Computer Applications, Robotics Impact factor: 2.337, year: 2016 http://library.utia.cas.cz/separaty/2016/ZOI/sorel-0459332.pdf

Isolation and Identification of Proteins Secreted by Cells Cultured within Synthetic Hydrogel-Based Matrices.

Science.gov (United States)

Sawicki, Lisa A; Choe, Leila H; Wiley, Katherine L; Lee, Kelvin H; Kloxin, April M

2018-03-12

Cells interact with and remodel their microenvironment, degrading large extracellular matrix (ECM) proteins (e.g., fibronectin, collagens) and secreting new ECM proteins and small soluble factors (e.g., growth factors, cytokines). Synthetic mimics of the ECM have been developed as controlled cell culture platforms for use in both fundamental and applied studies. However, how cells broadly remodel these initially well-defined matrices remains poorly understood and difficult to probe. In this work, we have established methods for widely examining both large and small proteins that are secreted by cells within synthetic matrices. Specifically, human mesenchymal stem cells (hMSCs), a model primary cell type, were cultured within well-defined poly(ethylene glycol) (PEG)-peptide hydrogels, and these cell-matrix constructs were decellularized and degraded for subsequent isolation and analysis of deposited proteins. Shotgun proteomics using liquid chromatography and mass spectrometry identified a variety of proteins, including the large ECM proteins fibronectin and collagen VI. Immunostaining and confocal imaging confirmed these results and provided visualization of protein organization within the synthetic matrices. Additionally, culture medium was collected from the encapsulated hMSCs, and a Luminex assay was performed to identify secreted soluble factors, including vascular endothelial growth factor (VEGF), endothelial growth factor (EGF), basic fibroblast growth factor (FGF-2), interleukin 8 (IL-8), and tumor necrosis factor alpha (TNF-α). Together, these methods provide a unique approach for studying dynamic reciprocity between cells and synthetic microenvironments and have the potential to provide new biological insights into cell responses during three-dimensional (3D) controlled cell culture.

Structure-based bayesian sparse reconstruction

KAUST Repository

Quadeer, Ahmed Abdul; Al-Naffouri, Tareq Y.

2012-01-01

Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical

The Antitriangular Factorization of Saddle Point Matrices

KAUST Repository

Pestana, J.

2014-01-01

Mastronardi and Van Dooren [SIAM J. Matrix Anal. Appl., 34 (2013), pp. 173-196] recently introduced the block antitriangular ("Batman") decomposition for symmetric indefinite matrices. Here we show the simplification of this factorization for saddle point matrices and demonstrate how it represents the common nullspace method. We show that rank-1 updates to the saddle point matrix can be easily incorporated into the factorization and give bounds on the eigenvalues of matrices important in saddle point theory. We show the relation of this factorization to constraint preconditioning and how it transforms but preserves the structure of block diagonal and block triangular preconditioners. © 2014 Society for Industrial and Applied Mathematics.

Binary Sparse Phase Retrieval via Simulated Annealing

Directory of Open Access Journals (Sweden)

Wei Peng

2016-01-01

Full Text Available This paper presents the Simulated Annealing Sparse PhAse Recovery (SASPAR algorithm for reconstructing sparse binary signals from their phaseless magnitudes of the Fourier transform. The greedy strategy version is also proposed for a comparison, which is a parameter-free algorithm. Sufficient numeric simulations indicate that our method is quite effective and suggest the binary model is robust. The SASPAR algorithm seems competitive to the existing methods for its efficiency and high recovery rate even with fewer Fourier measurements.

Emotional textile image classification based on cross-domain convolutional sparse autoencoders with feature selection

Science.gov (United States)

Li, Zuhe; Fan, Yangyu; Liu, Weihua; Yu, Zeqi; Wang, Fengqin

2017-01-01

We aim to apply sparse autoencoder-based unsupervised feature learning to emotional semantic analysis for textile images. To tackle the problem of limited training data, we present a cross-domain feature learning scheme for emotional textile image classification using convolutional autoencoders. We further propose a correlation-analysis-based feature selection method for the weights learned by sparse autoencoders to reduce the number of features extracted from large size images. First, we randomly collect image patches on an unlabeled image dataset in the source domain and learn local features with a sparse autoencoder. We then conduct feature selection according to the correlation between different weight vectors corresponding to the autoencoder's hidden units. We finally adopt a convolutional neural network including a pooling layer to obtain global feature activations of textile images in the target domain and send these global feature vectors into logistic regression models for emotional image classification. The cross-domain unsupervised feature learning method achieves 65% to 78% average accuracy in the cross-validation experiments corresponding to eight emotional categories and performs better than conventional methods. Feature selection can reduce the computational cost of global feature extraction by about 50% while improving classification performance.

Graphs and matrices

CERN Document Server

Bapat, Ravindra B

2014-01-01

This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reo...

Bayesian Nonparametric Clustering for Positive Definite Matrices.

Science.gov (United States)

Cherian, Anoop; Morellas, Vassilios; Papanikolopoulos, Nikolaos

2016-05-01

Symmetric Positive Definite (SPD) matrices emerge as data descriptors in several applications of computer vision such as object tracking, texture recognition, and diffusion tensor imaging. Clustering these data matrices forms an integral part of these applications, for which soft-clustering algorithms (K-Means, expectation maximization, etc.) are generally used. As is well-known, these algorithms need the number of clusters to be specified, which is difficult when the dataset scales. To address this issue, we resort to the classical nonparametric Bayesian framework by modeling the data as a mixture model using the Dirichlet process (DP) prior. Since these matrices do not conform to the Euclidean geometry, rather belongs to a curved Riemannian manifold,existing DP models cannot be directly applied. Thus, in this paper, we propose a novel DP mixture model framework for SPD matrices. Using the log-determinant divergence as the underlying dissimilarity measure to compare these matrices, and further using the connection between this measure and the Wishart distribution, we derive a novel DPM model based on the Wishart-Inverse-Wishart conjugate pair. We apply this model to several applications in computer vision. Our experiments demonstrate that our model is scalable to the dataset size and at the same time achieves superior accuracy compared to several state-of-the-art parametric and nonparametric clustering algorithms.

Assimilating irregularly spaced sparsely observed turbulent signals with hierarchical Bayesian reduced stochastic filters

International Nuclear Information System (INIS)

Brown, Kristen A.; Harlim, John

2013-01-01

In this paper, we consider a practical filtering approach for assimilating irregularly spaced, sparsely observed turbulent signals through a hierarchical Bayesian reduced stochastic filtering framework. The proposed hierarchical Bayesian approach consists of two steps, blending a data-driven interpolation scheme and the Mean Stochastic Model (MSM) filter. We examine the potential of using the deterministic piecewise linear interpolation scheme and the ordinary kriging scheme in interpolating irregularly spaced raw data to regularly spaced processed data and the importance of dynamical constraint (through MSM) in filtering the processed data on a numerically stiff state estimation problem. In particular, we test this approach on a two-layer quasi-geostrophic model in a two-dimensional domain with a small radius of deformation to mimic ocean turbulence. Our numerical results suggest that the dynamical constraint becomes important when the observation noise variance is large. Second, we find that the filtered estimates with ordinary kriging are superior to those with linear interpolation when observation networks are not too sparse; such robust results are found from numerical simulations with many randomly simulated irregularly spaced observation networks, various observation time intervals, and observation error variances. Third, when the observation network is very sparse, we find that both the kriging and linear interpolations are comparable

Wound care matrices for chronic leg ulcers: role in therapy

Directory of Open Access Journals (Sweden)

Sano H

2015-07-01

Full Text Available Hitomi Sano,1 Sachio Kouraba,2 Rei Ogawa11Department of Plastic, Reconstructive, and Aesthetic Surgery, Nippon Medical School, Tokyo, Japan; 2Sapporo Wound Care and Anti-Aging Laboratory, Sapporo, JapanAbstract: Chronic leg ulcers are a significant health care concern. Although deep wounds are usually treated by flap transfers, the operation is invasive and associates with serious complications. Skin grafts may be a less invasive means of covering wounds. However, skin grafts cannot survive on deep defects unless high-quality granulation tissue can first be generated in the defects. Technologies that generate high-quality granulation tissue are needed. One possibility is to use wound care matrices, which are bioengineered skin and soft tissue substitutes. Because they all support the healing process by providing a premade extracellular matrix material, these matrices can be termed “extracellular matrix replacement therapies”. The matrix promotes wound healing by acting as a scaffold for regeneration, attracting host cytokines to the wound, stimulating wound epithelialization and angiogenesis, and providing the wound bed with bioactive components. This therapy has lasting benefits as it not only helps large skin defects to be closed with thin skin grafts or patch grafts but also restores cosmetic appearance and proper function. In particular, since it acts as a layer that slides over the subcutaneous fascia, it provides skin elasticity, tear resistance, and texture. Several therapies and products employing wound care matrices for wound management have been developed recently. Some of these can be applied in combination with negative pressure wound therapy or beneficial materials that promote wound healing and can be incorporated into the matrix. To date, the clinical studies on these approaches suggest that wound care matrices promote spontaneous wound healing or can be used to facilitate skin grafting, thereby avoiding the need to use

Confidence of model based shape reconstruction from sparse data

DEFF Research Database (Denmark)

Baka, N.; de Bruijne, Marleen; Reiber, J. H. C.

2010-01-01

Statistical shape models (SSM) are commonly applied for plausible interpolation of missing data in medical imaging. However, when fitting a shape model to sparse information, many solutions may fit the available data. In this paper we derive a constrained SSM to fit noisy sparse input landmarks...

Proportionate Minimum Error Entropy Algorithm for Sparse System Identification

Directory of Open Access Journals (Sweden)

Zongze Wu

2015-08-01

Full Text Available Sparse system identification has received a great deal of attention due to its broad applicability. The proportionate normalized least mean square (PNLMS algorithm, as a popular tool, achieves excellent performance for sparse system identification. In previous studies, most of the cost functions used in proportionate-type sparse adaptive algorithms are based on the mean square error (MSE criterion, which is optimal only when the measurement noise is Gaussian. However, this condition does not hold in most real-world environments. In this work, we use the minimum error entropy (MEE criterion, an alternative to the conventional MSE criterion, to develop the proportionate minimum error entropy (PMEE algorithm for sparse system identification, which may achieve much better performance than the MSE based methods especially in heavy-tailed non-Gaussian situations. Moreover, we analyze the convergence of the proposed algorithm and derive a sufficient condition that ensures the mean square convergence. Simulation results confirm the excellent performance of the new algorithm.

Robust Algebraic Multilevel Methods and Algorithms

CERN Document Server

Kraus, Johannes

2009-01-01

This book deals with algorithms for the solution of linear systems of algebraic equations with large-scale sparse matrices, with a focus on problems that are obtained after discretization of partial differential equations using finite element methods. Provides a systematic presentation of the recent advances in robust algebraic multilevel methods. Can be used for advanced courses on the topic.

On Skew Circulant Type Matrices Involving Any Continuous Fibonacci Numbers

Directory of Open Access Journals (Sweden)

Zhaolin Jiang

2014-01-01

inverse matrices of them by constructing the transformation matrices. Furthermore, the maximum column sum matrix norm, the spectral norm, the Euclidean (or Frobenius norm, and the maximum row sum matrix norm and bounds for the spread of these matrices are given, respectively.

Immanant Conversion on Symmetric Matrices

Directory of Open Access Journals (Sweden)

Purificação Coelho M.

2014-01-01

Full Text Available Letr Σn(C denote the space of all n χ n symmetric matrices over the complex field C. The main objective of this paper is to prove that the maps Φ : Σn(C -> Σn (C satisfying for any fixed irre- ducible characters X, X' -SC the condition dx(A +aB = dχ·(Φ(Α + αΦ(Β for all matrices A,В ε Σ„(С and all scalars a ε C are automatically linear and bijective. As a corollary of the above result we characterize all such maps Φ acting on ΣИ(С.

On conjugate gradient type methods and polynomial preconditioners for a class of complex non-Hermitian matrices

Science.gov (United States)

Freund, Roland

1988-01-01

Conjugate gradient type methods are considered for the solution of large linear systems Ax = b with complex coefficient matrices of the type A = T + i(sigma)I where T is Hermitian and sigma, a real scalar. Three different conjugate gradient type approaches with iterates defined by a minimal residual property, a Galerkin type condition, and an Euclidian error minimization, respectively, are investigated. In particular, numerically stable implementations based on the ideas behind Paige and Saunder's SYMMLQ and MINRES for real symmetric matrices are proposed. Error bounds for all three methods are derived. It is shown how the special shift structure of A can be preserved by using polynomial preconditioning. Results on the optimal choice of the polynomial preconditioner are given. Also, some numerical experiments for matrices arising from finite difference approximations to the complex Helmholtz equation are reported.

A flexible framework for sparse simultaneous component based data integration

Directory of Open Access Journals (Sweden)

Van Deun Katrijn

2011-11-01

Full Text Available Abstract 1 Background High throughput data are complex and methods that reveal structure underlying the data are most useful. Principal component analysis, frequently implemented as a singular value decomposition, is a popular technique in this respect. Nowadays often the challenge is to reveal structure in several sources of information (e.g., transcriptomics, proteomics that are available for the same biological entities under study. Simultaneous component methods are most promising in this respect. However, the interpretation of the principal and simultaneous components is often daunting because contributions of each of the biomolecules (transcripts, proteins have to be taken into account. 2 Results We propose a sparse simultaneous component method that makes many of the parameters redundant by shrinking them to zero. It includes principal component analysis, sparse principal component analysis, and ordinary simultaneous component analysis as special cases. Several penalties can be tuned that account in different ways for the block structure present in the integrated data. This yields known sparse approaches as the lasso, the ridge penalty, the elastic net, the group lasso, sparse group lasso, and elitist lasso. In addition, the algorithmic results can be easily transposed to the context of regression. Metabolomics data obtained with two measurement platforms for the same set of Escherichia coli samples are used to illustrate the proposed methodology and the properties of different penalties with respect to sparseness across and within data blocks. 3 Conclusion Sparse simultaneous component analysis is a useful method for data integration: First, simultaneous analyses of multiple blocks offer advantages over sequential and separate analyses and second, interpretation of the results is highly facilitated by their sparseness. The approach offered is flexible and allows to take the block structure in different ways into account. As such

A flexible framework for sparse simultaneous component based data integration.

Science.gov (United States)

Van Deun, Katrijn; Wilderjans, Tom F; van den Berg, Robert A; Antoniadis, Anestis; Van Mechelen, Iven

2011-11-15

High throughput data are complex and methods that reveal structure underlying the data are most useful. Principal component analysis, frequently implemented as a singular value decomposition, is a popular technique in this respect. Nowadays often the challenge is to reveal structure in several sources of information (e.g., transcriptomics, proteomics) that are available for the same biological entities under study. Simultaneous component methods are most promising in this respect. However, the interpretation of the principal and simultaneous components is often daunting because contributions of each of the biomolecules (transcripts, proteins) have to be taken into account. We propose a sparse simultaneous component method that makes many of the parameters redundant by shrinking them to zero. It includes principal component analysis, sparse principal component analysis, and ordinary simultaneous component analysis as special cases. Several penalties can be tuned that account in different ways for the block structure present in the integrated data. This yields known sparse approaches as the lasso, the ridge penalty, the elastic net, the group lasso, sparse group lasso, and elitist lasso. In addition, the algorithmic results can be easily transposed to the context of regression. Metabolomics data obtained with two measurement platforms for the same set of Escherichia coli samples are used to illustrate the proposed methodology and the properties of different penalties with respect to sparseness across and within data blocks. Sparse simultaneous component analysis is a useful method for data integration: First, simultaneous analyses of multiple blocks offer advantages over sequential and separate analyses and second, interpretation of the results is highly facilitated by their sparseness. The approach offered is flexible and allows to take the block structure in different ways into account. As such, structures can be found that are exclusively tied to one data platform

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

Energy Technology Data Exchange (ETDEWEB)

Jiang, Lijian, E-mail: ljjiang@hnu.edu.cn [Institute of Mathematics, Hunan University, Changsha 410082 (China); Li, Qiuqi, E-mail: qiuqili@hnu.edu.cn [College of Mathematics and Econometrics, Hunan University, Changsha 410082 (China)

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

Electronic Spectroscopy of B Atoms and B2 Molecules Isolated in Para-H2, Normal-D2, Ne, Ar, Kr, and Xe Matrices

National Research Council Canada - National Science Library

Tam, Simon

2000-01-01

...), Ne, Ar, Kr, and Xe matrices, and of B2 molecules in Ne, Ar, Kr, and Xe matrices. The 2s(sup 2)3s((sup 2)S) left arrow 2s(sup 2)2p((sup 2)P) B atom Rydberg absorption suffers large gas-to-matrix blue shifts, increasing...

The 'golden' matrices and a new kind of cryptography

International Nuclear Information System (INIS)

Stakhov, A.P.

2007-01-01

We consider a new class of square matrices called the 'golden' matrices. They are a generalization of the classical Fibonacci Q-matrix for continuous domain. The 'golden' matrices can be used for creation of a new kind of cryptography called the 'golden' cryptography. The method is very fast and simple for technical realization and can be used for cryptographic protection of digital signals (telecommunication and measurement systems)

Feature selection and multi-kernel learning for sparse representation on a manifold

KAUST Repository

Wang, Jim Jing-Yan

2014-03-01

Sparse representation has been widely studied as a part-based data representation method and applied in many scientific and engineering fields, such as bioinformatics and medical imaging. It seeks to represent a data sample as a sparse linear combination of some basic items in a dictionary. Gao etal. (2013) recently proposed Laplacian sparse coding by regularizing the sparse codes with an affinity graph. However, due to the noisy features and nonlinear distribution of the data samples, the affinity graph constructed directly from the original feature space is not necessarily a reliable reflection of the intrinsic manifold of the data samples. To overcome this problem, we integrate feature selection and multiple kernel learning into the sparse coding on the manifold. To this end, unified objectives are defined for feature selection, multiple kernel learning, sparse coding, and graph regularization. By optimizing the objective functions iteratively, we develop novel data representation algorithms with feature selection and multiple kernel learning respectively. Experimental results on two challenging tasks, N-linked glycosylation prediction and mammogram retrieval, demonstrate that the proposed algorithms outperform the traditional sparse coding methods. © 2013 Elsevier Ltd.

Feature selection and multi-kernel learning for sparse representation on a manifold.

Science.gov (United States)

Wang, Jim Jing-Yan; Bensmail, Halima; Gao, Xin

2014-03-01

Sparse representation has been widely studied as a part-based data representation method and applied in many scientific and engineering fields, such as bioinformatics and medical imaging. It seeks to represent a data sample as a sparse linear combination of some basic items in a dictionary. Gao et al. (2013) recently proposed Laplacian sparse coding by regularizing the sparse codes with an affinity graph. However, due to the noisy features and nonlinear distribution of the data samples, the affinity graph constructed directly from the original feature space is not necessarily a reliable reflection of the intrinsic manifold of the data samples. To overcome this problem, we integrate feature selection and multiple kernel learning into the sparse coding on the manifold. To this end, unified objectives are defined for feature selection, multiple kernel learning, sparse coding, and graph regularization. By optimizing the objective functions iteratively, we develop novel data representation algorithms with feature selection and multiple kernel learning respectively. Experimental results on two challenging tasks, N-linked glycosylation prediction and mammogram retrieval, demonstrate that the proposed algorithms outperform the traditional sparse coding methods. Copyright © 2013 Elsevier Ltd. All rights reserved.

On the Eigenvalues and Eigenvectors of Block Triangular Preconditioned Block Matrices

KAUST Repository

Pestana, Jennifer

2014-01-01

Block lower triangular matrices and block upper triangular matrices are popular preconditioners for 2×2 block matrices. In this note we show that a block lower triangular preconditioner gives the same spectrum as a block upper triangular preconditioner and that the eigenvectors of the two preconditioned matrices are related. © 2014 Society for Industrial and Applied Mathematics.

Sparse representation, modeling and learning in visual recognition theory, algorithms and applications

CERN Document Server

Cheng, Hong

2015-01-01

This unique text/reference presents a comprehensive review of the state of the art in sparse representations, modeling and learning. The book examines both the theoretical foundations and details of algorithm implementation, highlighting the practical application of compressed sensing research in visual recognition and computer vision. Topics and features: provides a thorough introduction to the fundamentals of sparse representation, modeling and learning, and the application of these techniques in visual recognition; describes sparse recovery approaches, robust and efficient sparse represen

An Efficient GPU General Sparse Matrix-Matrix Multiplication for Irregular Data

DEFF Research Database (Denmark)

Liu, Weifeng; Vinter, Brian

2014-01-01

General sparse matrix-matrix multiplication (SpGEMM) is a fundamental building block for numerous applications such as algebraic multigrid method, breadth first search and shortest path problem. Compared to other sparse BLAS routines, an efficient parallel SpGEMM algorithm has to handle extra...... irregularity from three aspects: (1) the number of the nonzero entries in the result sparse matrix is unknown in advance, (2) very expensive parallel insert operations at random positions in the result sparse matrix dominate the execution time, and (3) load balancing must account for sparse data in both input....... Load balancing builds on the number of the necessary arithmetic operations on the nonzero entries and is guaranteed in all stages. Compared with the state-of-the-art GPU SpGEMM methods in the CUSPARSE library and the CUSP library and the latest CPU SpGEMM method in the Intel Math Kernel Library, our...

Comparison of Methods for Sparse Representation of Musical Signals

DEFF Research Database (Denmark)

Endelt, Line Ørtoft; la Cour-Harbo, Anders

2005-01-01

by a number of sparseness measures and results are shown on the ℓ1 norm of the coefficients, using a dictionary containing a Dirac basis, a Discrete Cosine Transform, and a Wavelet Packet. Evaluated only on the sparseness Matching Pursuit is the best method, and it is also relatively fast....

Joint-2D-SL0 Algorithm for Joint Sparse Matrix Reconstruction

Directory of Open Access Journals (Sweden)

Dong Zhang

2017-01-01

Full Text Available Sparse matrix reconstruction has a wide application such as DOA estimation and STAP. However, its performance is usually restricted by the grid mismatch problem. In this paper, we revise the sparse matrix reconstruction model and propose the joint sparse matrix reconstruction model based on one-order Taylor expansion. And it can overcome the grid mismatch problem. Then, we put forward the Joint-2D-SL0 algorithm which can solve the joint sparse matrix reconstruction problem efficiently. Compared with the Kronecker compressive sensing method, our proposed method has a higher computational efficiency and acceptable reconstruction accuracy. Finally, simulation results validate the superiority of the proposed method.

On Investigating GMRES Convergence using Unitary Matrices

Czech Academy of Sciences Publication Activity Database

Duintjer Tebbens, Jurjen; Meurant, G.; Sadok, H.; Strakoš, Z.

2014-01-01

Roč. 450, 1 June (2014), s. 83-107 ISSN 0024-3795 Grant - others:GA AV ČR(CZ) M100301201; GA MŠk(CZ) LL1202 Institutional support: RVO:67985807 Keywords : GMRES convergence * unitary matrices * unitary spectra * normal matrices * Krylov residual subspace * Schur parameters Subject RIV: BA - General Mathematics Impact factor: 0.939, year: 2014

"G.P.S Matrices" programme: A method to improve the mastery level of social science students in matrices operations

Science.gov (United States)

Lee, Ken Voon

2013-04-01

The purpose of this action research was to increase the mastery level of Form Five Social Science students in Tawau II National Secondary School in the operations of addition, subtraction and multiplication of matrices in Mathematics. A total of 30 students were involved. Preliminary findings through the analysis of pre-test results and questionnaire had identified the main problem faced in which the students felt confused with the application of principles of the operations of matrices when performing these operations. Therefore, an action research was conducted using an intervention programme called "G.P.S Matrices" to overcome the problem. This programme was divided into three phases. 'Gift of Matrices' phase aimed at forming matrix teaching aids. The second and third phases were 'Positioning the Elements of Matrices' and 'Strenghtening the Concept of Matrices'. These two phases were aimed at increasing the level of understanding and memory of the students towards the principles of matrix operations. Besides, this third phase was also aimed at creating an interesting learning environment. A comparison between the results of pre-test and post-test had shown a remarkable improvement in students' performances after implementing the programme. In addition, the analysis of interview findings also indicated a positive feedback on the changes in students' attitude, particularly in the aspect of students' understanding level. Moreover, the level of students' memory also increased following the use of the concrete matrix teaching aids created in phase one. Besides, teachers felt encouraging when conducive learning environment was created through students' presentation activity held in third phase. Furthermore, students were voluntarily involved in these student-centred activities. In conclusion, this research findings showed an increase in the mastery level of students in these three matrix operations and thus the objective of the research had been achieved.

Discussion of CoSA: Clustering of Sparse Approximations

Energy Technology Data Exchange (ETDEWEB)

Armstrong, Derek Elswick [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2017-03-07

The purpose of this talk is to discuss the possible applications of CoSA (Clustering of Sparse Approximations) to the exploitation of HSI (HyperSpectral Imagery) data. CoSA is presented by Moody et al. in the Journal of Applied Remote Sensing (“Land cover classification in multispectral imagery using clustering of sparse approximations over learned feature dictionaries”, Vol. 8, 2014) and is based on machine learning techniques.

Facial Expression Recognition via Non-Negative Least-Squares Sparse Coding

Directory of Open Access Journals (Sweden)

Ying Chen

2014-05-01

Full Text Available Sparse coding is an active research subject in signal processing, computer vision, and pattern recognition. A novel method of facial expression recognition via non-negative least squares (NNLS sparse coding is presented in this paper. The NNLS sparse coding is used to form a facial expression classifier. To testify the performance of the presented method, local binary patterns (LBP and the raw pixels are extracted for facial feature representation. Facial expression recognition experiments are conducted on the Japanese Female Facial Expression (JAFFE database. Compared with other widely used methods such as linear support vector machines (SVM, sparse representation-based classifier (SRC, nearest subspace classifier (NSC, K-nearest neighbor (KNN and radial basis function neural networks (RBFNN, the experiment results indicate that the presented NNLS method performs better than other used methods on facial expression recognition tasks.

Sparse Representation Based Multi-Instance Learning for Breast Ultrasound Image Classification

Directory of Open Access Journals (Sweden)

Lu Bing

2017-01-01

Full Text Available We propose a novel method based on sparse representation for breast ultrasound image classification under the framework of multi-instance learning (MIL. After image enhancement and segmentation, concentric circle is used to extract the global and local features for improving the accuracy in diagnosis and prediction. The classification problem of ultrasound image is converted to sparse representation based MIL problem. Each instance of a bag is represented as a sparse linear combination of all basis vectors in the dictionary, and then the bag is represented by one feature vector which is obtained via sparse representations of all instances within the bag. The sparse and MIL problem is further converted to a conventional learning problem that is solved by relevance vector machine (RVM. Results of single classifiers are combined to be used for classification. Experimental results on the breast cancer datasets demonstrate the superiority of the proposed method in terms of classification accuracy as compared with state-of-the-art MIL methods.

Sparse Representation Based Multi-Instance Learning for Breast Ultrasound Image Classification.

Science.gov (United States)

Bing, Lu; Wang, Wei

2017-01-01

We propose a novel method based on sparse representation for breast ultrasound image classification under the framework of multi-instance learning (MIL). After image enhancement and segmentation, concentric circle is used to extract the global and local features for improving the accuracy in diagnosis and prediction. The classification problem of ultrasound image is converted to sparse representation based MIL problem. Each instance of a bag is represented as a sparse linear combination of all basis vectors in the dictionary, and then the bag is represented by one feature vector which is obtained via sparse representations of all instances within the bag. The sparse and MIL problem is further converted to a conventional learning problem that is solved by relevance vector machine (RVM). Results of single classifiers are combined to be used for classification. Experimental results on the breast cancer datasets demonstrate the superiority of the proposed method in terms of classification accuracy as compared with state-of-the-art MIL methods.

CONVERGENCE OF POWERS OF CONTROLLABLE INTUITIONISTIC FUZZY MATRICES

OpenAIRE

Riyaz Ahmad Padder; P. Murugadas

2016-01-01

Convergences of powers of controllable intuitionistic fuzzy matrices have been stud¬ied. It is shown that they oscillate with period equal to 2, in general. Some equalities and sequences of inequalities about powers of controllable intuitionistic fuzzy matrices have been obtained.

Joint sparse representation for robust multimodal biometrics recognition.

Science.gov (United States)

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.

Robust Visual Tracking Via Consistent Low-Rank Sparse Learning

KAUST Repository

Zhang, Tianzhu

2014-06-19

Object tracking is the process of determining the states of a target in consecutive video frames based on properties of motion and appearance consistency. In this paper, we propose a consistent low-rank sparse tracker (CLRST) that builds upon the particle filter framework for tracking. By exploiting temporal consistency, the proposed CLRST algorithm adaptively prunes and selects candidate particles. By using linear sparse combinations of dictionary templates, the proposed method learns the sparse representations of image regions corresponding to candidate particles jointly by exploiting the underlying low-rank constraints. In addition, the proposed CLRST algorithm is computationally attractive since temporal consistency property helps prune particles and the low-rank minimization problem for learning joint sparse representations can be efficiently solved by a sequence of closed form update operations. We evaluate the proposed CLRST algorithm against 14 state-of-the-art tracking methods on a set of 25 challenging image sequences. Experimental results show that the CLRST algorithm performs favorably against state-of-the-art tracking methods in terms of accuracy and execution time.

Loop diagrams without γ matrices

International Nuclear Information System (INIS)

McKeon, D.G.C.; Rebhan, A.

1993-01-01

By using a quantum-mechanical path integral to compute matrix elements of the form left-angle x|exp(-iHt)|y right-angle, radiative corrections in quantum-field theory can be evaluated without encountering loop-momentum integrals. In this paper we demonstrate how Dirac γ matrices that occur in the proper-time ''Hamiltonian'' H lead to the introduction of a quantum-mechanical path integral corresponding to a superparticle analogous to one proposed recently by Fradkin and Gitman. Direct evaluation of this path integral circumvents many of the usual algebraic manipulations of γ matrices in the computation of quantum-field-theoretical Green's functions involving fermions

Efficient collaborative sparse channel estimation in massive MIMO

KAUST Repository

Masood, Mudassir

2015-08-12

We propose a method for estimation of sparse frequency selective channels within MIMO-OFDM systems. These channels are independently sparse and share a common support. The method estimates the impulse response for each channel observed by the antennas at the receiver. Estimation is performed in a coordinated manner by sharing minimal information among neighboring antennas to achieve results better than many contemporary methods. Simulations demonstrate the superior performance of the proposed method.

Efficient collaborative sparse channel estimation in massive MIMO

KAUST Repository

Masood, Mudassir; Afify, Laila H.; Al-Naffouri, Tareq Y.

2015-01-01

We propose a method for estimation of sparse frequency selective channels within MIMO-OFDM systems. These channels are independently sparse and share a common support. The method estimates the impulse response for each channel observed by the antennas at the receiver. Estimation is performed in a coordinated manner by sharing minimal information among neighboring antennas to achieve results better than many contemporary methods. Simulations demonstrate the superior performance of the proposed method.

Sparse dictionary learning of resting state fMRI networks.

Science.gov (United States)

Eavani, Harini; Filipovych, Roman; Davatzikos, Christos; Satterthwaite, Theodore D; Gur, Raquel E; Gur, Ruben C

2012-07-02

Research in resting state fMRI (rsfMRI) has revealed the presence of stable, anti-correlated functional subnetworks in the brain. Task-positive networks are active during a cognitive process and are anti-correlated with task-negative networks, which are active during rest. In this paper, based on the assumption that the structure of the resting state functional brain connectivity is sparse, we utilize sparse dictionary modeling to identify distinct functional sub-networks. We propose two ways of formulating the sparse functional network learning problem that characterize the underlying functional connectivity from different perspectives. Our results show that the whole-brain functional connectivity can be concisely represented with highly modular, overlapping task-positive/negative pairs of sub-networks.

Classification en référence à une matrice stochastique

OpenAIRE

Verdun , Stéphane; Cariou , Véronique; Qannari , El Mostafa

2009-01-01

International audience; Etant donné un tableau de données X portant sur un ensemble de n objets, et une matrice stochastique S qui peut être assimilée à une matrice de transition d'une chaîne de Markov, nous proposons une méthode de partitionnement consistant à appliquer la matrice S sur X de manière itérative jusqu'à convergence. Les classes formant la partition sont déterminées à partir des états stationnaires de la matrice stochastique. Cette matrice stochastique peut être issue d'une matr...

Low-Rank Sparse Coding for Image Classification

KAUST Repository

Zhang, Tianzhu; Ghanem, Bernard; Liu, Si; Xu, Changsheng; Ahuja, Narendra

2013-01-01

In this paper, we propose a low-rank sparse coding (LRSC) method that exploits local structure information among features in an image for the purpose of image-level classification. LRSC represents densely sampled SIFT descriptors, in a spatial neighborhood, collectively as low-rank, sparse linear combinations of code words. As such, it casts the feature coding problem as a low-rank matrix learning problem, which is different from previous methods that encode features independently. This LRSC has a number of attractive properties. (1) It encourages sparsity in feature codes, locality in codebook construction, and low-rankness for spatial consistency. (2) LRSC encodes local features jointly by considering their low-rank structure information, and is computationally attractive. We evaluate the LRSC by comparing its performance on a set of challenging benchmarks with that of 7 popular coding and other state-of-the-art methods. Our experiments show that by representing local features jointly, LRSC not only outperforms the state-of-the-art in classification accuracy but also improves the time complexity of methods that use a similar sparse linear representation model for feature coding.

Low-Rank Sparse Coding for Image Classification

KAUST Repository

Zhang, Tianzhu

2013-12-01

In this paper, we propose a low-rank sparse coding (LRSC) method that exploits local structure information among features in an image for the purpose of image-level classification. LRSC represents densely sampled SIFT descriptors, in a spatial neighborhood, collectively as low-rank, sparse linear combinations of code words. As such, it casts the feature coding problem as a low-rank matrix learning problem, which is different from previous methods that encode features independently. This LRSC has a number of attractive properties. (1) It encourages sparsity in feature codes, locality in codebook construction, and low-rankness for spatial consistency. (2) LRSC encodes local features jointly by considering their low-rank structure information, and is computationally attractive. We evaluate the LRSC by comparing its performance on a set of challenging benchmarks with that of 7 popular coding and other state-of-the-art methods. Our experiments show that by representing local features jointly, LRSC not only outperforms the state-of-the-art in classification accuracy but also improves the time complexity of methods that use a similar sparse linear representation model for feature coding.

Capture Matrices Handbook

Science.gov (United States)

2014-04-01

materials, the affinity ligand would need identification , as well as chemistries that graft the affinity ligand onto the surface of magnetic...ACTIVE CAPTURE MATRICES FOR THE DETECTION/ IDENTIFICATION OF PHARMACEUTICALS...6 As shown in Figure 2.3-1a, the spectra exhibit similar baselines and the spectral peaks lineup . Under these circumstances, the spectral

Regularized generalized eigen-decomposition with applications to sparse supervised feature extraction and sparse discriminant analysis

DEFF Research Database (Denmark)

Han, Xixuan; Clemmensen, Line Katrine Harder

2015-01-01

We propose a general technique for obtaining sparse solutions to generalized eigenvalue problems, and call it Regularized Generalized Eigen-Decomposition (RGED). For decades, Fisher's discriminant criterion has been applied in supervised feature extraction and discriminant analysis, and it is for...

Binary Positive Semidefinite Matrices and Associated Integer Polytopes

DEFF Research Database (Denmark)

Letchford, Adam N.; Sørensen, Michael Malmros

2012-01-01

We consider the positive semidefinite (psd) matrices with binary entries, along with the corresponding integer polytopes. We begin by establishing some basic properties of these matrices and polytopes. Then, we show that several families of integer polytopes in the literature-the cut, boolean qua...

Chain of matrices, loop equations and topological recursion

CERN Document Server

Orantin, Nicolas

2009-01-01

Random matrices are used in fields as different as the study of multi-orthogonal polynomials or the enumeration of discrete surfaces. Both of them are based on the study of a matrix integral. However, this term can be confusing since the definition of a matrix integral in these two applications is not the same. These two definitions, perturbative and non-perturbative, are discussed in this chapter as well as their relation. The so-called loop equations satisfied by integrals over random matrices coupled in chain is discussed as well as their recursive solution in the perturbative case when the matrices are Hermitean.

Robust sparse image reconstruction of radio interferometric observations with PURIFY

Science.gov (United States)

Pratley, Luke; McEwen, Jason D.; d'Avezac, Mayeul; Carrillo, Rafael E.; Onose, Alexandru; Wiaux, Yves

2018-01-01

Next-generation radio interferometers, such as the Square Kilometre Array, will revolutionize our understanding of the Universe through their unprecedented sensitivity and resolution. However, to realize these goals significant challenges in image and data processing need to be overcome. The standard methods in radio interferometry for reconstructing images, such as CLEAN, have served the community well over the last few decades and have survived largely because they are pragmatic. However, they produce reconstructed interferometric images that are limited in quality and scalability for big data. In this work, we apply and evaluate alternative interferometric reconstruction methods that make use of state-of-the-art sparse image reconstruction algorithms motivated by compressive sensing, which have been implemented in the PURIFY software package. In particular, we implement and apply the proximal alternating direction method of multipliers algorithm presented in a recent article. First, we assess the impact of the interpolation kernel used to perform gridding and degridding on sparse image reconstruction. We find that the Kaiser-Bessel interpolation kernel performs as well as prolate spheroidal wave functions while providing a computational saving and an analytic form. Secondly, we apply PURIFY to real interferometric observations from the Very Large Array and the Australia Telescope Compact Array and find that images recovered by PURIFY are of higher quality than those recovered by CLEAN. Thirdly, we discuss how PURIFY reconstructions exhibit additional advantages over those recovered by CLEAN. The latest version of PURIFY, with developments presented in this work, is made publicly available.

Sparse distributed representation of odors in a large-scale olfactory bulb circuit.

Directory of Open Access Journals (Sweden)

Yuguo Yu

Full Text Available In the olfactory bulb, lateral inhibition mediated by granule cells has been suggested to modulate the timing of mitral cell firing, thereby shaping the representation of input odorants. Current experimental techniques, however, do not enable a clear study of how the mitral-granule cell network sculpts odor inputs to represent odor information spatially and temporally. To address this critical step in the neural basis of odor recognition, we built a biophysical network model of mitral and granule cells, corresponding to 1/100th of the real system in the rat, and used direct experimental imaging data of glomeruli activated by various odors. The model allows the systematic investigation and generation of testable hypotheses of the functional mechanisms underlying odor representation in the olfactory bulb circuit. Specifically, we demonstrate that lateral inhibition emerges within the olfactory bulb network through recurrent dendrodendritic synapses when constrained by a range of balanced excitatory and inhibitory conductances. We find that the spatio-temporal dynamics of lateral inhibition plays a critical role in building the glomerular-related cell clusters observed in experiments, through the modulation of synaptic weights during odor training. Lateral inhibition also mediates the development of sparse and synchronized spiking patterns of mitral cells related to odor inputs within the network, with the frequency of these synchronized spiking patterns also modulated by the sniff cycle.

l1- and l2-Norm Joint Regularization Based Sparse Signal Reconstruction Scheme

Directory of Open Access Journals (Sweden)

Chanzi Liu

2016-01-01

Full Text Available Many problems in signal processing and statistical inference involve finding sparse solution to some underdetermined linear system of equations. This is also the application condition of compressive sensing (CS which can find the sparse solution from the measurements far less than the original signal. In this paper, we propose l1- and l2-norm joint regularization based reconstruction framework to approach the original l0-norm based sparseness-inducing constrained sparse signal reconstruction problem. Firstly, it is shown that, by employing the simple conjugate gradient algorithm, the new formulation provides an effective framework to deduce the solution as the original sparse signal reconstruction problem with l0-norm regularization item. Secondly, the upper reconstruction error limit is presented for the proposed sparse signal reconstruction framework, and it is unveiled that a smaller reconstruction error than l1-norm relaxation approaches can be realized by using the proposed scheme in most cases. Finally, simulation results are presented to validate the proposed sparse signal reconstruction approach.

Image fusion via nonlocal sparse K-SVD dictionary learning.

Science.gov (United States)

Li, Ying; Li, Fangyi; Bai, Bendu; Shen, Qiang

2016-03-01

Image fusion aims to merge two or more images captured via various sensors of the same scene to construct a more informative image by integrating their details. Generally, such integration is achieved through the manipulation of the representations of the images concerned. Sparse representation plays an important role in the effective description of images, offering a great potential in a variety of image processing tasks, including image fusion. Supported by sparse representation, in this paper, an approach for image fusion by the use of a novel dictionary learning scheme is proposed. The nonlocal self-similarity property of the images is exploited, not only at the stage of learning the underlying description dictionary but during the process of image fusion. In particular, the property of nonlocal self-similarity is combined with the traditional sparse dictionary. This results in an improved learned dictionary, hereafter referred to as the nonlocal sparse K-SVD dictionary (where K-SVD stands for the K times singular value decomposition that is commonly used in the literature), and abbreviated to NL_SK_SVD. The performance of the NL_SK_SVD dictionary is applied for image fusion using simultaneous orthogonal matching pursuit. The proposed approach is evaluated with different types of images, and compared with a number of alternative image fusion techniques. The resultant superior fused images using the present approach demonstrates the efficacy of the NL_SK_SVD dictionary in sparse image representation.

Detection of Pitting in Gears Using a Deep Sparse Autoencoder

Directory of Open Access Journals (Sweden)

Yongzhi Qu

2017-05-01

Full Text Available In this paper; a new method for gear pitting fault detection is presented. The presented method is developed based on a deep sparse autoencoder. The method integrates dictionary learning in sparse coding into a stacked autoencoder network. Sparse coding with dictionary learning is viewed as an adaptive feature extraction method for machinery fault diagnosis. An autoencoder is an unsupervised machine learning technique. A stacked autoencoder network with multiple hidden layers is considered to be a deep learning network. The presented method uses a stacked autoencoder network to perform the dictionary learning in sparse coding and extract features from raw vibration data automatically. These features are then used to perform gear pitting fault detection. The presented method is validated with vibration data collected from gear tests with pitting faults in a gearbox test rig and compared with an existing deep learning-based approach.

The Modern Origin of Matrices and Their Applications

Science.gov (United States)

Debnath, L.

2014-01-01

This paper deals with the modern development of matrices, linear transformations, quadratic forms and their applications to geometry and mechanics, eigenvalues, eigenvectors and characteristic equations with applications. Included are the representations of real and complex numbers, and quaternions by matrices, and isomorphism in order to show…

Flux Jacobian Matrices For Equilibrium Real Gases

Science.gov (United States)

Vinokur, Marcel

1990-01-01

Improved formulation includes generalized Roe average and extension to three dimensions. Flux Jacobian matrices derived for use in numerical solutions of conservation-law differential equations of inviscid flows of ideal gases extended to real gases. Real-gas formulation of these matrices retains simplifying assumptions of thermodynamic and chemical equilibrium, but adds effects of vibrational excitation, dissociation, and ionization of gas molecules via general equation of state.

Data depth and rank-based tests for covariance and spectral density matrices

KAUST Repository

Chau, Joris

2017-06-26

In multivariate time series analysis, objects of primary interest to study cross-dependences in the time series are the autocovariance or spectral density matrices. Non-degenerate covariance and spectral density matrices are necessarily Hermitian and positive definite, and our primary goal is to develop new methods to analyze samples of such matrices. The main contribution of this paper is the generalization of the concept of statistical data depth for collections of covariance or spectral density matrices by exploiting the geometric properties of the space of Hermitian positive definite matrices as a Riemannian manifold. This allows one to naturally characterize most central or outlying matrices, but also provides a practical framework for rank-based hypothesis testing in the context of samples of covariance or spectral density matrices. First, the desired properties of a data depth function acting on the space of Hermitian positive definite matrices are presented. Second, we propose two computationally efficient pointwise and integrated data depth functions that satisfy each of these requirements. Several applications of the developed methodology are illustrated by the analysis of collections of spectral matrices in multivariate brain signal time series datasets.

Data depth and rank-based tests for covariance and spectral density matrices

KAUST Repository

Chau, Joris; Ombao, Hernando; Sachs, Rainer von

2017-01-01

In multivariate time series analysis, objects of primary interest to study cross-dependences in the time series are the autocovariance or spectral density matrices. Non-degenerate covariance and spectral density matrices are necessarily Hermitian and positive definite, and our primary goal is to develop new methods to analyze samples of such matrices. The main contribution of this paper is the generalization of the concept of statistical data depth for collections of covariance or spectral density matrices by exploiting the geometric properties of the space of Hermitian positive definite matrices as a Riemannian manifold. This allows one to naturally characterize most central or outlying matrices, but also provides a practical framework for rank-based hypothesis testing in the context of samples of covariance or spectral density matrices. First, the desired properties of a data depth function acting on the space of Hermitian positive definite matrices are presented. Second, we propose two computationally efficient pointwise and integrated data depth functions that satisfy each of these requirements. Several applications of the developed methodology are illustrated by the analysis of collections of spectral matrices in multivariate brain signal time series datasets.

Multivariate analysis of nutritional information of foodstuff of plant origin for the selection of representative matrices for the analysis of pesticide residues

International Nuclear Information System (INIS)

Neves Bettencourt da Silva, Ricardo Jorge; Gomes Ferreira Crujo Camoes, Maria Filomena

2010-01-01

Testing safety of foodstuffs of plant origin involves the analysis of hundreds of pesticide residues. This control is only cost-effective through the use of methods validated for the analysis of many thousands of analyte/matrix combinations. Several documents propose representative matrices of groups of matrices from which the validity of the analytical method can be extrapolated to the represented matrices after summarised experimental check of within group method performance homogeneity. Those groups are based on an evolved expert consensus based on the empirical knowledge on the current analytical procedures; they are not exhaustive, they are not objectively defined and they propose a large list of representative matrices which makes their application difficult. This work proposes grouping 240 matrices, based on the nutritional composition pattern equivalence of the analytical portion right after hydration and before solvent extraction, aiming at defining groups that observe method performance homogeneity. This grouping was based on the combined outcome of three multivariate tools, namely: Principal Component Analysis, Hierarchical Cluster Analysis and K-Mean Cluster Analysis. These tools allowed the selection of eight groups for which representative matrices with average characteristics and objective criteria to test inclusion of new matrices were established. The proposed matrices groups are homogeneous to nutritional data not considered in their definition but correlated with the studied multivariate nutritional pattern. The developed grouping that must be checked with experimental test before use was tested against small deviations in food composition and for the integration of new matrices.

Pairwise Constraint-Guided Sparse Learning for Feature Selection.

Science.gov (United States)

Liu, Mingxia; Zhang, Daoqiang

2016-01-01

Feature selection aims to identify the most informative features for a compact and accurate data representation. As typical supervised feature selection methods, Lasso and its variants using L1-norm-based regularization terms have received much attention in recent studies, most of which use class labels as supervised information. Besides class labels, there are other types of supervised information, e.g., pairwise constraints that specify whether a pair of data samples belong to the same class (must-link constraint) or different classes (cannot-link constraint). However, most of existing L1-norm-based sparse learning methods do not take advantage of the pairwise constraints that provide us weak and more general supervised information. For addressing that problem, we propose a pairwise constraint-guided sparse (CGS) learning method for feature selection, where the must-link and the cannot-link constraints are used as discriminative regularization terms that directly concentrate on the local discriminative structure of data. Furthermore, we develop two variants of CGS, including: 1) semi-supervised CGS that utilizes labeled data, pairwise constraints, and unlabeled data and 2) ensemble CGS that uses the ensemble of pairwise constraint sets. We conduct a series of experiments on a number of data sets from University of California-Irvine machine learning repository, a gene expression data set, two real-world neuroimaging-based classification tasks, and two large-scale attribute classification tasks. Experimental results demonstrate the efficacy of our proposed methods, compared with several established feature selection methods.

Sparseness- and continuity-constrained seismic imaging

Science.gov (United States)

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 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.

Almost commuting self-adjoint matrices: The real and self-dual cases

Science.gov (United States)

Loring, Terry A.; Sørensen, Adam P. W.

2016-08-01

We show that a pair of almost commuting self-adjoint, symmetric matrices is close to a pair of commuting self-adjoint, symmetric matrices (in a uniform way). Moreover, we prove that the same holds with self-dual in place of symmetric and also for paths of self-adjoint matrices. Since a symmetric, self-adjoint matrix is real, we get a real version of Huaxin Lin’s famous theorem on almost commuting matrices. Similarly, the self-dual case gives a version for matrices over the quaternions. To prove these results, we develop a theory of semiprojectivity for real C*-algebras and also examine various definitions of low-rank for real C*-algebras.

Estimation of kinship coefficient in structured and admixed populations using sparse sequencing data.

Directory of Open Access Journals (Sweden)

Jinzhuang Dou

2017-09-01

Full Text Available Knowledge of biological relatedness between samples is important for many genetic studies. In large-scale human genetic association studies, the estimated kinship is used to remove cryptic relatedness, control for family structure, and estimate trait heritability. However, estimation of kinship is challenging for sparse sequencing data, such as those from off-target regions in target sequencing studies, where genotypes are largely uncertain or missing. Existing methods often assume accurate genotypes at a large number of markers across the genome. We show that these methods, without accounting for the genotype uncertainty in sparse sequencing data, can yield a strong downward bias in kinship estimation. We develop a computationally efficient method called SEEKIN to estimate kinship for both homogeneous samples and heterogeneous samples with population structure and admixture. Our method models genotype uncertainty and leverages linkage disequilibrium through imputation. We test SEEKIN on a whole exome sequencing dataset (WES of Singapore Chinese and Malays, which involves substantial population structure and admixture. We show that SEEKIN can accurately estimate kinship coefficient and classify genetic relatedness using off-target sequencing data down sampled to ~0.15X depth. In application to the full WES dataset without down sampling, SEEKIN also outperforms existing methods by properly analyzing shallow off-target data (~0.75X. Using both simulated and real phenotypes, we further illustrate how our method improves estimation of trait heritability for WES studies.

Combinatorial Algorithms for Computing Column Space Bases ThatHave Sparse Inverses

Energy Technology Data Exchange (ETDEWEB)

Pinar, Ali; Chow, Edmond; Pothen, Alex

2005-03-18

This paper presents a combinatorial study on the problem ofconstructing a sparse basis forthe null-space of a sparse, underdetermined, full rank matrix, A. Such a null-space is suitable forsolving solving many saddle point problems. Our approach is to form acolumn space basis of A that has a sparse inverse, by selecting suitablecolumns of A. This basis is then used to form a sparse null-space basisin fundamental form. We investigate three different algorithms forcomputing the column space basis: Two greedy approaches that rely onmatching, and a third employing a divide and conquer strategy implementedwith hypergraph partitioning followed by the greedy approach. We alsodiscuss the complexity of selecting a column basis when it is known thata block diagonal basis exists with a small given block size.

Image Super-Resolution Algorithm Based on an Improved Sparse Autoencoder

Directory of Open Access Journals (Sweden)

Detian Huang

2018-01-01

Full Text Available Due to the limitations of the resolution of the imaging system and the influence of scene changes and other factors, sometimes only low-resolution images can be acquired, which cannot satisfy the practical application’s requirements. To improve the quality of low-resolution images, a novel super-resolution algorithm based on an improved sparse autoencoder is proposed. Firstly, in the training set preprocessing stage, the high- and low-resolution image training sets are constructed, respectively, by using high-frequency information of the training samples as the characterization, and then the zero-phase component analysis whitening technique is utilized to decorrelate the formed joint training set to reduce its redundancy. Secondly, a constructed sparse regularization term is added to the cost function of the traditional sparse autoencoder to further strengthen the sparseness constraint on the hidden layer. Finally, in the dictionary learning stage, the improved sparse autoencoder is adopted to achieve unsupervised dictionary learning to improve the accuracy and stability of the dictionary. Experimental results validate that the proposed algorithm outperforms the existing algorithms both in terms of the subjective visual perception and the objective evaluation indices, including the peak signal-to-noise ratio and the structural similarity measure.

Propositional matrices as alternative representation of truth values ...

African Journals Online (AJOL)

The paper considered the subject of representation of truth values in symbolic logic. An alternative representation was given based on the rows and columns properties of matrices, with the operations involving the logical connectives subjected to the laws of algebra of propositions. Matrices of various propositions detailing ...

Diagnosis and prognosis of Ostheoarthritis by texture analysis using sparse linear models

DEFF Research Database (Denmark)

Marques, Joselene; Clemmensen, Line Katrine Harder; Dam, Erik

We present a texture analysis methodology that combines uncommitted machine-learning techniques and sparse feature transformation methods in a fully automatic framework. We compare the performances of a partial least squares (PLS) forward feature selection strategy to a hard threshold sparse PLS...... algorithm and a sparse linear discriminant model. The texture analysis framework was applied to diagnosis of knee osteoarthritis (OA) and prognosis of cartilage loss. For this investigation, a generic texture feature bank was extracted from magnetic resonance images of tibial knee bone. The features were...... used as input to the sparse algorithms, which dened the best features to retain in the model. To cope with the limited number of samples, the data was evaluated using 10 fold cross validation (CV). The diagnosis evaluation using sparse PLS reached a generalization area-under-the-ROC curve (AUC) of 0...