Results 1  10
of
469,309
The University of Florida sparse matrix collection
 NA DIGEST
, 1997
"... The University of Florida Sparse Matrix Collection is a large, widely available, and actively growing set of sparse matrices that arise in real applications. Its matrices cover a wide spectrum of problem domains, both those arising from problems with underlying 2D or 3D geometry (structural enginee ..."
Abstract

Cited by 536 (17 self)
 Add to MetaCart
for the development and performance evaluation of sparse matrix algorithms. The collection includes software for accessing and managing the collection, from MATLAB, Fortran, and C.
Robust face recognition via sparse representation
 IEEE TRANS. PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2008
"... We consider the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise. We cast the recognition problem as one of classifying among multiple linear regression models, and argue that new theory from sparse signa ..."
Abstract

Cited by 936 (40 self)
 Add to MetaCart
We consider the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise. We cast the recognition problem as one of classifying among multiple linear regression models, and argue that new theory from sparse
A Singular Value Thresholding Algorithm for Matrix Completion
, 2008
"... This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and arises in many important applications as in the task of reco ..."
Abstract

Cited by 555 (22 self)
 Add to MetaCart
toimplement algorithm that is extremely efficient at addressing problems in which the optimal solution has low rank. The algorithm is iterative and produces a sequence of matrices {X k, Y k} and at each step, mainly performs a softthresholding operation on the singular values of the matrix Y k. There are two
Parallel Numerical Linear Algebra
, 1993
"... We survey general techniques and open problems in numerical linear algebra on parallel architectures. We first discuss basic principles of parallel processing, describing the costs of basic operations on parallel machines, including general principles for constructing efficient algorithms. We illust ..."
Abstract

Cited by 773 (23 self)
 Add to MetaCart
illustrate these principles using current architectures and software systems, and by showing how one would implement matrix multiplication. Then, we present direct and iterative algorithms for solving linear systems of equations, linear least squares problems, the symmetric eigenvalue problem
A Data Locality Optimizing Algorithm
, 1991
"... This paper proposes an algorithm that improves the locality of a loop nest by transforming the code via interchange, reversal, skewing and tiling. The loop transformation algorithm is based on two concepts: a mathematical formulation of reuse and locality, and a loop transformation theory that unifi ..."
Abstract

Cited by 804 (16 self)
 Add to MetaCart
that unifies the various transforms as unimodular matrix transformations. The algorithm has been implemented in the SUIF (Stanford University Intermediate Format) compiler, and is successful in optimizing codes such as matrix multiplication, successive overrelaxation (SOR), LU decomposition without pivoting
For Most Large Underdetermined Systems of Linear Equations the Minimal ℓ1norm Solution is also the Sparsest Solution
 Comm. Pure Appl. Math
, 2004
"... We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that ..."
Abstract

Cited by 568 (10 self)
 Add to MetaCart
. In contrast, heuristic attempts to sparsely solve such systems – greedy algorithms and thresholding – perform poorly in this challenging setting. The techniques include the use of random proportional embeddings and almostspherical sections in Banach space theory, and deviation bounds for the eigenvalues
Online learning for matrix factorization and sparse coding
, 2010
"... Sparse coding—that is, modelling data vectors as sparse linear combinations of basis elements—is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the largescale matrix factorization problem that consists of learning the basis set in order to ad ..."
Abstract

Cited by 330 (31 self)
 Add to MetaCart
Sparse coding—that is, modelling data vectors as sparse linear combinations of basis elements—is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the largescale matrix factorization problem that consists of learning the basis set in order
Localityconstrained linear coding for image classification
 IN: IEEE CONFERENCE ON COMPUTER VISION AND PATTERN CLASSIFICATOIN
, 2010
"... The traditional SPM approach based on bagoffeatures (BoF) requires nonlinear classifiers to achieve good image classification performance. This paper presents a simple but effective coding scheme called Localityconstrained Linear Coding (LLC) in place of the VQ coding in traditional SPM. LLC util ..."
Abstract

Cited by 443 (20 self)
 Add to MetaCart
, achieving stateoftheart performance on several benchmarks. Compared with the sparse coding strategy [22], the objective function used by LLC has an analytical solution. In addition, the paper proposes a fast approximated LLC method by first performing a Knearestneighbor search and then solving a
Algorithms for simultaneous sparse approximation. Part II: Convex relaxation
, 2004
"... Abstract. A simultaneous sparse approximation problem requests a good approximation of several input signals at once using different linear combinations of the same elementary signals. At the same time, the problem balances the error in approximation against the total number of elementary signals th ..."
Abstract

Cited by 366 (5 self)
 Add to MetaCart
problems. The second part of the paper develops another algorithmic approach called convex relaxation, and it provides theoretical results on the performance of convex relaxation for simultaneous sparse approximation. Date: Typeset on March 17, 2005. Key words and phrases. Greedy algorithms, Orthogonal
SPARSKIT: a basic tool kit for sparse matrix computations  Version 2
, 1994
"... . This paper presents the main features of a tool package for manipulating and working with sparse matrices. One of the goals of the package is to provide basic tools to facilitate exchange of software and data between researchers in sparse matrix computations. Our starting point is the Harwell/Boei ..."
Abstract

Cited by 314 (22 self)
 Add to MetaCart
/Boeing collection of matrices for which we provide a number of tools. Among other things the package provides programs for converting data structures, printing simple statistics on a matrix, plotting a matrix profile, performing basic linear algebra operations with sparse matrices and so on. Work done partly
Results 1  10
of
469,309