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KSVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
, 2006
"... In recent years there has been a growing interest in the study of sparse representation of signals. Using an overcomplete dictionary that contains prototype signalatoms, signals are described by sparse linear combinations of these atoms. Applications that use sparse representation are many and inc ..."
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Cited by 935 (41 self)
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signal representations. Given a set of training signals, we seek the dictionary that leads to the best representation for each member in this set, under strict sparsity constraints. We present a new method—the KSVD algorithm—generalizing the umeans clustering process. KSVD is an iterative method
An improved algorithm for computing the singular value decomposition
 ACM Trans. Math. Software
, 1982
"... The most wellknown and widely used algorithm for computing the Singular Value Decomposition (SVD) A U ~V T of an m x n rectangular matrix A is the GolubReinsch algorithm (GRSVD). In this paper, an improved version of the original GRSVD algorithm is presented. The new algorithm works best for ..."
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Cited by 57 (0 self)
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The most wellknown and widely used algorithm for computing the Singular Value Decomposition (SVD) A U ~V T of an m x n rectangular matrix A is the GolubReinsch algorithm (GRSVD). In this paper, an improved version of the original GRSVD algorithm is presented. The new algorithm works best
The Singular Value Decomposition for Polynomial Systems
, 1995
"... This paper introduces singular value decomposition (SVD) algorithms for some standard polynomial computations, in the case where the coefficients are inexact or imperfectly known. We first give an algorithm for computing univariate GCD's which gives exact results for interesting nearby problems ..."
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Cited by 89 (9 self)
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This paper introduces singular value decomposition (SVD) algorithms for some standard polynomial computations, in the case where the coefficients are inexact or imperfectly known. We first give an algorithm for computing univariate GCD's which gives exact results for interesting nearby
A Stable And Fast Algorithm For Updating The Singular Value Decomposition
, 1994
"... . Let A 2 R m\Thetan be a matrix with known singular values and singular vectors, and let A 0 be the matrix obtained by appending a row to A. We present stable and fast algorithms for computing the singular values and the singular vectors of A 0 in O \Gamma (m + n) min(m;n) log 2 2 ffl \De ..."
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Cited by 57 (2 self)
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\Delta floating point operations, where ffl is the machine precision. Previous algorithms can be unstable and compute the singular values and the singular vectors of A 0 in O \Gamma (m + n) min 2 (m;n) \Delta floating point operations. 1. Introduction. The singular value decomposition (SVD
RELATIVEERROR CUR MATRIX DECOMPOSITIONS
 SIAM J. MATRIX ANAL. APPL
, 2008
"... Many data analysis applications deal with large matrices and involve approximating the matrix using a small number of “components.” Typically, these components are linear combinations of the rows and columns of the matrix, and are thus difficult to interpret in terms of the original features of the ..."
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Cited by 86 (17 self)
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and rows, respectively, of A, and U is a generalized inverse of their intersection.) For each algorithm, we show that with probability at least 1 − δ, ‖A − A ′ ‖F ≤ (1 + ɛ) ‖A − Ak‖F, where Ak is the “best ” rankk approximation provided by truncating the SVD of A, and where ‖X‖F is the Frobenius norm
An O(n²) algorithm for the bidiagonal SVD
, 2000
"... The RRR algorithm allows to compute the eigendecomposition of a symmetric tridiagonal matrix T with an O(n²) complexity. This article discusses how this method can be adapted to the bidiagonal SVD B = U \SigmaV T . It turns out that using the RRR algorithm as a black box to compute B T B = V \S ..."
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Cited by 3 (0 self)
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The RRR algorithm allows to compute the eigendecomposition of a symmetric tridiagonal matrix T with an O(n²) complexity. This article discusses how this method can be adapted to the bidiagonal SVD B = U \SigmaV T . It turns out that using the RRR algorithm as a black box to compute B T B = V
A systolic algorithm for QSVD updating
, 1991
"... : In earlier reports, a Jacobitype algorithm for SVD updating has been developed [8] and implemented on a systolic array [9]. Here, this is extended to a generalized decomposition for a matrix pair, viz. the quotient singular value decomposition (QSVD). Updating problems are considered where new ro ..."
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Cited by 8 (8 self)
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: In earlier reports, a Jacobitype algorithm for SVD updating has been developed [8] and implemented on a systolic array [9]. Here, this is extended to a generalized decomposition for a matrix pair, viz. the quotient singular value decomposition (QSVD). Updating problems are considered where new
Efficient Algorithms for Reducing Banded Matrices to Bidiagonal and Tridiagonal Form
, 1997
"... This paper presents efficient techniques for the orthogonal reduction of banded matrices to bidiagonal and symmetric tridiagonal form. The algorithms are numerically stable and well suited to parallel execution. Experiments on the Intel Paragon show that even on a single processor these methods usua ..."
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Cited by 1 (0 self)
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steps. First, a finite algorithm reduces the matrix to bidiagonal form, A \Gamma! B = U T 1 AV 1 , and then an iterative method (e.g., the Golub/Kahan procedure [8]) is used to compute the SVD of the bidiagonal matrix, B = U 2 \SigmaV T 2 . Thus, the SVD of A is given by A = (U 1 U 2 )\Sigma(V 1 V 2
THE GRADIENT PROJECTION ALGORITHM FOR ORTHOGONAL ROTATION
"... Let M be the manifold of all k by m columnwise orthonormal matrices and let f be a function defined on arbitrary k by m matrices. The general orthogonal rotation problem is to minimize f restricted to M. The most common problem is rotation to simple loadings in factor analysis. There f(T) = Q(AT) ..."
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) algorithm to be discussed is essentially the singular value decomposition (SVD) algorithm of Jennrich (2001). It, however, was not recognized that the SVD algorithm was in fact a GP algorithm until a remark to that effect appeared in a paper on oblique gradient projection algorithms (Jennrich, 2002
On Speech Enhancement Algorithms Based On Signal Subspace Methods
"... In this paper the signal subspace approach for nonparametric speech enhancement is considered. Several algorithms have been proposed in the litterature but only partly analyzed. Here, the different algorithms are compared, and the emphasis is put onto the limiting factors and practical behavior of t ..."
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approach for nonparametric speech enhancement is considered. Traditionally, the SVD is u...
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