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5,256
Rank-sparsity incoherence for matrix decomposition
, 2010
"... Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of applications in model and system identification, and is intractable ..."
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Cited by 230 (21 self)
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and low-rank matrices playing a prominent role. When the sparse and low-rank matrices are drawn from certain natural random ensembles, we show that the sufficient conditions for exact recovery are satisfied with high probability. We conclude with simulation results on synthetic matrix decomposition
Probability matrix decomposition models
- Psychometrika
, 1996
"... In this paper, we consider a class of models for two-way matrices with binary entries of 0 and l. First, we consider Boolean matrix decomposition, conceptualize it as a latent response model (LRM) and, by making use of this conceptualization, generalize it to a larger class of matrix decomposition m ..."
Abstract
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Cited by 11 (7 self)
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In this paper, we consider a class of models for two-way matrices with binary entries of 0 and l. First, we consider Boolean matrix decomposition, conceptualize it as a latent response model (LRM) and, by making use of this conceptualization, generalize it to a larger class of matrix decomposition
Matrix decompositions for quaternions
"... Abstract—Since quaternions have isomorphic representations in matrix form we investigate various well known matrix decompositions for quaternions. Keywords—Decompositions of quaternions, Schur, polar, SVD, Jordan, QR, LU. ..."
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Cited by 1 (0 self)
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Abstract—Since quaternions have isomorphic representations in matrix form we investigate various well known matrix decompositions for quaternions. Keywords—Decompositions of quaternions, Schur, polar, SVD, Jordan, QR, LU.
Interpretable nonnegative matrix decompositions
- In Proceeding of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
, 2008
"... A matrix decomposition expresses a matrix as a product of at least two factor matrices. Equivalently, it expresses each column of the input matrix as a linear combination of the columns in the first factor matrix. The interpretability of the decompositions is a key issue in data-analysis tasks. We p ..."
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Cited by 8 (1 self)
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A matrix decomposition expresses a matrix as a product of at least two factor matrices. Equivalently, it expresses each column of the input matrix as a linear combination of the columns in the first factor matrix. The interpretability of the decompositions is a key issue in data-analysis tasks. We
Jordan Matrix Decomposition
, 2008
"... In this paper I present the Jordan Matrix Decomposition Theorem which states that an arbitrary square matrix M over an algebraically closed field can be decomposed into the form M = SJS −1 where S is an invertible matrix and J is a matrix in a Jordan canonical form, i.e. a special type of block diag ..."
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In this paper I present the Jordan Matrix Decomposition Theorem which states that an arbitrary square matrix M over an algebraically closed field can be decomposed into the form M = SJS −1 where S is an invertible matrix and J is a matrix in a Jordan canonical form, i.e. a special type of block
Applying Matrix Decompositions to Counterterrorism
, 2004
"... Governments collect data in which they hope to find patterns of terrorist activity. It is hard to know what such patterns look like and, in any case, terrorists are actively trying to avoid leaving any distinctive traces. However, if they work as a group, it is impossible to avoid some correlation ..."
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Cited by 2 (0 self)
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among their attributes and actions. We show that such correlation can be detected, partly because it is likely to be qualitatively different from the correlations among groups with more innocent purpose. We show that matrix decompositions, in particular singular value decomposition and semidiscrete
FINDING STRUCTURE WITH RANDOMNESS: PROBABILISTIC ALGORITHMS FOR CONSTRUCTING APPROXIMATE MATRIX DECOMPOSITIONS
"... Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which demonstrates that randomization offers a powerful tool for ..."
Abstract
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Cited by 253 (6 self)
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Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which demonstrates that randomization offers a powerful tool
Probability Matrix Decomposition (PMD)...
"... check, psychometrics Probability Matrix Decomposition models may be used to model observed binary associations between two sets of elements. More specifically, to explain observed associations between two elements, it is assumed that B latent Ber-noulli variables are realized for each element and th ..."
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check, psychometrics Probability Matrix Decomposition models may be used to model observed binary associations between two sets of elements. More specifically, to explain observed associations between two elements, it is assumed that B latent Ber-noulli variables are realized for each element
Robust Matrix Decomposition with Outliers
, 2010
"... Suppose a given observation matrix can be decomposed as the sum of a low-rank matrix and a sparse matrix (outliers), and the goal is to recover these individual components from the observed sum. Such additive decompositions have applications in a variety of numerical problems including system identi ..."
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Cited by 16 (1 self)
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Suppose a given observation matrix can be decomposed as the sum of a low-rank matrix and a sparse matrix (outliers), and the goal is to recover these individual components from the observed sum. Such additive decompositions have applications in a variety of numerical problems including system
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