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Robust Matrix Decomposition with Sparse Corruptions
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@MISC{Hsu_robustmatrix,
author = {Daniel Hsu and Sham M. Kakade and Tong Zhang},
title = {Robust Matrix Decomposition with Sparse Corruptions},
year = {}
}
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Abstract
Abstract—Suppose a given observation matrix can be decomposed as the sum of a low-rank matrix and a sparse matrix, 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 identification, latent variable graphical modeling, and principal components analysis. We study conditions under which recovering such a decomposition is possible via a combination of ℓ1 norm and trace norm minimization. We are specifically interested in the question of how many sparse corruptions are allowed so that convex programming can still achieve accurate recovery, and we obtain stronger recovery guarantees than previous studies. Moreover, we do not assume that the spatial pattern of corruptions is random, which stands in contrast to related analyses under such assumptions via matrix completion. Index Terms—Matrix decompositions, sparsity, lowrank, outliers
Keyphrases
sparse corruption robust matrix decomposition index term matrix decomposition system identification low-rank matrix principal component analysis trace norm minimization observed sum previous study individual component spatial pattern many sparse corruption matrix completion abstract suppose convex programming latent variable graphical modeling observation matrix accurate recovery numerical problem recovery guarantee additive decomposition sparse matrix
