Fast convex optimization algorithms for exact recovery of a corrupted low-rank matrix

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Fast convex optimization algorithms for exact recovery of a corrupted low-rank matrix (2009)

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by Zhouchen Lin , Arvind Ganesh , John Wright , Leqin Wu , Minming Chen , Yi Ma

Venue:	In Intl. Workshop on Comp. Adv. in Multi-Sensor Adapt. Processing, Aruba, Dutch Antilles
Citations:	88 - 9 self

BibTeX

@INPROCEEDINGS{Lin09fastconvex,
    author = {Zhouchen Lin and Arvind Ganesh and John Wright and Leqin Wu and Minming Chen and Yi Ma},
    title = {Fast convex optimization algorithms for exact recovery of a corrupted low-rank matrix},
    booktitle = {In Intl. Workshop on Comp. Adv. in Multi-Sensor Adapt. Processing, Aruba, Dutch Antilles},
    year = {2009}
}

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Abstract

Abstract. This paper studies algorithms for solving the problem of recovering a low-rank matrix with a fraction of its entries arbitrarily corrupted. This problem can be viewed as a robust version of classical PCA, and arises in a number of application domains, including image processing, web data ranking, and bioinformatic data analysis. It was recently shown that under surprisingly broad conditions, it can be exactly solved via a convex programming surrogate that combines nuclear norm minimization and ℓ1-norm minimization. This paper develops and compares two complementary approaches for solving this convex program. The first is an accelerated proximal gradient algorithm directly applied to the primal; while the second is a gradient algorithm applied to the dual problem. Both are several orders of magnitude faster than the previous state-of-the-art algorithm for this problem, which was based on iterative thresholding. Simulations demonstrate the performance improvement that can be obtained via these two algorithms, and clarify their relative merits.

Keyphrases

corrupted low-rank matrix exact recovery fast convex optimization algorithm 1-norm minimization nuclear norm minimization accelerated proximal gradient algorithm image processing classical pca iterative thresholding bioinformatic data analysis previous state-of-the-art algorithm paper study convex program gradient algorithm several order dual problem application domain broad condition complementary approach performance improvement robust version relative merit data ranking low-rank matrix

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