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Robust principal component analysis?

Open access
Candès, Emmanuel J., Li, Xiaodong, Ma, Yi, Wright, John·2011·Journal of the ACM
DOI 10.1145/1970392.1970395
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Abstract

This article is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions, it is possible to recover both the low-rank and the sparse components exactly by solving a very convenient convex program called Principal Component Pursuit ; among all feasible decompositions, simply minimize a weighted combination of the nuclear norm and of the ℓ 1 norm. This suggests the possibility of a principled approach to robust principal component analysis since our methodology and results assert that one can recover the principal components of a data matrix even though a positive fraction of its entries are arbitrarily corrupted. This extends to the situation where a fraction of the entries are missing as well. We discuss an algorithm for solving this optimization problem, and present applications in the area of video surveillance, where our methodology allows for the detection of objects in a cluttered background, and in the area of face recognition, where it offers a principled way of removing shadows and specularities in images of faces.

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Metadata

Authors
Candès, E. J., Li, X., Ma, Y., & Wright, J.
Venue
Journal of the ACM
Publisher
Association for Computing Machinery (ACM)
Published
2011-05
Volume
58
Issue
3
Pages
1-37
ISSN
  • 0004-5411 (ISSN-L)
  • 1557-735X
DOI
10.1145/1970392.1970395
OpenAlex
W2145962650
Cited by
6,921
References
4
FWCI
357.14
Type
journal article
Language
en
Open access
green
Licence
www.acm.org/publications/policies/copyright_policy#Background (vor)
Funders
  • Office of Naval Research (N00014-09-1-0469N00014-08-1-0749N00014-09-1-0230)
  • Division of Electrical, Communications and Cyber Systems (IIS 08-49292ECCS 07-01676)
  • Division of Information and Intelligent Systems (IIS 08-49292ECCS 07-01676)

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Candès, E. J., Li, X., Ma, Y., & Wright, J. (2011). Robust principal component analysis? Journal of the ACM. https://doi.org/10.1145/1970392.1970395

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