### Robust principal component analysis?Robust principal component analysis?

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 Author Cands, Emmanuel J. ♦ Li, Xiaodong ♦ Ma, Yi ♦ Wright, John Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©2011 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword $ℓ_{1}-norm$ minimization ♦ Principal components ♦ Duality ♦ Low-rank matrices ♦ Nuclear-norm minimization ♦ Robustness vis-a-vis outliers ♦ Sparsity ♦ Video surveillance 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 $\textit{exactly}$ 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. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 2011-06-09 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 58 Issue Number 3 Page Count 37 Starting Page 1 Ending Page 37

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Source: ACM Digital Library