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Robust Principal Component Analysis?

11 Robust Principal Component Analysis? EMMANUEL J. CAND`ES and XIAODONG LI, Stanford UniversityYI MA, University of Illinois at Urbana-Champaign, Microsoft Research AsiaJOHN WRIGHT, Microsoft Research AsiaThis article is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of alow-rank Component and a sparse Component . Can we recover each Component individually? We prove thatunder some suitable assumptions, it is possible to recover both the low-rank and the sparse componentsexactlyby solving a very convenient convex program calledPrincipal Component Pursuit; among all feasibledecompositions, simply minimize a weighted combination of the nuclear norm and of the 1norm.

Their results are of a somewhat different nature; see Section 1.5 for a detailed explanation. Applications. There are many important applications in which the data under study can naturally be modeled as a low-rank plus a sparse contribution. All the statisti-cal applications, in which robust principal components are sought, of course fit our ...

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