Transcription of Robust Principal Component Analysis? - Columbia University
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Robust Principal Component Analysis? - Columbia University
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.
Robust Principal Component Analysis? 11:3 polynomial-time algorithm with strong performance guarantees under broad condi-tions.3 The problem we study here can be considered an idealized version of Robust PCA, in which we aim to recover a low-rank matrix L 0 from highly corrupted measure- ments M = L 0 + S 0.Unlike the small noise term N 0 in classical PCA, the …
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