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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. This sug-gests the possibility of a principled approach to Robust Principal Component analysis since our methodologyand results assert that one can recover the Principal components of a data matrix even though a positivefraction of its entries are arbitrarily corrupted.
data analysis, and bioinformatics, where some measurements may be arbitrarily cor-rupted (due to occlusions, malicious tampering, or sensor failures) or simply irrelevant to the low-dimensional structure we seek to identify. A number of natural approaches to robustifying PCA have been explored and proposed in the literature over several decades.
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