Transcription of Robust Principal Component Analysis?
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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.
performance. In Section 4, we will show how our method is able to effectively remove such defects in face images. —Latent Semantic Indexing. Web search engines often need to analyze and index the content of an enormous corpus of documents. A popular scheme is the Latent Semantic Indexing (LSI) [Dewester et al. 1990; Papadimitriou et al. 2000 ...
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