DMCA
Robust PCA via outlier pursuit (2010)
| Citations: | 90 - 9 self |
BibTeX
@TECHREPORT{Xu10robustpca,
author = {Huan Xu and Constantine Caramanis and Sujay Sanghavi},
title = {Robust PCA via outlier pursuit},
institution = {},
year = {2010}
}
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Abstract
Singular Value Decomposition (and Principal Component Analysis) is one of the most widely used techniques for dimensionality reduction: successful and efficiently computable, it is nevertheless plagued by a well-known, well-documented sensitivity to outliers. Recent work has considered the setting where each point has a few arbitrarily corrupted components. Yet, in applications of SVD or PCA such as robust collaborative filtering or bioinformatics, malicious agents, defective genes, or simply corrupted or contaminated experiments may effectively yield entire points that are completely corrupted. We present an efficient convex optimization-based algorithm we call Outlier Pursuit, that under some mild assumptions on the uncorrupted points (satisfied, e.g., by the standard generative assumption in PCA problems) recovers the exact optimal low-dimensional subspace, and identifies the corrupted points. Such identification of corrupted points that do not conform to the low-dimensional approximation, is of paramount interest in bioinformatics and financial applications, and beyond. Our techniques involve matrix decomposition using nuclear norm minimization, however, our results, setup, and approach, necessarily differ considerably from the existing line of work in matrix completion and matrix decomposition, since we develop an approach to recover the correct column space of the uncorrupted matrix, rather than the exact matrix itself. 1
Keyphrases
robust pca matrix decomposition corrupted point singular value decomposition defective gene low-dimensional approximation nuclear norm minimization uncorrupted matrix principal component analysis dimensionality reduction recent work financial application efficient convex optimization-based algorithm exact optimal low-dimensional subspace pca problem exact matrix matrix completion outlier pursuit correct column space well-documented sensitivity malicious agent entire point paramount interest standard generative assumption robust collaborative filtering mild assumption uncorrupted point
