• Corpus ID: 14523288

Robust Matrix Decomposition with Outliers

  title={Robust Matrix Decomposition with Outliers},
  author={Daniel J. Hsu and Sham M. Kakade and Tong Zhang},
Suppose a given observation matrix can be decomposed as the sum of a low-rank matrix and a sparse matrix (outliers), and the goal is to recover these individual components from the observed sum. Such additive decompositions have applications in a variety of numerical problems including system identification, latent variable graphical modeling, and principal components analysis. We study conditions under which recovering such a decomposition is possible via a combination of $\ell_1$ norm and… 
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It is proved that under some suitable assumptions, it is possible to recover both the low-rank and the sparse components exactly by solving a very convenient convex program called Principal Component Pursuit; among all feasible decompositions, this suggests the possibility of a principled approach to robust principal component analysis.
Stable Principal Component Pursuit
This result shows that the proposed convex program recovers the low-rank matrix even though a positive fraction of its entries are arbitrarily corrupted, with an error bound proportional to the noise level, the first result that shows the classical Principal Component Analysis, optimal for small i.i.d. noise, can be made robust to gross sparse errors.
Dense error correction for low-rank matrices via Principal Component Pursuit
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Exact matrix completion via convex optimization
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Recovering Low-Rank Matrices From Few Coefficients in Any Basis
  • D. Gross
  • Computer Science
    IEEE Transactions on Information Theory
  • 2011
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Handbook of geometry of Banach spaces
Basic concepts in the geometry of Banach spaces (W.B. Johnson, J. Lindenstrauss). Positive operators (Y.A. Abramovitch, C.D. Aliprantis). Lp spaces (D. Alspach, E. Odell). Convex geometry and