Robust matrix decomposition with sparse corruptions

Daniel Hsu, Sham M. Kakade, Tong Zhang

Research output: Contribution to journalArticlepeer-review


Suppose a given observation matrix can be decomposed as the sum of a low-rank matrix and a sparse matrix, 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 ℓ1 norm and trace norm minimization. We are specifically interested in the question of how many sparse corruptions are allowed so that convex programming can still achieve accurate recovery, and we obtain stronger recovery guarantees than previous studies. Moreover, we do not assume that the spatial pattern of corruptions is random, which stands in contrast to related analyses under such assumptions via matrix completion.

Original languageEnglish (US)
Article number5934412
Pages (from-to)7221-7234
Number of pages14
JournalIEEE Transactions on Information Theory
Issue number11
StatePublished - Nov 2011
Externally publishedYes


  • Low-rank
  • matrix decompositions
  • outliers
  • sparsity

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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