Matrix completion from noisy entries

Raghunandan H. Keshavan, Andrea Montanari, Sewoong Oh

Research output: Contribution to journalArticlepeer-review


Given a matrix M of low-rank, we consider the problem of reconstructing it from noisy observations of a small, random subset of its entries. The problem arises in a variety of applications, from collaborative filtering (the 'Netflix problem') to structure-from-motion and positioning. We study a low complexity algorithm introduced by Keshavan, Montanari, and Oh (2010), based on a combination of spectral techniques and manifold optimization, that we call here OptSpace. We prove performance guarantees that are order-optimal in a number of circumstances.

Original languageEnglish (US)
Pages (from-to)2057-2078
Number of pages22
JournalJournal of Machine Learning Research
StatePublished - Jul 2010
Externally publishedYes


  • Low-rank matrices
  • Manifold optimization
  • Matrix completion
  • Spectral methods

ASJC Scopus subject areas

  • Software
  • Artificial Intelligence
  • Control and Systems Engineering
  • Statistics and Probability


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