Matrix completion from a few entries

Raghunandan H. Keshavan, Sewoong Oh, Andrea Montanari

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Let M be an nα × n matrix of rank r « n, and assume that a uniformly random subset E of its entries is observed. We describe an efficient algorithm that reconstructs M from |E| = O(rn) observed entries with relative root mean square error RMSE ≤ C(α) (nr/|E|)1/2. Further, if r = O(1) and M is sufficiently unstructured, then it can be reconstructed exactly from |E| = O(n log n) entries. This settles (in the case of bounded rank) a question left open by Candès and Recht and improves over the guarantees for their reconstruction algorithm. The complexity of our algorithm is O(|E|r log n), which opens the way to its use for massive data sets. In the process of proving these statements, we obtain a generalization of a celebrated result by Friedman-Kahn-Szemerédi and Feige-Ofek on the spectrum of sparse random matrices.

Original languageEnglish (US)
Title of host publication2009 IEEE International Symposium on Information Theory, ISIT 2009
Pages324-328
Number of pages5
DOIs
StatePublished - Nov 19 2009
Event2009 IEEE International Symposium on Information Theory, ISIT 2009 - Seoul, Korea, Republic of
Duration: Jun 28 2009Jul 3 2009

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8102

Other

Other2009 IEEE International Symposium on Information Theory, ISIT 2009
CountryKorea, Republic of
CitySeoul
Period6/28/097/3/09

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

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  • Cite this

    Keshavan, R. H., Oh, S., & Montanari, A. (2009). Matrix completion from a few entries. In 2009 IEEE International Symposium on Information Theory, ISIT 2009 (pp. 324-328). [5205567] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2009.5205567