Orthogonal rank-one matrix pursuit for low rank matrix completion

Zheng Wang, Ming Jun Lai, Zhaosong Lu, Wei Fan, Hasan Davulcu, Jieping Ye

Research output: Contribution to journalArticlepeer-review

74 Scopus citations


In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend the orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our algorithm by introducing a novel weight updating rule to reduce the time and storage complexity. Both versions are computationally inexpensive for each matrix pursuit iteration and find satisfactory results in a few iterations. Another advantage of our proposed algorithm is that it has only one tunable parameter, which is the rank. It is easy to understand and to use by the user. This becomes especially important in large-scale learning problems. In addition, we rigorously show that both versions achieve a linear convergence rate, which is significantly better than the previous known results. We also empirically compare the proposed algorithms with several state-of-the-art matrix completion algorithms on many real-world datasets, including the large-scale recommendation dataset Netflix as well as the MovieLens datasets. Numerical results show that our proposed algorithm is more efficient than competing algorithms while achieving similar or better prediction performance.

Original languageEnglish (US)
Pages (from-to)A488-A514
JournalSIAM Journal on Scientific Computing
Issue number1
StatePublished - 2015
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2015 Society for Industrial and Applied Mathematics.


  • Low rank
  • Matching pursuit
  • Matrix completion
  • Rank minimization
  • Singular value decomposition


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