Matrix completion and low-rank SVD via fast alternating least squares

Trevor Hastie, Rahul Mazumder, Jason D. Lee, Reza Zadeh

Research output: Contribution to journalArticlepeer-review

123 Scopus citations

Abstract

The matrix-completion problem has attracted a lot of attention, largely as a result of the celebrated Netix competition. Two popular approaches for solving the problem are nuclear-norm-regularized matrix approximation (Candès and Tao, 2009; Mazumder et al., 2010), and maximum-margin matrix factorization (Srebro et al., 2005). These two procedures are in some cases solving equivalent problems, but with quite different algorithms. In this article we bring the two approaches together, leading to an efficient algorithm for large matrix factorization and completion that outperforms both of these. We develop a software package softImpute in R for implementing our approaches, and a distributed version for very large matrices using the Spark cluster programming environment.

Original languageEnglish (US)
Pages (from-to)3367-3402
Number of pages36
JournalJournal of Machine Learning Research
Volume16
StatePublished - Dec 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

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

Keywords

  • Alternating least squares
  • Matrix completion
  • Nuclear norm
  • SVD

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