Low-rank and sparse structure pursuit via alternating minimization

Quanquan Gu, Zhaoran Wang, Han Liu

Research output: Contribution to conferencePaper

35 Scopus citations

Abstract

In this paper, we present a nonconvex alternating minimization optimization algorithm for low-rank and sparse structure pursuit. Compared with convex relaxation based methods, the proposed algorithm is computationally more efficient for large scale problems. In our study, we define a notion of bounded difference of gradients, based on which we rigorously prove that with suitable initialization, the proposed nonconvex optimization algorithm enjoys linear convergence to the global optima and exactly recovers the underlying low rank and sparse matrices under standard conditions such as incoherence and sparsity conditions. For a wide range of statistical models such as multi-task learning and robust principal component analysis (RPCA), our algorithm provides a principled approach to learning the low rank and sparse structures with provable guarantee. Thorough experiments on both synthetic and real datasets backup our theory.

Original languageEnglish (US)
Pages600-609
Number of pages10
StatePublished - Jan 1 2016
Event19th International Conference on Artificial Intelligence and Statistics, AISTATS 2016 - Cadiz, Spain
Duration: May 9 2016May 11 2016

Conference

Conference19th International Conference on Artificial Intelligence and Statistics, AISTATS 2016
CountrySpain
CityCadiz
Period5/9/165/11/16

ASJC Scopus subject areas

  • Artificial Intelligence
  • Statistics and Probability

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  • Cite this

    Gu, Q., Wang, Z., & Liu, H. (2016). Low-rank and sparse structure pursuit via alternating minimization. 600-609. Paper presented at 19th International Conference on Artificial Intelligence and Statistics, AISTATS 2016, Cadiz, Spain.