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Modified subspace Barzilai-Borwein gradient method for non-negative matrix factorization

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  • Hongwei Liu
  • Xiangli Li

Abstract

Non-negative matrix factorization (NMF) is a problem to obtain a representation of data using non-negativity constraints. Since the NMF was first proposed by Lee, NMF has attracted much attention for over a decade and has been successfully applied to numerous data analysis problems. Recent years, many variants of NMF have been proposed. Common methods are: iterative multiplicative update algorithms, gradient descent methods, alternating least squares (ANLS). Since alternating least squares has nice optimization properties, various optimization methods can be used to solve ANLS’s subproblems. In this paper, we propose a modified subspace Barzilai-Borwein for subproblems of ANLS. Moreover, we propose a modified strategy for ANLS. Global convergence results of our algorithm are established. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Hongwei Liu & Xiangli Li, 2013. "Modified subspace Barzilai-Borwein gradient method for non-negative matrix factorization," Computational Optimization and Applications, Springer, vol. 55(1), pages 173-196, May.
    • Handle: RePEc:spr:coopap:v:55:y:2013:i:1:p:173-196
    DOI: 10.1007/s10589-012-9507-6
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    References listed on IDEAS

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    1. Daniel D. Lee & H. Sebastian Seung, 1999. "Learning the parts of objects by non-negative matrix factorization," Nature, Nature, vol. 401(6755), pages 788-791, October.
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    Cited by:

    1. Zexian Liu & Hongwei Liu, 2019. "An Efficient Gradient Method with Approximately Optimal Stepsize Based on Tensor Model for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 608-633, May.

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