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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Xidian University, Xi’an, 710071, P.R. China

    Hongwei Liu & Xiangli Li

  2. College of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, 541004, P.R. China

    Xiangli Li

Authors
  1. Hongwei Liu
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  2. Xiangli Li
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Correspondence to Xiangli Li.

Additional information

The project was supported by National Natural Science Foundation of China (Grant No. 61072144, 61179040).

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Liu, H., Li, X. Modified subspace Barzilai-Borwein gradient method for non-negative matrix factorization. Comput Optim Appl 55, 173–196 (2013). https://doi.org/10.1007/s10589-012-9507-6

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  • DOI: https://doi.org/10.1007/s10589-012-9507-6

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