Modified subspace BarzilaiBorwein gradient method for nonnegative matrix factorization
 Hongwei Liu,
 Xiangli Li
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Nonnegative matrix factorization (NMF) is a problem to obtain a representation of data using nonnegativity 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 BarzilaiBorwein 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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 Title
 Modified subspace BarzilaiBorwein gradient method for nonnegative matrix factorization
 Journal

Computational Optimization and Applications
Volume 55, Issue 1 , pp 173196
 Cover Date
 20130501
 DOI
 10.1007/s1058901295076
 Print ISSN
 09266003
 Online ISSN
 15732894
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Nonnegative matrix factorization
 Alternating least squares
 Active sets
 Nonmonotone technique
 Industry Sectors
 Authors

 Hongwei Liu ^{(1)}
 Xiangli Li ^{(1)} ^{(2)}
 Author Affiliations

 1. Department of Mathematics, Xidian University, Xi’an, 710071, P.R. China
 2. College of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, 541004, P.R. China