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Title: A nonmonotone alternating updating method for a class of matrix factorization problems
Authors: Yang, L 
Pong, TK 
Chen, X 
Issue Date: 2018
Source: SIAM journal on optimization, 2018, v. 28, no. 4, p. 3402-3430
Abstract: In this paper we consider a general matrix factorization model which covers a large class of existing models with many applications in areas such as machine learning and imaging sciences. To solve this possibly nonconvex, nonsmooth, and non-Lipschitz problem, we develop a nonmonotone alternating updating method based on a potential function. Our method essentially updates two blocks of variables in turn by inexactly minimizing this potential function, and updates another auxiliary block of variables using an explicit formula. The special structure of our potential function allows us to take advantage of efficient computational strategies for nonnegative matrix factorization to perform the alternating minimization over the two blocks of variables. A suitable line search criterion is also incorporated to improve the numerical performance. Under some mild conditions, we show that the line search criterion is well defined, and establish that the sequence generated is bounded and any cluster point of the sequence is a stationary point. Finally, we conduct some numerical experiments using real datasets to compare our method with some existing efficient methods for nonnegative matrix factorization and matrix completion. The numerical results show that our method can outperform these methods for these specific applications.
Keywords: Matrix factorization
Nonmonotone line search
Stationary point
Alternating updating
Publisher: Society for Industrial and Applied Mathematics
Journal: SIAM journal on optimization 
ISSN: 1052-6234
EISSN: 1095-7189
DOI: 10.1137/17M1130113
Rights: © 2018 Society for Industrial and Applied Mathematics.
Posted with permission of the publisher.
The following publication Yang, L., Pong, T. K., & Chen, X. (2018). A nonmonotone alternating updating method for a class of matrix factorization problems. SIAM Journal on Optimization, 28(4), 3402-3430 is available at https://doi.org/10.1137/17M1130113
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