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http://hdl.handle.net/10397/89217
| 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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