Novel Proximal Gradient Methods for Nonnegative Matrix Factorization with Sparsity Constraints

作     者：Teboulle, Marc Vaisbourd, Yakov 

作者机构：Tel Aviv Univ Sch Math Sci IL-69978 Ramat Aviv Israel 

出 版 物：《SIAM JOURNAL ON IMAGING SCIENCES》 (SIAM成像科学杂志)

年 卷 期：2020年第13卷第1期

页      面：381-421页

核心收录：

学科分类：1002[医学-临床医学] 070207[理学-光学] 07[理学] 08[工学] 0835[工学-软件工程] 0803[工学-光学工程] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 0702[理学-物理学] 

基　　金：Israel Science Foundation [1844-16] German-Israel Foundation [GIF-GI1253304.6-2014] 

主　　题：nonnegative matrix factorization sparsity constraints nonconvex nonsmooth composite minimization proximal gradient algorithms non-Euclidean Bregman distance Kurdyka-Losiajewicz property essentially cyclic block proximal gradient global convergence 

摘      要：We consider the nonnegative matrix factorization (NMF) problem with sparsity constraints formulated as a nonconvex composite minimization problem. We introduce four novel proximal gradient based algorithms proven globally convergent to a critical point and which are applicable to sparsity constrained NMF models. Our approach builds on recent results allowing one to lift the classical global Lipschitz continuity requirement through the use of a non-Euclidean Bregman based distance. Since under the proposed framework we are not restricted by the gradient Lipschitz continuity assumption, we can consider new decomposition settings of the NMF problem. Two of the derived schemes are genuine non-Euclidean proximal methods that tackle nonstandard decompositions of the NMF problem. The two other schemes are novel extensions of the well-known state-of-the-art methods (the multiplicative and hierarchical alternating least squares), thus allowing one to significantly broaden the scope of these algorithms. Numerical experiments illustrate the performance of the proposed methods.