An alternating projected gradient algorithm for nonnegative matrix factorization

作     者：Lin, Lu Liu, Zhong-Yun 

作者机构：Xiamen Univ Sch Math Sci Xiamen 361005 Peoples R China Changsha Univ Sci & Technol Sch Math Changsha 410076 Hunan Peoples R China 

出 版 物：《APPLIED MATHEMATICS AND COMPUTATION》 (应用数学和计算)

年 卷 期：2011年第217卷第24期

页      面：9997-10002页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：National Natural Science Foundation of China Scientific Research Foundation for the Returned Overseas Chinese Scholars State Education Ministry of China [890 ] Major Foundation of Educational Committee of Hunan Province [09A002 ] 

主　　题：Nonnegative matrix factorization Projected gradient algorithm Multiplicative updating method Low-rank decomposition 

摘      要：Due to the extensive applications of nonnegative matrix factorizations (NMFs) of nonnegative matrices, such as in image processing, text mining, spectral data analysis, speech processing, etc., algorithms for NMF have been studied for years. In this paper, we propose a new algorithm for NMF, which is based on an alternating projected gradient (APG) approach. In particular, no zero entries appear in denominators in our algorithm which implies no breakdown occurs, and even if some zero entries appear in numerators new updates can always be improved in our algorithm. It is shown that the effect of our algorithm is better than that of Lee and Seung s algorithm when we do numerical experiments on two known facial databases and one iris database. (C) 2011 Elsevier Inc. All rights reserved.