An alternating projected gradient algorithm for nonnegative matrix factorization

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• 作者：Lu Lin^a ; ^{llin@xmu.edu.cn"" rel=""nofollow} ; Zhong-Yun Liu^b ; ^{liuzhongyun@263.net"" rel=""nofollow}
• 关键词：Nonnegative matrix factorization ; Projected gradient algorithm ; Multiplicative updating method ; Low-rank decomposition
• 刊名：Applied Mathematics and Computation
• 出版年：2011
• 出版时间：15 August 2011
• 年：2011
• 卷：217
• 期：24
• 页码：9997-10002
• 全文大小：225 K

文摘

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.