Efficient Nonnegative Matrix Factorization via projected Newton method

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• 作者：Pinghua Gong ; ^{gph08@mails.tsinghua.edu.cn} ; ^{pinghuag@gmail.com}  ; [Author Vitae] ; Changshui Zhang ^{zcs@mail.tsinghua.edu.cn}  ; [Author Vitae]
• 关键词：Nonnegative Matrix Factorization ; Projected Newton method ; Quadratic convergence rate ; Nonnegative least squares ; Low rank
• 刊名：Pattern Recognition
• 出版年：2012
• 期刊代码：100_00313203
• 类别：cp
• 出版时间：September, 2012
• 卷：45
• 期：9
• 页码：3557-3565
• 文件大小：570 K

摘要

Nonnegative Matrix Factorization (NMF) is a popular decomposition technique in pattern analysis, document clustering, image processing and related fields. In this paper, we propose a fast NMF algorithm via Projected Newton Method (PNM). First, we propose PNM to efficiently solve a nonnegative least squares problem, which achieves a quadratic convergence rate under appropriate assumptions. Second, in the framework of an alternating optimization method, we adopt PNM as an essential subroutine to efficiently solve the NMF problem. Moreover, by exploiting the low rank assumption of NMF, we make PNM very suitable for solving NMF efficiently. Empirical studies on both synthetic and real-world (text and image) data demonstrate that PNM is quite efficient to solve NMF compared with several state of the art algorithms.