Global convergence of modified multiplicative updates for nonnegative matrix factorization
type: Item
instance of: scholarly article
title: Global convergence of modified multiplicative updates for nonnegative matrix factorization
zbMATH Open document ID: 1305.65135
author: Norikazu Takahashi
author: Ryota Hibi
published in: Computational Optimization and Applications
publication date: 2014-10-10T00:00:00Z
review text: The paper focuses on slightly modified versions of the original multiplicative updates for nonnegative matrix factorization (NMF) proposed by \textit{D. D. Lee} and \textit{H. S. Seung} [``Algorithms for non-negative matrix factorization'', in: Advances in neural information processing systems 13, 556--562 (2001)]. One considers not only the Euclidian distance-based multiplicative update but also the I-divergence-based one. The first section is an introduction in the nature of the subject. The second section introduces briefly the NMF optimization problems and the multipicatie updates of Lee and Seung. In the third section, the modified multipicative updates based on the idea of \textit{N. Gillis} and \textit{F. Glineur} [``Nonnegative factorization and the maximum edge biclique problem'', Preprint, \url{arXiv:0810.4225}] are first introduced and then convergence theorems for updates are presented. Also, one proposed algorithms based on the modified multiplicative updates, proving that they always stop within a finite number of iterations. In the fourth section, the global convergence theorems in the previous section are proved using \textit{W. I. Zangwill}'s global convergence theorem [Nonlinear programming: A unified approach. Cliffs, NJ: Prentice-Hall Inc (1969; Zbl 0195.20804)], which is a fundamental result in optimization theory. The main conclusions are within the fifth section.
reviewed by: Romulus Militaru
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 6353820
zbMATH Keywords: nonnegative matrix factorization
zbMATH Keywords: multiplicative updates
zbMATH Keywords: global convergence
zbMATH Keywords: finite termination
MaRDI profile type: Publication
full work available at URL: s10589-013-9593-0
OpenAlex ID: W1994292689
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DOI: 10.1007/S10589-013-9593-0
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description: scientific article; zbMATH DE number 6353820