A UNIFIED CONVERGENCE ANALYSIS OF THE MULTIPLICATIVE UPDATE ALGORITHM FOR NONNEGATIVE MATRIX FACTORIZATION

被引：0
|
作者：
Zhao, Renbo [1 ]
Tan, Vincent Y. F.
机构：
[1] Natl Univ Singapore, Dept Elect & Comp Engn, Singapore, Singapore
来源：
2017 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP) | 2017年
关键词：
Nonnegative Matrix Factorization; Multiplicative Update Algorithm; Convergence Analysis; Nonconvex Optimization; Stationary Points; ALPHA-BETA; OPTIMIZATION; DIVERGENCES;
D O I：
暂无
中图分类号：
O42 [声学];
学科分类号：
070206 ; 082403 ;
摘要：
The multiplicative update (MU) algorithm has been used extensively to estimate the basis and coefficient matrices in nonnegative matrix factorization (NMF) problems under a wide range of divergences and regularizations. However, theoretical convergence guarantees have only been derived for a few special divergences. In this work, we provide a conceptually simple, self-contained, and unified proof for the convergence of the MU algorithm applied on NMF with a wide range of divergences and regularizations. Our result shows the sequence of iterates (i.e., pairs of basis and coefficient matrices) produced by the MU algorithm converges to the set of stationary points of the NMF (optimization) problem. Our proof strategy has the potential to open up new avenues for analyzing similar problems.
引用
收藏
页码：2562 / 2566
页数：5
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