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A UNIFIED CONVERGENCE ANALYSIS OF THE MULTIPLICATIVE UPDATE ALGORITHM FOR NONNEGATIVE MATRIX FACTORIZATION
Conference proceeding   Open access

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

Renbo Zhao and Vincent Y. F. Tan
2017 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP), pp.2562-2566
International Conference on Acoustics Speech and Signal Processing ICASSP
01/01/2017
DOI: 10.1109/ICASSP.2017.7952619
url
https://arxiv.org/pdf/1609.00951View
Open Access

Abstract

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.
Acoustics Engineering Technology Engineering, Electrical & Electronic Science & Technology

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