Journal article
A Unified Convergence Analysis of the Multiplicative Update Algorithm for Regularized Nonnegative Matrix Factorization
IEEE transactions on signal processing, Vol.66(1), pp.129-138
01/01/2018
DOI: 10.1109/TSP.2017.2757914
Abstract
The multiplicative update (MU) algorithm has been extensively used to estimate the basis and coefficient matrices in nonnegative matrix factorization (NMF) problems under a wide range of divergences and regularizers. However, theoretical convergence guarantees have only been derived for a few special divergences without regularization. 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 regularizers. Our main 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 nonconvex NMF optimization problem. Our proof strategy has the potential to open up new avenues for analyzing similar problems in machine learning and signal processing.
Details
- Title: Subtitle
- A Unified Convergence Analysis of the Multiplicative Update Algorithm for Regularized Nonnegative Matrix Factorization
- Creators
- Renbo Zhao - National University of SingaporeVincent Y. F. Tan - National University of Singapore
- Resource Type
- Journal article
- Publication Details
- IEEE transactions on signal processing, Vol.66(1), pp.129-138
- Publisher
- IEEE
- DOI
- 10.1109/TSP.2017.2757914
- ISSN
- 1053-587X
- eISSN
- 1941-0476
- Grant note
- R-263-000-B37-133 / National University of Singapore Young Investigator
- Language
- English
- Date published
- 01/01/2018
- Academic Unit
- Business Analytics
- Record Identifier
- 9984446529002771
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