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A Unified Convergence Analysis of the Multiplicative Update Algorithm for Regularized Nonnegative Matrix Factorization.
- Source :
- IEEE Transactions on Signal Processing; Jan2018, Vol. 66 Issue 1, p129-138, 10p
- Publication Year :
- 2018
-
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. [ABSTRACT FROM PUBLISHER]
- Subjects :
- SIGNAL processing
NONNEGATIVE matrices
ALGORITHMS
FACTORIZATION
MACHINE learning
Subjects
Details
- Language :
- English
- ISSN :
- 1053587X
- Volume :
- 66
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Signal Processing
- Publication Type :
- Academic Journal
- Accession number :
- 127950169
- Full Text :
- https://doi.org/10.1109/TSP.2017.2757914