Nonnegative matrix factorization using ADMM: Algorithm and convergence analysis
Davood Hajinezhad, Tsung-Hui Chang, Xiangfeng Wang, Qingjiang Shi, Mingyi Hong
Abstract
The nonnegative matrix factorization (NMF) has been a popular model for a wide range of signal processing and machine learning problems. It is usually formulated as a nonconvex cost minimization problem. This work settles the convergence issue of a popular algorithm based on the alternating direction method of multipliers proposed in Boyd et al 2011. We show that the algorithm converges globally to the set of KKT solutions whenever certain penalty parameter ρ satisfies ρ > 1. We further extend the algorithm and its analysis to the problem where the observation matrix contains missing values. Numerical experiments on real and synthetic data sets demonstrate the effectiveness of the algorithms under investigation.
BibTeX
@inproceedings{icassp2016_nonnegativematri,
title = {Nonnegative matrix factorization using ADMM: Algorithm and convergence analysis},
author = {Davood Hajinezhad and Tsung-Hui Chang and Xiangfeng Wang and Qingjiang Shi and Mingyi Hong},
booktitle = {ICASSP 2016},
year = {2016}
}