Nonnegative matrix factorization using ADMM: Algorithm and convergence analysis

Davood Hajinezhad, Tsung Hui Chang, Xiangfeng Wang, Qingjiang Shi, Mingyi Hong

Research output: Chapter in Book/Report/Conference proceedingConference contribution

25 Scopus citations

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.

Original languageEnglish (US)
Title of host publication2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4742-4746
Number of pages5
ISBN (Electronic)9781479999880
DOIs
StatePublished - May 18 2016
Event41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Shanghai, China
Duration: Mar 20 2016Mar 25 2016

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2016-May
ISSN (Print)1520-6149

Other

Other41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016
CountryChina
CityShanghai
Period3/20/163/25/16

Keywords

  • ADMM
  • Convergence Analysis
  • Nonconvex Optimization
  • Nonnegative Matrix Factorization

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    Hajinezhad, D., Chang, T. H., Wang, X., Shi, Q., & Hong, M. (2016). Nonnegative matrix factorization using ADMM: Algorithm and convergence analysis. In 2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings (pp. 4742-4746). [7472577] (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 2016-May). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICASSP.2016.7472577