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 language | English (US) |
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Title of host publication | 2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings |
Publisher | Institute of Electrical and Electronics Engineers Inc. |
Pages | 4742-4746 |
Number of pages | 5 |
ISBN (Electronic) | 9781479999880 |
DOIs | |
State | Published - May 18 2016 |
Event | 41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Shanghai, China Duration: Mar 20 2016 → Mar 25 2016 |
Publication series
Name | ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings |
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Volume | 2016-May |
ISSN (Print) | 1520-6149 |
Other
Other | 41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 |
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Country/Territory | China |
City | Shanghai |
Period | 3/20/16 → 3/25/16 |
Bibliographical note
Publisher Copyright:© 2016 IEEE.
Keywords
- ADMM
- Convergence Analysis
- Nonconvex Optimization
- Nonnegative Matrix Factorization