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ICASSP
2011
IEEE

Stability analysis of multiplicative update algorithms for non-negative matrix factorization

10 years 10 months ago
Stability analysis of multiplicative update algorithms for non-negative matrix factorization
Multiplicative update algorithms have encountered a great success to solve optimization problems with non-negativity constraints, such as the famous non-negative matrix factorization (NMF) and its many variants. However, despite several years of research on the topic, the understanding of their convergence properties is still to be improved. In this paper, we show that Lyapunov’s stability theory provides a very enlightening viewpoint on the problem. We prove the stability of supervised NMF and study the more difficult case of unsupervised NMF. Numerical simulations illustrate those theoretical results, and the convergence speed of NMF multiplicative updates is analyzed.
Roland Badeau, Nancy Bertin, Emmanuel Vincent
Added 20 Aug 2011
Updated 20 Aug 2011
Type Journal
Year 2011
Where ICASSP
Authors Roland Badeau, Nancy Bertin, Emmanuel Vincent
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