| Stability analysis of multiplicative update algorithms and application to nonnegative matrix factorization. | |
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MedLine Citation:
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PMID: 20923731 Owner: NLM Status: In-Process |
Abstract/OtherAbstract:
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Multiplicative update algorithms have proved to be a great success in solving optimization problems with nonnegativity constraints, such as the famous nonnegative 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 exponential or asymptotic stability of the solutions to general optimization problems with nonnegative constraints, including the particular case of supervised NMF, and finally study the more difficult case of unsupervised NMF. The theoretical results presented in this paper are confirmed by numerical simulations involving both supervised and unsupervised NMF, and the convergence speed of NMF multiplicative updates is investigated. |
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Authors:
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Roland Badeau; Nancy Bertin; Emmanuel Vincent |
Publication Detail:
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Type: Journal Article; Research Support, Non-U.S. Gov't Date: 2010-10-04 |
Journal Detail:
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Title: IEEE transactions on neural networks / a publication of the IEEE Neural Networks Council Volume: 21 ISSN: 1941-0093 ISO Abbreviation: IEEE Trans Neural Netw Publication Date: 2010 Dec |
Date Detail:
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Created Date: 2010-12-07 Completed Date: - Revised Date: - |
Medline Journal Info:
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Nlm Unique ID: 101211035 Medline TA: IEEE Trans Neural Netw Country: United States |
Other Details:
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Languages: eng Pagination: 1869-81 Citation Subset: IM |
Affiliation:
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Institut Télécom, Télécom ParisTech, CNRS LTCI, Paris, France. roland.badeau@telecom-paristech.fr |
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From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine
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