Fast Nonnegative Matrix Factorization Algorithms Using Projected Gradient Approaches for Large-Scale Problems

Fast Nonnegative Matrix Factorization Algorithms Using Projected Gradient Approaches for Large-Scale Problems

Recently, a considerable growth of interest in projected gradient (PG) methods has been observed due to their high efficiency in solving large-scale convex minimization problems subject to linear constraints. Since the minimization problems underlying nonnegative matrix factorization (NMF) of large...

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Main Authors: Rafal Zdunek, Andrzej Cichocki
Format: Article
Language:English
Published: Hindawi Limited 2008-01-01
Series:Computational Intelligence and Neuroscience
Online Access:http://dx.doi.org/10.1155/2008/939567
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spelling doaj-0fe0e985fa304fddbbd72e195291616f2020-11-24T22:33:33ZengHindawi LimitedComputational Intelligence and Neuroscience1687-52651687-52732008-01-01200810.1155/2008/939567939567Fast Nonnegative Matrix Factorization Algorithms Using Projected Gradient Approaches for Large-Scale ProblemsRafal Zdunek0Andrzej Cichocki1Instiute of Telecommunications, Teleinformatics and Acoustics, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, PolandLaboratory for Advanced Brain Signal Processing, Brain Science Institute RIKEN, Wako-shi, Saitama 351-0198, JapanRecently, a considerable growth of interest in projected gradient (PG) methods has been observed due to their high efficiency in solving large-scale convex minimization problems subject to linear constraints. Since the minimization problems underlying nonnegative matrix factorization (NMF) of large matrices well matches this class of minimization problems, we investigate and test some recent PG methods in the context of their applicability to NMF. In particular, the paper focuses on the following modified methods: projected Landweber, Barzilai-Borwein gradient projection, projected sequential subspace optimization (PSESOP), interior-point Newton (IPN), and sequential coordinate-wise. The proposed and implemented NMF PG algorithms are compared with respect to their performance in terms of signal-to-interference ratio (SIR) and elapsed time, using a simple benchmark of mixed partially dependent nonnegative signals.http://dx.doi.org/10.1155/2008/939567
collection DOAJ
language English
format Article
sources DOAJ
author Rafal Zdunek
Andrzej Cichocki
spellingShingle Rafal Zdunek
Andrzej Cichocki
Fast Nonnegative Matrix Factorization Algorithms Using Projected Gradient Approaches for Large-Scale Problems
Computational Intelligence and Neuroscience
author_facet Rafal Zdunek
Andrzej Cichocki
author_sort Rafal Zdunek
title Fast Nonnegative Matrix Factorization Algorithms Using Projected Gradient Approaches for Large-Scale Problems
title_short Fast Nonnegative Matrix Factorization Algorithms Using Projected Gradient Approaches for Large-Scale Problems
title_full Fast Nonnegative Matrix Factorization Algorithms Using Projected Gradient Approaches for Large-Scale Problems
title_fullStr Fast Nonnegative Matrix Factorization Algorithms Using Projected Gradient Approaches for Large-Scale Problems
title_full_unstemmed Fast Nonnegative Matrix Factorization Algorithms Using Projected Gradient Approaches for Large-Scale Problems
title_sort fast nonnegative matrix factorization algorithms using projected gradient approaches for large-scale problems
publisher Hindawi Limited
series Computational Intelligence and Neuroscience
issn 1687-5265
1687-5273
publishDate 2008-01-01
description Recently, a considerable growth of interest in projected gradient (PG) methods has been observed due to their high efficiency in solving large-scale convex minimization problems subject to linear constraints. Since the minimization problems underlying nonnegative matrix factorization (NMF) of large matrices well matches this class of minimization problems, we investigate and test some recent PG methods in the context of their applicability to NMF. In particular, the paper focuses on the following modified methods: projected Landweber, Barzilai-Borwein gradient projection, projected sequential subspace optimization (PSESOP), interior-point Newton (IPN), and sequential coordinate-wise. The proposed and implemented NMF PG algorithms are compared with respect to their performance in terms of signal-to-interference ratio (SIR) and elapsed time, using a simple benchmark of mixed partially dependent nonnegative signals.
url http://dx.doi.org/10.1155/2008/939567
work_keys_str_mv AT rafalzdunek fastnonnegativematrixfactorizationalgorithmsusingprojectedgradientapproachesforlargescaleproblems
AT andrzejcichocki fastnonnegativematrixfactorizationalgorithmsusingprojectedgradientapproachesforlargescaleproblems
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