A multilevel approach for nonnegative matrix factorization

Nicolas Gillis () and François Glineur
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Nicolas Gillis: Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium

No 2010047, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: Nonnegative Matrix Factorization (NMF) is the problem of approximating a nonnegative matrix with the product of two low-rank nonnegative matrices and has been shown to be particularly useful in many applications, e.g., in text mining, image processing, computational biology, etc. In this paper, we explain how algorithms for NMF can be embedded into the framework of multi- level methods in order to accelerate their convergence. This technique can be applied in situations where data admit a good approximate representation in a lower dimensional space through linear transformations preserving nonnegativity. A simple multilevel strategy is described and is experi- mentally shown to speed up significantly three popular NMF algorithms (alternating nonnegative least squares, multiplicative updates and hierarchical alternating least squares) on several standard image datasets.

Keywords: nonnegative matrix factorization; algorithms; multigrid and multilevel methods; image processing (search for similar items in EconPapers)
Date: 2010-07-01
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (2)

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Working Paper: A multilevel approach for nonnegative matrix factorization (2011)
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Persistent link: https://EconPapers.repec.org/RePEc:cor:louvco:2010047

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