Accelerated multiplicative updates and hierarchical als algorithms for nonnegative matrix factorization

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

No 2011030, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: Nonnegative matrix factorization (NMF) is a data analysis technique used in a great variety of applications such as text mining, image processing, hyperspectral data analysis, computational biology, and clustering. In this paper, we consider two well-known algorithms designed to solve NMF problems, namely the multiplicative updates of Lee and Seung and the hierarchical alternating least squares of Cichocki et al. We propose a simple way to significantly accelerate their convergence, based on a careful analysis of the computational cost needed at each iteration. This acceleration technique can also be applied to other algorithms, which we illustrate on the projected gradient method of Lin. The efficiency of the accelerated algorithms is empirically demonstrated on image and text datasets, and compares favorably with a state-of-the-art alternating nonnegative least squares algorithm. Finally, we provide a theoretical argument based on the properties of NMF and its solutions that explains in particular the very good performance of HALS and its accelerated version observed in our numerical experiments.

Date: 2011-07-01
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Citations: View citations in EconPapers (7)

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Related works:
Working Paper: Accelerated multiplicative updates and hierarchical ALS algorithms for nonnegative matrix factorization (2012)
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