Block-Iterative Algorithms for Non-Negative Matrix Approximation

Sra, S

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Block-Iterative Algorithms for Non-Negative Matrix Approximation

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Sra, S
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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MPIK-TR-176.pdf
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Citation

Sra, S.(2008). Block-Iterative Algorithms for Non-Negative Matrix Approximation (176). Tübingen, Germany: Max Planck Institute for Biological Cybernetics.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-C761-F

Abstract

In this report we present new algorithms for non-negative matrix approximation (NMA),
commonly known as the NMF problem. Our methods improve upon the well-known methods of Lee
Seung [19] for both the Frobenius norm as well the Kullback-Leibler divergence versions of the problem.
For the latter problem, our results are especially interesting because it seems to have witnessed much
lesser algorithmic progress as compared to the Frobenius norm NMA problem. Our algorithms are
based on a particular block-iterative acceleration technique for EM, which preserves the multiplicative
nature of the updates and also ensures monotonicity. Furthermore, our algorithms also naturally apply
to the Bregman-divergence NMA algorithms of Dhillon and Sra [8]. Experimentally, we show that our
algorithms outperform the traditional Lee/Seung approach most of the time.