Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 33, Issue 6, Pages 3261-3281Publisher
SIAM PUBLICATIONS
DOI: 10.1137/110821172
Keywords
nonnegative matrix factorization; nonnegativity-constrained least squares; block principal pivoting method; active set method; lower rank approximation; dimension reduction
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Funding
- National Science Foundation [CCF-0732318, CCF-0808863]
- Samsung Foundation of Culture
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Nonnegative matrix factorization (NMF) is a dimension reduction method that has been widely used for numerous applications, including text mining, computer vision, pattern discovery, and bioinformatics. A mathematical formulation for NMF appears as a nonconvex optimization problem, and various types of algorithms have been devised to solve the problem. The alternating nonnegative least squares (ANLS) framework is a block coordinate descent approach for solving NMF, which was recently shown to be theoretically sound and empirically efficient. In this paper, we present a novel algorithm for NMF based on the ANLS framework. Our new algorithm builds upon the block principal pivoting method for the nonnegativity-constrained least squares problem that overcomes a limitation of the active set method. We introduce ideas that efficiently extend the block principal pivoting method within the context of NMF computation. Our algorithm inherits the convergence property of the ANLS framework and can easily be extended to other constrained NMF formulations. Extensive computational comparisons using data sets that are from real life applications as well as those artificially generated show that the proposed algorithm provides state-of-the-art performance in terms of computational speed.
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