Title:
Toward Faster Nonnegative Matrix Factorization: A New Algorithm and Comparisons
Toward Faster Nonnegative Matrix Factorization: A New Algorithm and Comparisons
Author(s)
Kim, Jingu
Park, Haesun
Park, Haesun
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Abstract
Nonnegative Matrix Factorization (NMF) is a dimension reduction method that has been widely used for
various tasks including text mining, pattern analysis, clustering, and cancer class discovery. The mathematical
formulation for NMF appears as a non-convex 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
some limitations of active set methods. We introduce ideas to efficiently extend the block principal pivoting
method within the context of NMF computation. Our algorithm inherits the convergence theory of the ANLS
framework and can easily be extended to other constrained NMF formulations. Comparisons of algorithms using
datasets that are from real life applications as well as those artificially generated show that the proposed new
algorithm outperforms existing ones in computational speed.
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Date Issued
2008
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Text
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Technical Report