2011 FastNonnegativeMatrixFactorizat

• (Kim & Park, 2011) ⇒ Jingu Kim, and Haesun Park. (2011). “Fast Nonnegative Matrix Factorization: An Active-Set-Like Method and Comparisons.” In: SIAM Journal on Scientific Computing, 33(6). doi:10.1137/110821172

Subject Headings: Alternating Least-Squares.

Cited By

• http://scholar.google.com/scholar?q=%222011%22+Fast+Nonnegative+Matrix+Factorization%3A+An+Active-Set-Like+Method+and+Comparisons
• http://dl.acm.org/citation.cfm?id=2340499.2340508&preflayout=flat#citedby

Quotes

Abstract

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.

References

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	Author	volume	Date Value	title	type	journal	titleUrl	doi	note	year
2011 FastNonnegativeMatrixFactorizat	Haesun Park Jingu Kim			Fast Nonnegative Matrix Factorization: An Active-Set-Like Method and Comparisons				10.1137/110821172		2011