| Title: | Toward Faster Nonnegative Matrix Factorization: A New Algorithm and Comparisons |
| Author: | Kim, Jingu ; Park, Haesun |
| 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. |
| Type: | Technical Report |
| URI: | http://hdl.handle.net/1853/25538 |
| Date: | 2008 |
| Contributor: |
Georgia Institute of Technology. College of Computing
Georgia Institute of Technology. Division of Computational Science and Engineering |
| Relation: | CSE Technical Reports ; GT-CSE-08-03 |
| Publisher: | Georgia Institute of Technology |
| Subject: |
Active set method
Alternating nonnegative least squares Block principal pivoting method Nonnegative matrix factorization |
| Files | Size | Format | View |
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| GT-CSE-08-03.pdf | 139.3Kb |
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