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Factoring nonnegative matrices with linear programs (2012)
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BibTeX
@MISC{Bittorf12factoringnonnegative,
author = {Victor Bittorf and Benjamin Recht and Christopher Ré},
title = {Factoring nonnegative matrices with linear programs},
year = {2012}
}
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Abstract
This paper describes a new approach for computing nonnegative matrix factorizations (NMFs) with linear programming. The key idea is a data-driven model for the factorization, in which the most salient features in the data are used to express the remaining features. More precisely, given a data matrix X, the algorithm identifies a matrix C that satisfies X ≈ CX and some linear constraints. The matrix C selects features, which are then used to compute a low-rank NMF of X. A theoretical analysis demonstrates that this approach has the same type of guarantees as the recent NMF algorithm of Arora et al. (2012). In contrast with this earlier work, the proposed method (1) has better noise tolerance, (2) extends to more general noise models, and (3) leads to efficient, scalable algorithms. Experiments with synthetic and real datasets provide evidence that the new approach is also superior in practice. An optimized C++ implementation of the new algorithm can factor a multi-Gigabyte matrix in a matter of minutes.
Keyphrases
linear program nonnegative matrix new approach nonnegative matrix factorization recent nmf algorithm low-rank nmf salient feature linear programming multi-gigabyte matrix key idea linear constraint new algorithm data-driven model optimized implementation scalable algorithm real datasets data matrix theoretical analysis noise tolerance general noise model
