2012 FastBregmanDivergenceNMFUsingTa

• (Li et al., 2012) ⇒ Liangda Li, Guy Lebanon, and Haesun Park. (2012). “Fast Bregman Divergence NMF Using Taylor Expansion and Coordinate Descent.” In: Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD-2012). ISBN:978-1-4503-1462-6 doi:10.1145/2339530.2339582

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Cited By

• http://scholar.google.com/scholar?q=%222012%22+Fast+Bregman+Divergence+NMF+Using+Taylor+Expansion+and+Coordinate+Descent
• http://dl.acm.org/citation.cfm?id=2339530.2339582&preflayout=flat#citedby

Quotes

Author Keywords

• Bregman divergences; euclidean distance; learning; non-negative matrix factorization; optimization; taylor series expansion

Abstract

Non-negative matrix factorization (NMF) provides a lower rank approximation of a matrix. Due to nonnegativity imposed on the factors, it gives a latent structure that is often more physically meaningful than other lower rank approximations such as singular value decomposition (SVD). Most of the algorithms proposed in literature for NMF have been based on minimizing the Frobenius norm. This is partly due to the fact that the minimization problem based on the Frobenius norm provides much more flexibility in algebraic manipulation than other divergences. In this paper we propose a fast NMF algorithm that is applicable to general Bregman divergences. Through Taylor series expansion of the Bregman divergences, we reveal a relationship between Bregman divergences and Euclidean distance. This key relationship provides a new direction for NMF algorithms with general Bregman divergences when combined with the scalar block coordinate descent method. The proposed algorithm generalizes several recently proposed methods for computation of NMF with Bregman divergences and is computationally faster than existing alternatives. We demonstrate the effectiveness of our approach with experiments conducted on artificial as well as real world data.

References

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	Author	volume	Date Value	title	type	journal	titleUrl	doi	note	year
2012 FastBregmanDivergenceNMFUsingTa	Liangda Li Guy Lebanon Haesun Park			Fast Bregman Divergence NMF Using Taylor Expansion and Coordinate Descent				10.1145/2339530.2339582		2012