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Conference Paper

Generalized Nonnegative Matrix Approximations with Bregman Divergences


Sra,  S
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Dhillon, I., & Sra, S. (2006). Generalized Nonnegative Matrix Approximations with Bregman Divergences. Advances in Neural Information Processing Systems 18: Proceedings of the 2005 Conference, 283-290.

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Nonnegative matrix approximation (NNMA) is a recent technique for dimensionality reduction and data analysis that yields a parts based, sparse nonnegative representation for nonnegative input data. NNMA has found a wide variety of applications, including text analysis, document clustering, face/image recognition, language modeling, speech processing and many others. Despite these numerous applications, the algorithmic development for computing the NNMA factors has been relatively efficient. This paper makes algorithmic progress by modeling and solving (using multiplicative updates) new generalized NNMA problems that minimize Bregman divergences between the input matrix and its lowrank approximation. The multiplicative update formulae in the pioneering work by Lee and Seung [11] arise as a special case of our algorithms. In addition, the paper shows how to use penalty functions for incorporating constraints other than nonnegativity into the problem. Further, some interesting extensions to the use of "link" functions for modeling nonlinear relationships are also discussed.