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Generalized Nonnegative Matrix Approximations with Bregman Divergences

2006

Conference Paper

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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.

Author(s): Dhillon, I. and Sra, S.
Book Title: Advances in neural information processing systems 18
Journal: Advances in Neural Information Processing Systems 18: Proceedings of the 2005 Conference
Pages: 283-290
Year: 2006
Month: May
Day: 0
Editors: Weiss, Y. , B. Sch{\"o}lkopf, J. Platt
Publisher: MIT Press

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

Event Name: Nineteenth Annual Conference on Neural Information Processing Systems (NIPS 2005)
Event Place: Vancouver, BC, Canada

Address: Cambridge, MA, USA
Digital: 0
ISBN: 0-262-23253-7
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

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BibTex

@inproceedings{5223,
  title = {Generalized Nonnegative Matrix Approximations with Bregman Divergences},
  author = {Dhillon, I. and Sra, S.},
  journal = {Advances in Neural Information Processing Systems 18: Proceedings of the 2005 Conference},
  booktitle = {Advances in neural information processing systems 18},
  pages = {283-290},
  editors = {Weiss, Y. , B. Sch{\"o}lkopf, J. Platt},
  publisher = {MIT Press},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {Cambridge, MA, USA},
  month = may,
  year = {2006},
  month_numeric = {5}
}