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Block Iterative Algorithms for Non-negative Matrix Approximation

2008

Conference Paper

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In this paper we present new algorithms for non-negative matrix approximation (NMA), commonly known as the NMF problem. Our methods improve upon the well-known methods of Lee & Seung~cite{lee00} for both the Frobenius norm as well the Kullback-Leibler divergence versions of the problem. For the latter problem, our results are especially interesting because it seems to have witnessed much lesser algorithmic progress as compared to the Frobenius norm NMA problem. Our algorithms are based on a particular textbf {block-iterative} acceleration technique for EM, which preserves the multiplicative nature of the updates and also ensures monotonicity. Furthermore, our algorithms also naturally apply to the Bregman-divergence NMA algorithms of~cite{suv.nips}. Experimentally, we show that our algorithms outperform the traditional Lee/Seung approach most of the time.

Author(s): Sra, S.
Book Title: ICDM 2008
Journal: Proceedings of the Eighth IEEE International Conference on Data Mining (ICDM 2008)
Pages: 1037-1042
Year: 2008
Month: December
Day: 0
Editors: Giannotti, F. , D. Gunopulos, F. Turini, C. Zaniolo, N. Ramakrishnan, X. Wu
Publisher: IEEE Service Center

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

DOI: 10.1109/ICDM.2008.77
Event Name: Eighth IEEE International Conference on Data Mining
Event Place: Pisa, Italy

Address: Piscataway, NJ, USA
Digital: 0
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: Web

BibTex

@inproceedings{5504,
  title = {Block Iterative Algorithms for Non-negative Matrix Approximation},
  author = {Sra, S.},
  journal = {Proceedings of the Eighth IEEE International Conference on Data Mining (ICDM 2008)},
  booktitle = {ICDM 2008},
  pages = {1037-1042},
  editors = {Giannotti, F. , D. Gunopulos, F. Turini, C. Zaniolo, N. Ramakrishnan, X. Wu},
  publisher = {IEEE Service Center},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {Piscataway, NJ, USA},
  month = dec,
  year = {2008},
  month_numeric = {12}
}