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Computational Intelligence and Neuroscience
Volume 2008, Article ID 168769, 10 pages
Research Article

Pattern Expression Nonnegative Matrix Factorization: Algorithm and Applications to Blind Source Separation

1School of Computer Science and Engineering, Xidian University, Xi'an 710071, China
2Department of Mathematics and Computer Science, Valdosta State University, Valdosta, GA 31698, USA
3The Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, VA 24061, USA

Received 1 November 2007; Accepted 18 April 2008

Academic Editor: Rafal Zdunek

Copyright © 2008 Junying Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Independent component analysis (ICA) is a widely applicable and effective approach in blind source separation (BSS), with limitations that sources are statistically independent. However, more common situation is blind source separation for nonnegative linear model (NNLM) where the observations are nonnegative linear combinations of nonnegative sources, and the sources may be statistically dependent. We propose a pattern expression nonnegative matrix factorization (PE-NMF) approach from the view point of using basis vectors most effectively to express patterns. Two regularization or penalty terms are introduced to be added to the original loss function of a standard nonnegative matrix factorization (NMF) for effective expression of patterns with basis vectors in the PE-NMF. Learning algorithm is presented, and the convergence of the algorithm is proved theoretically. Three illustrative examples on blind source separation including heterogeneity correction for gene microarray data indicate that the sources can be successfully recovered with the proposed PE-NMF when the two parameters can be suitably chosen from prior knowledge of the problem.