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

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 n...

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Bibliographic Details
Published in:Computational Intelligence and Neuroscience 2008, Vol.2008 (2008), p.3-12
Main Authors: Ma, Zhen, Wei, Le, Feng, Xuerong, Wang, Yue Joseph, Zhang, Junying
Format: Article
Language:English
Subjects:
Algorithms
Computer engineering
Computer science
Normal distribution
Random variables
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Summary: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.
ISSN:1687-5265
1687-5273
DOI:10.1155/2008/168769