Blind Source Separation with Pattern Expression NMF

Independent component analysis (ICA) is a widely applicable and effective approach in blind source separation (BSS) for basic ICA model, but with limitations that sources should be statistically independent, while more common situation is BSS for non-negative linear (NNL) model where observations are linear combinations of non-negative sources with non-negative coefficients and sources may be statistically dependent. By recognizing the fact that BSS for basic ICA model corresponds to matrix factorization problem, in this paper, a novel idea of BSS for NNL model is proposed that the BSS for NNL come'[ sponds to a non-negative matrix factorization problem and the non-negative matrix factorization (NMF) technique is utilized. For better expression of the patterns of the sources, the NMF is further extended to pattern expression NMF (PE-NMF) and its algorithm is presented. Finally, the experimental results are presented which show the effectiveness and efficiency of the PE-NMF to BSS for a variety of applications which follow NNL model.