Non-negative matrix factorization algorithms for blind source sepertion in speech recognition

The performance of the Speech recognition degrades in the presence of the multiple sources/speakers or unwanted signals such as noise. To separate the source from the other signals called as Blind Source Separation many algorithms are proposed in the literature such as Independent Component Analysis (ICA), Principle Component Analysis (PCA), Non-Negative matrix Factorization (NMF). In this paper we provide the theoretical study of the different algorithms for NMF factorization such as Least Square Error (LSE) divergence, Kullback-Leibler (KL) divergence, Itakura-saito (IS) divergence, Non-negative hidden Markov model(N-HMM), Bayesian NMF, NMF with Automatic Relevance Determinant and Complex NMF applicable for the 2-dimensional data matrix. The performance evaluation of the supervised learning and un-supervised learning is evaluated.