Alpha-divergence two-dimensional nonnegative matrix factorization for biomedical blind source separation

An alpha-divergence two-dimensional nonnegative matrix factorization (NMF2D) for biomedical signal separation is presented. NMF2D is a popular approach for retrieving low-rank approximations of nonnegative data such as image pixel, audio signal, data mining, pattern recognition and so on. In this paper, we concentrate on biomedical signal separation by using NMF2D with alpha-divergence family which decomposes a mixture into two-dimensional convolution factor matrices that represent temporal code and the spectral basis. The proposed iterative estimation algorithm (alpha-divergence algorithm) is initialized with random values, and it updated using multiplicative update rules until the values converge. Simulation experiments were carried out by comparing the original and estimated signal in term of signal-to-distortion ratio (SDR). The performances have been evaluated by including and excluding the sparseness constraint which sparseness is favored by penalizing nonzero gains. As a result, the proposed algorithm improved the iteration speed and sparseness constraints produce slight improvement of SDR.