Blind Source Separation and Equiprobabilistic Topographic Maps

Recently, a number of heuristic techniques have been devised in order to overcome some of the limitations of the Blind Source Separation (BSS) algorithms that are rooted in the theory of Independent Component Analysis (ICA). They are usually based on topographic maps and designed to separate mixtures of signals with either sub-Gaussian or super-Gaussian source densities. In the sub-Gaussian case, the coordinates of the winning neurons in the topographic map represent the estimates of the source signal amplitudes. In the super-Gaussian case, one relies on the topographic map's ability to detect the source directions in mixture space which, in turn, correspond to the column vectors of the mixing matrix in the linear case. We will introduce a new topographic map-based heuristic for super-Gaussian BSS. It relies on the tendency of the mixture samples to cluster around the source directions. We will demonstrate its performance on linear and mildly non-linear mixtures of speech signals, including the case where there are less mixtures than sources to be separated (non-square BSS).