Maximum likelihood blind source separation: A context-sensitive generalization of ICA

In the square linear blind source separation problem, one must find a linear unmixing operator which can detangle the result x(i)(t) of mixing n unknown independent sources s(i)(t) through an unknown n x n mixing matrix A(t) of causal linear filters: x(i) = Sigma(j) a(ij) * s(j). We cast the problem as one of maximum likelihood density estimation, and in that framework introduce an algorithm that searches for independent components using both temporal and spatial cues. We call the resulting algorithm ''Contextual ICA,'' after the (Bell and Sejnowski 1995) Infomax algorithm, which we show to be a special case of cICA. Because cICA can make use of the temporal structure of its input, it is able separate in a number of situations where standard methods cannot, including sources with low kurtosis, colored Gaussian sources, and sources which have Gaussian histograms.