Maximum Likelihood Blind Source Separation: A Context-Sensitive Generalization of ICA

Part of Advances in Neural Information Processing Systems 9 (NIPS 1996)

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Barak Pearlmutter, Lucas Parra


In the square linear blind source separation problem, one must find a linear unmixing operator which can detangle the result Xi(t) of mixing n unknown independent sources 8i(t) through an unknown n x n mixing matrix A( t) of causal linear filters: Xi = E j aij * 8 j . We cast the problem as one of maximum likelihood density estima(cid:173) tion, 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 kur(cid:173) tosis, colored Gaussian sources, and sources which have Gaussian histograms.

1 The Blind Source Separation Problem

Consider a set of n indepent sources 81 (t), . .. ,8n (t). We are given n linearly dis(cid:173) torted sensor reading which combine these sources, Xi = E j aij8j, where aij is a filter between source j and sensor i, as shown in figure 1a. This can be expressed as

Xi(t) = 2: 2: aji(r)8j(t - r) = 2: aji * 8j