A Context-Sensitive Generalization of ICA
Source separation arises in a surprising number of signal processing applications, from speech 
recognition to EEG analysis. In the square linear blind source separation problem without time delays, 
one must find an unmixing matrix which can detangle the result of mixing n unknown independent sources 
through an unknown n x n mixing matrix. The recently introduced ICA blind source separation algorithm 
(Baram and Roth 1994; Bell and Sejnowski 1995) is a powerful and surprisingly simple technique for solving 
this problem. ICA is all the more remarkable for performing so well despite making absolutely no use of the 
temporal structure of its input! This paper presents a new algorithm, contextual ICA, which derives from a 
maximum likelihood density estimation formulation of the problem. cICA can incorporate arbitrarily complex 
adaptive history-sensitive source models, and thereby make use of the temporal structure of its input. 
This allows it to separate in a number of situations where standard ICA cannot, including sources with low 
kurtosis, colored gaussian sources, and sources which have gaussian histograms. Since ICA is a special case 
of cICA, the MLE derivation provides as a corollary a rigorous derivation of classic ICA.