Independent Components Analysis for Step-wise Separation of Signals
We introduce a method for the step-wise extraction of each of N source signals from a set of M N signal mixtures. The mixtures x = (x1; : : : ; xM) T are formed by combining diierent proportions of the independent sources s = (s1; : : : ; sN) T using an M N mixing matrix A, so that x = As. Porrill and Stone Porrill and Stone, 1997] showed that K N signals (s1; : : : ; sK) T could be extracted using a K M rectangular un0mixing matrix W by maximising the joint entropy of K whitened, unmixed signals Y = (Wx), where is a monotonic, non-linear function. Rather than extracting K N signals simultaneously, we use a step-wise procedure in which each step consists of extracting K = 1 source signal, and then subtracting that signal from the signal mixtures. The relation between this ICA method and exploratory projection pursuit is discussed. The method is demonstrated on acoustic data.