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Non-linear cross-correlations

Ever since the seminal paper by Jutten and Hérault [80] (and Jutten's PhD paper [79]), several authors have used the principle of canceling non-linear cross-correlations to obtain the independent components [80,28,33,32]. Such non-linear cross-correlations are of the form $E\{g_1(y_i)g_2(y_j)\}$, where g1 and g2 are some suitably chosen odd non-linearities. If yi and yj are independent, these cross-correlations are zero, under the assumption that the yiand yj have symmetric densities. Often the objective function is here formulated only implicitly, and an exact objective function may not even exist. The non-linearities must be chosen according to the pdf's of the independent components; some guidelines are given in [92,100,131].

Aapo Hyvarinen