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 y_i and y_j are independent, these cross-correlations are zero, under the assumption that the y_iand y_j 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].