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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
,
where *g*_{1} and *g*_{2} 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*_{i}and *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].

*Aapo Hyvarinen*

*1999-04-23*