I.C.A.: conditions on cumulants and information theoretic approach.
Jean‐Pierre Nadal, Néstor Parga · 1997
. In this contribution we present new conditions on cross cumulants which guarantee that blind source separation has been performed, and we relate these conditions to the maximization of mutual information as a criterion for ICA. Submitted to ESANN97 1. Introduction Independent Component Analysis (ICA), and in particular Blind Source Separation (BSS), can be obtained from the maximization of mutual information, as first shown in [Nadal and Parga, 1994][1]. This result was obtained for a deterministic processing system, with an arbitrary input-output relationship. Technically, a small additive noise was considered in order to define the mutual information between the inputs and the outputs variable. Then the zero noise limit was taken in order to extract the relevant "contrast" cost function for the deterministic case. The relevance for BSS was stressed out: in the particular case where the inputs are linear combinations of independent random variables ("sources"), one can use a feedf...