A Fast Indscal Analysis for Blind Underdetermined Mixture Identification from Several Even Higher Order Cumulants

A new class of cumulant-based methods is presented in order to blindly identify potentially underdetermined mixtures of statistically independent sources. These algorithms perform a joint canonical decomposition (CAND) of several higher order cumulants through a fast CAND of a special 3-way array. From a signal processing viewpoint, the proposed methods are shown (i) to have a better estimation resolution and (ii) to be able to process more sources than the other classical cumulant-based techniques. Secondly, from a numerical analysis viewpoint, we show how to accelerate the iterative CAND procedures by using efficiently potential symmetries between loading matrices. This yields a fast individual differences scaling (INDSCAL) scheme. Eventually, a numerical complexity study is performed.