Independent component analysis based on higher-order statistics only

Most conventional techniques for independent component analysis (or blind source separation) resort to second-order statistics to decorrelate the observed data. The prewhitening step makes these algorithms sensitive to the presence of additive Gaussian noise. A higher-order-only technique is presented. The identification problem is approached in a (linear and multilinear) algebraic framework: our derivation starts with the observation that the solution can be obtained from the canonical decomposition (CANDECOMP) of a higher-order cumulant tensor. Next, it is demonstrated that the CANDECOMP components follow from the simultaneous diagonalization, by congruence transformation, of a set of matrices. A reformulation in terms of orthogonal unknowns leads to a simultaneous Schur decomposition, which is solved by a Givens-type iteration. The technique can be considered as the higher-order-only equivalent of the popular JADE-algorithm.