Independent component analysis based on higher-order statistics only

Authors:
L. De Lathauwer;B. De Moor;J. Vandewalle
Affiliations:
-;-;-
Venue:
SSAP '96 Proceedings of the 8th IEEE Signal Processing Workshop on Statistical Signal and Array Processing (SSAP '96)
Year:
1996

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Abstract

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.