Uniqueness of complex and multidimensional independent component analysis

Abstract

A complex version of the Darmois-Skitovitch theorem is proved using a multivariate extension of the latter by Ghurye and Olkin. This makes it possible to calculate the indeterminacies of independent component analysis (ICA) with complex variables and coefficients. Furthermore, the multivariate Darmois-Skitovitch theorem is used to show uniqueness of multidimensional ICA, where only groups of sources are mutually independent.