Independent component analysis: extrema-correspondence properties for higher-order moment functions

This paper compares the use of the kurtosis function and higher-order moment functions for the extraction of independent components from a hybrid mixture. The kurtosis function, based on the 4-th order moments, is a theoretically attractive contrast function since it possess a traceable extrema-correspondence. Numerical motivations have lead many researchers to look into contrast functions involving higher-order moments. To facility the study, we define super-ness and sub-ness of non-Gaussian processes as terms that are dependent not only only on the nature of the signals themselves, but also on the the contrast functions used. In terms of the extrema-correspondence, we report some noteworthy discrepancies between the kurtosis and higher-order moment functions. Finally, we verify that for even-positive-integer and equal-moment components, both the necessary and sufficient conditions are valid