Cumulant-based independence measures for linear mixtures

This paper deals with independence measures for linear mixtures of mutually independent random variables. Such measures, also known as contrasts, constitute useful criteria in solving blind source separation problems. By making use of the Schur convexity properties, we show that it is possible to define a wide-ranging class of contrast functions based on the auto-cumulants of the components of the random vector being considered. Among the most appealing characteristics of these new contrast functions is that they can be used to combine cumulants of different orders in a flexible way. Furthermore, extensions of existing cross-cumulant-base contrasts are proposed. Finally, some particularization of our approach to measures of decorrelation is considered. A general characterization of these decorrelation measures using strictly Schur convex functions is provided.