Extraction of independent components from hybrid mixture: KuicNet learning algorithm and applications

Abstract

A hybrid mixture is a mixture of supergaussian, gaussian, and subgaussian independent components (ICs). This paper addresses extraction of ICs from a hybrid mixture. There are two kinds of (single-output vs. all-outputs) kurtosis function to be considered as a contrast function. We advocate the former approach due to its (1) simple and closed-form analysis, and (2) numerical convergence and computational saving. Via this approach, all (and only) the positive local maxima (resp. negative local minima) can yield supergaussian (resp, subgaussian) ICs from any mixture (Kung 1997). We also propose a network algorithm, kurtosis-based independent component network (KuicNet), for recursively extracting ICs. Numerical and convergence properties are analyzed and several application examples demonstrated.