An information-theoretic perspective to kernel independent components analysis

In this paper, we investigate the intriguing relationship between information-theoretic learning (ITL), based on weighted Parzen window density estimator, and kernel-based learning algorithms. We prove the equivalence between kernel independent component analysis (kernel ICA) and the Cauchy-Schwartz (C-S) independence measure. This link gives a theoretical motivation for the selection of the Mercer kernel, based on density estimation. Demonstrating this equivalence requires introducing a weighted kernel density estimator, a modification of Parzen windowing. We also discuss the role of the weights in the weighted Parzen windowing and kernel ICA.