Multivariate PDF matching via kernel density estimation

In this work, a measure of similarity based on the matching of multivariate probability density functions (PDFs) is proposed. In consonance with the information theoretic learning (ITL) framework, the affinity comparison between the joint PDFs is performed using a quadratic distance, estimated with the aid of the Parzen window method with Gaussian kernels. The motivation underlying this proposal is to introduce a criterion capable of quantifying, to a significant extent, the statistical dependence present on information sources endowed with temporal and/or spatial structure, like audio, images and coded data. The measure is analyzed and compared with the canonical ITL-based approach - correntropy - for a set of blind equalization scenarios. The comparison includes elements like surface analysis, performance comparison in terms of bit error rate and a qualitative discussion concerning image processing. It is also important to remark that the study includes the application of two computational intelligence paradigms: extreme learning machines and differential evolution. The results indicate that the proposal can be, in some scenarios, a more informative formulation than correntropy.