Correntropy: A Localized Similarity Measure

The measure of similarity normally utilized in statistical signal processing is based on second order moments. In this paper, we reveal the probabilistic meaning of correntropy as a new localized similarity measure based on information theoretic learning (ITL) and kernel methods. As such it has vastly different properties when compared with mean square error (MSE) that can be very useful in nonlinear, non-Gaussian signal processing. Two examples are presented to illustrate the technique.