Correntropy: Properties and Applications in Non-Gaussian Signal Processing

The optimality of second-order statistics depends heavily on the assumption of Gaussianity. In this paper, we elucidate further the probabilistic and geometric meaning of the recently defined correntropy function as a localized similarity measure. A close relationship between correntropy and M-estimation is established. Connections and differences between correntropy and kernel methods are presented. As such correntropy has vastly different properties compared with second-order statistics that can be very useful in non-Gaussian signal processing, especially in the impulsive noise environment. Examples are presented to illustrate the technique.