  As a robust nonlinear similarity measure in kernel space, correntropy has
received increasing attention in domains of machine learning and signal
processing. In particular, the maximum correntropy criterion (MCC) has recently
been successfully applied in robust regression and filtering. The default
kernel function in correntropy is the Gaussian kernel, which is, of course, not
always the best choice. In this work, we propose a generalized correntropy that
adopts the generalized Gaussian density (GGD) function as the kernel (not
necessarily a Mercer kernel), and present some important properties. We further
propose the generalized maximum correntropy criterion (GMCC), and apply it to
adaptive filtering. An adaptive algorithm, called the GMCC algorithm, is
derived, and the mean square convergence performance is studied. We show that
the proposed algorithm is very stable and can achieve zero probability of
divergence (POD). Simulation results confirm the theoretical expectations and
demonstrate the desirable performance of the new algorithm.
