Kernel adaptive filtering under generalized Maximum Correntropy Criterion

Owing to their universal approximation capability and online learning manner, kernel adaptive filters have been widely used in nonlinear systems modeling. Under Gaussian assumption, traditional kernel adaptive algorithms utilize the well-known mean square error(MSE) as a cost function to get optimal solutions. For non-Gaussian situations, MSE will not properly represent the statistics of the error, and hence degrade the performance. In recent years, an information theoretic learning(ITL) based criterion called Maximum Correntropy Criterion(MCC) has been proposed and applied in robust adaptive filtering. The correntropy is a generalized correlation measure in kernel space, which uses Gaussian kernel as a default kernel function. Of course, Gaussian kernel is not always the best choice. Recently, a more flexible definition of correntropy, called generalized correntropy, has been proposed. With a proper shape parameter, the generalized correntropy may get better performance than original correntropy with Gaussian kernel. In this paper, we take advantages of both kernel methods and generalized correntropy to develop a new kernel adaptive algorithm called Generalized Kernel Maximum Correntropy(GKMC) algorithm. We analyze theoretically the stability and steady-state performance of the new algorithm. In addition, we propose a Quantized GKMC(QGKMC) algorithm to curb the growth of the network size in GKMC while maintaining the performance. Simulation results confirm the theoretical expectations and show superior performance compared with existing methods.