An adaptive kernel width update for correntropy

Correntropy, as an adaptive criterion of Information Theoretic Learning (ITL), has been successfully used in signal processing and machine learning. How to appropriately select the kernel width of correntropy is a crucial problem in correntropy applications. Existing kernel width selection methods are not suitable enough for this problem. In this paper, we develop an adaptive method for kernel width selection in correntropy. Based on the Middleton´s non-Gaussian models, this method utilizes the kurtosis as a ratio to adjust the standard deviation of the prediction error to obtain the kernel width online. The superior performance of the new method has been demonstrated by simulation examples in the noisy frequency doubling and echo cancelation problems.