Recursive Minimum Kernel Mixture Mean p-Power Error Algorithm Based on the Nyström Method

Abstract

In this brief, a novel kernel mixture mean $p$ -power error (KMP) criterion is proposed by combining the mixture of two Gaussian functions into the kernel function of kernel mean $p$ -power error. The mixture correntropy (MC) measure can be viewed as a special case of the KMP with $p = 2$ . And the KMP with an appropriate $p$ can provide better accuracy than MC for robust learning. Some properties of KMP are presented for discussion. The Nystrom method is an efficient method for curbing the growth of network size of kernel adaptive filters (KAFs), and the recursive update form can improve the tracking ability of KAFs. To this end, we apply the Nystrom method and recursive update form to the KMP criterion, generating a novel recursive minimum kernel mixture mean $p$ -power error algorithm based on the Nystrom method (NysRMKMP). Monte Carlo simulations on chaotic time-series prediction illustrate the desirable accuracy and robustness of NysRMKMP.