Online Sequential Extreme Learning Machine Algorithm Based on the Generalized Maximum Correntropy Criterion

Abstract

Under Gaussian assumption, online sequential extreme learning machine (OS-ELM) can achieve optimal performance. However, OS-ELM is based on the mean square error (MSE) criterion which is not a good choice for non-Gaussian signals. In this paper, a novel OS-ELM algorithm based on the generalized maximum correntropy criterion (OS-ELM-GMCC) is derived. Since the maximum correntropy criterion (MCC) can be generalized by the generalized maximum correntropy criterion (GMCC), the GMCC-based adaptive filtering algorithms with an appropriate shape parameter achieve better filtering performance than the MCC-based ones in the presence of non-Gaussian noise. As the important parameters, the number of hidden node, the shape parameter and scale parameter are discussed by simulations. Simulations in the context of the two examples including the system identification and Mackey-Glass (MG) chaotic time series demonstrate the superiority of OS-ELM-GMCC over OS-ELM and OS-ELM-MC.