Generalized Maximum Correntropy-Based Echo State Network for Robust Nonlinear System Identification

Abstract

In this paper, we propose a robust method for non-linear system identification that incorporates robustness to echo state networks (ESNs). In particular, the ESNs utilize generalized correntropy as a loss function to get optimal solutions. Generalized correntropy is a more flexible extension of correntropy in information theoretic learning (ITL). Generalized correntropy induced metric (GCIM) is robust to outliers with a proper shape parameter. The ESNs with GCIM can provide the anti-noise capacity and are insensitive outliers which are prevalent in real-world tasks. They also inherit the basic architecture of echo state network but replaces the commonly used mean square error (MSE) criterion with GCIM. The stochastic gradient descent method is adopted to optimize the generalized correntropy-based cost function. Numerical simulations are given to show that the proposed algorithm is robust to the non-Gaussian noise and outliers.