Robust echo state networks based on correntropy induced loss function

In this paper, a robust echo state network with correntropy induced loss function (CLF) is presented. CLF is robust to outliers through the mechanism of correntropy which is widely applied in information theoretic learning. The proposed method can improve the anti-noise capacity of echo state network and overcome its problem of being sensitive outliers which are prevalent in real-world tasks. The echo state network with CLF inherits the basic architecture of echo state network, but replaces the commonly used mean square error (MSE) criterion with CLF. The stochastic gradient descent method is adopted to optimize the objective function. The proposed method is subsequently verified in nonlinear system identification and chaotic time-series prediction. Experimental results demonstrate that our method is robust to outliers and outperforms the echo state networks with Bayesian regression and Huber loss function.