A Correntropy-Based Echo State Network with Application to Time Series Prediction

As a category of recurrent neural networks, echo state networks (ESNs) have been the topic of in-depth investigations and extensive applications in a diverse array of fields, with spectacular triumphs achieved. Nevertheless, the traditional ESN and the majority of its variants are devised in the light of the second-order statistical information of data (e.g., variance and covariance), while more information is neglected. In the context of information theoretic learning, correntropy demonstrates the capacity to grab more information from data. Therefore, under the guidelines of the maximum correntropy criterion, this paper proposes a correntropy-based echo state network (CESN) in which the first-order and higher-order information of data is captured, promoting robustness to noise. Furthermore, an incremental learning algorithm for the CESN is presented, which has the expertise to update the CESN when new data arrives, eliminating the need to retrain the network from scratch. Finally, experiments on benchmark problems and comparisons with existing works are provided to verify the effectiveness and superiority of the proposed CESN.