A mirrored echo state network with application to time series prediction

In recent years, the echo state network (ESN) has been increasingly developed and investigated. In this paper, for the first time, a mirrored algorithm is proposed to optimize input weights, and then a mirrored echo state network (MESN) is constructed, where the order of determining weights is exchanged, forming a mirror symmetry with the traditional ESN. Combining the mirrored algorithm and the traditional ESN training method, a novel weight determination scheme is proposed for the MESN, where multiple pseudoinverse processes are involved and utilized, and then the optimal input weights and retrained output weights are acquired. To meet the echo state property, the reservoir connection weights are determined with the assistance of the singular value decomposition. Moreover, the stepwise incremental method and the achievements of predecessors are combined and used, based on which the structure of the reservoir is determined. Finally, experiments on the Mackey-Glass system (MGS), as well as two real-world datasets, along with comparisons with existing works, are conducted, and the results demonstrate the superiority and stability of the proposed MESN in predicting MGS with large chaotic factors and more complex real-world problems.