Fuzzy-Weighted Echo State Networks

Abstract

A novel echo state network (ESN), referred to as a fuzzy-weighted echo state network (FWESN), is proposed by using the structural information of data sets to improve the performance of the classical ESN. The information is incorporated into the classical ESN via the concept of Takagi–Sugeno (TS) models/rules. We employ the fuzzy c-mean clustering method to extract the information based on the given data set. The antecedent part of the TS model is determined by the information. Then, we obtain new fuzzy rules by replacing the affine models in the consequent part of each TS rule with a classical ESN. Consequently, the output of the proposed FWESN is calculated through inferring these new fuzzy rules by a fuzzy-weighted mechanism. The corresponding reservoir is consisted of the sub-reservoirs of the new fuzzy rules. Furthermore, we prove that the FWESN has an echo state property by setting the largest spectrum radium of all the internal weight matrices in the sub-reservoirs less than one. Finally, a nonlinear dynamic system and five nonlinear time series are employed to validate the FWESN.