Effect of hybrid circle reservoir injected with wavelet-neurons on performance of echo state network

The Echo State Network (ESN) has attracted wide attention for its superior performance in chaos time-series prediction. However, the complicated ESN topologies and the random reservoirs are difficult to implement in practice. We propose a hybrid circle reservoir (HCR) ESN architecture that comprises the following features: (1) built with low complexity circle reservoir; (2) partly injected with wavelet-neurons; (3) uses fixed connection weights in both input matrix and dynamic reservoir matrix. The HCR model has been successfully applied to solve six application problems, and the results are used to compare with the existing low complexity simple circle reservoir (SCR) ESN. Furthermore, we analyze the performance of the new model under different ratios of wavelet-neurons, different circle distributions and different input sign patterns. Simulation results show that the HCR model achieves significantly better performance in prediction accuracy than the SCR model. Additionally, the HCR model has similar low complexity as the SCR. Moreover, the short-term memory capacity (MC) in the HCR is close to the theoretical optimal MC value.