A new echo state network with variable memory length

This paper proposes a new echo state network (ESN) with variable memory length. For input-driven applications, existing ESNs do not fully consider the characteristics of input signals and usually ignore output feedback connections. Therefore, the echo state property of ESN cannot be completely satisfied for a certain period of time, and thus ESNs cannot provide higher accuracy and faster convergence speed for time-series prediction. To overcome the abovementioned problems of existing ESNs, we propose a variable memory length echo state network (VML-ESN) that can adaptively adjust the state update pattern according to the autocorrelation characteristic of the input signals. For different input signals, the reservoir of VML-ESN is composed of different leaky integrator units with multiple delays. Therefore, the reservoir of VML-ESN has a variable state update equation for different types of input signals. A sufficient condition is given to guarantee that the VML-ESN model has the echo state property. The extended Kalman filtering (EKF) method is utilized to obtain the global optimal parameters of VML-ESN. To validate the effectiveness of VML-ESN, we use VML-ESN to predict different types of time series. Simulation results showed that VML-ESN can greatly improve the prediction accuracy and training time for different input signals.