Echo state network-based visibility graph method for nonlinear time series prediction

For an echo state network (ESN), the reservoir topology plays a very important role in network performance. However, the computing capability of classical random structure is limited, and it can not meet the prediction accuracy requirement of some highly complicated prediction tasks. Therefore, different algorithms to construct new reservoir topology based on complex network theory have been proposed, amongst of which, the visibility graph algorithm shows to be more effective and simple. In this paper, a new ESN based on the visibility graph (VGESN) is proposed to perform the prediction of Mackey-Glass chaotic system (MGS) and nonlinear autoregressive moving average (NARMA) time series. Furthermore, the network features of associated graphs are analysed, including the small-world feature and scale- free property. The simulation results indicate that the proposed VGESN has better prediction performance compared with traditional ESN. The analytical results of network characteristics also reveal that the MGS associated graph has small-world feature, while the NARMA associated graph has both small-world and scale-free property.