Multivariate chaotic system modeling based on nonuniform state space reconstruction and echo state network

A new learning framework is proposed for multivariate chaotic system modeling. In order to construct suitable input variables, we put forward a scheme of input variable selection based on nonuniform state space reconstruction. A new criteria based on low dimensional approximation of joint mutual information is derived, which is solved by evolutionary computation approach efficiently with low computation complexity. Then, echo state network is adopted as prediction model, which has powerful capability for nonlinear predicting. To improve generalization performance and stability of the predictive model, we introduce feature selection in the training process. Feature selection method can control complexity of the network and prevent overfitting. The model is applied to the prediction of real world time series. The simulation results show the effectiveness and practicality of the proposed method.