ICA-based radial basis function network for multivariate chaotic time series forecasting

The paper presents a method for prediction of multivariate chaotic time series, using radial basis function (RBF) neural network with the input phase space preprocessed by independent component analysis (ICA). Firstly, C-C method is used to respectively compute the embedding dimension and delay time for all variables, and we get a reconstructed initial multivariate input vector space which may be highly correlated. Then the ICA method is expanded to find a linear representation of reconstructed input data so that the components are statistically independent. This representation of capturing the essential structure of the input data may reduce the initial dimension and simplify the computation. Furthermore, RBF network is trained to make prediction on the basis of approximating both the functional relation between different variables and the map between current state and future state. The method has been applied in simulation on Lorenz equation. We make one-step to ten-step predictions respectively. And prediction accuracy (E_PA) and root-mean-square error (E_RMSE) is used to measure the performance of proposed prediction model. We also make comparison between the model and the direct RBF prediction with the same node numbers. The simulation results showed the effectiveness of the method.