L1/2 norm regularized echo state network for chaotic time series prediction

Abstract

Echo state network contains a randomly connected hidden layer and an adaptable output layer. It can overcome the problems associated with the complex computation and local optima. But there may be ill-posed problem when large reservoir state matrix is used to calculate the output weights by least square estimation. In this study, we use L1/2 regularization to calculate the output weights to get a sparse solution in order to solve the ill-posed problem and improve the generalized performance. In addition, an operation of iterated prediction is conducted to test the effectiveness of the proposed L1/2ESN for capturing the dynamics of the chaotic time series. Experimental results illustrate that the predictor has been designed properly. It outperforms other modified ESN models in both sparsity and accuracy.