A multivariate time series prediction model based on subspace echo state network

Considering that there may be ill-posed solutions in the pseudo-inverse algorithm for using echo state network to predict the multivariate chaotic time series, we introduce a new approach towards ESNs, termed Fast Subspace Decomposition Echo State Network model (FSDESN) herein. The model uses a Krylov subspace decomposition algorithm, on the basis of an efficient Lanczos type iteration, to extract the subspace of large-scale reservoir matrix, and then calculate the output weights by replacing the original state space with its subspace. By this way, it brings a jump on computational complexity compared with conventional eigenvalue decomposition algorithm. In addition, FSDESN model eliminates approximate collinear components so as to solve the ill-posed problem and avoid over-training. Furthermore, it improves the generalization performance of single ESN. Simulation results on basis of two sets of multivariate chaotic time series substantiate the effectiveness and characteristics of FSDESN. ©, 2014, Jisuanji Xuebao/Chinese Journal of Computers. All right reserved.