Chaotic time series prediction using phase space reconstruction based conceptor network

The Conceptor network is a new framework of reservoir computing (RC), in addition to the features of easy training, global convergence, it can online learn new classes of input patterns without complete re-learning from all the training data. The conventional connection topology and weights of the hidden layer (reservoir) of RC are initialized randomly, and are fixed to be no longer fine-tuned after initialization. However, it has been demonstrated that the reservoir connection of RC plays an important role in the computational performance of RC. Therefore, in this paper, we optimize the Conceptor's reservoir connection and propose a phase space reconstruction (PSR) -based reservoir generation method. We tested the generation method on time series prediction task, and the experiment results showed that the proposed PSR-based method can improve the prediction accuracy of Conceptor networks. Further, we compared the PSR-based Conceptor with two Conceptor networks of other typical reservoir topologies (random connected, cortex-like connected), and found that all of their prediction accuracy showed a nonlinear decline trend with increasing storage load, but in comparison, our proposed PSR-based method has the best accuracy under different storage loads.