Modular state space of echo state network

Echo state network (ESN) mainly consists of a reservoir with a large number of neurons that are randomly connected and a linear readout (output) that is easily adapted. From this point, the reservoir will reconstruct the input signals in the high-dimensional state space. In this paper, modular state space of echo state network (MSSESN) is proposed. First, the state space is divided into several subspaces and each of which is called “a module”. And then, linear readout of ESN is replaced by piecewise output function which maps each module states individually to the actual output. Furthermore, unlike iterative prediction in ESN, the feedback connections from the output neuron to the reservoir are eliminated, which establishes a direct relationship between the reservoir and output. Finally, the final results can be obtained by assembling the outputs of each module. Different from previous reservoir computing methods, MSSESN takes advantage of the modularity and reservoir mechanisms. It is theoretically analyzed and tested by the benchmark prediction of Mackey–Glass and Lorenz time series. The results have proven the effectiveness of this methodology.