Predicting Chaotic Time Series Using Neural and Neurofuzzy Models: A Comparative Study
Neural Processing Letters
Training Recurrent Networks by Evolino
Neural Computation
Chaotic Time Series Prediction Using a Neuro-Fuzzy System with Time-Delay Coordinates
IEEE Transactions on Knowledge and Data Engineering
Pruning and regularization in reservoir computing
Neurocomputing
Prediction of multivariate chaotic time series with local polynomial fitting
Computers & Mathematics with Applications
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Architectural and Markovian factors of echo state networks
Neural Networks
Prediction of chaotic time series based on the recurrent predictor neural network
IEEE Transactions on Signal Processing
A tighter bound for the echo state property
IEEE Transactions on Neural Networks
Support Vector Echo-State Machine for Chaotic Time-Series Prediction
IEEE Transactions on Neural Networks
Collective Behavior of a Small-World Recurrent Neural System With Scale-Free Distribution
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
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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.