KT-RC: Kernel time-delayed reservoir computing for time series prediction

Reservoir computing (RC) is an efficient recurrent neural network (RNN) method. However, the performance and prediction results of traditional RCs are susceptible to several factors, such as their network structure, parameter setting, and selection of input features. In this study, we employ a kernel time-delayed RC (KT-RC) method for time series prediction. The KT-RC transforms input vectors linearly to obtain a high-dimensional set of time-delayed linear eigenvectors, which are then transformed by various kernel functions to represent the nonlinear characteristics of the input signal. Finally, the Bayesian optimization algorithm adjusts the few remaining weights and kernel parameters to minimize the manual adjustment process. The advantages of KT-RC can be summarized as follows: 1) KT-RC solves the problems of uncertainty in weight matrices and difficulty in large-scale parameter selection in the input and hidden layers of RCs. 2) The KT module can avoid massive reservoir hyperparameters and effectively reduce the hidden layer size of the traditional RC. 3) The proposed KT-RC shows good performance, strong stability, and robustness in several synthetic and real-world datasets for one-step-ahead and multistep-ahead time series prediction. The simulation results confirm that KT-RC not only outperforms some gate-structured RNNs, kernel vector regression models, and recently proposed prediction models but also requires fewer parameters to be initialized and can reduce the hidden layer size of the traditional RCs. The source code is available at https://github.com/whs7713578/RC.