K-order echo-type spiking neural P systems for time series forecasting

Abstract

Nonlinear spiking neural P (NSNP) systems are variants of neural-like membrane computing models, abstracted by nonlinear spiking mechanisms of biological neurons. NSNP systems can show rich nonlinear dynamics. This study proposes a new variant of NSNP systems, called $k$-order NSNP systems, and derives their mathematical models. The $k$-order NSNP systems are able to remember the states of the previous $k$ moments. Based on the $k$-order NSNP systems, we propose a new recurrent-like model, called $k$-order echo-type spiking neural P systems or termed kESNP model. Structurally, the $k$ESNP model is a $k$-order NSNP system equipped with an input layer and an output layer. Inspired by echo state networks (ESN), this $k$ESNP model is trained by ridge regression algorithm. Six time series are used as benchmark data sets to evaluate the $k$ESNP model and it is compared with 33 baseline prediction methods. The experimental results demonstrate that the proposed $k$ESNP model is sufficient for the task of time series forecasting.