Is Single Enough? A Joint Spatiotemporal Feature Learning Framework for Multivariate Time Series Prediction

A fuzzy cognitive map (FCM) is a simple but effective tool for modeling and predicting time series. This article focuses on the problem of multivariate time series prediction (TSP), which is essential and challenging in data mining. Although several FCM-based approaches have been designed to solve this problem, their feature extraction module designed for single mode falls short in capturing the nonlinear spatiotemporal dependencies among variates, thereby resulting in low prediction accuracy in forecasting multivariate time series, which shows that the single mode learning is not enough. Therefore, in this article, we propose a joint spatiotemporal feature learning framework for multivariate TSP, where a mix-resolution spatial module consisting of multiple sparse autoencoders (SAEs) is designed to extract the feature series with different spatial resolutions, and a mix-order spatiotemporal module concluding multiple high-order FCMs (HFCMs) is designed to model the spatiotemporal dynamics of these feature series. Finally, the outputs of the two modules are concatenated to predict future values. We refer to this framework as the spatiotemporal FCM (STFCM). Especially, an efficient learning algorithm is designed to update the integral weights of STFCM based on the batch gradient descent algorithm when it deems necessary. We validate the performance of the STFCM on four real-world datasets. Compared with the existing state-of-the-art (SOTA) methods, the experimental results not only show the advantages of the two designed modules in the STFCM but also show the excellent performance of the STFCM.