QSTGNN: Quaternion Spatio-Temporal Graph Neural Networks

Spatio-temporal time series forecasting has attracted great attentions in various fields, including climate, power, and traffic forecasting. Recently, Spatio-temporal Graph Neural Networks (STGNNs) have shown promising performances in modeling spatial dependencies based on graph neural networks (GNNs) and temporal dependencies based on temporal learning modules. However, most STGNNs do not effectively integrate explicit and implicit relationships between nodes, nor do they adequately capture long and short-term time dependencies. To address these challenges, this paper presents a Quaternion Spatio-temporal Graph Neural Network (QSTGNN). Specifically, the quaternion spatio-temporal graph is constructed firstly, such that the information of both short and long-term time steps are preserved in quaternion feature tensor, and information of multiple explicit graphs and implicit graph are integrated in quaternion graph adjacency matrix. Then, two modules are designed: a 1D quaternion convolution module and a quaternion graph convolution module. In the 1D quaternion convolution module, complex temporal correlations among short and long-term time steps can be well exploited by 1D quaternion convolution operator based on the quaternion Hamilton product. In the quaternion graph convolution module, quaternion graph convolution is designed to characterize nonlinear dependencies among multiple spatial graphs, including explicit and implicit graphs. Extensive experiments are conducted on six datasets, and the results show that QSTGNN achieves state-of-the-art performances over the existing ten methods. Explainable analysis presents that multiple spatial correlations can accurately illustrate the traffic flow and road functional information in real traffic roads.