Geometric Algebra Multi-Order Graph Neural Network for Traffic Prediction

Accurate traffic prediction is crucial for urban traffic management. Spatial-temporal graph neural networks, which combine graph neural networks with time series processing, have been extensively employed in traffic prediction. However, traditional graph neural networks only capture pairwise spatial relationships between road network nodes, neglecting high-order interactions among multiple nodes. Meanwhile, most work for extracting temporal dependencies suffers from implicit modeling and overlooks the internal and external dependencies of time series. To address these challenges, we propose a Geometric Algebraic Multi-order Graph Neural Network (GA-MGNN). Specifically, in the temporal dimension, we design a convolution kernel based on the rotation matrix of geometric algebra, which not only learns internal dependencies between different time steps in time series but also external dependencies between time series and convolution kernels. In the spatial dimension, we construct a tokenized hypergraph and integrate dynamic graph convolution with attention hypergraph convolution to comprehensively capture multi-order spatial dependencies. Additionally, we design a segmented loss function based on traffic periodic information to further improve prediction accuracy. Extensive experiments on seven real-world datasets demonstrate that GA-MGNN outperforms state-of-the-art baselines.