Designing Specialized Two-Dimensional Graph Spectral Filters for Spatial-Temporal Graph Modeling

Spatial-temporal graph modeling is challenging due to the diverse node interactions across spatial and temporal dimensions. Recent studies typically adopt Graph Neural Networks (GNNs) to perform node-level aggregation at different time steps, acting as a series of low-pass graph spectral filters, for node interaction modeling. However, these filters, confined to the spatial dimension, are ill-suited for processing signals of nodes with inherent spatial-temporal interdependencies. Moreover, oversimplified low-pass filtering fails to fully exploit information from diverse node interactions. To address these issues, we propose a Spatial-Temporal Spectral Graph Neural Network (STSGNN), which designs specialized two-dimensional (2-D) graph spectral filters for comprehensive spatial-temporal graph modeling. First, based on the normalized Laplacian spectrum of spatial and temporal graphs, we extend the existing graph spectral theory from a univariate spatial dimension to a bivariate spatial-temporal dimension through a 2-D Discrete Graph Fourier Transform (2-D DGFT). Then, we leverage the bivariate Bernstein polynomial approximation, with learned basis coefficients, to design 2-D filters with specialized spectral properties for unified spatial-temporal signal filtering. Finally, the filtered signals, with refined spatial-temporal representations, are fed into well-designed pyramidal gated convolution modules to acquire multiple ranges of spatial-temporal dependencies. Experiments on traffic and meteorological prediction tasks demonstrate that STSGNN achieves state-of-the-art performance. Additionally, we visualize the 2-D filters learned from inputs with distinct spatial-temporal characteristics to enhance the model's interpretability.