提出新型动态图网络，高效建模时空序列的复杂关联。
A Dynamic Stiefel Graph Neural Network for Efficient Spatio-Temporal Time Series Forecasting
- 用施蒂费尔流形约束图傅里叶变换矩阵，提升模型表达力。
- 在7个数据集上优于当前最佳方法，计算开销更低。
- 适合需要高效处理大规模时空数据的研究者使用。
时空时间序列（STTS）被广泛应用于各类场景。然而，由于时间和空间维度中存在复杂的动态相关性，准确预测STTS仍具挑战。现有图神经网络在建模动态时空关系时难以兼顾效果与效率。为此，我们提出动态时空施蒂费尔图神经网络（DST-SGNN），以高效处理STTS。DST-SGNN首先引入新颖的施蒂费尔图谱卷积（SGSC）和施蒂费尔图傅里叶变换（SGFT），其中SGFT矩阵被约束在施蒂费尔流形上，使SGSC可视为一种滤波图谱卷积。同时提出线性动态图优化算法（LDGOSM），可高效学习动态图的SGFT矩阵，显著降低计算复杂度。最后设计多层SGSC（MSGSC），有效捕捉复杂的时空相关性。在7个时空数据集上的大量实验表明，DST-SGNN在性能上超越当前最优方法，同时保持较低的计算成本。
原文摘要 · Abstract (English)
Spatio-temporal time series (STTS) have been widely used in many applications. However, accurately forecasting STTS is challenging due to complex dynamic correlations in both time and space dimensions. Existing graph neural networks struggle to balance effectiveness and efficiency in modeling dynamic spatio-temporal relations. To address this problem, we propose the Dynamic Spatio-Temporal Stiefel Graph Neural Network (DST-SGNN) to efficiently process STTS. For DST-SGNN, we first introduce the novel Stiefel Graph Spectral Convolution (SGSC) and Stiefel Graph Fourier Transform (SGFT). The SGFT matrix in SGSC is constrained to lie on the Stiefel manifold, and SGSC can be regarded as a filtered graph spectral convolution. We also propose the Linear Dynamic Graph Optimization on Stiefel Manifold (LDGOSM), which can efficiently learn the SGFT matrix from the dynamic graph and significantly reduce the computational complexity. Finally, we propose a multi-layer SGSC (MSGSC) that efficiently captures complex spatio-temporal correlations. Extensive experiments on seven spatio-temporal datasets show that DST-SGNN outperforms state-of-the-art methods while maintaining relatively low computational costs.
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