The effectiveness of Spatio-temporal Graph Neural Networks (STGNNs) in time-series applications is often limited by their dependence on fixed, hand-crafted input graph structures. Motivated by insights from the Topological Data Analysis (TDA) paradigm, of which real-world data exhibits multi-scale patterns, we construct several graphs using \textit{Persistent Homology Filtration} -- a mathematical framework describing the multiscale structural properties of data points. Then, we use the constructed graphs as an input to create an ensemble of Graph Neural Networks. The ensemble aggregates the signals from the individual learners via an attention-based routing mechanism, thus systematically encoding the inherent multiscale structures of data. Four different real-world experiments on seismic activity prediction and traffic forecasting (PEMS-BAY, METR-LA) demonstrate that our approach consistently outperforms single-graph baselines while providing interpretable insights.

翻译：时空图神经网络（STGNNs）在时间序列应用中的有效性常常受限于其对固定、手工构建的输入图结构的依赖。受拓扑数据分析（TDA）范式的启发——该范式认为现实世界数据展现出多尺度模式——我们使用\textit{持久同调过滤}（一种描述数据点多尺度结构特性的数学框架）构建了多个图。然后，我们将构建的图作为输入，创建了一个图神经网络集成。该集成通过一种基于注意力的路由机制聚合来自各个学习器的信号，从而系统地编码数据固有的多尺度结构。在地震活动预测和交通流量预测（PEMS-BAY, METR-LA）上的四项不同真实世界实验表明，我们的方法在提供可解释性见解的同时，始终优于单图基线模型。