用拓扑方法生成多尺度图结构，提升时间序列预测精度。
Persistent Homology-induced Graph Ensembles for Time Series Regressions
- 基于持久同调构造数据的多尺度图结构
- 在地震预测与交通流量任务中优于单图基线
- 支持可解释性分析，适合需要结构洞察的应用
时空图神经网络在时间序列应用中的表现常受限于对固定人工图结构的依赖。受拓扑数据分析范式启发，真实数据具有多尺度特征，我们利用持久同调滤波构建多个图结构，并将其作为输入构建图神经网络集成模型。该集成通过注意力路由机制聚合各子模型信号，系统编码数据的内在多尺度结构。在地震活动预测及交通预测（PEMS-BAY、METR-LA）四项真实世界实验中，本方法持续优于单图基线，并提供可解释性洞见。
原文摘要 · Abstract (English)
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 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.
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