Persistent Homology-induced Graph Ensembles for Time Series Regressions

• URL: http://arxiv.org/abs/2503.14240v2
• Date: Wed, 19 Mar 2025 10:33:40 GMT
• Title: Persistent Homology-induced Graph Ensembles for Time Series Regressions
• Authors: Viet The Nguyen, Duy Anh Pham, An Thai Le, Jans Peter, Gunther Gust,
• Abstract summary: We create an ensemble of Graph Neural Networks based on Persistent Homology filtration.<n>The ensemble aggregates the signals from the individual learners via an attention-based routing mechanism.<n>Four different real-world experiments on seismic activity prediction and traffic forecasting demonstrate that our approach consistently outperforms single-graph baselines.
• Score: 1.5728609542259502
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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