Persistent Homology-induced Graph Ensembles for Time Series Regressions
This work addresses the problem of improving time-series regression accuracy for applications such as traffic forecasting and seismic prediction by introducing a method to encode multiscale data structures, representing an incremental advancement over existing STGNN approaches.
The paper tackles the limitation of fixed graph structures in Spatio-temporal Graph Neural Networks for time-series applications by constructing multiple graphs using Persistent Homology Filtration and using them in an ensemble with attention-based routing. The result is consistent outperformance of single-graph baselines in experiments on seismic activity prediction and traffic forecasting datasets like PEMS-BAY and METR-LA.
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.