# Persistent Homology-induced Graph Ensembles for Time Series Regressions

arXiv: https://arxiv.org/abs/2503.14240 · HTML: https://mlsanity.com/paper/2503.14240/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 39 references that are in the map.
- First posted on arXiv 18 Mar 2025.

## Builds on (most cited first, 16 of 16)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Graph Neural Network for Traffic Forecasting: A Survey](https://mlsanity.com/paper/2101.11174/) (2021)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [1D Convolutional Neural Networks and Applications: A Survey](https://mlsanity.com/paper/1905.03554/) (2019)
- [Pre-training Enhanced Spatial-temporal Graph Neural Network for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2206.09113/) (2022)
- [Fused Gromov-Wasserstein distance for structured objects: theoretical foundations and mathematical properties](https://mlsanity.com/paper/1811.02834/) (2018)
- [Spatio-Temporal Meta-Graph Learning for Traffic Forecasting](https://mlsanity.com/paper/2211.14701/) (2022)
- [A Survey on Graph Structure Learning: Progress and Opportunities](https://mlsanity.com/paper/2103.03036/) (2021)
- [Spatial-Temporal-Decoupled Masked Pre-training for Spatiotemporal Forecasting](https://mlsanity.com/paper/2312.00516/) (2023)
- [Uncovering the Topology of Time-Varying fMRI Data using Cubical Persistence](https://mlsanity.com/paper/2006.07882/) (2020)
- [Graph Neural Networks for Multivariate Time Series Regression with Application to Seismic Data](https://mlsanity.com/paper/2201.00818/) (2022)
- [Boosting Graph Pooling with Persistent Homology](https://mlsanity.com/paper/2402.16346/) (2024)

## Built on by (most cited first, 3 of 3)

- [On topological descriptors for graph products](https://mlsanity.com/paper/2511.08846/) (2025)
- [Do Deep Ensembles Actually Capture Uncertainty in Graph Neural Networks?](https://mlsanity.com/paper/2605.22593/) (2026)
- [TopoCast: A Topological Fidelity Framework for Evaluating Transformer-Based Time Series Forecasting](https://mlsanity.com/paper/2606.25439/) (2026)

## Abstract (arXiv)

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.