# Explaining the Power of Topological Data Analysis in Graph Machine Learning

arXiv: https://arxiv.org/abs/2401.04250 · HTML: https://mlsanity.com/paper/2401.04250/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 66 references that are in the map.
- First posted on arXiv 8 Jan 2024.

## Builds on (most cited first, 24 of 24)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Adversarial Attacks on Neural Networks for Graph Data](https://mlsanity.com/paper/1805.07984/) (2018)
- [Techniques for Interpretable Machine Learning](https://mlsanity.com/paper/1808.00033/) (2018)
- [A Survey on Graph Kernels](https://mlsanity.com/paper/1903.11835/) (2019)
- [A roadmap for the computation of persistent homology](https://mlsanity.com/paper/1506.08903/) (2015)
- [Ripser: efficient computation of Vietoris-Rips persistence barcodes](https://mlsanity.com/paper/1908.02518/) (2019)
- [Deep Learning with Topological Signatures](https://mlsanity.com/paper/1707.04041/) (2017)
- [Learning metrics for persistence-based summaries and applications for graph classification](https://mlsanity.com/paper/1904.12189/) (2019)
- [Graph Kernels: A Survey](https://mlsanity.com/paper/1904.12218/) (2019)
- [Stochastic Convergence of Persistence Landscapes and Silhouettes](https://mlsanity.com/paper/1312.0308/) (2013)
- [Convolutional Kernel Networks for Graph-Structured Data](https://mlsanity.com/paper/2003.05189/) (2020)
- [Beyond Deep Residual Learning for Image Restoration: Persistent Homology-Guided Manifold Simplification](https://mlsanity.com/paper/1611.06345/) (2016)
- [RipsNet: a general architecture for fast and robust estimation of the persistent homology of point clouds](https://mlsanity.com/paper/2202.01725/) (2022)
- [Approximated and User Steerable tSNE for Progressive Visual Analytics](https://mlsanity.com/paper/1512.01655/) (2015)
- [The Power of the Weisfeiler-Leman Algorithm for Machine Learning with Graphs](https://mlsanity.com/paper/2105.05911/) (2021)
- [Revisiting Robustness in Graph Machine Learning](https://mlsanity.com/paper/2305.00851/) (2023)
- [Using persistent homology and dynamical distances to analyze protein binding](https://mlsanity.com/paper/1412.1394/) (2014)
- [Graph Kernel Neural Networks](https://mlsanity.com/paper/2112.07436/) (2021)
- [Harnessing the power of Topological Data Analysis to detect change points in time series](https://mlsanity.com/paper/1910.12939/) (2019)
- [Reduction Algorithms for Persistence Diagrams of Networks: CoralTDA and PrunIT](https://mlsanity.com/paper/2211.13708/) (2022)

## Built on by (most cited first, 1 of 1)

- [PHLP: Sole Persistent Homology for Link Prediction - Interpretable Feature Extraction](https://mlsanity.com/paper/2404.15225/) (2024)

## Abstract (arXiv)

Topological Data Analysis (TDA) has been praised by researchers for its ability to capture intricate shapes and structures within data. TDA is considered robust in handling noisy and high-dimensional datasets, and its interpretability is believed to promote an intuitive understanding of model behavior. However, claims regarding the power and usefulness of TDA have only been partially tested in application domains where TDA-based models are compared to other graph machine learning approaches, such as graph neural networks. We meticulously test claims on TDA through a comprehensive set of experiments and validate their merits. Our results affirm TDA's robustness against outliers and its interpretability, aligning with proponents' arguments. However, we find that TDA does not significantly enhance the predictive power of existing methods in our specific experiments, while incurring significant computational costs. We investigate phenomena related to graph characteristics, such as small diameters and high clustering coefficients, to mitigate the computational expenses of TDA computations. Our results offer valuable perspectives on integrating TDA into graph machine learning tasks.