Explaining the Power of Topological Data Analysis in Graph Machine Learning

TL;DR

This paper rigorously evaluates the strengths and limitations of Topological Data Analysis in graph machine learning, confirming its robustness and interpretability but highlighting its limited impact on predictive accuracy and high computational costs.

Contribution

It provides a comprehensive experimental validation of TDA's claims, analyzing its performance, computational challenges, and potential integration strategies in graph learning.

Findings

TDA is robust against outliers and interpretable.

TDA does not significantly improve predictive accuracy in tested scenarios.

TDA incurs high computational costs, especially with certain graph characteristics.

Abstract

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.