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

Explaining the Power of Topological Data Analysis in Graph Machine Learning