Stability analysis of intersection graphs and it’s application for hyperparameter tuning in TDA Mapper

TDA Mapper (also referred to as topological data visualisation or topological clustering), is a method that yields an approximation of a Reeb graph of a data manifold, and has been used successfully in applications across different fields over several last decades.

In spite of TDA Mapper showing great promise, it's wide spread adoption has been limited. This is primarily due to practioners' ad-hoc approach to parameter tuning.

This is unsurprising, since all unsupervised learning algorithms face the same issue due to absence of ground truth labels, and TDA Mapper even more so, due to existence of hyper parameters along with parameters. Model selection is, therefore, highly non-trivial.

In this talk I will present stability analysis as a systematic tool for hyper-parameter tuning on Mapper Graphs, discuss appropriate distance metrics on these mathematical structures, and conclude with few applications.