Random Persistence Diagram Generation (Virtual)

Topological data analysis (TDA) studies the shape patterns of data. Persistent homology (PH) is a widely used method in TDA that summarizes homological features of data at multiple scales and stores them in persistence diagrams (PDs).

However, a sufficiently large amount of PDs that allow performing statistical analysis is typically unavailable or requires inordinate computational resources.

In this talk, I will present a novel sampling method for random persistence diagram generation (RPDG) that augments topological summaries of the data, thus facilitating statistical inference with a limited amount of data.

RPDG is underpinned by (i) a model based on pairwise interacting point processes for inference of PDs, and (ii) by a reversible jump Markov chain Monte Carlo algorithm for generating samples of PDs. This framework is applicable to a wide variety of datasets. I will present an application to a materials science problem.