Mathematics Colloquium
Farzana Nasrin
University of Hawaii
Title: Title: Random Persistence Diagram Generation
Date: Friday, February 4, 2022
Place and Time: Zoom, 3:05-3:55 pm
Abstract.
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.