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Activity Number: 542 - Advances in Topological and Geometric Data Analysis
Type: Topic Contributed
Date/Time: Thursday, August 11, 2022 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract #322747
Title: Random Persistence Diagram Generation and Materials
Author(s): Vasileios Maroulas and Theodore Papamarkou and Farzana Nasrin and Minh Quang Le*
Companies: University of Tennesse, Knoxville and The University of Manchester and University of Hawaii and University of Tennesse, Knoxville
Keywords: reversible jump MCMC; interacting point process; persistent homology; materials science

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). In this talk, we will discuss a random persistence diagram generation (RPDG) method that generates a sequence of random PDs from the ones produced by the data. RPDG is underpinned by (i) a model based on pairwise interacting point processes for inference of persistence diagrams, and (ii) by a reversible jump Markov chain Monte Carlo (RJ-MCMC) algorithm for generating samples of PDs. A first example, which is based on a synthetic dataset, demonstrates the efficacy of RPDG and provides a detailed comparison with other existing methods for sampling PDs. A second example demonstrates the utility of RPDG to solve a materials science problem given a real dataset of small sample size.

Authors who are presenting talks have a * after their name.

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