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

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). 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 (RJMCMC) 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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