A Random Persistence Diagram Generator
Abstract
Topological data analysis (TDA) studies the shape patterns of data. Persistent homology 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 paper, we propose a random persistence diagram generator (RPDG) method that generates a sequence of random PDs from the ones produced by the data. RPDG is underpinned by a model based on pairwise interacting point processes, and a reversible jump Markov chain Monte Carlo (RJ-MCMC) algorithm. A first example, which is based on a synthetic dataset, demonstrates the efficacy of RPDG and provides a comparison with another method 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.
Keywords
Cite
@article{arxiv.2104.07737,
title = {A Random Persistence Diagram Generator},
author = {Theodore Papamarkou and Farzana Nasrin and Austin Lawson and Na Gong and Orlando Rios and Vasileios Maroulas},
journal= {arXiv preprint arXiv:2104.07737},
year = {2022}
}
Comments
17 pages, 6 figures and 3 tables