A Random Persistence Diagram Generator

TL;DR

This paper introduces RPDG, a novel method for generating random persistence diagrams using pairwise interacting point processes and RJ-MCMC, useful for data analysis and scientific applications.

Contribution

The paper presents a new probabilistic model and algorithm for sampling persistence diagrams, enhancing topological data analysis capabilities.

Findings

RPDG effectively generates realistic PD samples on synthetic data.

RPDG demonstrates utility in a materials science problem with small sample size.

Comparison shows RPDG outperforms existing sampling methods.

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.