A random persistence diagram generator

Theodore Papamarkou, Farzana Nasrin, Austin Lawson, Na Gong, Orlando Rios, Vasileios Maroulas

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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.

Original languageEnglish
Article number88
JournalStatistics and Computing
Volume32
Issue number5
DOIs
Publication statusPublished - 7 Oct 2022

Keywords

  • Interacting point processes
  • Materials microstructure analysis
  • Reversible jump Markov chain Monte Carlo
  • Topological data analysis

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