A random persistence diagram generator

Theodore Papamarkou; Farzana Nasrin; Austin LawsonNa GongOrlando RiosVasileios Maroulas

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A random persistence diagram generator

机译：A random persistence diagram generator

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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.

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来源
《Statistics and computing》 |2022年第5期|88.1-88.15|共15页
作者
Theodore Papamarkou; Farzana Nasrin; Austin LawsonNa GongOrlando RiosVasileios Maroulas;
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作者单位

University of Tennessee||University of Manchester;

University of Hawai’i;

University of Tennessee;

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原文格式 PDF
正文语种英语
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关键词
Interacting point processes; Topological data analysis; Reversible jump Markov chain Monte Carlo; Materials microstructure analysis;

A random persistence diagram generator

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