A Random Persistence Diagram Generator
This work addresses a specific need in topological data analysis for generating random persistence diagrams, which is incremental as it builds on existing methods for sampling persistence diagrams.
The authors tackled the problem of generating random persistence diagrams from data in topological data analysis by proposing a random persistence diagram generator method based on pairwise interacting point processes and a reversible jump Markov chain Monte Carlo algorithm, demonstrating its efficacy on a synthetic dataset and utility in a materials science problem with a small real dataset.
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.