2021/04/15 by Theodore Papamarkou, Farzana Nasrin, Papamarkou, Theodore +9 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · #55N31 #60G55 #62R40 #Algebraic Topology (math.AT) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Metabolomics and Mass Spectrometry Studies #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2104.07737
openalex publication_date 2021/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.