TY - JOUR
T1 - A random persistence diagram generator
AU - Papamarkou, Theodore
AU - Nasrin, Farzana
AU - Lawson, Austin
AU - Gong, Na
AU - Rios, Orlando
AU - Maroulas, Vasileios
N1 - Funding Information:
The work has been partially supported by the ARO W911NF-21-1-0094 (VM); NSF DMS-2012609 (VM), and ARL Co-operative Agreement # W911NF-19-2-0328 (VM). The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied of the Army Research Laboratory or the US Government. The US Government is authorized to reproduce and distribute reprints for Government purposes not withstanding any copyright notation herein.
Funding Information:
The work has been partially supported by the ARO W911NF-21-1-0094 (VM); NSF DMS-2012609 (VM), and ARL Co-operative Agreement # W911NF-19-2-0328 (VM). The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied of the Army Research Laboratory or the US Government. The US Government is authorized to reproduce and distribute reprints for Government purposes not withstanding any copyright notation herein.
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2022/10/7
Y1 - 2022/10/7
N2 - 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.
AB - 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.
KW - Interacting point processes
KW - Materials microstructure analysis
KW - Reversible jump Markov chain Monte Carlo
KW - Topological data analysis
U2 - 10.1007/s11222-022-10141-y
DO - 10.1007/s11222-022-10141-y
M3 - Article
SN - 0960-3174
VL - 32
JO - Statistics and Computing
JF - Statistics and Computing
IS - 5
M1 - 88
ER -