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.

翻译：地形数据分析(TDA)研究数据的形状模式。持久性同系物是TDA广泛使用的一种方法,它总结了多种尺度数据的同质特征,并将其储存在持久性图示(PDs)中。在本文中,我们建议采用随机持久性图示生成器(RPDG)方法,从数据产生的数据中产生随机的PD序列。RPDG以基于双向相互作用点过程的模型和可逆跳的马尔科夫链-蒙特卡洛(RJ-MC)算法(RJ-MC)为基础。第一个例子是以合成数据集为基础的,它展示了RPDG的功效,并提供了与另一种样本PDs方法的比较。第二个例子是RPDG在解决材料科学问题的有用性,因为实际的样本规模较小。