A random persistence diagram generator
A random persistence diagram generator
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DOI：
10.1007/s11222-022-10141-y
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发表时间：
2021-04
影响因子：
2.2
通讯作者：
T. Papamarkou;Farzana Nasrin;A. Lawson;Na Gong;Orlando Rios;V. Maroulas
中科院分区：
文献类型：
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作者：
T. Papamarkou;Farzana Nasrin;A. Lawson;Na Gong;Orlando Rios;V. Maroulas
拓扑数据分析(TDA)研究数据的形状模式。持久同源是TDA中广泛使用的一种方法，它总结了数据在多个尺度上的同源特征，并将它们存储在持久图(PD)中。在本文中，我们提出了一种随机持续图生成器(RPDG)方法，它从数据产生的随机持续图序列生成随机持续图序列。RPDG基于两两相互作用的点过程模型和可逆跳跃马尔可夫链蒙特卡罗(RJ-MCMC)算法。第一个例子基于一个合成数据集，它展示了RPDG的有效性，并提供了与另一种抽样PD的方法的比较。第二个例子演示了RPDG在给出一个小样本的真实数据集的情况下解决材料科学问题的实用性。
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.