论文标题
贝叶斯的持续图的拓扑特征估计
Bayesian estimation of topological features of persistence diagrams
论文作者
论文摘要
持续的同源性是拓扑数据分析中的一种常见技术，可提供有关样品空间的几何和拓扑信息。所有这些信息（称为拓扑特征）均以持久图总结，主要兴趣是确定最持久的信息，因为它们与Betti数字值相对应。鉴于采样过程中固有的随机性以及持久图的空间的复杂结构为值，因此betti数字的估计并不简单。这项工作中遵循的方法利用了功能的寿命，并根据随机分区提供了完整的贝叶斯聚类模型，以估计贝蒂数字。还提出了一项模拟研究。
Persistent homology is a common technique in topological data analysis providing geometrical and topological information about the sample space. All this information, known as topological features, is summarized in persistence diagrams, and the main interest is in identifying the most persisting ones since they correspond to the Betti number values. Given the randomness inherent in the sampling process, and the complex structure of the space where persistence diagrams take values, estimation of Betti numbers is not straightforward. The approach followed in this work makes use of features' lifetimes and provides a full Bayesian clustering model, based on random partitions, in order to estimate Betti numbers. A simulation study is also presented.
