论文标题
多参数持久性简介
An Introduction to Multiparameter Persistence
论文作者
论文摘要
在拓扑数据分析（TDA）中，经常通过构建过滤后的拓扑空间来研究数据的形状，然后使用持久同源性检查其结构。但是，单个过滤空间通常无法充分捕获数据中感兴趣的结构，并且有人被考虑考虑多参数持久性，该持久性将其与配备多参数过滤的数据相关联。多参数持久性已成为TDA中最活跃的研究领域之一，在几个方面取得了令人兴奋的进步。在本文中，我们介绍了多参数的持久性并调查了最近的一些进展，重点是在不久的将来可能导致实际应用的想法。
In topological data analysis (TDA), one often studies the shape of data by constructing a filtered topological space, whose structure is then examined using persistent homology. However, a single filtered space often does not adequately capture the structure of interest in the data, and one is led to consider multiparameter persistence, which associates to the data a space equipped with a multiparameter filtration. Multiparameter persistence has become one of the most active areas of research within TDA, with exciting progress on several fronts. In this article, we introduce multiparameter persistence and survey some of this recent progress, with a focus on ideas likely to lead to practical applications in the near future.
