In this chapter, we discuss applications of topological data analysis (TDA) to spatial systems. We briefly review the recently proposed level-set construction of filtered simplicial complexes, and we then examine persistent homology in two cases studies: street networks in Shanghai and hotspots of COVID-19 infections. We then summarize our results and provide an outlook on TDA in spatial systems.

中文翻译：

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空间系统的拓扑数据分析

在本章中，我们讨论了拓扑数据分析（TDA）在空间系统中的应用。我们简要回顾了最近提出的过滤简单复合体的水平集构造，然后在两个案例研究中研究了持久的同源性：上海的街道网络和COVID-19感染的热点。然后，我们总结我们的结果，并对空间系统中的TDA进行展望。