Topological data analysis (TDA) is a rising field in the intersection of mathematics, statistics, and computer science/data science. The cornerstone of TDA is persistent homology, which produces a summary of topological information called a persistence diagram. To utilize machine and deep learning methods on persistence diagrams, These diagrams are further summarized by transforming them into functions. In this paper we investigate the stability and injectivity of a class of smooth, one-dimensional functional summaries called Gaussian persistence curves.

翻译：地形数据分析(TDA)是数学、统计和计算机科学/数据科学交汇处的一个不断上升的领域,TDA的基石是持久性同系学,它产生一个叫做持久性图的地形信息摘要。为了在持久性图中使用机器和深层学习方法,这些图表通过将其转换为函数而得到进一步总结。在本文中,我们调查了所谓高斯持久性曲线的光滑、单维功能摘要的稳定性和输入性。