论文标题
高斯持久性曲线
Gaussian Persistence Curves
论文作者
论文摘要
拓扑数据分析（TDA）是数学，统计和计算机科学/数据科学交集的上升领域。 TDA的基石是持续的同源性，它产生了称为持久图的拓扑信息的摘要。为了利用机器和深度学习方法，通过将它们转换为函数，进一步总结了这些图。在本文中，我们研究了一类平滑的一维功能摘要的稳定性和注入性，称为高斯持久性曲线。
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.
