关于有限度量空间的弱isometry概念
On the notion of weak isometry for finite metric spaces
摘要：
有限度量空间是许多数据分析问题的研究对象。我们研究有限度量空间之间弱等距的概念，以分析在距离函数的严格递增重标度下不变的空间的性质。在本文中，我们分析了一些可能的完整和不完整的弱等距不变量，我们介绍了一个相异性措施，评估多远两个空间是弱等距。此外，我们将这些想法与持久同源理论进行比较，以研究两者之间的关系。
英文摘要：
Finite metric spaces are the object of study in many data analysis problems. We examine the concept of weak isometry between finite metric spaces, in order to analyse properties of the spaces that are invariant under strictly increasing rescaling of the distance functions. In this paper, we analyse some of the possible complete and incomplete invariants for weak isometry and we introduce a dissimilarity measure that asses how far two spaces are from being weakly isometric. Furthermore, we compare these ideas with the theory of persistent homology, to study how the two are related.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
