论文标题
关于有限公制空间的弱等距概念
On the notion of weak isometry for finite metric spaces
论文作者
论文摘要
在许多数据分析问题中，有限的度量空间是研究的对象。我们检查了有限度量空间之间弱等轴测图的概念，以分析在严格增加距离函数重新缩放下不变的空间的性质。在本文中，我们分析了一些弱等轴测图可能的完整且不完整的不变式，并引入了一种差异度措施，该测量方法可以使两个空间距离弱等距较弱。此外，我们将这些思想与持续同源性理论进行了比较，以研究两者的相关性。
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.
