On the cosine similarity and orthogonality between persistence diagrams
Azmeer Nordin, Mohd Salmi Md Noorani, Nurulkamal Masseran, Mohd Sabri Ismail, Nur Firyal Roslan
拓扑数据分析是一种通过拓扑学研究数据集形状的方法。 它的主要研究对象是持久性图,它代表了数据集在不同空间分辨率下的拓扑特征。 可以通过图表的相似性来比较多个数据集,以了解它们相对于彼此的行为。 瓶颈和Wasserstein距离通常被用作指示相似性的工具。 在本文中,我们介绍了余辛相似性,作为持久性图和调查其属性之间相似性的新指标。 此外,它导致了持久性图之间的正交性的新概念。 事实证明,正交性是指余烬相似性下的持久性图之间的完美差异。 通过数据演示,显微相似性比标准距离更准确,以测量持久性图之间的相似性。
Topological data analysis is an approach to study shape of a data set by means of topology. Its main object of study is the persistence diagram, which represents the topological features of the data set at different spatial resolutions. Multiple data sets can be compared by the similarity of their diagrams to understand their behaviors in relative to each other. The bottleneck and Wasserstein distances are often used as a tool to indicate the similarity. In this paper, we introduce cosine simila...