论文标题
关于持续同源性的新的非架构的指标
A New Non-archimedean Metric on Persistent Homology
论文作者
论文摘要
在本文中，我们定义了一种关于所有程度的持续同源类别的新的非一切型公制结构，称为Cophenetic Metric。然后，我们表明零持续的同源性以及具有许多不同指标的辅助度量和分层聚类算法的确提供了基于我们在不同数据集中获得的实验结果提供统计上可验证的相应拓扑信息。我们还观察到，来自辅助距离的产生簇确实会以不同的评估措施（例如轮廓分数和兰德指数）的方式发光。此外，由于为所有同源度定义了cophenetic度量，因此现在可以通过根树在所有程度上显示持续的同源性类别的相互关系。
In this article, we define a new non-archimedean metric structure, called cophenetic metric, on persistent homology classes of all degrees. We then show that zeroth persistent homology together with the cophenetic metric and hierarchical clustering algorithms with a number of different metrics do deliver statistically verifiable commensurate topological information based on experimental results we obtained on different datasets. We also observe that the resulting clusters coming from cophenetic distance do shine in terms of different evaluation measures such as silhouette score and the Rand index. Moreover, since the cophenetic metric is defined for all homology degrees, one can now display the inter-relations of persistent homology classes in all degrees via rooted trees.
