A new non-archimedean metric on persistent homology

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 together with the and hierarchical clustering algorithms number different metrics do deliver statistically verifiable commensurate topological information based experimental results obtained datasets. also observe resulting clusters coming from distance shine in terms evaluation measures such as silhouette score Rand index. Moreover, since is defined for degrees, one can now display inter-relations degrees via rooted trees.