A new non-archimedean metric on persistent homology

İsmail Güzel*, Atabey Kaygun

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1963-1983
Number of pages21
JournalComputational Statistics
Volume37
Issue number4
DOIs
Publication statusPublished - Sept 2022

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

Funding

The first author was supported by Research Fund Project Number TDK-2020-42698 of the Istanbul Technical University.

FundersFunder number
Istanbul Teknik Üniversitesi

    Keywords

    • Cophenetic distance
    • Hierarchical clustering
    • Machine learning
    • Persistent homology
    • Topological data analysis

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