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Finding Ultrametricity in Data using Topology

Author

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  • Patrick Erik Bradley

    (Karlsruher Institut für Technologie (KIT), Institut für Photogrammetrie und Fernerkundung (IPF))

Abstract

The topological ultrametricity index can be approximated by the expected survival time of a dataset in the state of being ultrametric while only distances up to a given value are considered. It is observed that the quotient of the number of connected components by the number of maximal cliques in the Vietoris-Rips graph initially is the survival function of a Weibull distribution. This is shown for some codings of Fisher’s Iris data as well as for random samples in the Euclidean hypercube.

Suggested Citation

  • Patrick Erik Bradley, 2017. "Finding Ultrametricity in Data using Topology," Journal of Classification, Springer;The Classification Society, vol. 34(1), pages 76-84, April.
    • Handle: RePEc:spr:jclass:v:34:y:2017:i:1:d:10.1007_s00357-017-9228-8
    DOI: 10.1007/s00357-017-9228-8
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    References listed on IDEAS

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    1. Fionn Murtagh, 2004. "On Ultrametricity, Data Coding, and Computation," Journal of Classification, Springer;The Classification Society, vol. 21(2), pages 167-184, September.
    2. Patrick Bradley, 2008. "Degenerating Families of Dendrograms," Journal of Classification, Springer;The Classification Society, vol. 25(1), pages 27-42, June.
    3. Fionn Murtagh, 2009. "The Remarkable Simplicity of Very High Dimensional Data: Application of Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 26(3), pages 249-277, December.
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    Cited by:

    1. Douglas L. Steinley, 2019. "Editorial: Journal of Classification Vol. 36–2," Journal of Classification, Springer;The Classification Society, vol. 36(2), pages 175-176, July.
    2. Patrick Erik Bradley, 2019. "On the Logistic Behaviour of the Topological Ultrametricity of Data," Journal of Classification, Springer;The Classification Society, vol. 36(2), pages 266-276, July.

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