Finding Ultrametricity in Data using Topology

Patrick Erik Bradley ()
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Patrick Erik Bradley: Karlsruher Institut für Technologie (KIT), Institut für Photogrammetrie und Fernerkundung (IPF)

Journal of Classification, 2017, vol. 34, issue 1, No 5, 76-84

Abstract: 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.

Keywords: Ultrametric; Topology; Weibull distribution; Vietoris-Rips graph (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s00357-017-9228-8

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