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Finding Ultrametricity in Data using Topology

Finding Ultrametricity in Data using Topology 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Classification Springer Journals

Finding Ultrametricity in Data using Topology

Journal of Classification , Volume 34 (1) – Mar 20, 2017

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References (23)

Publisher
Springer Journals
Copyright
Copyright © 2017 by Classification Society of North America
Subject
Statistics; Statistical Theory and Methods; Pattern Recognition; Bioinformatics; Signal,Image and Speech Processing; Psychometrics; Marketing
ISSN
0176-4268
eISSN
1432-1343
DOI
10.1007/s00357-017-9228-8
Publisher site
See Article on Publisher Site

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.

Journal

Journal of ClassificationSpringer Journals

Published: Mar 20, 2017

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