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Data Analysis, Machine Learning and ApplicationsFamilies of Dendrograms

Data Analysis, Machine Learning and Applications: Families of Dendrograms [A conceptual framework for cluster analysis from the viewpoint of p-adic geometry is introduced by describing the space of all dendrograms for n datapoints and relating it to the moduli space of p-adic Riemannian spheres with punctures using a method recently applied by Murtagh (2004b). This method embeds a dendrogram as a subtree into the Bruhat-Tits tree associated to the p-adic numbers, and goes back to Cornelissen et al. (2001) in p-adic geometry. After explaining the definitions, the concept of classifiers is discussed in the context of moduli spaces, and upper bounds for the number of hidden vertices in dendrograms are given.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Data Analysis, Machine Learning and ApplicationsFamilies of Dendrograms

Editors: Preisach, Christine; Burkhardt, Hans; Schmidt-Thieme, Lars; Decker, Reinhold

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References (10)

Publisher
Springer Berlin Heidelberg
Copyright
© Springer-Verlag Berlin Heidelberg 2008
ISBN
978-3-540-78239-1
Pages
95 –102
DOI
10.1007/978-3-540-78246-9_12
Publisher site
See Chapter on Publisher Site

Abstract

[A conceptual framework for cluster analysis from the viewpoint of p-adic geometry is introduced by describing the space of all dendrograms for n datapoints and relating it to the moduli space of p-adic Riemannian spheres with punctures using a method recently applied by Murtagh (2004b). This method embeds a dendrogram as a subtree into the Bruhat-Tits tree associated to the p-adic numbers, and goes back to Cornelissen et al. (2001) in p-adic geometry. After explaining the definitions, the concept of classifiers is discussed in the context of moduli spaces, and upper bounds for the number of hidden vertices in dendrograms are given.]

Published: Jan 1, 2008

Keywords: Modulus Space; Ultrametric Analysis; Ultrametric Space; Arbitrary Positive Real Number; Projective Linear Transformation

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