Families of dendrograms
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.
Cite
@article{arxiv.0707.4072,
title = {Families of dendrograms},
author = {Patrick Erik Bradley},
journal= {arXiv preprint arXiv:0707.4072},
year = {2009}
}
Comments
7 pages, 3 figures. To appear in: Proceedings of the 31st Annual Conference of the German Classification Society on Data Analysis, Machine Learning, and Applications, Freiburg im Breisgau, 7-9 March 2007. Springer series Studies in Classification, Data Analysis, and Knowledge Organization