Advertisement

Families of Dendrograms

  • Patrick Erik Bradley
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

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.

Keywords

Modulus Space Ultrametric Analysis Ultrametric Space Arbitrary Positive Real Number Projective Linear Transformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. BERKOVICH, V.G. (1990): Spectral Theory and Analytic Geometry over Non-Archimedean Fields. Mathematical Surveys and Monographs, 33, AMS.Google Scholar
  2. BRADLEY, P.E. (2006): Degenerating families of dendrograms. Preprint. BRADLEY, P.E. (2007): Mumford dendrograms. Preprint.Google Scholar
  3. CORNELISSEN, G. and KATO, F. (2005): The p-adic icosahedron. Notices of the AMS, 52, 720-727.zbMATHMathSciNetGoogle Scholar
  4. CORNELISSEN, G., KATO, F. and KONTOGEORGIS, A. (2001): Discontinuous groups in positive characteristic and automorphisms of Mumford curves. Mathematische Annalen, 320,55-85.zbMATHCrossRefMathSciNetGoogle Scholar
  5. DRAGOVICH, B. AND DRAGOVICH, A. (2006): A p-Adic Model of DNA-Sequence and Genetic Code. Preprint arXiv:q-bio.GN/0607018.Google Scholar
  6. GOUVÊA, F.Q. (2003): p-adic numbers: an introduction. Universitext, Springer.Google Scholar
  7. HERRLICH, F (1980): Endlich erzeugbare p-adische diskontinuierliche Gruppen. Archiv der Mathematik, 35, 505-515.zbMATHCrossRefMathSciNetGoogle Scholar
  8. MURTAGH, F. (2004): On ultrametricity, data coding, and computation. Journal of Classifi-cation, 21, 167-184.zbMATHMathSciNetGoogle Scholar
  9. MURTAGH, F. (2004): Thinking ultrametrically. In: D. Banks, L. House, F.R. McMorris, P. Arabie, and W. Gaul (Eds.): Classification, Clustering and Data Mining, Springer, 3-14.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Patrick Erik Bradley
    • 1
  1. 1.Institut für Industrielle BauproduktionKarlsruheGermany

Personalised recommendations