On quadripolar Robinson dissimilarity matrices

  • Frank Critchley
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Summary

The class of quadripolar Robinson dissimilarity matrices is studied. The additive tree visual representation of such matrices is generally to be preferred. Local and global characterisations are described, as well as links between them. The local characterisation is given in terms of sub-matrices of order four. There are only three possible types of such sub-matrix and, allowing for a certain natural duality, only seven essentially different sub-matrices of order five. The global characterisation rests on the idea of connected external exchangeability. Visual displays are used for illustration throughout.

Keywords

Pyramid Suffix Furnas 

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References

  1. BATBEDAT, A. (1989) Les dissimilarités médas ou arbas, Statistique et Analyse des Données 14, 1–18 Google Scholar
  2. BATBEDAT, A. (1991) Phylogenie et dendrogrammes, Journées de Statistique, Strasbourg.Google Scholar
  3. BATBEDAT, A. (1992) Les distances quadrangulaires qui ont une orientation, RAIRO-Rech. Oper., 26, 15–29.Google Scholar
  4. CRITCHLEY, F. (1993) On exchangeability-based equivalence relations induced by strongly Robinson and, in particular, by quadripolar Robinson dissimilarity matrices. To appear in: B. Van Cutsem (ed.): Classifícation and Dissimilarity Analysis. Springer-Verlag, Berlin.Google Scholar
  5. CRITCHLEY, F. and FICHET, B. (1993) The partial order by inclusion of the principal classes of dissimilarity on a finite set and some of their basic properties. To appear in: B. Van Cutsem (ed.): Classifícation and Dissimilarity Analysis. Springer-Verlag, Berlin.Google Scholar
  6. DIDAY, E. (1984) Une representation visuelle des classes empiétantes: les pyramides, Research Report No. 291, INRIA-Rocquencourt.Google Scholar
  7. DURAND, C. (1989) Ordres et graphes pseudo-hiérarchiques: théorie et optimisation algorithmique, These de l’Université de Provence, Marseille.Google Scholar
  8. FICHET, B. (1984) Sur une extension des hierarchies et son équivalence avec certaines matrices de Robinson, Journées de Statistique, Montpellier.Google Scholar
  9. LECLERC, B. (1993) Tree-Robinson dissimilarities This volume. Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Frank Critchley
    • 1
  1. 1.School of Mathematics and StatisticsUniversity of BirminghamBirminghamUK

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