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An order-theoretic unification and generalisation of certain fundamental bijections in mathematical classification. II

  • Frank Critchley
  • Bernard Van Cutsem
Part of the Lecture Notes in Statistics book series (LNS, volume 93)

Abstract

In chapter 4 of this book, the simple but general Theorem 4.5.1 was established and shown to have a variety of important applications in mathematical classification. In particular, it was seen to unify and generalise four bijections reported in the literature concerning dendrograms and generalised dendrograms, numerically stratified clusterings and residual maps

Keywords

Nonempty Subset Level Foliation Dual Result Follow Diagram Commute Proper Filter 
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.

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References

  1. Coppi, R., Bolasco, S. (1989), Multiway Data Analysis, North-Holland, Amsterdam.MATHGoogle Scholar
  2. Critchley, F. (1983), Ziggurats and dendrograms, Warwick Statistics Research Report n° 43, U.K.Google Scholar
  3. Critchley, F., Van Cutsem, B. (1992), An order-theoretic unification and generalisation of certain fundamental bijections in mathematical classification — II, Joint Research Report, University of Warwick, U.K., and Université Joseph Fourier, Grenoble, France.Google Scholar
  4. Critchley, F., Van Cutsem, B. (1994), An order-theoretic unification and generalisation of certain fundamental bijections in mathematical classification — I, In Van Cutsem, B., ed., Classification and Dissimilarity Analysis, Ch. 4, Lecture Notes in Statistics, Springer-Verlag, New York.Google Scholar
  5. Jardine, N., Sibson, R. (1971), Mathematical Taxonomy, Wiley, London.MATHGoogle Scholar
  6. Van Cutsem, B. (1983a), Décomposition D’une ultramétrique: ultrametriques simples et semi-simples, Rapport de Recherche nº 388, Laboratoire IMAG, Grenoble, FranceGoogle Scholar
  7. Van Cutsem, B. (1983b), Ultramétriques, distances, ø-distances maximum dominées par une dissimilarite donnee, Statist. Anal. Données, 8, pp. 42–63MATHGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1994

Authors and Affiliations

  • Frank Critchley
    • 1
  • Bernard Van Cutsem
    • 2
  1. 1.University of BirminghamUK
  2. 2.Université Joseph FourierGrenobleFrance

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