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.
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References
BATBEDAT, A. (1989) Les dissimilarités médas ou arbas, Statistique et Analyse des Données 14, 1–18
BATBEDAT, A. (1991) Phylogenie et dendrogrammes, Journées de Statistique, Strasbourg.
BATBEDAT, A. (1992) Les distances quadrangulaires qui ont une orientation, RAIRO-Rech. Oper., 26, 15–29.
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.): ClassifÃcation and Dissimilarity Analysis. Springer-Verlag, Berlin.
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.): ClassifÃcation and Dissimilarity Analysis. Springer-Verlag, Berlin.
DIDAY, E. (1984) Une representation visuelle des classes empiétantes: les pyramides, Research Report No. 291, INRIA-Rocquencourt.
DURAND, C. (1989) Ordres et graphes pseudo-hiérarchiques: théorie et optimisation algorithmique, These de l’Université de Provence, Marseille.
FICHET, B. (1984) Sur une extension des hierarchies et son équivalence avec certaines matrices de Robinson, Journées de Statistique, Montpellier.
LECLERC, B. (1993) Tree-Robinson dissimilarities This volume.
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© 1994 Springer-Verlag Berlin Heidelberg
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Critchley, F. (1994). On quadripolar Robinson dissimilarity matrices. In: Diday, E., Lechevallier, Y., Schader, M., Bertrand, P., Burtschy, B. (eds) New Approaches in Classification and Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51175-2_9
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DOI: https://doi.org/10.1007/978-3-642-51175-2_9
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