Abstract
We consider two or more ultrametric distance matrices defined over different, possibly overlapping, subsets. These matrices are merged into one ultrametric matrix defined over the whole set. Necessary and sufficient conditions for uniqueness of the merging are established. when these conditions are not satisfied, consistent algorithms are given.
Resume
Etant données au moins deux matrices de distances ultramétriques définies sur des sous-ensembles disjoints ou non, on les fusionne pour obtenir une ultramétrique définie sur l'ensemble tout entier. On donne des conditions nécessaires et suffisantes pour que l'extension soit unique. Quand ces conditions ne sont pas satisfaites on donne des algorithmes dont on montre qu'ils sont consistants.
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References
BARTHELEMY, J. P., LECLERC, B., and MONJARDET, B. (1986), “On the Use of Ordered Sets in Problems of Comparison and Consensus of Classifications,”Journal of Classification, 3, 187–224.
BARTHELEMY, J. P., and GUENOCHE, A. (1988),Les Arbres et les Representations des Proximités, Paris: Masson.
BROSSIER, G. (1986), “Etudes des Matrices de Proximité Rectangulaires en vue de la Classification,”Revue de Statistique Appliquée, XXXV, 43–68.
COOMBS, C. H. (1964),A Theory of Data, New York: Wiley.
DE SOETE, G., DESARBO, W. S., FURNAS, G. W., and CARROLL, J. D. (1984), “The Estimation of Ultrametric and Path Length Tress from Rectangular Proximity Data,”Psychometrika, 49, 289–310.
FURNAS, G. W. (1980), “Objects and Their Features: The Metric Representation of Two-Class Data,” Unpublished Ph.D. Dissertation, Stanford University.
GORDON, A. D. (1986), “Consensus Supertrees: The Synthesis of Rooted Trees Containing Overlapping Sets of Labeled Leaves,”Journal of Classification, 3, 335–348.
JAMBU, M., and LEBEAUX, M. O. (1983),Cluster Analysis and Data Analysis, Amsterdam: North-Holland.
ZUPAN, J. (1982),Clustering of Large Data Sets, Letchworth: Research Studies Press.
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The author thanks B. Monjardet and two anonymous referees for their helpful comments.
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Brossier, G. Piecewise hierarchical clustering. Journal of Classification 7, 197–216 (1990). https://doi.org/10.1007/BF01908716
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DOI: https://doi.org/10.1007/BF01908716