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A Contribution to the Study of the Metric and Euclidean Structures of Dissimilarities

Published online by Cambridge University Press:  01 January 2025

Francis Caillez  and
Pascale Kuntz
Francis Caillez
Affiliation:
Institut National de la Recherche Agronomique
Pascale Kuntz*
Affiliation:
Ecole Nationale Supérieure des Télécommunications de Bretagne
*
Requests for reprints should be sent to Pascale Kuntz, Ecole Nationale Suprrieure des Trlrcommunications de Bretagne, BP 832, 29285 BREST Cedex, FRANCE.
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Abstract

This paper is concerned with the geometric properties of dissimilarity coefficients defined on finite sets and especially with their Euclidean nature. We present several particular transformations which preserve Euclideanarity and we complete, through the study of a one-parameter family, the current knowledge of the metric and Euclidean structure of coefficients based on binary data. These results are directly deduced from two theorems which prove the positive semi-definite status of some quadratic forms which play a large role in some definitions of dissimilarity commonly used.

Keywords

dissimilaritymetricEuclidean representationpositive semidefinite matricesmetric transformations
Type
Original Paper
Information
Psychometrika , Volume 61 , Issue 2 , June 1996 , pp. 241 - 253
Copyright
Copyright © 1996 The Psychometric Society

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Footnotes

The authors wish to thank B. Fichet for his helpful suggestions, the associate Editor and an anonymous reviewer for comments and highly constructive criticisms on earlier drafts of the paper.

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