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The Analytical Solution of the Additive Constant Problem

Published online by Cambridge University Press:  01 January 2025

Francis Cailliez
Francis Cailliez*
Affiliation:
Centre Technique Forestier Tropical
*
Reprint requests should be addressed to Francis Cailliez, Centre Technique Forestier Tropical, 45 Bis, avenue de la Belle Gabrielle, 94130 Nogent Sur Marne, France.
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Abstract

If d is a measure of dissimilarity on a finite set with n elements, the smallest positive constant c* such that d + c has an euclidean representation for all c ≥c* is shown to be the largest eigen-value of a matrix of size 2n.

Keywords

additive constantmultidimensional scaling
Type
Notes And Comments
Information
Psychometrika , Volume 48 , Issue 2 , June 1983 , pp. 305 - 308
Copyright
Copyright © 1983 The Psychometric Society

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References

Cailliez, F. & Pagès, J. P. Introduction à L'Analyse des Donnèes. SMASH, 9 rue Duban 75016 Paris, 1976.Google Scholar
de Leeuw, J. & Heiser, W. Theory of multidimensional scaling. In Krishnaiah, P. R. & Kanal, L. N. (Eds.), Handbook of statistics (Vol. 2), Amsterdam: North-Holland Publishing Company, 1982.Google Scholar