Dissimilarites de type spherique et positionnement multidimensionnel normé

Issue		RAIRO Oper. Res. Volume 33, Number 4, October-December 1999


Page(s)		569 - 581
DOI		10.1051/ro:1999124

DOI: 10.1051/ro:1999124

RAIRO Rech. Opér. (vol. 33, n $^\circ$ 4, 1999, pp. 569-581)

Dissimilarites de type spherique et positionnement multidimensionnel normé

Farid Beninel

IUT Departement STID, Centre d'Activites de Noron, Université de Poitiers, 8 rue Archimede, 79000 Niort.

Abstract:

Our concern here, is the characterization of dissimilarity indexes defined over finite sets, whose spatial representation is spherical. Consequently, we propose a methodology (Normed MultiDimensional Scaling) to determine the spherical euclidean representation of a set of items best accounting for the initial dissimilarity between items. This methodology has the advantage of being graphically readable on individual qualities of projection like the normed PCA, of which it constitutes a generalization. Moreover, it avoids the arbitrary character of spherical encoding which the use of similitude functions currently used in MDS, implies.

Résumé:

On s'interesse a la caracterisation des mesures de dissimilarite sur ensembles finis admettant une representation euclidienne spherique. On propose, en consequence, une methodologie de determination de la representation euclidienne spherique associee a un ensemble d'items et restituant au mieux les dissimilarites inter items. Cette methodologie presente l'avantage de la lisibilite graphique des qualites individuelles de projection a l'instar de l'ACP normee dont elle constitue une generalisation. En outre, elle evite l'arbitraire du codage spherique que suppose l'usage des fonctions de similitude couramment utilisees en MDS.

Keywords: Dissimilarity, Euclidean image, MDS, metric analysis, spherical dissimilarity, Euclidean transformation, similitude functions.

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