Abstract
We consider dissimilarities which are defined only on some pairs of items. Such situations may occur in some problems like unfolding or merging, or can be encountered as an intermediate step of a more general transformation. We give necessary and sufficient conditions for the existence of extensions with good properties and characterize the family of such extensions. Using partial dissimilarities we construct a dissimilarity-into-distance transformation family.
Résumé
On s'intéresse aux dissimilarités qui ne sont définies que sur certaines paires d'éléments. Cette situation se rencontre dans certains types de problèmes tel que les déploiments ou les mélanges. Elle peut également intervenir comme une étape intermédiaire d'une transformation plus générale. On donne des conditions nécessaires et suffisantes pour qu'il existe des extensions ayant de bonnes propriétés et on caractérise la famille obtenue. Par l'intermédiaire des dissimilarités partielles on construit une famille de transformation d'une dissimilarité en une distance.
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The author thanks the editor and two anonymous referees for their suggestions and their helpful comments.
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Brossier, G. Partial dissimilarities with application to clustering. Journal of Classification 11, 37–58 (1994). https://doi.org/10.1007/BF01201022
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DOI: https://doi.org/10.1007/BF01201022