Abstract
Given the marginal description of two partitionsC andY of the same set, an index of agreement between the two partitions is given by the number of pairs appearing together in an equivalence class in both partitions. LetC be fixed andY an unknown partition represented by its marginal description. We consider the following problem: finding the distribution of objects (conditioned by the marginal description ofY) which maximizes the agreement betweenC andY. We discuss some approaches that have proposed, and we obtain a heuristic procedure from the solution of a linear transportation problem.
Résumé
Soit une mesure d'association entre deux partitions,C etY, du même ensemble. Supposons queC soit fixée et que pourY nous ne possédions que la distribution de ses classes (nombre et taille de chaque classe). Considérons le problème suivant: déterminer la distribution des objets dans les classes deY de façon à maximiser les accords entre les classes deC et celles deY. Nous présentons quelques approches proposées dans la litérature et dérivons une procédure heuristique à partir de la solution d'un problème de transport.
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Messatfa, H. An algorithm to maximize the agreement between partitions. Journal of Classification 9, 5–15 (1992). https://doi.org/10.1007/BF02618465
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DOI: https://doi.org/10.1007/BF02618465