The median procedure in cluster analysis and social choice theory |
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Authors: | Jean Pierre Barthelemy Bernard Monjardet |
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Institution: | Ecole Nationale Supérieure des Télécommunications, 46 Rue Barrault, 75013 Paris, France;Université Paris V et Centre de Mathématique Sociale, 54 Boulevard Raspail, 75270 Paris Cedex 06, France |
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Abstract: | Classical approachs for fitting and aggregation problems, specially in cluster analysis, social choice theory and paired comparisons methods, consist in the minimization of a remoteness function between relational data and a relational model. The notion of median, with its algebraic, metric, geometrical and statistical aspects, allow a unified treatment of many of base problems. Properties of median procedures are organized according to four directions: stabilities and axiomatic characterizations; Arrow-like properties; combinatorial properties; effective computational possibilities. Finally, interesting mathematical problems, related to the notion of median are surveyed. |
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Keywords: | Cluster analysis Aggregation Median Social choice theory Distance |
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