We define a new distance measure for ranking data by using a mixture of copula functions. This distance evaluates the dissimilarity between subjects expressing their preferences by rankings in order to segment them by hierarchical cluster analysis. The proposed distance builds upon the Spearman’s grade correlation coefficient on a transformation, operated by the copula function, of the rank denoting the leveloftheimportanceassignedbysubjectsunderclassificationtokobjects. Themixturesofcopulaeareaflexiblewaytomodeldifferenttypesofdependencestructuresin thedataandtoconsiderdifferentsituationsintheclassificationprocess. For example, by using mixtures of copulae with lower and upper tail dependence,we emphasize the agreement on extreme ranks, when extreme ranks are considered more important.
Bonanomi, A., Nai Ruscone, M., Osmetti, S. A., MIXTURE OF COPULAE BASED APPROACH FOR DEFINING THE SUBJECTS DISTANCE IN CLUSTER ANALYSIS, in Cladag 2017 Book of Short Papers, (Milano, Università di Milano Bicocca, 13-15 September 2017), Universitas Studiorum S.r.l. Casa Editrice, Mantova 2017: 1-4 [http://hdl.handle.net/10807/120365]
MIXTURE OF COPULAE BASED APPROACH FOR DEFINING THE SUBJECTS DISTANCE IN CLUSTER ANALYSIS
Bonanomi, Andrea;Osmetti, Silvia Angela
2017
Abstract
We define a new distance measure for ranking data by using a mixture of copula functions. This distance evaluates the dissimilarity between subjects expressing their preferences by rankings in order to segment them by hierarchical cluster analysis. The proposed distance builds upon the Spearman’s grade correlation coefficient on a transformation, operated by the copula function, of the rank denoting the leveloftheimportanceassignedbysubjectsunderclassificationtokobjects. Themixturesofcopulaeareaflexiblewaytomodeldifferenttypesofdependencestructuresin thedataandtoconsiderdifferentsituationsintheclassificationprocess. For example, by using mixtures of copulae with lower and upper tail dependence,we emphasize the agreement on extreme ranks, when extreme ranks are considered more important.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.