Mixture of copulae based approach for defining the subjects distance in cluster analysis

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 level of the importance assigned by subjects under classification to k objects. The mixtures of copulae are a flexible way to model different types of dependence structures in the data and to consider different situations in the classification process. 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