Dissimilarity functions for rank-invariant hierarchical clustering of continuous variables

A theoretical framework is presented for a (copula-based) notion of dissimilarity between continuous random vectors and its main properties are studied. The proposed assigns the smallest value to pair that comonotonic. Various this studied, with special attention those prone hierarchical agglomerative methods, such as reducibility. Some insights provided use measure in clustering algorithms simulation study presented. Real case studies illustrate features whole methodology.