Hierarchical clustering of modal ordinal symbolic data objects
Résumé
The problem of analysing the dispersion of a set of objects described by ordinal modal symbolic data is addressed in order to obtain homogeneous groups, which are evaluated by a consensus measure. Based on a generalized @ function a consensus measure for objects and for sets of objects described by modal ordinal data is defined. A variability measure for sets of subsets of objects based in the consensus measure of their members is proposed. A dissimilarity measure between objects and between set of objects based on this consensus variability measure is also given. It is proven that the Leik consensus measure is a @ function. An ascending hierarchical clustering algorithm is presented. The criterion to be minimized in each step is based on the decrease of the consensus variability. An example with modal ordinal data of 34 teachers that were evaluated by their students is presented.