ABSTRACT
This chapter presents a divisive top-down clustering method designed for histogram-valued data. The method provides a hierarchy on a set of units together with a characterization of each cluster in the form of a conjunction of properties on the descriptive variables, which are necessary and sufficient conditions for cluster belonging (monothetic clustering). At each step, a cluster is chosen to be split, to minimize intra-cluster dispersion, which is measured by the sum of squared Mallows distances between pairs of members of each cluster. The criterion is minimized across the bipartitions induced by a set of binary questions. Since interval-valued variables constitute a special case of histogram-valued variables, the method applies to data described by either kind of variables. An application illustrates the proposed approach.
