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In this paper we propose a divisive top-down clustering method designed for interval and histogram-valued data. The method provides a hierarchy on a set of objects together with a monothetic characterization of each formed cluster. At each step, a cluster is split so as to minimize intra-cluster dispersion, which is measured using a distance suitable for the considered variable types. The criterion is minimized across the bipartitions induced by a set of binary questions. Since interval-valued variables may be considered a special case of histogram-valued variables, the method applies to data described by either kind of variables, or by variables of both types. An example illustrates the proposed approach.

DIVISIVE MONOTHETIC CLUSTERING FOR INTERVAL AND HISTOGRAM-VALUED DATA