On the number of clusters

A large number of classification and clustering methods for defining and calculating optimal or well-suited partitions for data sets are available. Perhaps the most difficult problem facing the user of cluster analysis techniques in practice is the objective assessment of the stability and validity of the clusters found by the numerical technique used. The problem of determining the ''true'' number of clusters has been called the fundamental problem of cluster validity. The aim of this paper is to compare three methods based on the hypervolume criterion with other well-known methods. To illustrate and compare their behaviour, these procedures for determining the number of clusters are applied to artificially constructed bivariate data containing various types of structure. To provide a variety of solutions six clustering methods are used. We finally conclude by pointing out the performance of each method and by giving some recommendations to help potential users of these techniques.