A Stopping Rule and Clustering Method of Wide Applicability

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Abstract
A new method for determining the number of groups in a numerical classification is proposed. Extensive tests of the criterion for the correct or optimum number of groups are reported. The criterion may be used with any definition of similarity whose possible values are bounded by zero and unity, and with any agglomerative clustering method, whether it be hierarchical or nonhierarchical. It may also be used in conjunction with divisive clustering methods for which the similarity coefficients can conveniently be obtained. The procedure is based on the average similarity of an individual with the members of its group, including itself, and readily lends itself to interactive computation if one wishes to find the partition that maximizes the overall average similarity for a given number of groups. In that sense, the procedure may also be considered to be a clustering method.