Abstract
Combinatorial cluster analysis includes the single linkage, complete linkage, and other methods, all of which arrange individuals as a dendrogram. Consider the application of any of these methods to a set of n individuals, which are represented by points in m-dimensional Euclidean space Rm. Suppose that the positions of n- individuals are fixed, but that one is allowed to vary. Then the form of the resulting dendrogram depends on the position of the n-th individual. We show that the different possible forms divide Rm into domains; within each domain, the lengths assigned to individuals vary, and therefore the clusters will differ. The domains are bounded by m-dimensional spheres and (m-1)-dimensional hyperplanes.
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