0.700 0.500 —

Cophenetic Such a matrix is often called a cophenetic matrix (Sokal & Rohlf, 1962; Jain & Dubes, matrix 1988). The ordering of objects in the cophenetic matrix is irrelevant; any order that suits the researcher is acceptable. The same applies to dendrograms; the order of the objects may be changed at will, provided that the dendrogram is redrawn to accommodate the new ordering.

For a partition of the data set (as in the A"-means method, below), the resulting groups of objects are not related through a dendrogram. A cophenetic matrix may nevertheless be obtained. Consider the groups (212, 214) and (233, 431, 432) obtained by cutting the dendrogram of Fig. 8.2 at similarity level S = 0.25, ignoring the hierarchical structure of the two clusters. The cophenetic matrices would be:

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