Cophenetic matrix

Cophenetic The cophenetic similarity (or distance) of two objects x1 and x2 is defined as the similarity similarity (or distance) level at which objects x1 and x2 become members of the same cluster during the course of clustering (Jain & Dubes, 1988), as depicted by connected subgraphs or a dendrogram (Fig. 2a, b). Any dendrogram can be uniquely represented by a matrix in which the similarity (or distance) for a pair of objects is their cophenetic similarity (or distance). Consider the single linkage clustering dendrogram of Fig. 8.2. The clustering levels, read directly on the dendrogram, lead to the following matrices of similarity (S) and distance (D, where D = 1 - S):

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