Consider the context of a dendrogram clustering. Let us call original dissimilarities the distances between the individuals. After constructing the dendrogram we define the cophenetic dissimilarity between two individuals as the distance between the clusters to which these individuals belong.
Some people consider that the correlation between the original dissimilarities and the cophenetic dissimilarities (called cophenetic correlation) is a "suitability index" of the classification. This sounds totally puzzling to me. My objection does not rely on the particular choice of the Pearson correlation, but on the general idea that any link between the original dissimilarities and the cophenetic dissimilarities could be related to the suitability of the classification.
Do you agree with me, or could you present some argument supporting the use of the cophenetic correlation as a suitability index for the dendrogram classification ?