# On cophenetic correlation for dendrogram clustering

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 ?

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You don't explain your objection to the (quite intuitive)general idea that any link between the original dissimilarities and the cophenetic dissimilarities could be related to the suitability of the classification. Classification should reflect original dissimilarities. Dendrogramic classification's basic feature to do this is via cophenetic dissimilarity. Is there smth. wrong? –  ttnphns Jul 26 '12 at 11:24
By the way, one should not mix concept of hierarchical (agglometative) clustering with hierarchical (dendrogramic) classification. The clustering produces its dendrogram as a process report; it doesn't claim it to be hierarchical classification result. –  ttnphns Jul 26 '12 at 11:32
Cophenetic correlation was proposed for "dogmatic" classifications only - where the classification should reflect pairwise dissimilarities, thence the notion of usefulness of (cophenetic) correlation follows immideately. –  ttnphns Jul 26 '12 at 11:51
You might want to read this paper on cophenetic correlation –  ttnphns Jul 26 '12 at 11:54
@StéphaneLaurent I have nothing to contribute as an answer to your question but I have been reading the dialog. Nothing you said sounded offensive to me. Also you said you didn't know the difference between classification and clustering and I haven't seen that simple question answered. It is the differece between what the machine learning people call supervised and unsupervised learning. In classification you know all the class labels for your data and use that information to construct a classification rule for future cases that don't have labels. In cluster you have no labelling. –  Michael Chernick Jul 26 '12 at 18:45