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I applied the same hierarchical clustering (weighted) on two data sets: The first is a 'raw' data set, on which I didn't do anything, and the second on the same data set after I filtered it by removing some items I believe mislead the clustering. I computed the cophenetic correlation coefficients on both methods. But is this relevant? Given that the data sets are linked, but different.

Also, I read that 'This coefficient has also been proposed for use as a test for nested clusters'. Is there a method using the cophenetic correlation coefficient to know whether a cluster could be further divided into more clusters?

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