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There are many cluster validity index (cvi) requiring the global mean in their calculations, such as the Calinski-Harabasz index. I was wondering is this type of cvis applicable to k-medoids clustering? If yes, should the global mean or the global medoid be used in the calculation of these cvis?

Much appreciated for any answers!

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  • $\begingroup$ You can and may assess any cluster solution produced by any clustering method with thre CH or a similar criterion, if the variables are continuous/interval or the distance matrix (if it is the matrix what you have) is euclidean distances. But keep in mind that (as Anony-Mousse said) the optimality function assessed by those criteria, the between/within squared scatter, is quite different from the function that k-medoid method tried to optimize producing the cluster solution. K-means would be another story: almost corresponding function. $\endgroup$ – ttnphns Jul 29 at 16:09
  • $\begingroup$ Imagine you have such data with many data points so that cluster and the global medoids are close to the corresponding means. Then you might apply CH or such without asking. But then you might have been using k-means as well, probably... $\endgroup$ – ttnphns Jul 29 at 16:16
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The mean is the optimal estimator of locality for squared errors.

So it is the best estimate of a set of points for minimizing squared Euclidean distances, as done in k-means.

It's not the point with the smallest Euclidean distances (that would be the Weber point) nor the optimum point for most other distances.

Hence, using the cluster mean with other distances is questionable in my opinion...

If you want to evaluate k-medoids, choosing the medoids of the entire data set is a reasonable replacement.

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