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How to obtain CriterionFunction value in clustering

Mathematica has different related functions to perform clustering including ClusterClassify[] and FindClusters[]. Is it possible to obtain the value of its CriterionFunction?

As a simple example:

data = ExampleData[{"MachineLearning", "FisherIris"}, "Data"];

X = data[[All, 1]];

c = ClusterClassify[X, Method -> "NeighborhoodContraction", CriterionFunction -> "Silhouette"];

I would like to obtain the internal index corresponding to the CriterionFunction used in this case, which is the Silhouette coefficient.

Thanks in advance for any help!

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