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I've been using the CH criterion to determine the optimal number of clusters for some data I'm working with. I know that in general you would evaluate the criterion for a number of different choices of clusters, and choose the number of clusters which gives the highest CH value, or one where there is a large increase in CH score.

For my data, the optimal number of clusters is 2. Plotting the CH score against number of clusters, I can see the score decreases very quickly if you increase the number of clusters.

My question is this: Since the CH criterion does not evaluate for 1 cluster, how can I be sure using 2 clusters is better than one cluster? I.e how can one determine if there is evidence for any clustering at all in the data?

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