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Well, of course density-based clustering validation gives a higher score to a density-based clustering algorithm. For this example, we only know that DBCV gives a better clustering because it's obvious from plotting the data. In ten dimensions, how do you know which algorithm and which metric will give the best result?

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Of course, visualization is infeasible in such cases. So mostly, we prefer dimensionality reduction using techniques like t-SNE. And there is obviously no guidelines on which algo/metric will work better. In case of missing labels, one has to approach with intrinsic measures and in such cases, the evaluation is entirely subjective.

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Hi Jean, where did you find out about this disadvantage of the Silhouette, in what article? I need to cite this in my dissertation.

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