I was considering using the silhouette score, however its complexity is $O(mn^2)$ which can quickly become prohibitive with the size of the dataset.
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Are you asking about some internal clustering validation criteria? If yes, see https://stats.stackexchange.com/a/358937/3277. Pay attention to Clalinski-Harabasz, Davies-Bouldin. – ttnphns Sep 20 '18 at 11:31
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Thank you. Are there references listing the complexity of those different validation metrics (my computational ressources are limited...)? – Tanguy Sep 20 '18 at 18:29