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Finding the right number of clusters

Hello,

It depends, *which clustering method you will use*.
Model-based Clustering algorithms have the BIC criterion implemented
(Mclust).
Partition Based clustering algorithms have other criterias (Sum of
Squares withhin and between clusters and you can easely implement other
criterias).
Most of the criterias in fuzzy clustering are very different.
With hierarchical clustering algorithms, you can also determine the
number of cluster, very different from the other methods.
Note that there is no optimal criteria for all these different methods
and it is not so easy to find the optimal number of clusters - the
optimal number of clusters depends on your data and which criteria you
have to use depends also on your data.

Best,
Matthias