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Techniques for Determining Cluster Counts

Stephanie Glen has an image which describes different techniques for figuring out how many clusters you have:

If you want to determine the optimal number of clusters in your analysis, you’re faced with an overwhelming number of (mostly subjective) choices. Note that there’s no “best” method, no “correct” k, and there isn’t even a consensus as to the definition of what a “cluster” is. With that said, this picture focuses on three popular methods that should fit almost every need: Silhouette, Elbow, and Gap Statistic.

Click through for the picture and references.