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Beyond visual inspection, '''internal validation metrics''' can provide more objective guidance:
* '''Elbow Method''': By plotting a measure of within-cluster variation against the number of clusters, the
* '''Silhouette Score''': This evaluates how similar a data point is to its own cluster compared to other clusters. Higher average silhouette scores indicate better-defined clusters.
* '''Gap Statistic''': This compares the observed within-cluster dispersion to that expected under a null reference distribution. The optimal number of clusters is often where the gap statistic is highest, adjusted for variability.
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