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Selecting the Optimal Number of Clusters in K-Means Clustering

There are two main ways to select the optimal number of clusters (kk) for K-means clustering:

  1. Elbow Method: Plot the explained variation as a function of the number of clusters and pick the "elbow" of the curve as the number of clusters to use.
  2. Silhouette Score: Calculated using the silhouette coefficient: xymax(x,y)\frac{x - y}{\max(x, y)} where xx is the mean distance to the instances of the next closest cluster, and yy is the mean distance to the other instances in the same cluster. The kk value with the highest average silhouette score is selected.

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Updated 2026-07-01

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Data Science