Clustering - Silhouette Score

The Silhouette Score is a metric used to evaluate the quality of a clustering result. It measures how well each data point fits within its assigned cluster compared to other clusters.

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🔍 What does the Silhouette Score tell you?

For each data point, the silhouette value combines two ideas:

1. Cohesion (a)

   • How close the point is to other points in its own cluster.

   • Lower distance = better cohesion.

2. Separation (b)

   • How far the point is from points in the nearest other cluster.

   • Higher distance = better separation.

The silhouette value for a point is:

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📏 Range of the Silhouette Score

• +1 → Excellent clustering
  (Well-separated clusters; point is far from other clusters)

• 0 → Overlapping clusters
  (Point is on or near the decision boundary)

• –1 → Incorrect clustering
  (Point is closer to another cluster than its own)

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🧪 When is it used?

• To evaluate clustering algorithms like:

  • K-Means

  • Hierarchical clustering

  • DBSCAN (if labels are well-formed)

• To choose the optimal number of clusters k.

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📊 Example (with intuition)

If you change the number of clusters in K-Means and compute the silhouette score for each value, the k with the highest average silhouette score is often the best choice.

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🧠 Summary

The Silhouette Score measures:

How similar an object is to its own cluster compared to other clusters.

It’s a simple yet powerful tool for validating clustering results.