Compute Silhouette Score

Metrics & Evaluation

Medium

Implement a function to compute the Silhouette Score for clustering. The Silhouette Score measures how well each point fits within its cluster compared to other clusters.

For each sample i:

a(i): average distance to all other points in the same cluster (intra-cluster distance)
b(i): minimum average distance to points in any other cluster (nearest inter-cluster distance)

The silhouette for point i is:

s(i) = \frac{b(i) - a(i)}{\max(a(i), b(i))}

The final score is the mean of all s(i).

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Examples

Input: X=[[0,0],[0,1],[1,0],[5,5],[5,6],[6,5]], labels=[0,0,0,1,1,1]

Output: ≈ 0.79

Hint 1

Use broadcasting to compute all-pairs Euclidean distances efficiently.

Hint 2

Use boolean masking to efficiently compute intra-cluster and inter-cluster means.

Requirements

Must work for any number of clusters (K ≥ 2)
Distance metric: Euclidean
Fully vectorized (no nested loops)
Return a single float in range [-1, 1]

Constraints

2 ≤ n_samples ≤ 500
Use only NumPy

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