Silhouette score

The problem, from first principles

Clustering has no labels to score against, so quality must be judged from the data itself: are points close to their own cluster and far from the others? The silhouette score summarises that for each point and averages it.

From theory to code

Implement silhouette_score(X, labels) using Euclidean distance.

Constraints

• X has shape (n_samples, n_features); labels is a length-n_samples integer cluster assignment.
• For a point, a is its mean distance to the other points in its own cluster, and b is the smallest mean distance to the points of any other cluster.
• A point alone in its cluster has silhouette 0. If max(a, b) == 0, its silhouette is 0.
• Return 0.0 when there are fewer than two clusters. Return the mean silhouette as a Python float.

Hints

Open one at a time. Each gives away a little more than the last.