Silhouette Score for Clustering

How good is a clustering when there are no labels? The silhouette compares how close each point is to its own cluster versus the nearest other cluster.

For point i: a = mean distance to the other points in its cluster, b = the smallest mean distance to the points of any other cluster, and $s_i = \frac{b - a}{\max(a, b)}$. A point alone in its cluster gets $s_i = 0$.

Implement (with Euclidean distances):

• silhouette_samples(X, labels): the array of $s_i$
• silhouette_score(X, labels): their mean
• best_k(X, label_sets): given a dict {k: labels}, the k with the highest score (ties: smallest k)