Clustering often has no ground-truth class label, so evaluation must ask whether the proposed groups are internally coherent and useful for the intended purpose.

One internal measure is the silhouette coefficient. For example $i$, let $a(i)$ be its average distance to points in its own cluster and $b(i)$ the smallest average distance to points in any other cluster. Then

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

Values near $1$ indicate a point much closer to its own cluster than to alternatives. Values near $0$ indicate an ambiguous boundary, and negative values suggest it may fit another cluster better.

Internal scores are not universal definitions of good clustering. A partition can score well geometrically while being useless for the domain, and different distance choices can change the conclusion.

When downstream use is known, external utility may be more informative: for example, do customer segments support meaningfully different actions? Stability under resampling can also reveal whether clusters are robust or artifacts of a particular sample.

Clustering evaluation therefore combines structural evidence with the purpose for which the grouping was created.