SilhouetteKoeffizient

SilhouetteKoeffizient, also known as the silhouette coefficient, is a metric used to evaluate the quality of clustering results. It measures how similar an object is to its own cluster (cohesion) compared to other clusters (separation). For each data point i, the coefficient s(i) is defined as (b(i) − a(i)) / max{a(i), b(i)}, where a(i) is the average distance from i to all other points in the same cluster, and b(i) is the smallest average distance from i to points in any other cluster. The value of s(i) ranges from –1 to 1; values close to 1 indicate that the point is well matched to its own cluster and poorly matched to neighboring clusters, values near 0 suggest overlapping clusters, and negative values imply possible misclassification.

The overall silhouette score of a clustering is obtained by averaging s(i) over all points. High average scores (typically above 0.5) are interpreted as evidence of a meaningful partition, whereas low or negative averages signal that the chosen number of clusters or the clustering algorithm may be unsuitable.

The silhouette coefficient is applicable to a wide range of clustering methods, including k‑means, hierarchical clustering, and density‑based approaches, provided a distance metric can be defined. It is frequently used for selecting the optimal number of clusters by computing the score for different values of k and choosing the one with the highest average silhouette.

Despite its usefulness, the silhouette coefficient has limitations. It assumes convex cluster shapes and may be biased by the choice of distance metric. In high‑dimensional spaces the distances can become less informative, leading to misleading silhouette values. Consequently, it is often combined with other validation techniques such as the Davies‑Bouldin index or visual assessment when evaluating clustering performance.