An upper bound on the silhouette evaluation metric for clustering

ArXi:2509.08625v5 Announce Type: replace The silhouette coefficient quantifies, for each observation, the balance between within-cluster cohesion and between-cluster separation, taking values in the range [-1,1]. The average silhouette width (ASW) is a widely used internal measure of clustering quality, with higher values indicating cohesive and well-separated clusters. However, the dataset-specific maximum of ASW is typically unknown, and the standard upper limit of 1 is rarely attainable.