New bounds on the cohesion of complete-link and other linkage methods for agglomeration clustering

Abstract: Linkage methods are among the most popular algorithms for hierarchical clustering. Despite their relevance the current knowledge regarding the quality of the clustering produced by these methods is limited. Here, we improve the currently available bounds on the maximum diameter of the clustering obtained by complete-link for metric spaces. One of our new bounds, in contrast to the existing ones, allows us to separate complete-link from single-link in terms of approximation for the diameter, which corroborates the common perception that the former is more suitable than the latter when the goal is producing compact clusters. We also show that our techniques can be employed to derive upper bounds on the cohesion of a class of linkage methods that includes the quite popular average-link.