A Characterization of Linkage-Based Hierarchical Clustering
Margareta Ackerman, Shai Ben-David; 17(232):1−17, 2016.
AbstractThe class of linkage-based algorithms is perhaps the most popular class of hierarchical algorithms. We identify two properties of hierarchical algorithms, and prove that linkage- based algorithms are the only ones that satisfy both of these properties. Our characterization clearly delineates the difference between linkage-based algorithms and other hierarchical methods. We formulate an intuitive notion of locality of a hierarchical algorithm that distinguishes between linkage-based and
globalhierarchical algorithms like bisecting $k$-means, and prove that popular divisive hierarchical algorithms produce clusterings that cannot be produced by any linkage-based algorithm.