Applicability and Interpretability of Ward's Hierarchical Agglomerative Clustering With or Without Contiguity Constraints

Hierarchical agglomerative clustering (HAC) with Ward's linkage has been widely used since its introduction by Ward (Journal of the American Statistical Association, 58(301), 236-244,1963). This article reviews extensions of HAC to various input data and contiguity-constrained HAC, and provides applicability conditions. In addition, different versions of the graphical representation of the results as a dendrogram are also presented and their properties are clarified. We clarify and complete the results already available in an heterogeneous literature using a uniform background. In particular, this study reveals an important distinction between a consistency property of the dendrogram and the absence of crossover within it. Finally, a simulation study shows that the constrained version of HAC can sometimes provide more relevant results than its unconstrained version despite the fact that the constraint leads to optimize the objective criterion on a reduced set of solutions at each step. Overall, this article provides comprehensive recommendations, both for the use of HAC and constrained HAC depending on the input data, and for the representation of the results.

Automated summary

This article discusses the various extensions of hierarchical agglomerative clustering (HAC) with Ward's linkage, applicability conditions, and different versions of graphical representation as dendrograms. It also highlights the distinction between the consistency property and absence of crossover within the dendrogram. The study shows that the constrained version of HAC can sometimes provide more relevant results despite optimizing the objective criterion on a reduced set of solutions.