  Hierarchical Agglomerative Classification (HAC) with Ward's linkage has been
widely used since its introduction in Ward (1963). The present article reviews
the different extensions of the method to various input data and the
constrained framework, while providing applicability conditions. In addition,
various versions of the graphical representation of the results as a dendrogram
are also presented and their properties are clarified. While some of these
results can sometimes be found in an heteroclite literature, we clarify and
complete them all 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 latter optimizes the objective
criterion on a reduced set of solutions at each step. Overall, the article
provides comprehensive recommandations for the use of HAC and constrained HAC
depending on the input data as well as for the representation of the results.
