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.

中文翻译：

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有或没有连续性约束的 Ward 分层凝聚聚类的适用性和可解释性

自从在 Ward (1963) 中引入以来，带有 Ward 链接的分层凝聚分类 (HAC) 已被广泛使用。本文回顾了该方法对各种输入数据和约束框架的不同扩展，同时提供了适用条件。此外，还提供了作为树状图的结果图形表示的各种版本，并阐明了它们的属性。虽然有时可以在异质岩文献中找到其中一些结果，但我们使用统一的背景来澄清和完善它们。特别是，这项研究揭示了树状图的一致性属性与其中不存在交叉之间的重要区别。最后，一项模拟研究表明，HAC 的约束版本有时可以提供比其无约束版本更相关的结果，尽管后者在每个步骤的一组减少的解决方案上优化了客观标准。总体而言，本文根据输入数据以及结果的表示，对 HAC 和受约束的 HAC 的使用提供了全面的建议。