Agglomerative hierarchical clustering can be implemented with several strategies that differ in the way elements of a collection are grouped together to build a hierarchy of clusters. Here we introduce versatile linkage, a new infinite system of agglomerative hierarchical clustering strategies based on generalized means, which go from single linkage to complete linkage, passing through arithmetic average linkage and other clustering methods yet unexplored such as geometric linkage and harmonic linkage. We compare the different clustering strategies in terms of cophenetic correlation, mean absolute error, and also tree balance and space distortion, two new measures proposed to describe hierarchical trees. Unlike the $\beta$-flexible clustering system, we show that the versatile linkage family is space-conserving.

中文翻译：

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多功能链接：凝聚层次聚类的一系列空间节约策略

凝聚层次聚类可以通过几种不同的策略来实现，这些策略的不同之处在于将集合元素组合在一起以构建聚类层次结构。在这里，我们介绍了通用链接，一种新的基于广义手段的凝聚层次聚类策略的无限系统，从单一链接到完全链接，通过算术平均链接和其他尚未探索的聚类方法，如几何链接和谐波链接。我们在 cophenetic 相关性、平均绝对误差以及树平衡和空间失真方面比较了不同的聚类策略，这两种新措施被提议用于描述分层树。与 $\beta$ 灵活的聚类系统不同，我们展示了多功能链接家族是空间守恒的。