In this paper we offer a new perspective on the well established agglomerative clustering algorithm, focusing on recovery of hierarchical structure. We recommend a simple variant of the standard algorithm, in which clusters are merged by maximum average dot product and not, for example, by minimum distance or within-cluster variance. We demonstrate that the tree output by this algorithm provides a bona fide estimate of generative hierarchical structure in data, under a generic probabilistic graphical model. The key technical innovations are to understand how hierarchical information in this model translates into tree geometry which can be recovered from data, and to characterise the benefits of simultaneously growing sample size and data dimension. We demonstrate superior tree recovery performance with real data over existing approaches such as UPGMA, Ward's method, and HDBSCAN.

翻译：本文为成熟的凝聚式聚类算法提供了一种新视角，聚焦于层级结构的恢复。我们推荐标准算法的一种简单变体，其中聚类合并依据最大平均点积，而非例如最小距离或簇内方差。我们证明，在通用概率图模型下，该算法输出的树状结构能有效估计数据中生成的层级结构。关键技术突破在于：理解该模型中的层级信息如何转化为可从数据恢复的树形几何结构，并刻画样本量与数据维度同步增长的优势。通过真实数据实验，我们展示了该方法在树状结构恢复性能上优于现有方法（如UPGMA、Ward法与HDBSCAN）。