Hierarchical clustering with dot products recovers hidden tree structure

Published: 21 Sept 2023, Last Modified: 02 Nov 2023NeurIPS 2023 spotlightEveryoneRevisionsBibTeX
Keywords: agglomerative clustering, generative model, graphical model, hierarchical clustering, high-dimensional data
TL;DR: A new perspective on recovery of tree structure from data.
Abstract: 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.
Supplementary Material: zip
Submission Number: 12822