Hierarchical clustering with dot products recovers hidden tree structure
- URL: http://arxiv.org/abs/2305.15022v3
- Date: Fri, 1 Mar 2024 16:25:54 GMT
- Title: Hierarchical clustering with dot products recovers hidden tree structure
- Authors: Annie Gray, Alexander Modell, Patrick Rubin-Delanchy, Nick Whiteley
- Abstract summary: 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.
- Score: 53.68551192799585
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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