# On the cohesion and separability of average-link for hierarchical agglomerative clustering

arXiv: https://arxiv.org/abs/2411.05097 · HTML: https://mlsanity.com/paper/2411.05097/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 33 references that are in the map.
- First posted on arXiv 7 Nov 2024.

## Builds on (most cited first, 11 of 11)

- [A cost function for similarity-based hierarchical clustering](https://mlsanity.com/paper/1510.05043/) (2015)
- [Hierarchical Clustering better than Average-Linkage](https://mlsanity.com/paper/1808.02227/) (2018)
- [Scalable Hierarchical Agglomerative Clustering](https://mlsanity.com/paper/2010.11821/) (2020)
- [Hierarchical Agglomerative Graph Clustering in Nearly-Linear Time](https://mlsanity.com/paper/2106.05610/) (2021)
- [An Objective for Hierarchical Clustering in Euclidean Space and its Connection to Bisecting K-means](https://mlsanity.com/paper/2008.13235/) (2020)
- [Hierarchical Agglomerative Graph Clustering in Poly-Logarithmic Depth](https://mlsanity.com/paper/2206.11654/) (2022)
- [TeraHAC: Hierarchical Agglomerative Clustering of Trillion-Edge Graphs](https://mlsanity.com/paper/2308.03578/) (2023)
- [Hierarchical Clustering for Euclidean Data](https://mlsanity.com/paper/1812.10582/) (2018)
- [Optimization of Inter-group Criteria for Clustering with Minimum Size Constraints](https://mlsanity.com/paper/2401.07091/) (2024)
- [Analysis of Ward's Method](https://mlsanity.com/paper/1907.05094/) (2019)
- [ParChain: A Framework for Parallel Hierarchical Agglomerative Clustering using Nearest-Neighbor Chain](https://mlsanity.com/paper/2106.04727/) (2021)

## Built on by (most cited first, 2 of 2)

- [Metric Design != Metric Behavior: Improving Metric Selection for the Unbiased Evaluation of Dimensionality Reduction](https://mlsanity.com/paper/2507.02225/) (2025)
- [OmniFC: Rethinking Federated Clustering via Lossless and Secure Distance Reconstruction](https://mlsanity.com/paper/2505.13071/) (2025)

## Abstract (arXiv)

Average-link is widely recognized as one of the most popular and effective methods for building hierarchical agglomerative clustering. The available theoretical analyses show that this method has a much better approximation than other popular heuristics, as single-linkage and complete-linkage, regarding variants of Dasgupta's cost function [STOC 2016]. However, these analyses do not separate average-link from a random hierarchy and they are not appealing for metric spaces since every hierarchical clustering has a 1/2 approximation with regard to the variant of Dasgupta's function that is employed for dissimilarity measures [Moseley and Yang 2020]. In this paper, we present a comprehensive study of the performance of average-link in metric spaces, regarding several natural criteria that capture separability and cohesion and are more interpretable than Dasgupta's cost function and its variants. We also present experimental results with real datasets that, together with our theoretical analyses, suggest that average-link is a better choice than other related methods when both cohesion and separability are important goals.