# Improved Hierarchical Clustering on Massive Datasets with Broad Guarantees

arXiv: https://arxiv.org/abs/2101.04818 · HTML: https://mlsanity.com/paper/2101.04818/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jan 2021.

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

- [Sublinear Algorithms for Hierarchical Clustering](https://mlsanity.com/paper/2206.07633/) (2022)
- [Latent Taxonomies: How Property Induction Develops in Language Model Pre-training](https://mlsanity.com/paper/2610.15836/) (2026)

## Abstract (arXiv)

Hierarchical clustering is a stronger extension of one of today's most influential unsupervised learning methods: clustering. The goal of this method is to create a hierarchy of clusters, thus constructing cluster evolutionary history and simultaneously finding clusterings at all resolutions. We propose four traits of interest for hierarchical clustering algorithms: (1) empirical performance, (2) theoretical guarantees, (3) cluster balance, and (4) scalability. While a number of algorithms are designed to achieve one to two of these traits at a time, there exist none that achieve all four. Inspired by Bateni et al.'s scalable and empirically successful Affinity Clustering [NeurIPs 2017], we introduce Affinity Clustering's successor, Matching Affinity Clustering. Like its predecessor, Matching Affinity Clustering maintains strong empirical performance and uses Massively Parallel Communication as its distributed model. Designed to maintain provably balanced clusters, we show that our algorithm achieves good, constant factor approximations for Moseley and Wang's revenue and Cohen-Addad et al.'s value. We show Affinity Clustering cannot approximate either function. Along the way, we also introduce an efficient k-sized maximum matching algorithm in the MPC model.