# Optimization of Inter-group Criteria for Clustering with Minimum Size Constraints

arXiv: https://arxiv.org/abs/2401.07091 · HTML: https://mlsanity.com/paper/2401.07091/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 25 references that are in the map.
- First posted on arXiv 13 Jan 2024.

## Builds on (most cited first, 7 of 7)

- [A cost function for similarity-based hierarchical clustering](https://mlsanity.com/paper/1510.05043/) (2015)
- [Better Guarantees for k-Means and Euclidean k-Median by Primal-Dual Algorithms](https://mlsanity.com/paper/1612.07925/) (2016)
- [Diversity in Machine Learning](https://mlsanity.com/paper/1807.01477/) (2018)
- [Approximate Hierarchical Clustering via Sparsest Cut and Spreading Metrics](https://mlsanity.com/paper/1609.09548/) (2016)
- [Hierarchical Clustering via Spreading Metrics](https://mlsanity.com/paper/1610.09269/) (2016)
- [Individual Preference Stability for Clustering](https://mlsanity.com/paper/2207.03600/) (2022)
- [Connecting Spectral Clustering to Maximum Margins and Level Sets](https://mlsanity.com/paper/1812.06397/) (2018)

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

- [On the cohesion and separability of average-link for hierarchical agglomerative clustering](https://mlsanity.com/paper/2411.05097/) (2024)
- [Scalable Algorithms for Individual Preference Stable Clustering](https://mlsanity.com/paper/2403.10365/) (2024)

## Abstract (arXiv)

Internal measures that are used to assess the quality of a clustering usually take into account intra-group and/or inter-group criteria. There are many papers in the literature that propose algorithms with provable approximation guarantees for optimizing the former. However, the optimization of inter-group criteria is much less understood. Here, we contribute to the state-of-the-art of this literature by devising algorithms with provable guarantees for the maximization of two natural inter-group criteria, namely the minimum spacing and the minimum spanning tree spacing. The former is the minimum distance between points in different groups while the latter captures separability through the cost of the minimum spanning tree that connects all groups. We obtain results for both the unrestricted case, in which no constraint on the clusters is imposed, and for the constrained case where each group is required to have a minimum number of points. Our constraint is motivated by the fact that the popular Single Linkage, which optimizes both criteria in the unrestricted case, produces clusterings with many tiny groups. To complement our work, we present an empirical study with 10 real datasets, providing evidence that our methods work very well in practical settings.