# Individual Fairness in Hierarchical Clustering

arXiv: https://arxiv.org/abs/2608.25586 · HTML: https://mlsanity.com/paper/2608.25586/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 25 references that are in the map.
- First posted on arXiv 26 Aug 2026.

## Builds on (most cited first, 5 of 5)

- [A cost function for similarity-based hierarchical clustering](https://mlsanity.com/paper/1510.05043/) (2015)
- [Individual Fairness for k-Clustering](https://mlsanity.com/paper/2002.06742/) (2020)
- [A Scalable Algorithm for Individually Fair K-means Clustering](https://mlsanity.com/paper/2402.06730/) (2024)
- [Linear Programming based Approximation to Individually Fair k-Clustering with Outliers](https://mlsanity.com/paper/2412.10923/) (2024)
- [Local Search-based Individually Fair Clustering with Outliers](https://mlsanity.com/paper/2510.06130/) (2025)

## Abstract (arXiv)

Hierarchical clustering produces ultrametric representations that impose strong global geometric constraints and may distort local similarities in ways that disproportionately affect individual data points. We study hierarchical clustering under an individual fairness requirement that bounds relative distortion within local k-nearest neighborhoods. We formulate this requirement as a feasibility problem over dominated ultrametrics and characterize the minimal multiplicative slack required for feasibility. We identify a sharp local threshold, prove stability under bounded perturbations, establish monotonicity in k, and show an intrinsic Theta(log n) separation between local and global realizability. Experiments on synthetic and real world datasets support our theoretical results.