Individual Fairness in Hierarchical Clustering

2026-08-26

AI Summary

研究通过限制局部k-最近邻域内的相对扭曲，解决层次聚类中个体公平性问题，并提出可行性问题及理论分析。

Abstract

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 $Θ(\log n)$ separation between local and global realizability. Experiments on synthetic and real world datasets support our theoretical results.

Problem

• Individual Fairness
• Hierarchical Clustering
• Ultrametric Representations
• Local Similarities
• Relative Distortion

Innovation

• individual fairness
• hierarchical clustering
• dominated ultrametrics
• multiplicative slack
• local k-nearest neighborhoods