发表机构
Indian Institute of Technology, Gandhinagar（印度理工学院甘地纳格尔分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对层次聚类扭曲局部相似性影响单个数据点的问题，将个体公平性要求限制在k近邻范围，刻画可行性所需松弛量并通过实验验证相关理论结果。
AI 中文摘要
层次聚类会生成超度量表示，该表示施加了强全局几何约束，可能以不成比例影响单个数据点的方式扭曲局部相似性。我们在个体公平性要求下研究层次聚类，该要求将相对扭曲限制在局部k近邻范围内。我们将此要求表述为受控超度量上的可行性问题，并刻画了可行性所需的最小乘性松弛量。我们确定了一个尖锐的局部阈值，证明了有界扰动下的稳定性，建立了k的单调性，并展示了局部与全局可实现性之间存在内在的Θ(log n)差距。在合成数据集和真实世界数据集上的实验验证了我们的理论结果。
英文摘要
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.
