In recent years, there has been a surge in effort to formalize notions of fairness in machine learning. We focus on clustering -- one of the fundamental tasks in unsupervised machine learning. We propose a new axiom that captures proportional representation fairness (PRF). We make a case that the concept achieves the raison d'{\^{e}}tre of several existing concepts in the literature in an arguably more convincing manner. Our fairness concept is not satisfied by existing fair clustering algorithms. We design efficient algorithms to achieve PRF both for unconstrained and discrete clustering problems.

翻译：近年来，机器学习的公平性概念形式化研究激增。本文聚焦于无监督机器学习中的基础任务——聚类，提出了一种刻画比例代表性公平性（PRF）的新公理。我们论证了该概念以更令人信服的方式实现了文献中若干现有概念的核心要旨。现有公平聚类算法未能满足我们的公平性概念。为此，我们针对无约束聚类和离散聚类问题设计了实现PRF的高效算法。