Ensuring fairness in machine learning algorithms is a challenging and important task. We consider the problem of clustering a set of points while ensuring fairness constraints. While there have been several attempts to capture group fairness in the k-clustering problem, fairness at an individual level is not well-studied. We introduce a new notion of individual fairness in k-clustering based on features that are not necessarily used for clustering. We show that this problem is NP-hard and does not admit a constant factor approximation. We then design a randomized algorithm that guarantees approximation both in terms of minimizing the clustering distance objective as well as individual fairness under natural restrictions on the distance metric and fairness constraints. Finally, our experimental results validate that our algorithm produces lower clustering costs compared to existing algorithms while being competitive in individual fairness.

中文翻译：

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k-聚类中基于特征的个体公平性

确保机器学习算法的公平性是一项具有挑战性且重要的任务。我们考虑在确保公平性约束的同时对一组点进行聚类的问题。虽然在 k 聚类问题中已经有几次尝试捕捉群体公平性，但个人层面的公平性还没有得到很好的研究。我们基于不一定用于聚类的特征在 k 聚类中引入了个体公平的新概念。我们表明这个问题是 NP-hard 问题，并且不允许常数因子近似。然后，我们设计了一个随机算法，在距离度量和公平性约束的自然限制下，在最小化聚类距离目标以及个体公平性方面保证近似。最后，