这篇论文用协方差方法解决了子组公平聚类的计算难题，COVA-FC比现有方法更快更稳定，做公平聚类研究可以看看。
论文定义了子组公平性差距，并推导出协方差代理精确匹配该差距。提出COVA-FC算法，通过连续松弛实现梯度优化，解决多敏感属性下子组数量指数增长和少数实例问题。实验在基准数据集上显示COVA-FC在成本和公平性之间取得竞争性权衡，并在子组和更高阶边际设置中提升计算效率。
COVAriance-Induced Fairness Gap Penalty for Subgroup-Fair Clustering
Fair clustering aims to make cluster assignments independent of sensitive attributes, but this goal becomes challenging when multiple sensitive attributes jointly define many subgroups. In such settings, directly extending existing fair clustering algorithms is computationally expensive or numerically unstable, especially when the number of subgroups grows exponentially and some subgroups contain only a few instances. To address these challenges, we define a subgroup-fairness gap for clustering and derive a covariance-based surrogate that exactly matches this gap. We then introduce a continuous relaxation of the surrogate, enabling efficient gradient-based optimization and yielding our proposed algorithm, COVA-FC. We also show that subgroup fairness alone does not imply marginal fairness, and extend our framework to capture a subgroup-marginal-fairness gap. Experiments on benchmark datasets show that COVA-FC achieves competitive cost-fairness trade-offs and improves computational efficiency over existing baselines in both subgroup and higher-order marginal settings.