We show that the popular k-means clustering algorithm (Lloyd's heuristic), used for a variety of scientific data, can result in outcomes that are unfavorable to subgroups of data (e.g., demographic groups). Such biased clusterings can have deleterious implications for human-centric applications such as resource allocation. We present a fair k-means objective and algorithm to choose cluster centers that provide equitable costs for different groups. The algorithm, Fair-Lloyd, is a modification of Lloyd's heuristic for k-means, inheriting its simplicity, efficiency, and stability. In comparison with standard Lloyd's, we find that on benchmark datasets, Fair-Lloyd exhibits unbiased performance by ensuring that all groups have equal costs in the output k-clustering, while incurring a negligible increase in running time, thus making it a viable fair option wherever k-means is currently used.

中文翻译：

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社会公平 k 均值聚类

我们表明，用于各种科学数据的流行 k 均值聚类算法（劳埃德启发式算法）可能会导致对数据子组（例如人口统计组）不利的结果。这种有偏见的聚类可能会对以人为中心的应用程序（例如资源分配）产生有害影响。我们提出了一个公平的 k-means 目标和算法来选择为不同群体提供公平成本的集群中心。Fair-Lloyd 算法是对 K-means 的 Lloyd 启发式的修改，继承了其简单性、效率和稳定性。与标准 Lloyd's 相比，我们发现在基准数据集上，Fair-Lloyd 通过确保所有组在输出 k 聚类中具有相同的成本，同时运行时间的增加可以忽略不计，从而表现出无偏性能，