We study the problem of differentially private (DP) $k$-means clustering in Euclidean space. Previous solutions rely on summing the private data directly, which induces a sensitivity proportional to the domain. We introduce PE-means, an extension of the private evolution (PE) algorithm (an increasingly popular method for synthetic data generation), to the problem of $k$-means clustering. The key advantage of PE is that it only computes a private histogram with constant sensitivity to guide the evolution. Our adaptation of PE includes new evolutionary operators for clustering, as well as other algorithmic improvements of independent interest. Overall, PE-means achieves an average improvement of 20% in clustering loss over state-of-the-art baselines.

翻译：我们研究欧几里得空间中差分隐私$k$-均值聚类问题。现有解决方案依赖于直接对私有数据求和，这会导致与域成正比的敏感度。我们提出PE-means，将私有进化算法（一种日益流行的合成数据生成方法）扩展到$k$-均值聚类问题。PE的关键优势在于它仅计算具有恒定敏感度的私有直方图来引导进化过程。我们对PE的适配包括用于聚类的新型进化算子，以及其他具有独立价值的算法改进。总体而言，PE-means在聚类损失上相比最先进的基线方法实现了平均20%的提升。