在线差分隐私一致性聚类
Online Differentially Private Consistent Clustering
AI总结：
该研究针对在线流环境下的差分隐私聚类问题，提出通用归约方法，使算法在近似比、空间与时间性能上优于或匹配现有方法，且继承了非私有聚类算法的一致性属性。
AI中文摘要：
我们研究在线流环境下的差分隐私（DP）k-均值与k-中位数聚类问题。该模型中，点按顺序到达，每一步需输出k个中心的集合，以优化当前已观测到所有点的聚类目标。我们提出一种通用归约方法，将敏感输入流转换为私有流，该私有流是输入流的半核心集。这意味着任何（非私有）在线聚类算法作为后处理步骤运行时，均可针对原始聚类目标实现良好的效用。我们的算法在近似比、空间使用量和运行时间上与现有算法[Epasto等人，2026；Dupré la Tour等人，2024]相当或更优。该归约方法的关键特性是继承了底层非私有聚类算法的理想属性，例如一致性[Lattanzi和Vassilvitskii，2017]——这是此前差分隐私算法未满足的属性。
英文摘要：
We study differentially private (DP) $k$-means and $k$-median clustering in the online streaming setting. In this model, points arrive sequentially, and at each time step, we need to output a set of $k$ centers that optimizes the clustering objective for all points seen so far. We give a generic reduction that transforms the (sensitive) input stream into a private stream, which is a semi-coreset of the input stream. This implies that any (non-private) online clustering algorithm, run as a post-processing step, can achieve good utility for the original clustering objective. Our algorithm matches or improves upon the approximation ratio, space usage, and running time of existing algorithms [Epasto et al., 2026, Dupré la Tour et al., 2024]. A key aspect of our reduction is that it inherits desirable properties of the underlying non-private clustering algorithm, such as consistency [Lattanzi and Vassilvitskii, 2017]--a property not satisfied by previous DP algorithms.
