This study aims to alleviate the trade-off between utility and privacy in the task of differentially private clustering. Existing works focus on simple clustering methods, which show poor clustering performance for non-convex clusters. By utilizing Morse theory, we hierarchically connect the Gaussian sub-clusters to fit complex cluster distributions. Because differentially private sub-clusters are obtained through the existing methods, the proposed method causes little or no additional privacy loss. We provide a theoretical background that implies that the proposed method is inductive and can achieve any desired number of clusters. Experiments on various datasets show that our framework achieves better clustering performance at the same privacy level, compared to the existing methods.

翻译：本研究旨在缓解差分隐私聚类任务中效用与隐私之间的权衡问题。现有工作主要关注简单的聚类方法，这些方法对非凸聚类的表现较差。通过利用莫尔斯理论，我们层次化地连接高斯子聚类以拟合复杂的聚类分布。由于差分隐私子聚类可通过现有方法获得，本方法几乎不造成额外的隐私损失。我们提供了理论背景，表明所提方法具有归纳性，能够实现任意所需的聚类数量。在多种数据集上的实验证明，与现有方法相比，我们的框架在相同隐私水平下取得了更好的聚类性能。