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.

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