  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.
