$DPM:$ Clustering Sensitive Data through Separation

Clustering is an important tool for data exploration with the goal to subdivide a data set into disjoint clusters that fit well into the underlying data structure. When dealing with sensitive data, privacy-preserving algorithms aim to approximate the non-private baseline while minimising the leakage of sensitive information. State-of-the-art privacy-preserving clustering algorithms tend to output clusters that are good in terms of the standard metrics, inertia, silhouette score, and clustering accuracy, however, the clustering result strongly deviates from the non-private KMeans baseline. In this work, we present a privacy-preserving clustering algorithm called DPM that recursively separates a data set into clusters based on a geometrical clustering approach. In addition, DPM estimates most of the data-dependent hyper-parameters in a privacypreserving way. We prove that DPM preserves Differential Privacy and analyse the utility guarantees of DPM . Finally, we conduct an extensive empirical evaluation for synthetic and real-life data sets. We show that DPM achieves state-of-the-art utility on the standard clustering metrics and yields a clustering result much closer to that of the popular non-private KMeans algorithm without requiring the number of classes.