Differentially-Private Clustering of Easy Instances
This work addresses the challenge of practical differentially private clustering for data analysts, though it is incremental as it builds on existing methods by targeting easier cases.
The paper tackled the problem of differentially private clustering by focusing on easy instances with significant cluster separation, proposing a framework that applies non-private algorithms and privately combines results, achieving improved sample complexity bounds for Gaussian mixtures and k-means.
Clustering is a fundamental problem in data analysis. In differentially private clustering, the goal is to identify $k$ cluster centers without disclosing information on individual data points. Despite significant research progress, the problem had so far resisted practical solutions. In this work we aim at providing simple implementable differentially private clustering algorithms that provide utility when the data is "easy," e.g., when there exists a significant separation between the clusters. We propose a framework that allows us to apply non-private clustering algorithms to the easy instances and privately combine the results. We are able to get improved sample complexity bounds in some cases of Gaussian mixtures and $k$-means. We complement our theoretical analysis with an empirical evaluation on synthetic data.