A Convergent Differentially Private k-Means Clustering Algorithm

Preserving differential privacy (DP) for the iterative clustering algorithms has been extensively studied in the interactive and the non-interactive settings. However, existing interactive differentially private clustering algorithms suffer from a non-convergence problem, i.e., these algorithms may not terminate without a predefined number of iterations. This problem severely impacts the clustering quality and the efficiency of the algorithm. To resolve this problem, we propose a novel iterative approach in the interactive settings which controls the orientation of the centroids movement over the iterations to ensure the convergence by injecting DP noise in a selected area. We prove that, in the expected case, our approach converges to the same centroids as Lloyd's algorithm in at most twice the iterations of Lloyd's algorithm. We perform experimental evaluations on real-world datasets to show that our algorithm outperforms the state-of-the-art of the interactive differentially private clustering algorithms with a guaranteed convergence and better clustering quality to meet the same DP requirement.