Differentially Private k-Means Clustering with Guaranteed Convergence
This addresses privacy risks in iterative clustering for data analysts by ensuring algorithm termination and better performance, though it is incremental as it builds on existing DP methods.
The paper tackles the non-convergence problem in interactive differentially private k-means clustering algorithms by proposing a novel framework that controls centroid movement orientation with DP noise injection, proving convergence in at most twice the iterations of Lloyd's algorithm and showing improved clustering quality on real-world datasets.
Iterative clustering algorithms help us to learn the insights behind the data. Unfortunately, this may allow adversaries to infer the privacy of individuals with some background knowledge. In the worst case, the adversaries know the centroids of an arbitrary iteration and the information of n-1 out of n items. To protect individual privacy against such an inference attack, preserving differential privacy (DP) for the iterative clustering algorithms has been extensively studied in the 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 a differentially private algorithm. To resolve this problem, in this paper, we propose a novel differentially private clustering framework in the interactive settings which controls the orientation of the movement of the centroids over the iterations to ensure the convergence by injecting DP noise in a selected area. We prove that, in the expected case, algorithm under our framework converges 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 guaranteed convergence and better clustering quality to meet the same DP requirement.