Making Old Things New: A Unified Algorithm for Differentially Private Clustering
This provides a unified solution for differentially private clustering, addressing the need for efficient and private data analysis in scenarios with evolving data, though it is incremental as it builds on an existing algorithm.
The paper tackles the problem of designing differentially private clustering algorithms across various privacy models by showing that a 20-year-old algorithm can be slightly modified to work for any of them, matching almost all previously known results while improving some and extending to a new continual observation setting.
As a staple of data analysis and unsupervised learning, the problem of private clustering has been widely studied under various privacy models. Centralized differential privacy is the first of them, and the problem has also been studied for the local and the shuffle variation. In each case, the goal is to design an algorithm that computes privately a clustering, with the smallest possible error. The study of each variation gave rise to new algorithms: the landscape of private clustering algorithms is therefore quite intricate. In this paper, we show that a 20-year-old algorithm can be slightly modified to work for any of these models. This provides a unified picture: while matching almost all previously known results, it allows us to improve some of them and extend it to a new privacy model, the continual observation setting, where the input is changing over time and the algorithm must output a new solution at each time step.