Differentially Private Federated Clustering Over Non-IID Data

In this article, we investigate the federated clustering (FedC) problem, which aims to accurately partition unlabeled data samples distributed over massive clients into finite clusters under the orchestration of a parameter server (PS), meanwhile considering data privacy. Though it is an NP-hard optimization problem involving real variables denoting cluster centroids and binary variables denoting the cluster membership of each data sample, we judiciously reformulate the FedC problem into a nonconvex optimization problem with only one convex constraint, accordingly yielding a soft clustering solution. Then, a novel FedC algorithm using differential privacy (DP) technique, referred to as DP- FedC, is proposed in which partial clients participation (PCP) and multiple local model updating steps are also considered. Furthermore, various attributes of the proposed DP- FedC are obtained through theoretical analyses of privacy protection and convergence rate, especially for the case of nonidentically and independently distributed (non-i.i.d.) data, that ideally serve as the guidelines for the design of the proposed DP- FedC. Then, some experimental results on two real datasets are provided to demonstrate the efficacy of the proposed DP- FedC together with its much superior performance over some state-of-the-art FedC algorithms, and the consistency with all the presented analytical results.