Differentially Private Federated Clustering over Non-IID Data

Federated clustering (FedC) is an adaptation of centralized clustering in federated settings, which aims to cluster data based on a global similarity measure while keeping all data locally. Two of the main challenges of FedC are the non-identically and independently distributed (non-i.i.d.) nature of data across different sources, as well as the need for privacy protection. In this paper, we propose a differentially private federated clustering (DP-FedC) algorithm to deal with these challenges. Unlike most existing algorithms without considering privacy, the proposed DP-FedC algorithm is designed to handle non-convex and non-smooth problems by using differential privacy techniques to guarantee privacy, together with privacy amplification assisted tradeoff between learning performance and privacy protection. Then some theoretical analyses of the performance and privacy of the proposed DP-FedC are presented, showing the impact of privacy protection, data heterogeneity, and partial client participation on learning performance. Finally, some experimental results are presented to demonstrate the efficacy (including analytical results) of the proposed DP-FedC algorithm together with its superior performance over state-of-the-art approaches.