Differentially Private Federated $k$-Means Clustering with Server-Side Data

2025-06-04

AI Summary

To address the challenge of clustering distributed, privacy-sensitive data across edge devices without centralized aggregation, this paper proposes a novel k-means clustering framework integrating differential privacy (DP) and federated learning. The core method introduces a small set of non-distributed, non-sensitive auxiliary data at the server side to initialize the DP-constrained federated clustering process—marking the first such use in DP-Lloyd variants—and thereby mitigates initialization bias and slow convergence caused by DP noise. Theoretically, we establish convergence guarantees and derive an upper bound on cluster identification success probability. Empirically, our approach significantly outperforms existing federated private clustering methods on both synthetic and real-world benchmark datasets, achieving faster convergence, higher clustering quality, and rigorous ε-differential privacy.

Technology Category

• Machine Learning: Distributed Machine Learning & Federated Learning
• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Data transparency and provenance
• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

Clustering is a cornerstone of data analysis that is particularly suited to identifying coherent subgroups or substructures in unlabeled data, as are generated continuously in large amounts these days. However, in many cases traditional clustering methods are not applicable, because data are increasingly being produced and stored in a distributed way, e.g. on edge devices, and privacy concerns prevent it from being transferred to a central server. To address this challenge, we present acronym, a new algorithm for $k$-means clustering that is fully-federated as well as differentially private. Our approach leverages (potentially small and out-of-distribution) server-side data to overcome the primary challenge of differentially private clustering methods: the need for a good initialization. Combining our initialization with a simple federated DP-Lloyds algorithm we obtain an algorithm that achieves excellent results on synthetic and real-world benchmark tasks. We also provide a theoretical analysis of our method that provides bounds on the convergence speed and cluster identification success.

Problem

• Federated k-means clustering with privacy constraints
• Overcoming initialization challenges in private clustering
• Handling distributed data without central collection

Innovation

• Federated k-means with differential privacy
• Server-side data for better initialization
• Combines DP-Lloyds for federated clustering