OmniFC: Rethinking Federated Clustering via Lossless and Secure Distance Reconstruction

TL;DR

OmniFC introduces a secure, model-agnostic federated clustering framework that accurately reconstructs global distances without privacy leakage, effectively handling data heterogeneity and improving robustness over existing methods.

Contribution

It presents a novel, unified approach using Lagrange coded computing for lossless distance reconstruction in federated clustering, enhancing privacy, robustness, and generality.

Findings

Achieves exact global distance matrix reconstruction without data leakage

Demonstrates superior robustness and effectiveness across benchmarks

Decouples federated clustering from model-specific proxies

Abstract

Federated clustering (FC) aims to discover global cluster structures across decentralized clients without sharing raw data, making privacy preservation a fundamental requirement. There are two critical challenges: (1) privacy leakage during collaboration, and (2) robustness degradation due to aggregation of proxy information from non-independent and identically distributed (Non-IID) local data, leading to inaccurate or inconsistent global clustering. Existing solutions typically rely on model-specific local proxies, which are sensitive to data heterogeneity and inherit inductive biases from their centralized counterparts, thus limiting robustness and generality. We propose Omni Federated Clustering (OmniFC), a unified and model-agnostic framework. Leveraging Lagrange coded computing, our method enables clients to share only encoded data, allowing exact reconstruction of the global distance matrix--a fundamental representation of sample relationships--without leaking private information, even under client collusion. This construction is naturally resilient to Non-IID data distributions. This approach decouples FC from model-specific proxies, providing a unified extension mechanism applicable to diverse centralized clustering methods. Theoretical analysis confirms both reconstruction fidelity and privacy guarantees, while comprehensive experiments demonstrate OmniFC's superior robustness, effectiveness, and generality across various benchmarks compared to state-of-the-art methods. Code will be released.