Abstract: Federated clustering is vulnerable to data heterogeneity under non-independent and non-identically distributed (Non-IID) conditions, making it difficult to maintain robust model performance. Traditional multi-round iterative clustering methods incur high communication overhead and privacy risks, making them unsuitable for resource-constrained environments. To address this issue, this paper proposes federated Bayesian weighted clustering (FedBWC), a one-shot federated clustering method designed to handle heterogeneity in cluster distributions. On the client side, a Bayesian Gaussian mixture model (BGM) with variational inference is applied to local data to adaptively identify effective clusters and extract their centers along with corresponding confidence weights. On the server side, weighted K-means aggregation is performed with only a single communication round, where dynamic weight assignment enhances the representativeness of global centers. Systematic experiments were conducted on six benchmark datasets (Thyroid, Balance Scale, Digits, Waveform, USPS, and PenDigits). The results show that under strong heterogeneity conditions (Dirichlet parameter = 0.3), FedBWC achieves average improvements of 21.6% in V-measure, 28.7% in ARI, and 22.6% in AMI over the baseline methods, while retaining a performance advantage of more than 5% under moderate heterogeneity conditions (Dirichlet parameter = 0.5). Overall, FedBWC significantly outperforms existing methods and provides an efficient and robust solution for federated clustering in complex heterogeneous environments.

Key words: federated clustering, federated learning, data heterogeneity, privacy protection, Bayesian Gaussian mixture