Federated Hierarchical Clustering with Automatic Selection of Optimal Cluster Numbers

Hierarchical federated learning (HFL) leverages edge servers for partial aggregation in edge computing. Yet existing FL methods lack mechanisms for jointly optimizing cluster assignment and client selection under data heterogeneity. This paper proposes Fed-BAC, which integrates additive cluster personalization with a two-level bandit framework: contextual bandits at the cloud learn server-to-cluster assignments, while Thompson Sampling at each edge server identifies high-contributing clients. The additive decomposition enables the sharing of knowledge between groups through a globally aggregated network, while cluster-specific networks capture distribution variations. Across three classification benchmarks (CIFAR-10, SVHN, Fashion-MNIST) under moderate ($α= 0.5$) and severe ($α= 0.1$) Dirichlet non-IID partitioning, Fed-BAC achieves distributed accuracy gains of up to +35.5pp over HierFAVG and +8.4pp over IFCA, while requiring only 80% client participation, converging 1.5 to 4.8$\times$ faster depending on dataset and accuracy target, and improving cross-server fairness. These gains are further validated at 5$\times$ deployment scale on CIFAR-10. The advantage of Fed-BAC increases with heterogeneity severity, confirming that additive cluster personalization becomes increasingly valuable as data distributions diverge.

Federated clustering methods that do not require the global number of clusters $K$ still assume that each client knows its local number $K_g$. This assumption is hard to justify when clients know no more about their data than the server does, as in fault diagnosis across independently operated industrial sites. We propose a two-phase framework in which neither count is known: each client first estimates $K_g$ from its own data, and an aggregator that requires local counts, such as FedGEM, then uses these estimates in place of the true values. For the first phase we introduce Adaptive Split--Merge (ASM), which grows a spherical Gaussian mixture by BIC-driven splitting and then merges excess components. ASM uses no labels, selects its hyperparameters on held-out client data only, and makes no assumption about how clusters are shared across clients. We derive a closed-form split criterion whose critical cluster size falls with anisotropy and rises with dimension, and show empirically that over-fragmentation grows with the number of points per cluster, which federation divides among clients. Across eight datasets, ASM with FedGEM attains a mean ARI of 0.333, against 0.256 for the next best label-free estimator and 0.361 when the true local counts are supplied. It also gives the most reliable global estimates of $K$ and is robust when client size is decoupled from local cardinality.

Clustering high-dimensional data is a fundamental task in unsupervised machine learning with applications to a variety of domains. In the centralized data scenario, this task is commonly solved using deep clustering methods that utilize deep neural network architectures to learn clustering-friendly latent space representations. In Federated Learning, where data is distributed between clients and is private, deep clustering methods are less explored. In particular, recently introduced federated deep clustering methods, despite showing very promising performance, still fall short in reliably providing good performance if data across clients are non-identically-independently distributed. In this work, we introduce a generalization of Deep Clustering Networks to the federated scenario, named FedDCN, that simultaneously optimizes a reconstruction loss and a clustering loss. To ensure robustness and latent space alignment in non-identically-independently distributed data scenarios, FedDCN generates synthetic data augmentations, and its learning objective includes a geometric regularization for latent space alignment. Through experimental evaluation, the effectiveness of the approach under IID and non-IID assumptions is demonstrated, and future research directions are identified.