Federated Community Detection in Bipartite Networks

Clustered Federated Learning (FL) partitions a client population into groups of similar local distributions and trains one specialized model per cluster, mitigating client drift that degrades single-model methods under non-IID data. Prior methods discover cluster structure inside the training loop through gradient similarity, loss evaluation, or EM-style updates, thus increasing communication overhead, exposing gradients to inversion attacks, and providing no mechanism to assign clients absent from training. We propose RIPPLE, a clustered FL framework in which cluster assignment is computed entirely offline from a spectral characterization of each client's local data: a variance-weighted principal-component prototype embedded via the Wavelet Scattering Transform and decoded by a Gaussian Mixture VAE trained server-side on synthetic client populations before federation begins. Per-round communication cost matches FedAvg exactly, and a client absent from training obtains a personalized model from a single forward pass, without gradient computation, model evaluation, or extra communication round. We prove that the gap between RIPPLE's surrogate clustered objective and the oracle is bounded by a computable quantity decaying with client sample size and independent of federation duration; per-cluster convergence matches the minimax-optimal rate for non-convex smooth objectives. Across five benchmarks spanning controlled and realistic heterogeneity, RIPPLE consistently outperforms all baselines, with margins growing on the most realistic partitions.

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.

This paper studies robust estimation for Independent Component Analysis (ICA) in the federated learning setting, where data are locally distributed across clients and may exhibit substantial heterogeneity. The goal is to recover a common global mixing matrix by aggregating local estimators computed by individual clients. The main difficulty is that local ICA estimators are identifiable only up to sign flips and column permutations and may have highly heterogeneous estimation quality. We propose a novel three-step aggregation method that first aligns the permutations across all local estimators via a particular spectral clustering approach, then aligns the signs within each estimated cluster via another tailored spectral approach, and finally applies the geometric median for robust aggregation. The proposed estimator is shown to remain accurate even when a substantial fraction of local estimators are of low quality or inconsistent, as long as each cluster contains a majority of accurate estimators. This contrasts with its analogue based on simple averaging, whose performance is determined by the worst local estimator. In the homogeneous setting, the robust estimator is also shown to be minimax optimal, up to a logarithmic factor, both when the number of clients remains fixed and when it diverges. The theoretical findings are corroborated by simulation studies and a real-data analysis.