Federated Clustering with Unknown Local and Global Cluster Cardinalities

Federated clustering methods that do not require the global number of clusters K still assume that each client knows its local number Kg. 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 Kg 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.