# Federated Clustering with Unknown Local and Global Cluster Cardinalities

arXiv: https://arxiv.org/abs/2609.36762 · HTML: https://mlsanity.com/paper/2609.36762/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 19 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 8 of 8)

- [An Efficient Framework for Clustered Federated Learning](https://mlsanity.com/paper/2006.04088/) (2020)
- [Clustered Federated Learning: Model-Agnostic Distributed Multi-Task Optimization under Privacy Constraints](https://mlsanity.com/paper/1910.01991/) (2019)
- [Heterogeneity for the Win: One-Shot Federated Clustering](https://mlsanity.com/paper/2103.00697/) (2021)
- [Towards Federated Clustering: A Federated Fuzzy c-Means Algorithm (FFCM)](https://mlsanity.com/paper/2201.07316/) (2022)
- [Statistical Model Aggregation via Parameter Matching](https://mlsanity.com/paper/1911.00218/) (2019)
- [Asynchronous Federated Clustering with Unknown Number of Clusters](https://mlsanity.com/paper/2412.20341/) (2024)
- [Federated K-means Clustering](https://mlsanity.com/paper/2310.01195/) (2023)
- [A Federated Generalized Expectation-Maximization Algorithm for Mixture Models with an Unknown Number of Components](https://mlsanity.com/paper/2601.21160/) (2026)

## Abstract (arXiv)

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.