# Federated Soft Clustering via Generalized Total Variation Minimization

arXiv: https://arxiv.org/abs/2609.19202 · HTML: https://mlsanity.com/paper/2609.19202/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 26 references that are in the map.
- First posted on arXiv 16 Sep 2026.

## Builds on (most cited first, 11 of 11)

- [An Efficient Framework for Clustered Federated Learning](https://mlsanity.com/paper/2006.04088/) (2020)
- [Federated Multi-Task Learning under a Mixture of Distributions](https://mlsanity.com/paper/2108.10252/) (2021)
- [Training generative neural networks via Maximum Mean Discrepancy optimization](https://mlsanity.com/paper/1505.03906/) (2015)
- [Personalized Federated Learning under Mixture of Distributions](https://mlsanity.com/paper/2305.01068/) (2023)
- [Towards the Theory of Unsupervised Federated Learning: Non-asymptotic Analysis of Federated EM Algorithms](https://mlsanity.com/paper/2310.15330/) (2023)
- [Distributed Estimation, Information Loss and Exponential Families](https://mlsanity.com/paper/1410.2653/) (2014)
- [Distributed Learning of Finite Gaussian Mixtures](https://mlsanity.com/paper/2010.10412/) (2020)
- [Federated Gaussian Mixture Models](https://mlsanity.com/paper/2506.01780/) (2025)
- [Robust Federated Personalised Mean Estimation for the Gaussian Mixture Model](https://mlsanity.com/paper/2504.19955/) (2025)
- [Federated k-Means over Networks](https://mlsanity.com/paper/2510.09718/) (2025)
- [Transfer Learning in High-Dimensional Clustering: Minimax Thresholds and Applications in Single-Cell Data](https://mlsanity.com/paper/2607.25031/) (2026)

## Abstract (arXiv)

We study federated soft clustering over federated learning (FL) networks of devices that each hold a private local dataset and fit a personalized Gaussian mixture model (GMM). Generalized total variation minimization (GTVMin) couples the local maximum likelihood problems through a graph regularizer that penalizes a discrepancy between the models of connected nodes. The choice of discrepancy measure is a key design decision: we compare a squared Euclidean distance between model parameters, which requires component matching, with two measures that compare the local model distributions directly and hence need no matching: a Monte-Carlo approximated Kullback-Leibler (KL) divergence and a closed-form maximum mean discrepancy (MMD). All three resulting GTVMin instances are optimized by synchronous projected gradient updates; for the smooth MMD instance we provide a convergence guarantee to stationary points. We characterize their computational cost and evaluate their robustness to data heterogeneity.