Federated Soft Clustering via Generalized Total Variation Minimization
Abstract
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.
Versions
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BibTeX
@misc{abdurakhmanova2026federated,
title = {{Federated Soft Clustering via Generalized Total Variation Minimization}},
author = {Shamsiiat Abdurakhmanova and Alexander Jung},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19202},
eprint = {2609.19202},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19202},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Federated Soft Clustering via Generalized Total Variation Minimization
AU - Shamsiiat Abdurakhmanova
AU - Alexander Jung
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.19202
UR - https://arxiv.org/abs/2609.19202
AB - 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.
ER -