# Analysis of Total Variation Minimization for Clustered Federated Learning

arXiv: https://arxiv.org/abs/2403.06298 · HTML: https://mlsanity.com/paper/2403.06298/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 23 references that are in the map.
- First posted on arXiv 10 Mar 2024.

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

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Federated Multi-Task Learning](https://mlsanity.com/paper/1705.10467/) (2017)
- [cpSGD: Communication-efficient and differentially-private distributed SGD](https://mlsanity.com/paper/1805.10559/) (2018)
- [Distributed optimization over time-varying directed graphs](https://mlsanity.com/paper/1303.2289/) (2013)
- [CoCoA: A General Framework for Communication-Efficient Distributed Optimization](https://mlsanity.com/paper/1611.02189/) (2016)
- [Network Lasso: Clustering and Optimization in Large Graphs](https://mlsanity.com/paper/1507.00280/) (2015)
- [Localized Linear Regression in Networked Data](https://mlsanity.com/paper/1903.11178/) (2019)
- [Clustered Federated Learning via Generalized Total Variation Minimization](https://mlsanity.com/paper/2105.12769/) (2021)
- [Inexact First-Order Primal-Dual Algorithms](https://mlsanity.com/paper/1803.10576/) (2018)
- [Plug In and Learn: Federated Intelligence over a Smart Grid of Models](https://mlsanity.com/paper/2302.04363/) (2023)

## Built on by (most cited first, 1 of 1)

- [Federated Learning for Predicting Mild Cognitive Impairment to Dementia Conversion](https://mlsanity.com/paper/2503.03489/) (2025)

## Abstract (arXiv)

A key challenge in federated learning applications is the statistical heterogeneity of local datasets. Clustered federated learning addresses this challenge by identifying clusters of local datasets that are approximately homogeneous. One recent approach to clustered federated learning is generalized total variation minimization (GTVMin). This approach requires a similarity graph which can be obtained by domain expertise or in a data-driven fashion via graph learning techniques. Under a widely applicable clustering assumption, we derive an upper bound the deviation between GTVMin solutions and their cluster-wise averages. This bound provides valuable insights into the effectiveness and robustness of GTVMin in addressing statistical heterogeneity within federated learning environments.