# CLoVE: Personalized Federated Learning through Clustering of Loss Vector Embeddings

arXiv: https://arxiv.org/abs/2506.22427 · HTML: https://mlsanity.com/paper/2506.22427/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 50 references that are in the map.
- First posted on arXiv 27 Jun 2025.

## Builds on (most cited first, 30 of 30)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Federated Learning with Non-IID Data](https://mlsanity.com/paper/1806.00582/) (2018)
- [Towards Federated Learning at Scale: System Design](https://mlsanity.com/paper/1902.01046/) (2019)
- [LEAF: A Benchmark for Federated Settings](https://mlsanity.com/paper/1812.01097/) (2018)
- [Federated Multi-Task Learning](https://mlsanity.com/paper/1705.10467/) (2017)
- [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)
- [Towards Personalized Federated Learning](https://mlsanity.com/paper/2103.00710/) (2021)
- [Adaptive Personalized Federated Learning](https://mlsanity.com/paper/2003.13461/) (2020)
- [FedProto: Federated Prototype Learning across Heterogeneous Clients](https://mlsanity.com/paper/2105.00243/) (2021)
- [Three Approaches for Personalization with Applications to Federated Learning](https://mlsanity.com/paper/2002.10619/) (2020)
- [Improving Federated Learning Personalization via Model Agnostic Meta Learning](https://mlsanity.com/paper/1909.12488/) (2019)
- [Federated Learning of a Mixture of Global and Local Models](https://mlsanity.com/paper/2002.05516/) (2020)
- [FedALA: Adaptive Local Aggregation for Personalized Federated Learning](https://mlsanity.com/paper/2212.01197/) (2022)
- [Multi-Center Federated Learning: Clients Clustering for Better Personalization](https://mlsanity.com/paper/2108.08647/) (2021)
- [Efficient Parameter-free Clustering Using First Neighbor Relations](https://mlsanity.com/paper/1902.11266/) (2019)
- [Personalized Federated Learning with Feature Alignment and Classifier Collaboration](https://mlsanity.com/paper/2306.11867/) (2023)
- [Heterogeneity for the Win: One-Shot Federated Clustering](https://mlsanity.com/paper/2103.00697/) (2021)
- [Flexible Clustered Federated Learning for Client-Level Data Distribution Shift](https://mlsanity.com/paper/2108.09749/) (2021)
- [Efficient Distribution Similarity Identification in Clustered Federated Learning via Principal Angles Between Client Data Subspaces](https://mlsanity.com/paper/2209.10526/) (2022)
- [Provably Personalized and Robust Federated Learning](https://mlsanity.com/paper/2306.08393/) (2023)
- [Spectral Co-Distillation for Personalized Federated Learning](https://mlsanity.com/paper/2401.17124/) (2024)
- [Interaction-Aware Gaussian Weighting for Clustered Federated Learning](https://mlsanity.com/paper/2502.03340/) (2025)
- [Alternating Minimization for Mixed Linear Regression](https://mlsanity.com/paper/1310.3745/) (2013)

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

- [CLAD: A Clustered Label-Agnostic Federated Learning Framework for Joint Anomaly Detection and Attack Classification](https://mlsanity.com/paper/2605.06571/) (2026)

## Abstract (arXiv)

We propose CLoVE (Clustering of Loss Vector Embeddings), a novel algorithm for Clustered Federated Learning (CFL). In CFL, clients are naturally grouped into clusters based on their data distribution. However, identifying these clusters is challenging, as client assignments are unknown. CLoVE utilizes client embeddings derived from model losses on client data, and leverages the insight that clients in the same cluster share similar loss values, while those in different clusters exhibit distinct loss patterns. Based on these embeddings, CLoVE is able to iteratively identify and separate clients from different clusters and optimize cluster-specific models through federated aggregation. Key advantages of CLoVE over existing CFL algorithms are (1) its simplicity, (2) its applicability to both supervised and unsupervised settings, and (3) the fact that it eliminates the need for near-optimal model initialization, which makes it more robust and better suited for real-world applications. We establish theoretical convergence bounds, showing that CLoVE can recover clusters accurately with high probability in a single round and converges exponentially fast to optimal models in a linear setting. Our comprehensive experiments comparing with a variety of both CFL and generic Personalized Federated Learning (PFL) algorithms on different types of datasets and an extensive array of non-IID settings demonstrate that CLoVE achieves highly accurate cluster recovery in just a few rounds of training, along with state-of-the-art model accuracy, across a variety of both supervised and unsupervised PFL tasks.