\section{Conclusion}\label{sec:conclusion}

% We propose \algname, which uses a soft clustering model to enable federated training of personalized models in a decentralized setting. \algname~models each FL client's data as a mixture of cluster distributions and aims to learn a separate model for data corresponding to each cluster, with post-training finetuning to learn a personalized model for each client based on the cluster models. \algname~requires each client to train only one cluster model in each training round and thus scales well with the number of clusters. We theoretically show that \algname~can reach a consensus for each cluster. Our experiments on real-world datasets show that \algname~outperforms previously proposed algorithms for personalized, decentralized FL and can even approach the accuracy achieves by centralized FL training. 
We propose \textbf{\algname}, a soft clustering approach that enables federated training of personalized models in a decentralized setting. \textbf{\algname}~models each FL client's data as a mixture of cluster distributions and aims to learn a distinct model for each cluster. In the final phase, all models are aggregated and further personalized for each client. Importantly, \textbf{\algname}~requires each client to train only one cluster model per training round, ensuring scalability with the number of clusters, and works well when communication resource is limited. We theoretically demonstrate that \textbf{\algname}~can achieve consensus within each cluster. Our experiments on real-world datasets show that \textbf{\algname}~outperforms previous algorithms for personalized, decentralized FL and performs well even in \textit{low-connectivity} networks. For future extensions, this work can serve as a foundation for various applications, such as environmental monitoring in IoT, object identification in mixed reality, or autonomous driving, all of which benefit from the low latency of direct communication and collaborative learning across adjacent devices with similar data.

%\subsection*{Future Work}

%The decentralized fashion of \algname and the communication/parameter exchange with local clients make it a perfect solution for learning on geographically dependent data. In environmental monitoring and learning, the data observed by each client may be geographically dependent. Nearby clients may share different but highly related data. Since the nature of \algname relies on communication between devices in physical proximity, we expect it to allow devices with similar data to learn from each other, leading to the training of accurate models. With proper modeling of the data dependencies, a theoretical guarantee may also be derived in such a scenario. Other application of interest might be augmented and virtual reality (AR/VR) for person/object Identification, where the camera data is also highly depends on the location while these applications often require low latencies where decentralized communication might be a better choice.
% The decentralized nature of \algname~and its communication/parameter exchange with local clients make it an ideal solution for learning on geographically dependent data. In environmental monitoring and learning, the data observed by each client may be geographically dependent, with nearby clients sharing different but highly related data. Since \algname~relies on communication between devices in physical proximity, it enables devices with similar data to learn from each other, resulting in the training of accurate models. With proper modeling of the data dependencies, a theoretical guarantee may also be derived in such scenarios. Other applications of interest include augmented and virtual reality (AR/VR) for person/object identification, where camera data is highly dependent on location. These applications often require low latencies, making decentralized communication a better choice.