A Convergent Federated Clustering Algorithm without Initial Condition

In this paper, we define a new clustering framework for FL based on the (optimal) local models of the users: two users belong to the same cluster if their local models are close. We propose an algorithm, \emph{Successive Refine Federated Clustering Algorithm} (\texttt{SR-FCA}), that treats each user as a singleton cluster as an initialization, and then successively refine the cluster estimation via exploiting similarity with other users. In any intermediate step, \texttt{SR-FCA} uses an {\em error-tolerant} federated learning algorithm within each cluster to exploit simultaneous training and to correct clustering errors. Unlike some prominent prior works, such as ~\cite{ghoshefficient2021}, \texttt{SR-FCA} does not require any \emph{good} initialization (or warm start), both in theory and practice. We show that with proper choice of learning rate, \texttt{SR-FCA} incurs arbitrarily small clustering error. Additionally, \texttt{SR-FCA} does not require the knowledge of the number of clusters apriori like some prior works. We also validate the performance of our algorithm on real-world FL datasets including FEMNIST and Shakespeare in non-convex problems and show the benefits of \texttt{SR-FCA} over several baselines.