Federated k-Means over Networks

We study federated clustering, where interconnected devices collaboratively cluster the data points of private local datasets. Focusing on hard clustering via the k-means principle, we formulate federated k-means as an instance of generalized total variation minimization (GTVMin). This leads to a federated k-means algorithm in which each device updates its local cluster centroids by solving a regularized k-means problem with a regularizer that enforces consistency between neighbouring devices. The resulting algorithm is privacy-friendly, as only aggregated information is exchanged.