  Federated learning has recently garnered significant attention, especially
within the domain of supervised learning. However, despite the abundance of
unlabeled data on end-users, unsupervised learning problems such as clustering
in the federated setting remain underexplored. In this paper, we investigate
the federated clustering problem, with a focus on federated k-means. We outline
the challenge posed by its non-convex objective and data heterogeneity in the
federated framework. To tackle these challenges, we adopt a new perspective by
studying the structures of local solutions in k-means and propose a one-shot
algorithm called FeCA (Federated Centroid Aggregation). FeCA adaptively refines
local solutions on clients, then aggregates these refined solutions to recover
the global solution of the entire dataset in a single round. We empirically
demonstrate the robustness of FeCA under various federated scenarios on both
synthetic and real-world data. Additionally, we extend FeCA to representation
learning and present DeepFeCA, which combines DeepCluster and FeCA for
unsupervised feature learning in the federated setting.
