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.

翻译：联邦学习近来受到广泛关注，尤其在监督学习领域。然而，尽管终端用户拥有大量未标记数据，联邦环境下的无监督学习问题（如聚类）仍未得到充分探索。本文研究联邦聚类问题，重点关注联邦k均值算法。我们阐述了其在联邦框架中因非凸目标函数和数据异构性所带来的挑战。为应对这些挑战，我们采用新视角，通过研究k均值局部解的结构，提出了一种名为FeCA（联邦质心聚合）的单轮算法。FeCA自适应地优化客户端上的局部解，然后聚合这些优化后的解，以单轮通信恢复整个数据集的全局解。我们在合成数据和真实数据上的多种联邦场景下实证验证了FeCA的鲁棒性。此外，我们将FeCA扩展至表示学习领域，提出了DeepFeCA，该方法结合DeepCluster与FeCA，用于联邦环境下的无监督特征学习。