Federated learning (FL) is a decentralized machine learning paradigm in which multiple clients collaboratively train a shared model without sharing their local private data. However, real-world applications of FL frequently encounter challenges arising from the non-identically and independently distributed (non-IID) local datasets across participating clients, which is particularly pronounced in the field of medical imaging, where shifts in image feature distributions significantly hinder the global model's convergence and performance. To address this challenge, we propose FedMP, a novel method designed to enhance FL under non-IID scenarios. FedMP employs stochastic feature manifold completion to enrich the training space of individual client classifiers, and leverages class-prototypes to guide the alignment of feature manifolds across clients within semantically consistent subspaces, facilitating the construction of more distinct decision boundaries. We validate the effectiveness of FedMP on multiple medical imaging datasets, including those with real-world multi-center distributions, as well as on a multi-domain natural image dataset. The experimental results demonstrate that FedMP outperforms existing FL algorithms. Additionally, we analyze the impact of manifold dimensionality, communication efficiency, and privacy implications of feature exposure in our method.
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