Federated Learning (FL) has emerged as a decentralized machine learning technique, allowing clients to train a global model collaboratively without sharing private data. However, most FL studies ignore the crucial challenge of heterogeneous domains where each client has a distinct feature distribution, which is popular in real-world scenarios. Prototype learning, which leverages the mean feature vectors within the same classes, has become a prominent solution for federated learning under domain shift. However, existing federated prototype learning methods focus soley on inter-domain prototypes and neglect intra-domain perspectives. In this work, we introduce a novel federated prototype learning method, namely I$^2$PFL, which incorporates $\textbf{I}$ntra-domain and $\textbf{I}$nter-domain $\textbf{P}$rototypes, to mitigate domain shift from both perspectives and learn a generalized global model across multiple domains in federated learning. To construct intra-domain prototypes, we propose feature alignment with MixUp-based augmented prototypes to capture the diversity within local domains and enhance the generalization of local features. Additionally, we introduce a reweighting mechanism for inter-domain prototypes to generate generalized prototypes that reduce domain shift while providing inter-domain knowledge across multiple clients. Extensive experiments on the Digits, Office-10, and PACS datasets illustrate the superior performance of our method compared to other baselines.

翻译：联邦学习作为一种去中心化的机器学习技术，允许客户端在不共享私有数据的情况下协作训练全局模型。然而，多数联邦学习研究忽略了异构领域这一关键挑战，即每个客户端具有不同的特征分布——这在实际场景中普遍存在。原型学习通过利用同一类别内的平均特征向量，已成为应对领域偏移下联邦学习的重要解决方案。然而，现有的联邦原型学习方法仅关注域间原型，忽视了域内视角。本研究提出一种新颖的联邦原型学习方法——I$^2$PFL，该方法融合$\textbf{域内}$与$\textbf{域间}$$\textbf{原型}$，从双重视角缓解领域偏移，并在联邦学习中学习跨多个领域的泛化全局模型。为构建域内原型，我们提出基于MixUp增强原型的特征对齐方法，以捕捉局部领域内的多样性并增强局部特征的泛化能力。此外，我们引入域间原型的重加权机制，通过生成泛化原型来降低领域偏移，同时提供跨多个客户端的域间知识。在Digits、Office-10和PACS数据集上的大量实验表明，相较于其他基线方法，本方法具有更优越的性能。