Federated learning (FL) has emerged with increasing popularity to collaborate distributed medical institutions for training deep networks. However, despite existing FL algorithms only allow the supervised training setting, most hospitals in realistic usually cannot afford the intricate data labeling due to absence of budget or expertise. This paper studies a practical yet challenging FL problem, named textit{Federated Semi-supervised Learning} (FSSL), which aims to learn a federated model by jointly utilizing the data from both labeled and unlabeled clients (i.e., hospitals). We present a novel approach for this problem, which improves over traditional consistency regularization mechanism with a new inter-client relation matching scheme. The proposed learning scheme explicitly connects the learning across labeled and unlabeled clients by aligning their extracted disease relationships, thereby mitigating the deficiency of task knowledge at unlabeled clients and promoting discriminative information from unlabeled samples. We validate our method on two large-scale medical image classification datasets. The effectiveness of our method has been demonstrated with the clear improvements over state-of-the-arts as well as the thorough ablation analysis on both tasksfootnote{Code will be made available at url{https://github.com/liuquande/FedIRM}}.
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