Most existing federated learning methods assume that clients have fully labeled data to train on, while in reality, it is hard for the clients to get task-specific labels due to users' privacy concerns, high labeling costs, or lack of expertise. This work considers the server with a small labeled dataset and intends to use unlabeled data in multiple clients for semi-supervised learning. We propose a new framework with a generalized model, Federated Incremental Learning (FedIL), to address the problem of how to utilize labeled data in the server and unlabeled data in clients separately in the scenario of Federated Learning (FL). FedIL uses the Iterative Similarity Fusion to enforce the server-client consistency on the predictions of unlabeled data and uses incremental confidence to establish a credible pseudo-label set in each client. We show that FedIL will accelerate model convergence by Cosine Similarity with normalization, proved by Banach Fixed Point Theorem. The code is available at https://anonymous.4open.science/r/fedil.
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