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In this paper, the content popularity prediction problem in fog radio access networks (F-RANs) is investigated. Based on clustered federated learning, we propose a novel mobility-aware popularity prediction policy, which integrates content popularities in terms of local users and mobile users. For local users, the content popularity is predicted by learning the hidden representations of local users and contents. Initial features of local users and contents are generated by incorporating neighbor information with self information. Then, dual-channel neural network (DCNN) model is introduced to learn the hidden representations by producing deep latent features from initial features. For mobile users, the content popularity is predicted via user preference learning. In order to distinguish regional variations of content popularity, clustered federated learning (CFL) is employed, which enables fog access points (F-APs) with similar regional types to benefit from one another and provides a more specialized DCNN model for each F-AP. Simulation results show that our proposed policy achieves significant performance improvement over the traditional policies.