Personalization aims to characterize individual preferences and is widely applied across many fields. However, conventional personalized methods operate in a centralized manner and potentially expose the raw data when pooling individual information. In this paper, with privacy considerations, we develop a flexible and interpretable personalized framework within the paradigm of Federated Learning, called PPFL (Population Personalized Federated Learning). By leveraging canonical models to capture fundamental characteristics among the heterogeneous population and employing membership vectors to reveal clients' preferences, it models the heterogeneity as clients' varying preferences for these characteristics and provides substantial insights into client characteristics, which is lacking in existing Personalized Federated Learning (PFL) methods. Furthermore, we explore the relationship between our method and three main branches of PFL methods: multi-task PFL, clustered FL, and decoupling PFL, and demonstrate the advantages of PPFL. To solve PPFL (a non-convex constrained optimization problem), we propose a novel random block coordinate descent algorithm and present the convergence property. We conduct experiments on both pathological and practical datasets, and the results validate the effectiveness of PPFL.
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