Credible grouping of heterogeneous clients for personalized federated learning via block-term decomposition

Clustered federated learning (FL) has demonstrated promising results in personalized modeling by grouping clients with similar data distribution into the same cluster. However, existing methods either fix the client grouping before training, which limits the flexibility of grouping, or determine the grouping during training, which suffers from inefficiency. Moreover, intra-cluster models are typically obtained via simple weighted aggregation, which tends to dilute important model information and introduce aggregation bias. To address these issues, we propose FedBTD, a novel FL framework based on Block-Term Decomposition (BTD), which credibly groups clients and performs nonlinear intra-group aggregation. By compressing clients’ classification predictor layers into tensors and applying BTD, FedBTD extracts structural patterns to identify similar clients and derive group-wise models, enabling effective knowledge sharing while filtering out irrelevant information. Unlike traditional clustering methods, FedBTD supports dynamic regrouping during training and avoids information loss from linear aggregation. Extensive experiments across various heterogeneous data settings show that FedBTD consistently outperforms 17 state-of-the-art FL methods.