Personalized Federated Learning with Heat-Kernel Enhanced Tensorized Multi-View Clustering

This paper proposes a personalized federated learning framework integrating heat-kernel enhanced tensorized multi-view fuzzy c-means clustering with tensor decomposition techniques. The approach combines heat-kernel coefficients adapted from quantum field theory with PARAFAC2 and Tucker decomposition to transform distance metrics and efficiently represent high-dimensional multi-view structures. Two main algorithms, FedHK-PARAFAC2 and FedHK-Tucker, are developed to extract shared and view-specific features while preserving inter-view relationships. The framework addresses data heterogeneity, privacy preservation, and communication efficiency challenges in federated learning environments. Theoretical analysis provides convergence guarantees, privacy bounds, and complexity analysis. The integration of heat-kernel methods with tensor decomposition in a federated setting offers a novel approach for effective multi-view data analysis while ensuring data privacy.