FedHK-MVFC: Federated Heat Kernel Multi-View Clustering

In the realm of distributed AI and privacy-focused medical applications, we propose a framework for multi-view clustering that links quantum field theory with federated healthcare analytics. Our method uses heat-kernel coefficients from spectral analysis to convert Euclidean distances into geometry-aware similarity measures, capturing the structure of diverse medical data. We lay this out through the Heat Kernel Distance (HKD) transformation with convergence guarantees. Two algorithms are developed: Heat Kernel-Enhanced Multi-View Fuzzy Clustering (HK-MVFC) for central analysis, and Federated Heat Kernel Multi-View Fuzzy Clustering (FedHK-MVFC) for secure, privacy-preserving learning across hospitals using differential privacy and secure aggregation to facilitate HIPAA-compliant collaboration. Tests on synthetic datasets of cardiovascular patients show an $8-12 \%$ increase in clustering accuracy, $70 \%$ reduced communication, and $98.2 \%$ efficiency retention over centralized methods. Validated on 10,000 patient records across two hospitals, it proves useful for collaborative phenotyping involving ECG, cardiac imaging, and behavioral data. Our theoretical contributions include update rules with proven convergence, adaptive view weighting, and privacy-preserving protocols. This presents a new standard for geometry-aware federated learning in healthcare, turning advanced math into workable solutions for analyzing sensitive medical data while ensuring both rigor and clinical relevance.