FedHK-MVFC: Federated Heat Kernel Multi-View Clustering

TL;DR

This work introduces HK-MVFC, a heat-kernel based multi-view fuzzy clustering framework, and its federated extension FedHK-MVFC for privacy-preserving collaboration across distributed healthcare sites. By replacing Euclidean distances with geometry-aware kernel distances derived from heat-kernel coefficients, the method captures intrinsic data manifold structure and supports adaptive view weighting to handle view heterogeneity. Theoretical contributions include convergence guarantees, adaptive weighting analysis, and privacy-preserving protocols (differential privacy and secure aggregation) within a federated learning setting. Experiments on synthetic multi-view cardiovascular data show improved clustering accuracy, reduced communication, and robust performance under data heterogeneity, illustrating practical potential for collaborative phenotyping while safeguarding sensitive medical information. The framework further outlines real-world extensions to healthcare, Future Internet scenarios, and cross-domain applications, highlighting the balance between geometric fidelity, privacy, and scalability.

Abstract

In the realm of distributed artificial intelligence (AI) and privacy-focused medical applications, this paper proposes a multi-view clustering framework that links quantum field theory with federated healthcare analytics. The method uses heat kernel coefficients from spectral analysis to convert Euclidean distances into geometry-aware similarity measures that capture the structure of diverse medical data. The framework is presented through the heat kernel distance (HKD) transformation, which has convergence guarantees. Two algorithms have been developed: The first, Heat Kernel-Enhanced Multi-View Fuzzy Clustering (HK-MVFC), is used for central analysis. The second, Federated Heat Kernel Multi-View Fuzzy Clustering (FedHK-MVFC), is used for secure, privacy-preserving learning across hospitals. FedHK-MVFC uses differential privacy and secure aggregation to enable HIPAA-compliant collaboration. Tests on synthetic cardiovascular patient datasets demonstrate increased clustering accuracy, reduced communication, and retained efficiency compared to centralized methods. After being validated on 10,000 synthetic patient records across two hospitals, the methods proved useful for collaborative phenotyping involving electrocardiogram (ECG) data, cardiac imaging data, and behavioral data. The proposed methods' theoretical contributions include update rules with proven convergence, adaptive view weighting, and privacy-preserving protocols. These contributions establish a new standard for geometry-aware federated learning in healthcare, translating advanced mathematics into practical solutions for analyzing sensitive medical data while ensuring rigor and clinical relevance.

Figures (11)

• Figure 1: Flowchart of the HK-MVFC Algorithm (Algorithm \ref{['alg:HK_MVFC']}). The algorithm iteratively updates membership matrix, cluster centers, and view weights using heat kernel-enhanced distances until convergence.
• Figure 2: Flowchart of the FedHK-MVFC Algorithm (Algorithm \ref{['alg:FedHK_MVFC_Main']}). The federated workflow involves iterative server-client communication with local heat kernel-enhanced clustering and global model aggregation.
• Figure 3: Two-view, four-cluster multi-view dataset featuring unique cluster shapes, each with precisely 10,000 instances (4 clusters x 2,500 samples per cluster): (a) View 1 displaying four unique cluster shapes, including circular, horizontal, crescent/banana, and spiral/S-curve formations. (b) View 2 illustrating four distinct shapes like diamond/rhombus, ring/donut, cross/plus, and heart configurations. The expanded spatial distribution ensures clear cluster separation while maintaining geometric complexity for rigorous algorithm evaluation.
• Figure 4: Multi-view federated clustering visualization showing data distribution across two hospitals. Hospital A (Client 1) contributes 8,500 patient records while Hospital B (Client 2) contributes 1,500 patient records. Each hospital provides two complementary views: View 1 contains physiological measurements (ECG features, blood pressure, laboratory biomarkers, physical examination), while View 2 encompasses imaging and behavioral data (cardiac MRI, echocardiogram, lifestyle factors, risk profiles). The federated learning framework enables collaborative patient phenotyping while preserving data privacy across institutions.
• Figure 5: Medical Federated Scenario: Multi-Hospital Cardiovascular Patient Analysis using FedHK-MVFC. Hospital A (8,500 records) and Hospital B (1,500 records) collaborate to identify patient phenotypes while preserving data privacy. The heat-kernel enhanced framework enables effective clustering across complementary medical views (physiological measurements and imaging/behavioral data) without sharing sensitive patient information.

Theorems & Definitions (6)

• Theorem 1: HK-MVFC Update Rules
• Remark 1
• proof
• Theorem 2: FedHK-MVFC Update Rules
• Remark 2
• proof