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

Kristina P. Sinaga

TL;DR

This work tackles clustering over heterogeneous, multi-view data distributed across federated clients by marrying heat-kernel enhanced distance measures with tensor-based representations. It introduces two personalized federated algorithms, FedHK-PARAFAC2 and FedHK-Tucker, that unify multi-view fuzzy clustering with PARAFAC2 and Tucker decompositions to capture shared and view-specific structure while preserving privacy. The framework deploys Federated Kernel Euclidean Distance (FKED) and tensorized TKED, along with FedH-KC heat-kernel coefficients, enabling private, efficient clustering with personalized updates and secure aggregation. Theoretical analysis provides convergence guarantees, privacy bounds, and complexity assessments, underscoring the practicality of tensorized, privacy-preserving, personalized federated clustering for high-dimensional, multi-view data. Potential applications span healthcare, IoT, and collaborative intelligence, where privacy and personalization are paramount.

Abstract

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.

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

TL;DR

This work tackles clustering over heterogeneous, multi-view data distributed across federated clients by marrying heat-kernel enhanced distance measures with tensor-based representations. It introduces two personalized federated algorithms, FedHK-PARAFAC2 and FedHK-Tucker, that unify multi-view fuzzy clustering with PARAFAC2 and Tucker decompositions to capture shared and view-specific structure while preserving privacy. The framework deploys Federated Kernel Euclidean Distance (FKED) and tensorized TKED, along with FedH-KC heat-kernel coefficients, enabling private, efficient clustering with personalized updates and secure aggregation. Theoretical analysis provides convergence guarantees, privacy bounds, and complexity assessments, underscoring the practicality of tensorized, privacy-preserving, personalized federated clustering for high-dimensional, multi-view data. Potential applications span healthcare, IoT, and collaborative intelligence, where privacy and personalization are paramount.

Abstract

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.

Paper Structure

This paper contains 49 sections, 12 theorems, 83 equations, 3 figures, 2 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Federated Learning and Clustering
  4. Multi-View Clustering
  5. Heat Kernel Methods and Quantum-Inspired Learning
  6. Tensor Decomposition Methods
  7. Mathematical Preliminaries
  8. Federated Learning and Clustering
  9. Multi-View Clustering
  10. Federated Multi-View Learning and Privacy Preservation
  11. Tensor Decomposition Methods
  12. The Basic Background of Tensors
  13. The Higher Order Singular Value Decomposition (HOSVD)
  14. Tensor Distance
  15. Summary and Research Gaps
  16. ...and 34 more sections

Key Result

Theorem 1

For the federated objective function $J_{E-FKMVC}$ defined in Eq. eqn:E-FKMVC, the necessary conditions for optimality yield the following update rules for client $\ell$: Membership Matrix Update: Cluster Centers Update: View Weights Update: where the updates are performed iteratively until convergence, subject to the normalization constraints in Eqs. eqn:fed_constraint1 and eqn:fed_constraint2.

Figures (3)

  • Figure 1: The Illustration of A 3-Dimensional of a Red-Green-Blue (RGB) Image
  • Figure 2: The Illustration of MV Data in Tensor Space
  • Figure 3: The Illustration of Rank-One Third-Order Tensor $\mathcal{A} = x \circ y \circ z$

Theorems & Definitions (22)

  • Theorem 1: E-FKMVC Update Rules
  • proof
  • Theorem 2: The FedHK-PARAFAC2 Update Rules
  • proof : The Proof of Theorem \ref{['thm:tensorized_updates']}
  • Theorem 3: The FedHK-Tucker Update Rules
  • proof : The Proof of Theorem \ref{['thm:tucker_updates']}
  • Definition 1: Federated Heat-Kernel Enhanced Multi-View Clustering with Personalization
  • Definition 2: Federated Aggregation Protocol
  • Definition 3: Tensorized Federated Aggregation Protocol
  • Theorem 4: Local Convergence
  • ...and 12 more