Heterogeneity-Aware Knowledge Sharing for Graph Federated Learning

TL;DR

FedSSA tackles heterogeneity in Graph Federated Learning by independently addressing node-feature and structural heterogeneity. It combines a variational graph autoencoder to infer class-wise feature distributions and cluster clients semantically, with a spectral-GNN framework that uses a spectral energy descriptor to cluster by topology and align local versus cluster-level spectral filters. The method yields linear convergence to a small error floor and achieves state-of-the-art performance across 11 benchmark datasets with both non-overlapping and overlapping partitioning. This dual sharing mechanism enhances both privacy-preserving collaboration and model effectiveness in diverse graph settings, offering robust, scalable improvements for real-world GFL deployments.

Abstract

Graph Federated Learning (GFL) enables distributed graph representation learning while protecting the privacy of graph data. However, GFL suffers from heterogeneity arising from diverse node features and structural topologies across multiple clients. To address both types of heterogeneity, we propose a novel graph Federated learning method via Semantic and Structural Alignment (FedSSA), which shares the knowledge of both node features and structural topologies. For node feature heterogeneity, we propose a novel variational model to infer class-wise node distributions, so that we can cluster clients based on inferred distributions and construct cluster-level representative distributions. We then minimize the divergence between local and cluster-level distributions to facilitate semantic knowledge sharing. For structural heterogeneity, we employ spectral Graph Neural Networks (GNNs) and propose a spectral energy measure to characterize structural information, so that we can cluster clients based on spectral energy and build cluster-level spectral GNNs. We then align the spectral characteristics of local spectral GNNs with those of cluster-level spectral GNNs to enable structural knowledge sharing. Experiments on six homophilic and five heterophilic graph datasets under both non-overlapping and overlapping partitioning settings demonstrate that FedSSA consistently outperforms eleven state-of-the-art methods.

Figures (13)

• Figure 1: The overview of our proposed FedSSA. (a) Semantic Knowledge Sharing: A variational model infers class-wise node feature distributions on each client. Clients are clustered based on inferred distributions, and local distributions are aligned with cluster-level distributions. (b) Structural Knowledge Sharing: Spectral GNNs are employed alongside a spectral energy measure to characterize local structural topologies. Clients are clustered by spectral energy, which enables alignment between local and cluster-level spectral GNNs.
• Figure 2: The graphical model of our proposed variational model, where $\mathbf{Z}_m$ is a latent variable, $\mathbf{X}_m$ and $\mathbf{Y}_m$ are observed variables.
• Figure 3: Ablation studies under overlapping partitioning setting with 30 clients.
• Figure 4: Convergence curves on two datasets under non-overlapping partitioning setting with 10 clients.
• Figure 5: Accuracy curves with standard deviation bands on Cora dataset under different values of $K_\mathrm{node}$, $K_\mathrm{struct}$, $\lambda_1$, and $\lambda_2$.

Theorems & Definitions (20)

• Theorem 4.2: Convergence of FedSSA
• Corollary 4.3: Convergence Rate
• Remark 4.4
• Lemma 4.6: Cluster-level Jacobian Bounds
• proof
• Lemma 4.7: KL Divergence Bound
• proof
• Lemma 4.8: Gradient Error from Semantic Alignment
• proof
• Lemma 4.9: Lipschitz Constant of the Spectral Filter