Homophily Heterogeneity Matters in Graph Federated Learning: A Spectrum Sharing and Complementing Perspective
Wentao Yu
TL;DR
This work tackles the challenge of homophily heterogeneity in Graph Federated Learning by introducing FedGSP, which leverages a spectral GNN to separate and share low-frequency (generic) and high-frequency (complementary) spectral information across clients. It builds a Federated Collaboration Graph to model inter-client relationships and theoretically ties heterogeneity to the complementarity ratio, justifying simultaneous pursuit of similarity and complementarity. The method jointly optimizes collaboration strengths and federates polynomial-basis coefficients to achieve robust performance across both homophilic and heterophilic graphs, with extensive experiments showing improvements over 11 baselines and demonstrating efficiency and stability. The approach has practical impact for privacy-preserving, distributed graph learning scenarios where client data exhibit diverse homophily patterns and spectral properties.
Abstract
Since heterogeneity presents a fundamental challenge in graph federated learning, many existing methods are proposed to deal with node feature heterogeneity and structure heterogeneity. However, they overlook the critical homophily heterogeneity, which refers to the substantial variation in homophily levels across graph data from different clients. The homophily level represents the proportion of edges connecting nodes that belong to the same class. Due to adapting to their local homophily, local models capture inconsistent spectral properties across different clients, significantly reducing the effectiveness of collaboration. Specifically, local models trained on graphs with high homophily tend to capture low-frequency information, whereas local models trained on graphs with low homophily tend to capture high-frequency information. To effectively deal with homophily heterophily, we introduce the spectral Graph Neural Network (GNN) and propose a novel Federated learning method by mining Graph Spectral Properties (FedGSP). On one hand, our proposed FedGSP enables clients to share generic spectral properties (i.e., low-frequency information), allowing all clients to benefit through collaboration. On the other hand, inspired by our theoretical findings, our proposed FedGSP allows clients to complement non-generic spectral properties by acquiring the spectral properties they lack (i.e., high-frequency information), thereby obtaining additional information gain. Extensive experiments conducted on six homophilic and five heterophilic graph datasets, across both non-overlapping and overlapping settings, validate the superiority of our method over eleven state-of-the-art methods. Notably, our FedGSP outperforms the second-best method by an average margin of 3.28% on all heterophilic datasets.