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$S^2$FGL: Spatial Spectral Federated Graph Learning
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Proposes S²FGL, a subgraph federated graph learning framework combining a prototype-based global knowledge repository (NLIR) with spectral alignment of low/high-frequency projections (FGMA) to address label signal disruption and spectral client drift.
Problem
Subgraph federated graph learning loses label signals across edges removed by partitioning (spatial) and suffers spectral heterogeneity across clients that causes divergent GNN propagation (spectral client drift), degrading global generalizability.
Approach
Spatial side: select structurally and semantically representative nodes (SALC score via PPR) to build global class prototypes and distill similarity distributions to them (FKD loss). Spectral side: build a kNN feature-similarity Laplacian for local and frozen global models and align low- and high-frequency eigenvector projections of features (FGMA loss).
Key results
- S²FGL reaches 83.4% on Cora, 76.0% on CiteSeer and 88.6% on PubMed, outperforming the best baseline on each homophilic dataset by about 0.9 to 1.7 points.
- On heterophilic datasets S²FGL obtains 74.8% on Texas (+2.0 over FedAvg) and 80.5% on Minesweeper.
- Ablation on Cora and CiteSeer shows NLIR alone gives 83.2/75.6, FGMA alone 82.6/75.0, and both together 83.4/76.0 (FedAvg 81.9/74.3).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use S²FGL instead of FedAvg | ACM-GCN · Cora | accuracy: 81.9 ± 0.7 -> 83.4 ± 0.2 | Helped |
| use S²FGL instead of FedAvg | ACM-GCN · CiteSeer | accuracy: 74.3 ± 0.4 -> 76.0 ± 0.3 | Helped |
| use S²FGL instead of FedAvg | ACM-GCN · PubMed | accuracy: 87.3 ± 0.3 -> 88.6 ± 0.2 | Helped |
| use S²FGL instead of FedAvg | ACM-GCN · Texas | accuracy: 72.8 ± 2.2 -> 74.8 ± 2.3 | Helped |
| use S²FGL instead of FedAvg | ACM-GCN · Wisconsin | accuracy: 77.6 ± 2.7 -> 79.0 ± 1.0 | Mixed |
| use S²FGL instead of FedAvg | ACM-GCN · Minesweeper | accuracy: 79.6 ± 0.1 -> 80.5 ± 0.1 | Helped |
| add NLIR and FGMA (ablation) | S²FGL · Cora | accuracy: 81.9 ± 0.7 -> 83.4 ± 0.2 | Helped |
| add NLIR and FGMA (ablation) | S²FGL · CiteSeer | accuracy: 74.3 ± 0.4 -> 76.0 ± 0.3 | Helped |
| add FGMA (ablation) | S²FGL with NLIR · Cora | accuracy: 83.2 ± 0.4 -> 83.4 ± 0.2 | Helped |
| add NLIR (ablation) | S²FGL with FGMA · CiteSeer | accuracy: 75.0 ± 0.2 -> 76.0 ± 0.3 | Helped |
Limitations
- Improvements over the strongest baselines are modest (often under 1 point) and some gaps are within standard deviation.
- Ablation is limited to Cora and CiteSeer; hyperparameter and client-scale studies are also limited to those datasets.
- Several analysis claims (SIS trends, spectral heterogeneity) reference figures and are not fully specified in the text.
Experimental setup
Datasets: Cora CiteSeer PubMed Texas Wisconsin Minesweeper
Benchmarks: Cora CiteSeer PubMed Texas Wisconsin Minesweeper
Metrics: node classification accuracy
Baselines: FedAvg FedProx FedNova FedFa FedSage+ FedStar FedPub FGSSL FedGTA FGGP
Builds on: FedAvg personalized PageRank ACM-GCN Louvain community detection
Closest papers by meaning
- Virtual Nodes Can Help: Tackling Distribution Shifts in Federated Graph Learning (AAAI 2025 · similarity 0.92)
- FedSSP: Federated Graph Learning with Spectral Knowledge and Personalized Preference (NeurIPS 2024 · similarity 0.91)
- Less is More: Federated Graph Learning with Alleviating Topology Heterogeneity from A Causal Perspective (ICML 2025 · similarity 0.91)
- FedSPA: Generalizable Federated Graph Learning under Homophily Heterogeneity (CVPR 2025 · similarity 0.90)
- Subgraph Federated Learning via Spectral Methods (NeurIPS 2025 · similarity 0.89)
- Federated Graph-Level Clustering Network (AAAI 2025 · similarity 0.89)
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