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Propagate and Inject: Revisiting Propagation-Based Feature Imputation for Graphs with Partially Observed Features
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Identifies low-variance channels produced by propagation-based feature imputation and proposes FISF, which injects synthetic random features into those channels and diffuses them with distance-encoded weights to restore variance and improve node classification and link prediction under high missing rates.
Problem
Graph learning with missing node features at extreme missing rates; propagation-based imputation (FP, PCFI) yields near-constant low-variance channels that carry little information for downstream GNNs.
Approach
Detect low-variance channels after pre-diffusion, inject one synthetic feature (uniform random value) per such channel at a missing node, and re-diffuse using a distance-encoding-based transition weight so the synthetic value spreads widely and increases channel variance.
Key results
- At 99.5% structural missing rate, FISF reaches 79.29% accuracy on Cora vs 71.86% for FP and 74.62% for PCFI.
- FISF achieves state-of-the-art ROC AUC in several link prediction settings at rm=0.995; FISF+NIP is best in four of ten settings.
- FISF with only 0.1% of features performs similarly to or better than FISF with full features on Cora, CiteSeer and PubMed.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add synthetic features to low-variance channels and diffuse them with distance encoding | PCFI imputation · Semi-supervised node classification, structural missing, rm = 0.995 | accuracy (%): 74.62 ± 1.78 -> 79.29 ± 1.72 (Cora); 66.06 ± 3.26 -> 69.68 ± 2.47 (CiteSeer); 74.47 ± 2.54 -> 76.90 ± 1.50 (PubMed); 87. | Helped |
| add synthetic features to low-variance channels and diffuse them with distance encoding | PCFI imputation · Semi-supervised node classification, uniform missing, rm = 0.995 | accuracy (%): 78.82 ± 1.48 -> 79.09 ± 1.73 (Cora); 68.94 ± 1.95 -> 69.52 ± 1.81 (CiteSeer); 76.28 ± 2.52 -> 77.53 ± 1.28 (PubMed); 88. | Helped |
| add synthetic features to low-variance channels and diffuse them with distance encoding | PCFI imputation · Link prediction, structural missing, rm = 0.995 | ROC AUC score (%): 86.75 ± 0.84 -> 87.26 ± 1.44 (Cora); 79.38 ± 1.81 -> 84.12 ± 1.17 (CiteSeer); 82.49 ± 0.82 -> 83.19 ± 0.78 (PubMed); 96. | Helped |
| add synthetic features to low-variance channels and diffuse them with distance encoding | PCFI imputation · Link prediction, uniform missing, rm = 0.995 | ROC AUC score (%): 87.35 ± 1.28 -> 87.44 ± 0.80 (Cora); 82.33 ± 1.88 -> 83.45 ± 2.53 (CiteSeer); 84.68 ± 0.75 -> 85.33 ± 0.47 (PubMed); 97. | Mixed |
| add NIP after FISF (ablation) | FISF · Link prediction, rm = 0.995 | ROC AUC score (%): Cora structural: 87.26 ± 1.44 -> 87.16 ± 1.46; CiteSeer structural: 84.12 ± 1.17 -> 84.20 ± 1.70; Photo structural: 95.8 | Mixed |
| replace PCFI pre-diffusion with FP pre-diffusion (ablation) | FISF · Semi-supervised node classification, rm = 0.995 | accuracy (%): Structural average: 77.24 -> 77.04; uniform average: 77.73 -> 77.55 | Mixed |
| use FP instead of distance encoding for synthetic-feature diffusion (ablation) | FISF · Semi-supervised node classification, structural missing, rm = 0.995 | accuracy (%): 71.86 ± 2.82 -> 78.25 ± 1.38 (Cora); 58.61 ± 1.74 -> 68.52 ± 1.82 (CiteSeer); 71.96 ± 3.06 -> 74.40 ± 2.64 (PubMed); 85. | Helped |
| add fewer synthetic-feature channels than F · ropt% (ablation) | PCFI+FISF+ · Semi-supervised node classification, structural missing, rm = 0.995 | accuracy (%): Vanilla PCFI: 74.62 ± 1.78; 0.125F · ropt%: 77.04 ± 1.42; 0.25F · ropt%: 77.50 ± 0.92; 0.5F · ropt%: 78.56 ± 1.07; F · r | Helped |
Surprising findings
- Removing the highest-variance channels causes significant accuracy degradation while removing low-variance channels barely affects performance.
- FISF with 0.1% observed features matches or outperforms full-feature FISF on several citation datasets.
Limitations
- FISF has O(N^2 F) time and O(N^2) memory complexity from distance encoding, making it costly on large graphs.
- Gains diminish as the missing rate decreases.
- Evaluated only on node classification and link prediction; medical tabular experiments are referenced but not central.
Experimental setup
Datasets: Cora CiteSeer PubMed OGBN-Arxiv Amazon-Photo Amazon-Computers
Benchmarks: Cora CiteSeer PubMed OGBN-Arxiv Amazon-Photo Amazon-Computers
Metrics: accuracy ROC AUC AP
Baselines: LP GCNMF GRAFENNE MEGAE FP PCFI
Builds on: Feature Propagation (FP) PCFI GCN GAE
Closest papers by meaning
- Confidence-Based Feature Imputation for Graphs with Partially Known Features (ICLR 2023 · similarity 0.92)
- FSD-CAP: Fractional Subgraph Diffusion with Class-Aware Propagation for Graph Feature Imputation (ICLR 2026 · similarity 0.91)
- Attribute-Missing Graph Clustering Network (AAAI 2024 · similarity 0.86)
- Disentangling Invariant Subgraph via Variance Contrastive Estimation under Distribution Shifts (ICML 2025 · similarity 0.85)
- Editing Partially Observable Networks via Graph Diffusion Models (ICML 2024 · similarity 0.85)
- Missing Data Imputation by Reducing Mutual Information with Rectified Flows (NeurIPS 2025 · similarity 0.85)
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