FSD-CAP: Fractional Subgraph Diffusion with Class-Aware Propagation for Graph Feature Imputation

TL;DR

FSD-CAP tackles the problem of imputing missing node features in graphs under extreme sparsity. It introduces a two-stage framework that combines a fractional diffusion operator with progressive subgraph diffusion and a class-aware refinement stage to stabilize diffusion and enforce semantic consistency. The method demonstrates strong empirical gains in semi-supervised node classification and link prediction across five datasets, including large-scale and heterophilous graphs, with robustness to 99.5% feature missing. Overall, FSD-CAP provides a scalable, diffusion-based solution that approaches fully observed performance in challenging sparse regimes and offers principled convergence guarantees for its local-to-global diffusion process.

Abstract

Imputing missing node features in graphs is challenging, particularly under high missing rates. Existing methods based on latent representations or global diffusion often fail to produce reliable estimates, and may propagate errors across the graph. We propose FSD-CAP, a two-stage framework designed to improve imputation quality under extreme sparsity. In the first stage, a graph-distance-guided subgraph expansion localizes the diffusion process. A fractional diffusion operator adjusts propagation sharpness based on local structure. In the second stage, imputed features are refined using class-aware propagation, which incorporates pseudo-labels and neighborhood entropy to promote consistency. We evaluated FSD-CAP on multiple datasets. With $99.5\%$ of features missing across five benchmark datasets, FSD-CAP achieves average accuracies of $80.06\%$ (structural) and $81.01\%$ (uniform) in node classification, close to the $81.31\%$ achieved by a standard GCN with full features. For link prediction under the same setting, it reaches AUC scores of $91.65\%$ (structural) and $92.41\%$ (uniform), compared to $95.06\%$ for the fully observed case. Furthermore, FSD-CAP demonstrates superior performance on both large-scale and heterophily datasets when compared to other models.

Figures (12)

• Figure 1: FSD-CAP Pipeline: Given graph $\mathcal{G}$ and partially observed feature matrix $X$, FSD-CAP recovers the full matrix $\hat{X}$. (i) FSD: Starting from observed nodes, it gradually expands the radius of the subgraph and performs progressive subgraph diffusion using fractional diffusion operators $\mathbf A^{\gamma,0}$, $\mathbf A^{\gamma,1}$, $\mathbf A^{\gamma,2}$, producing a preliminary imputed feature matrix. (ii) CAP: Based on the FSD-imputed features, pseudo-labels are assigned by a classifier to form class-wise graphs, each associated with class-specific $X^c$ and $\mathbf W^c$. Feature propagation within each class graph yields the final output $\hat{X}$.
• Figure 2: Node classification accuracy (%) comparison on Cora and CiteSeer datasets with $mr\in \{0.6,0.7,0.8,0.9,0.95,0.995\}$. The top row displays results for structural missing, while the bottom row shows results for uniform missing. Methods that encounter out-of-memory errors or are not applicable to specific missing scenarios are excluded from the corresponding plots.
• Figure 3: Sensitivity of node classification accuracy to the retention coefficient $\lambda$ and fractional exponent $\gamma$ on Cora and Photo datasets.
• Figure 4: Sensitivity of link prediction performance to the retention coefficient $\lambda$ and fractional exponent $\gamma$ on the Cora dataset.
• Figure 5: Sensitivity of link prediction performance to the retention coefficient $\lambda$ and fractional exponent $\gamma$ on the Photo dataset.

Theorems & Definitions (14)

• Proposition 1: Limiting behavior of $\mathbf{A}^\gamma$
• Remark 1: Super-diffusion and nearest-neighbor routing
• Theorem 1: Fractional diffusion on feature propagation
• Theorem 2: Convergence of subgraph diffusion
• Theorem 3: Global convergence via progressive subgraph expansion
• Definition 1: Neighborhood label information entropy
• Proposition A.1: Limiting behavior of $\mathbf{A}^\gamma$
• proof
• Theorem A.1: Fractional diffusion on feature propagation
• proof