SPGCL: Effective Graph Contrastive Learning via SVD-Guided Structural Perturbation

TL;DR

SPGCL tackles robustness in graph representation learning under structural noise by introducing a two-stage augmentation that couples stochastic edge removal with SVD-guided recovery to produce a sparse, informative perturbed view. A contrastive fusion module then aligns node embeddings across the original and perturbed views using node-level InfoNCE and a global similarity constraint, enforcing both local and global structural consistency. Empirical results across ten real-world datasets show that SPGCL consistently outperforms state-of-the-art GCL and graph-structure learning methods, with pronounced gains on heterophilous graphs and robustness under increasing structural noise. The approach offers explicit control over perturbation magnitude and preserves high-order structural patterns, making it a practical and generalizable solution for robust graph representation learning.

Abstract

Graph Neural Networks (GNNs) can be highly sensitive to structural noise, including spurious or missing edges caused by adversarial attacks or non-adversarial imperfections. Existing graph contrastive learning methods typically rely on either random perturbations (e.g., edge dropping) to generate diverse views or purely spectral augmentations (e.g., SVD) to preserve global structural priors. However, random perturbations are structure-agnostic and may remove critical edges, while SVD-based views often become dense and lack sufficient diversity. To bridge this gap, we propose SPGCL, a robust graph contrastive learning framework via SVD-guided structural perturbation. SPGCL couples lightweight stochastic edge removal with an SVD-guided refinement step that can recover mistakenly removed informative edges and introduce semantically meaningful missing links while avoiding graph densification through sparse top-ranked edge selection and merging. By balancing edge removal and recovery rates, SPGCL explicitly controls structural discrepancy between views so that contrastive signals reflect semantic structural differences rather than edge-count gaps. We further incorporate a contrastive fusion module regularized by a global similarity constraint to better align the two views. Extensive experiments on ten benchmark datasets demonstrate that SPGCL consistently improves robustness and accuracy of base GNNs, outperforming state-of-the-art graph contrastive learning and structure learning methods.

Figures (3)

• Figure 1: Overview of the proposed SPGCL framework. (a) SVD-guided structured perturbation. Starting from the original adjacency $\mathbf{A}$, we first apply Edge Drop to obtain the remaining graph $\mathbf{A}_R$ and the removed edges $\Delta \mathbf{A}$. We then perform truncated SVD on $\mathbf{A}_R$ and estimate the singular-value perturbation via a first-order approximation, constructing a topology-aware score matrix$\widetilde{\mathbf{A}}$. To avoid graph densi-fication, we select the Top-$P$ highest-scored candidate edges (excluding edges in $\mathcal{E}_R$) to form a sparse addition matrix $\mathbf{A}_P$, and merge it with $\mathbf{A}_R$ to produce the sparse perturbed view $\mathbf{A}_E = \mathbf{A}_R + \alpha \mathbf{A}_P$ Eq \ref{['eq:a_e']}. (b) Siamese GNN encoder. A shared encoder $f_\theta$ extracts layer-wise node representations from the original view ($\mathbf{A}$) and the perturbed view ($\mathbf{A}_E$). (c) Contrastive learning-based fusion. We apply an InfoNCE-based alignment loss $\mathcal{L}_I$ at each encoder layer for multi-level node-wise agreement, while enforcing a global similarity-matrix consistency loss $\mathcal{L}_c$only on the final layer to regularize global structural patterns. All components are jointly optimized with the task loss.
• Figure 2: t-SNE visualization of node embeddings on CoraML. While baselines (a-d) show blurred boundaries, SPGCL (e) exhibits distinct class separation and compact intra-class clustering, demonstrating the effectiveness of the proposed fusion strategy.
• Figure 3: Sensitivity analysis of $p$ and $q$.