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Enhancing the Resilience of Graph Neural Networks to Topological Perturbations in Sparse Graphs

Shuqi He, Jun Zhuang, Ding Wang, Luyao Peng, Jun Song

TL;DR

This work addresses the vulnerability of graph neural networks to topological perturbations by introducing TraTopo, a label-inference framework that fuses Bayesian label transitions with topology-aware propagation and random-walk based link analysis. It leverages a shortest-path mechanism to reduce inference overhead and a novel improved topology sampler to better handle sparse graphs, achieving superior node classification performance under adversarial, random, and missing-link perturbations. The method integrates asymmetric Dirichlet-based label transitions, Gibbs sampling, and dynamic reweighting to align inferred labels with true labels, supported by extensive experiments on multiple datasets. Overall, TraTopo advances robust GNN design by combining probabilistic reasoning with topology-guided sampling to maintain high accuracy and low uncertainty in challenging, perturbed graph environments.

Abstract

Graph neural networks (GNNs) have been extensively employed in node classification. Nevertheless, recent studies indicate that GNNs are vulnerable to topological perturbations, such as adversarial attacks and edge disruptions. Considerable efforts have been devoted to mitigating these challenges. For example, pioneering Bayesian methodologies, including GraphSS and LlnDT, incorporate Bayesian label transitions and topology-based label sampling to strengthen the robustness of GNNs. However, GraphSS is hindered by slow convergence, while LlnDT faces challenges in sparse graphs. To overcome these limitations, we propose a novel label inference framework, TraTopo, which combines topology-driven label propagation, Bayesian label transitions, and link analysis via random walks. TraTopo significantly surpasses its predecessors on sparse graphs by utilizing random walk sampling, specifically targeting isolated nodes for link prediction, thus enhancing its effectiveness in topological sampling contexts. Additionally, TraTopo employs a shortest-path strategy to refine link prediction, thereby reducing predictive overhead and improving label inference accuracy. Empirical evaluations highlight TraTopo's superiority in node classification, significantly exceeding contemporary GCN models in accuracy.

Enhancing the Resilience of Graph Neural Networks to Topological Perturbations in Sparse Graphs

TL;DR

This work addresses the vulnerability of graph neural networks to topological perturbations by introducing TraTopo, a label-inference framework that fuses Bayesian label transitions with topology-aware propagation and random-walk based link analysis. It leverages a shortest-path mechanism to reduce inference overhead and a novel improved topology sampler to better handle sparse graphs, achieving superior node classification performance under adversarial, random, and missing-link perturbations. The method integrates asymmetric Dirichlet-based label transitions, Gibbs sampling, and dynamic reweighting to align inferred labels with true labels, supported by extensive experiments on multiple datasets. Overall, TraTopo advances robust GNN design by combining probabilistic reasoning with topology-guided sampling to maintain high accuracy and low uncertainty in challenging, perturbed graph environments.

Abstract

Graph neural networks (GNNs) have been extensively employed in node classification. Nevertheless, recent studies indicate that GNNs are vulnerable to topological perturbations, such as adversarial attacks and edge disruptions. Considerable efforts have been devoted to mitigating these challenges. For example, pioneering Bayesian methodologies, including GraphSS and LlnDT, incorporate Bayesian label transitions and topology-based label sampling to strengthen the robustness of GNNs. However, GraphSS is hindered by slow convergence, while LlnDT faces challenges in sparse graphs. To overcome these limitations, we propose a novel label inference framework, TraTopo, which combines topology-driven label propagation, Bayesian label transitions, and link analysis via random walks. TraTopo significantly surpasses its predecessors on sparse graphs by utilizing random walk sampling, specifically targeting isolated nodes for link prediction, thus enhancing its effectiveness in topological sampling contexts. Additionally, TraTopo employs a shortest-path strategy to refine link prediction, thereby reducing predictive overhead and improving label inference accuracy. Empirical evaluations highlight TraTopo's superiority in node classification, significantly exceeding contemporary GCN models in accuracy.
Paper Structure (29 sections, 9 equations, 3 figures, 6 tables, 4 algorithms)

This paper contains 29 sections, 9 equations, 3 figures, 6 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. RELATED WORK
  3. Graph Neural Networks
  4. Adversarial Robustness
  5. Noisy Labels
  6. Random Walk and PageRank
  7. PRELIMINARIES
  8. GNN-based Node Classification
  9. Random walk algorithm
  10. Random walk with restart
  11. PageRank
  12. METHOD
  13. Bayesian Label Transition with Asymmetric Dirichlet Distributions
  14. Shortest path-based approximated method
  15. Improved Topology Sampler
  16. ...and 14 more sections

Figures (3)

  • Figure 1: The diagram of Bayesian label transition, $V$ signifies nodes and $N$ indicates the number of nodes. $Z$ includes inferred $\bar{\mathcal{Z}}$ and true labels $Z$, and $Y$ encompasses both manually-annotated labels $Y_m$ and automatically-generated labels $Y_a$ labels. The $K$ class label transition, controlled by matrix $\phi$ and parameter $\alpha$, Black arrows depict variable dependencies, while dotted arrows indicate this symbol can be subdivided into two different meanings.
  • Figure 2: The diagram of Concentric circles representing the shortest paths between nodes
  • Figure 3: The diagram of the Topological sample, displays a network delineated by three sampling techniques: majority, degree, and random. Green nodes, chosen by majority rule, reflect dominant characteristics within their network vicinity. Green nodes, chosen by majority rule, reflect dominant characteristics within their network vicinity. Blue nodes, sampled randomly, lack selection criteria, embodying stochastic choice.