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GraphSB: Boosting Imbalanced Node Classification on Graphs through Structural Balance

Zhixiao Wang, Chaofan Zhu, Qihan Feng, Jian Zhang, Xiaobin Rui, Philip S Yu

TL;DR

GraphSB tackles imbalanced node classification by addressing the underlying imbalanced graph structure rather than solely balancing data or altering learning. It introduces Structural Balance, a two-stage framework with Structure Enhancement to mine hard minority samples and strengthen minority connectivity, followed by Relation Diffusion to propagate minority context and capture higher-order structure. The approach is supported by theoretical insights into majority-class dominance and minority assimilation, and experimental results across eight datasets show consistent gains, including a reported average accuracy improvement of 4.57% when SB is integrated as a plug-in. The method is scalable, simple to adopt in existing pipelines, and demonstrates strong robustness on both mid-size and large-scale graphs, indicating practical impact for real-world imbalanced graph learning tasks.

Abstract

Imbalanced node classification is a critical challenge in graph learning, where most existing methods typically utilize Graph Neural Networks (GNNs) to learn node representations. These methods can be broadly categorized into the data-level and the algorithm-level. The former aims to synthesize minority-class nodes to mitigate quantity imbalance, while the latter tries to optimize the learning process to highlight minority classes. However, neither of them addresses the inherently imbalanced graph structure, which is a fundamental factor that incurs majority-class dominance and minority-class assimilation in GNNs. Our theoretical analysis further supports this critical insight. Therefore, we propose GraphSB (Graph Structural Balance), a novel framework that incorporates Structural Balance as a key strategy to address the underlying imbalanced graph structure before node synthesis. Structural Balance performs a two-stage structure optimization: Structure Enhancement that mines hard samples near decision boundaries through dual-view analysis and enhances connectivity for minority classes through adaptive augmentation, and Relation Diffusion that propagates the enhanced minority context while simultaneously capturing higher-order structural dependencies. Thus, GraphSB balances structural distribution before node synthesis, enabling more effective learning in GNNs. Extensive experiments demonstrate that GraphSB significantly outperforms the state-of-the-art methods. More importantly, the proposed Structural Balance can be seamlessly integrated into state-of-the-art methods as a simple plug-and-play module, increasing their accuracy by an average of 4.57%.

GraphSB: Boosting Imbalanced Node Classification on Graphs through Structural Balance

TL;DR

GraphSB tackles imbalanced node classification by addressing the underlying imbalanced graph structure rather than solely balancing data or altering learning. It introduces Structural Balance, a two-stage framework with Structure Enhancement to mine hard minority samples and strengthen minority connectivity, followed by Relation Diffusion to propagate minority context and capture higher-order structure. The approach is supported by theoretical insights into majority-class dominance and minority assimilation, and experimental results across eight datasets show consistent gains, including a reported average accuracy improvement of 4.57% when SB is integrated as a plug-in. The method is scalable, simple to adopt in existing pipelines, and demonstrates strong robustness on both mid-size and large-scale graphs, indicating practical impact for real-world imbalanced graph learning tasks.

Abstract

Imbalanced node classification is a critical challenge in graph learning, where most existing methods typically utilize Graph Neural Networks (GNNs) to learn node representations. These methods can be broadly categorized into the data-level and the algorithm-level. The former aims to synthesize minority-class nodes to mitigate quantity imbalance, while the latter tries to optimize the learning process to highlight minority classes. However, neither of them addresses the inherently imbalanced graph structure, which is a fundamental factor that incurs majority-class dominance and minority-class assimilation in GNNs. Our theoretical analysis further supports this critical insight. Therefore, we propose GraphSB (Graph Structural Balance), a novel framework that incorporates Structural Balance as a key strategy to address the underlying imbalanced graph structure before node synthesis. Structural Balance performs a two-stage structure optimization: Structure Enhancement that mines hard samples near decision boundaries through dual-view analysis and enhances connectivity for minority classes through adaptive augmentation, and Relation Diffusion that propagates the enhanced minority context while simultaneously capturing higher-order structural dependencies. Thus, GraphSB balances structural distribution before node synthesis, enabling more effective learning in GNNs. Extensive experiments demonstrate that GraphSB significantly outperforms the state-of-the-art methods. More importantly, the proposed Structural Balance can be seamlessly integrated into state-of-the-art methods as a simple plug-and-play module, increasing their accuracy by an average of 4.57%.
Paper Structure (33 sections, 6 theorems, 40 equations, 10 figures, 6 tables)

This paper contains 33 sections, 6 theorems, 40 equations, 10 figures, 6 tables.

Key Result

Theorem 1

For a path of length $L$ in a class-imbalanced graph with imbalance ratio $\beta$ and degree disparity $\tau$, the expected path weight satisfies: where $\mathcal{W}_L$ denotes the weight of information propagated along a path of length $L$. $W^{(L)} = \prod_{\ell=1}^L \nabla\phi_\ell \nabla\psi_\ell$ represents the cumulative weight matrix product.

Figures (10)

  • Figure 1: Imbalanced node learning on graphs
  • Figure 2: Overview of the GraphSB framework.
  • Figure 3: Ablation study on SE and RD.
  • Figure 4: Visualization on PubMed.
  • Figure 5: Impact of diffusion steps $K$ and coefficient $\alpha$.
  • ...and 5 more figures

Theorems & Definitions (12)

  • Definition 1
  • Theorem 1
  • Definition 2
  • Theorem 2
  • Definition 3
  • Theorem 3
  • Theorem 3
  • proof
  • Theorem 3
  • proof
  • ...and 2 more