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SStaGCN: Simplified stacking based graph convolutional networks

Jia Cai, Zhilong Xiong, Shaogao Lv

TL;DR

GCNs face over-smoothing and struggle with heterogeneous graphs. SStaGCN proposes a simple yet effective framework that uses stacking-based feature extraction from diverse base classifiers, followed by aggregation (mean, attention, or voting) and a vanilla GCN, to improve discriminability and robustness. A theoretical generalization bound is provided, and extensive experiments on six real-world datasets show substantial gains in accuracy and efficiency, with voting often offering the strongest performance and reduced smoothing. The approach offers a flexible, scalable path for applying GCNs to varied graph structures and can be extended to regression tasks.

Abstract

Graph convolutional network (GCN) is a powerful model studied broadly in various graph structural data learning tasks. However, to mitigate the over-smoothing phenomenon, and deal with heterogeneous graph structural data, the design of GCN model remains a crucial issue to be investigated. In this paper, we propose a novel GCN called SStaGCN (Simplified stacking based GCN) by utilizing the ideas of stacking and aggregation, which is an adaptive general framework for tackling heterogeneous graph data. Specifically, we first use the base models of stacking to extract the node features of a graph. Subsequently, aggregation methods such as mean, attention and voting techniques are employed to further enhance the ability of node features extraction. Thereafter, the node features are considered as inputs and fed into vanilla GCN model. Furthermore, theoretical generalization bound analysis of the proposed model is explicitly given. Extensive experiments on $3$ public citation networks and another $3$ heterogeneous tabular data demonstrate the effectiveness and efficiency of the proposed approach over state-of-the-art GCNs. Notably, the proposed SStaGCN can efficiently mitigate the over-smoothing problem of GCN.

SStaGCN: Simplified stacking based graph convolutional networks

TL;DR

GCNs face over-smoothing and struggle with heterogeneous graphs. SStaGCN proposes a simple yet effective framework that uses stacking-based feature extraction from diverse base classifiers, followed by aggregation (mean, attention, or voting) and a vanilla GCN, to improve discriminability and robustness. A theoretical generalization bound is provided, and extensive experiments on six real-world datasets show substantial gains in accuracy and efficiency, with voting often offering the strongest performance and reduced smoothing. The approach offers a flexible, scalable path for applying GCNs to varied graph structures and can be extended to regression tasks.

Abstract

Graph convolutional network (GCN) is a powerful model studied broadly in various graph structural data learning tasks. However, to mitigate the over-smoothing phenomenon, and deal with heterogeneous graph structural data, the design of GCN model remains a crucial issue to be investigated. In this paper, we propose a novel GCN called SStaGCN (Simplified stacking based GCN) by utilizing the ideas of stacking and aggregation, which is an adaptive general framework for tackling heterogeneous graph data. Specifically, we first use the base models of stacking to extract the node features of a graph. Subsequently, aggregation methods such as mean, attention and voting techniques are employed to further enhance the ability of node features extraction. Thereafter, the node features are considered as inputs and fed into vanilla GCN model. Furthermore, theoretical generalization bound analysis of the proposed model is explicitly given. Extensive experiments on public citation networks and another heterogeneous tabular data demonstrate the effectiveness and efficiency of the proposed approach over state-of-the-art GCNs. Notably, the proposed SStaGCN can efficiently mitigate the over-smoothing problem of GCN.
Paper Structure (14 sections, 4 theorems, 28 equations, 7 figures, 11 tables, 1 algorithm)

This paper contains 14 sections, 4 theorems, 28 equations, 7 figures, 11 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. The proposed approach: SStaGCN
  4. Graph convolutional networks
  5. Stacking
  6. The proposed approach
  7. Generalization bound
  8. Experiments
  9. Datasets
  10. Baselines
  11. Setting
  12. Results
  13. Visualization
  14. Conclusion

Key Result

Theorem 3.1

Suppose $\|{\bf x}_i\|_2\leq R, i=1,\cdots, N$, $\|W^{(0)}\|_F\leq B_1$, $\|W^{(1)}\|_F\leq B_2$. Denote $N(v)$ the number of neighbors of node $v\in \Omega$ (the set of node indices with observed labels), let $q=\max\{N(v)\}$, $f: \mathcal{X}\rightarrow \mathbb{R}$ be any given predictor of a class

Figures (7)

  • Figure 1: Workflow of the SStaGCN model.
  • Figure 2: Visualization of classification features by the GCN (left) and the features after conducting stacking and aggregation steps in the SStaGCN model (right) on CiteSeer dataset, node colors denote classes.
  • Figure 3: Visualization of classification features by the GCN (left) and the features after conducting stacking and aggregation steps in the SStaGCN model (right) on DBLP dataset, node colors denote classes.
  • Figure 4: Visualization of final classification features via GCN on Cora dataset with $2$, $3$, $4$, $5$, $6$, $7$ layers, node colors denote classes.
  • Figure 5: Visualization of final classification features via SStaGCN on Cora dataset with $2$, $3$, $4$, $5$, $6$, $7$ layers, node colors denote classes.
  • ...and 2 more figures

Theorems & Definitions (5)

  • Theorem 3.1
  • Remark 3.1
  • Lemma 5.1
  • Lemma 5.2
  • Lemma 5.3