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Through the Dual-Prism: A Spectral Perspective on Graph Data Augmentation for Graph Classification

Yutong Xia, Runpeng Yu, Yuxuan Liang, Xavier Bresson, Xinchao Wang, Roger Zimmermann

TL;DR

The paper interrogates graph data augmentation through a spectral lens, addressing graph-property distortion and limited structural changes in existing methods. It introduces the Dual-Prism (DP) augmentation, with DP-Noise and DP-Mask, which selectively perturb high-frequency Laplacian eigenvalues while preserving low-frequency components to maintain core graph properties. Through extensive experiments across supervised, semi-supervised, unsupervised, and transfer learning on 21 real-world datasets, DP methods achieve state-of-the-art or near-state-of-the-art performance in many settings, demonstrating improved generalization and diversity. The work highlights the practical significance of spectral-aware augmentation for robust graph classification and suggests a new direction for leveraging graph spectra in data augmentation.

Abstract

Graph Neural Networks have become the preferred tool to process graph data, with their efficacy being boosted through graph data augmentation techniques. Despite the evolution of augmentation methods, issues like graph property distortions and restricted structural changes persist. This leads to the question: Is it possible to develop more property-conserving and structure-sensitive augmentation methods? Through a spectral lens, we investigate the interplay between graph properties, their augmentation, and their spectral behavior, and observe that keeping the low-frequency eigenvalues unchanged can preserve the critical properties at a large scale when generating augmented graphs. These observations inform our introduction of the Dual-Prism (DP) augmentation methods, including DP-Noise and DP-Mask, which retain essential graph properties while diversifying augmented graphs. Extensive experiments validate the efficiency of our approach, providing a new and promising direction for graph data augmentation.

Through the Dual-Prism: A Spectral Perspective on Graph Data Augmentation for Graph Classification

TL;DR

The paper interrogates graph data augmentation through a spectral lens, addressing graph-property distortion and limited structural changes in existing methods. It introduces the Dual-Prism (DP) augmentation, with DP-Noise and DP-Mask, which selectively perturb high-frequency Laplacian eigenvalues while preserving low-frequency components to maintain core graph properties. Through extensive experiments across supervised, semi-supervised, unsupervised, and transfer learning on 21 real-world datasets, DP methods achieve state-of-the-art or near-state-of-the-art performance in many settings, demonstrating improved generalization and diversity. The work highlights the practical significance of spectral-aware augmentation for robust graph classification and suggests a new direction for leveraging graph spectra in data augmentation.

Abstract

Graph Neural Networks have become the preferred tool to process graph data, with their efficacy being boosted through graph data augmentation techniques. Despite the evolution of augmentation methods, issues like graph property distortions and restricted structural changes persist. This leads to the question: Is it possible to develop more property-conserving and structure-sensitive augmentation methods? Through a spectral lens, we investigate the interplay between graph properties, their augmentation, and their spectral behavior, and observe that keeping the low-frequency eigenvalues unchanged can preserve the critical properties at a large scale when generating augmented graphs. These observations inform our introduction of the Dual-Prism (DP) augmentation methods, including DP-Noise and DP-Mask, which retain essential graph properties while diversifying augmented graphs. Extensive experiments validate the efficiency of our approach, providing a new and promising direction for graph data augmentation.
Paper Structure (21 sections, 10 figures, 9 tables, 1 algorithm)

This paper contains 21 sections, 10 figures, 9 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. A Spectral Lens on Graph Data Augmentations
  4. Spectral Analysis Insights
  5. Methodology
  6. Proposed Augmentation Methods
  7. Empirical Evidence
  8. Theoretical Backing and Insights
  9. Experiments
  10. Supervised Learning
  11. Semi-supervised Learning
  12. Unsupervised Representation Learning
  13. Transfer Learning
  14. Conclusion
  15. Acknowledgements
  16. ...and 6 more sections

Figures (10)

  • Figure 1: Visualization of (a) a graph from the IMDB-BINARY dataset and its augmented graphs via (b) DropEdge rong2019dropedge, (c) DP-Noise (ours), and (d) DP-Mask (ours). Dashed line: Dropped edge. Red line: Added edge. (e) Five properties of these graphs. $r$: radius. $d$: diameter. conn.: connectivity. ASPL: average shortest path length. #peri: number of periphery. Ori.: Original. D.E.: DropEdge. DP-N: DP-Noise. DP-M: DP-Mask. (f) The eigenvalues of these four graphs.
  • Figure 2: (a) A toy graph $\mathcal{G}$ consisting of eight nodes. (b) Absolute variation in eigenvalues of $\mathcal{G}$ when adding an edge at diverse positions. The red and blue rectangles represent when adding the corresponding edges in $\mathcal{G}$ and the change of the eigenvalues. (c) A real-world case in the REDDIT-BINARY dataset where, when dropping 20% and 50%, the high frequency is more vulnerable.
  • Figure 3: (a) Training loss of GIN model on REDDIT-BINARY when graphs are augmented by masking different eigenvalues. (b) Graph classification performance on IMDB-BINARY under various hyperparameters. The lines represent the average accuracy, while the shaded areas indicate the error margins.
  • Figure 4: (a) Diameter and (b) radius distributions of different classes in REDD-M12. When (c) adding or (d) removing an edge, variation of the spectral domain $\Delta L_2$, $1/\lambda_1$ of $\mathcal{G}'$, ASPL and diameter $d$ of $\mathcal{G}'$.
  • Figure 5: The framework of our Dual-Prism (DP) for graph data augmentation.
  • ...and 5 more figures