G-Mixup: Graph Data Augmentation for Graph Classification (2202.07179v2)

Abstract: This work develops \emph{mixup for graph data}. Mixup has shown superiority in improving the generalization and robustness of neural networks by interpolating features and labels between two random samples. Traditionally, Mixup can work on regular, grid-like, and Euclidean data such as image or tabular data. However, it is challenging to directly adopt Mixup to augment graph data because different graphs typically: 1) have different numbers of nodes; 2) are not readily aligned; and 3) have unique typologies in non-Euclidean space. To this end, we propose $\mathcal{G}$-Mixup to augment graphs for graph classification by interpolating the generator (i.e., graphon) of different classes of graphs. Specifically, we first use graphs within the same class to estimate a graphon. Then, instead of directly manipulating graphs, we interpolate graphons of different classes in the Euclidean space to get mixed graphons, where the synthetic graphs are generated through sampling based on the mixed graphons. Extensive experiments show that $\mathcal{G}$-Mixup substantially improves the generalization and robustness of GNNs.

• The paper introduces a novel graph data augmentation method using graphon mixup to interpolate between classes for improved GNN performance.
• The methodology preserves critical discriminative motifs through rigorous theoretical analysis, ensuring representative synthetic graphs.
• Empirical evaluations show up to 12% accuracy gains over baselines across diverse datasets and GNN architectures.

An Expert Overview of $\mathcal{G}$-Mixup: Graph Data Augmentation for Graph Classification

The paper "$\mathcal{G}$-Mixup: Graph Data Augmentation for Graph Classification" introduces a novel approach for augmenting graph data, aimed at improving the generalization and robustness of Graph Neural Networks (GNNs) for graph classification tasks. The authors address the challenges posed by graph data's inherent irregularity and non-Euclidean nature by leveraging graphons, which represent the generators for graph instances. The paper proposes a method to mix graphons from different classes to create synthetic graph data that facilitates between-graph data augmentation.

Key Contributions

1. Graphon-Based Mixup: The method, termed $\mathcal{G}$-Mixup, proposes leveraging graphons — regular, scalable functions in Euclidean space — to interpolate between different classes of graph data, circumventing the challenges posed by graphs' irregular topology. This enables the generation of synthetic graphs that retain key characteristics from parent classes.
2. Theoretical Foundation: The paper provides rigorous theoretical analysis ensuring that synthetic graphs generated via graphon mixup preserve discriminative motifs, which are the substructures most critical for classification. This guarantees that augmented data remains representative of the underlying class properties.
3. Empirical Results: Extensive experiments underscore the efficacy of $\mathcal{G}$-Mixup in enhancing GNNs. The method yields substantial improvements in classification accuracy across diverse datasets when compared to existing data augmentation strategies such as DropEdge, Subgraph, and Manifold Mixup, demonstrating both enhanced generalization and training stability.

Strong Numerical Results and Claims

The numerical results presented in the paper provide evidence of up to 12% improvement in accuracy compared to baseline methods. These gains are notable across various datasets and GNN backbones, reinforcing the utility of graphon mixup for graph classification.

Implications and Future Directions

The approach opens up promising pathways for graph data augmentation, particularly in scenarios where class imbalance or insufficient data diversity undermines model performance. Practically, $\mathcal{G}$-Mixup can be instrumental in domains like chemistry and social networks where graphs exhibit complex and diverse topologies but share fundamental class-defining structures.

Theoretically, the integration of graphons as a basis for between-graph augmentation presents opportunities to further explore and refine graph-based machine learning methodologies. Future investigations could explore optimizing graphon estimation processes or exploring the applicability of graphon mixup in unsupervised settings, such as graph clustering or anomaly detection.

Conclusion

$\mathcal{G}$-Mixup introduces a powerful augmentation technique that leverages the latent regularity of graphons to enhance the generalization capabilities of GNNs. The paper solidifies its contributions through both theoretical insights and robust empirical validation, marking a significant step forward in graph-based learning approaches. As the domain of AI continues to evolve, methodologies like $\mathcal{G}$-Mixup highlight the immense potential for innovation in graph data processing, promising to influence both academic research and practical application landscapes.