[Paper Review] Data Augmentation View on Graph Convolutional Network and the Proposal of Monte Carlo Graph Learning

Hande Dong, Zhaolin Ding+3 more|arXiv (Cornell University)|Jun 23, 2020

Advanced Graph Neural Networks24 references4 citations

TL;DR

This paper proposes Monte Carlo Graph Learning (MCGL), a new graph learning paradigm that interprets graph convolutional networks (GCNs) through data augmentation in label space. By propagating training labels through graph structures via Monte Carlo sampling, MCGL expands the training set and trains traditional classifiers, demonstrating superior performance on clean graphs with non-linear boundaries or community structures, while being more sensitive to graph noise than GCNs.

ABSTRACT

Today, there are two major understandings for graph convolutional networks, i.e., in the spectral and spatial domain. But both lack transparency. In this work, we introduce a new understanding for it -- data augmentation, which is more transparent than the previous understandings. Inspired by it, we propose a new graph learning paradigm -- Monte Carlo Graph Learning (MCGL). The core idea of MCGL contains: (1) Data augmentation: propagate the labels of the training set through the graph structure and expand the training set; (2) Model training: use the expanded training set to train traditional classifiers. We use synthetic datasets to compare the strengths of MCGL and graph convolutional operation on clean graphs. In addition, we show that MCGL's tolerance to graph structure noise is weaker than GCN on noisy graphs (four real-world datasets). Moreover, inspired by MCGL, we re-analyze the reasons why the performance of GCN becomes worse when deepened too much: rather than the mainstream view of over-smoothing, we argue that the main reason is the graph structure noise, and experimentally verify our view. The code is available at https://github.com/DongHande/MCGL.

Motivation & Objective

• To provide a new, transparent interpretation of graph convolutional networks (GCNs) through the lens of data augmentation.
• To address the lack of interpretability in spectral and spatial domain interpretations of GCNs.
• To propose a novel graph learning paradigm—Monte Carlo Graph Learning (MCGL)—that operates in label space via pseudo-label propagation.
• To investigate the trade-offs between MCGL and GCN in terms of robustness to graph structure noise and performance on different data characteristics.
• To re-evaluate the cause of GCN performance degradation with depth, arguing it is due to structural noise rather than over-smoothing.

Proposed method

• MCGL performs K-step Monte Carlo sampling from training nodes, propagating their labels to sampled neighbors to generate pseudo-labeled training samples.
• The expanded training set, consisting of original and pseudo-labeled nodes, is used to train a base classifier (e.g., MLP, SVM, LR).
• The method relies on the local homogeneity assumption: connected nodes are likely to share the same label, making label propagation reasonable.
• Label propagation is limited to K steps to avoid over-trust in distant or noisy neighbors, preventing incorrect pseudo-labeling.
• The core mechanism treats graph structure as a data augmentation tool in label space, contrasting with GCN’s representation-space augmentation.
• MCGL is evaluated on synthetic and real-world datasets to compare performance and robustness with GCN under varying noise levels.

Experimental results

Research questions

• RQ1 Can graph convolutional operations be meaningfully interpreted as a form of data augmentation in label space?
• RQ2 How does MCGL compare to GCN in performance on clean graphs with non-linear decision boundaries or community structures?
• RQ3 Why does GCN performance degrade when depth increases, and is it primarily due to over-smoothing or structural noise?
• RQ4 How does MCGL’s robustness to graph structure noise compare to that of GCN?
• RQ5 Can insights from MCGL’s depth limitations help explain the depth limitations of GCN?

Key findings

• On clean graphs, MCGL outperforms GCN on datasets with non-linear decision boundaries or community structures, while GCN performs better on high-variance datasets.
• MCGL is more sensitive to graph structure noise than GCN, showing lower tolerance on four real-world noisy datasets.
• The performance degradation of GCN with increasing depth is primarily caused by graph structure noise, not over-smoothing, as empirically validated.
• MCGL cannot be made too deep because bad edges lead to an increasing number of incorrectly labeled pseudo-samples, degrading model performance.
• The depth limitation of GCN is fundamentally linked to the same noise issue that limits MCGL, suggesting a shared underlying cause.
• The data augmentation view of GCN provides a more transparent and interpretable understanding than spectral or spatial interpretations.