Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning

TL;DR

This paper provides deeper theoretical insights into Graph Convolutional Networks (GCNs), revealing their connection to Laplacian smoothing, addressing over-smoothing issues, and proposing co-training and self-training methods to enhance semi-supervised learning with limited labels.

Contribution

The paper uncovers the Laplacian smoothing interpretation of GCNs, analyzes their limitations, and introduces co-training and self-training techniques to improve performance with few labels.

Findings

GCNs are a form of Laplacian smoothing.

Over-smoothing occurs with many convolutional layers.

Proposed methods significantly improve GCN performance with limited labels.

Abstract

Many interesting problems in machine learning are being revisited with new deep learning tools. For graph-based semisupervised learning, a recent important development is graph convolutional networks (GCNs), which nicely integrate local vertex features and graph topology in the convolutional layers. Although the GCN model compares favorably with other state-of-the-art methods, its mechanisms are not clear and it still requires a considerable amount of labeled data for validation and model selection. In this paper, we develop deeper insights into the GCN model and address its fundamental limits. First, we show that the graph convolution of the GCN model is actually a special form of Laplacian smoothing, which is the key reason why GCNs work, but it also brings potential concerns of over-smoothing with many convolutional layers. Second, to overcome the limits of the GCN model with shallow architectures, we propose both co-training and self-training approaches to train GCNs. Our approaches significantly improve GCNs in learning with very few labels, and exempt them from requiring additional labels for validation. Extensive experiments on benchmarks have verified our theory and proposals.