Co-embedding of Nodes and Edges with Graph Neural Networks

Graph, as an important data representation, is ubiquitous in many real world applications ranging from social network analysis to biology. How to correctly and effectively learn and extract information from graph is essential for a large number of machine learning tasks. Graph embedding is a way to transform and encode the data structure in high dimensional and non-Euclidean feature space to a low dimensional and structural space, which is easily exploited by other machine learning algorithms. We have witnessed a huge surge of such embedding methods, from statistical approaches to recent deep learning methods such as the graph convolutional networks (GCN). Deep learning approaches usually outperform the traditional methods in most graph learning benchmarks by building an end-to-end learning framework to optimize the loss function directly. However, most of the existing GCN methods can only perform convolution operations with node features, while ignoring the handy information in edge features, such as relations in knowledge graphs. To address this problem, we present CensNet, Convolution with Edge-Node Switching graph neural network, for learning tasks in graph-structured data with both node and edge features. CensNet is a general graph embedding framework, which embeds both nodes and edges to a latent feature space. By using line graph of the original undirected graph, the role of nodes and edges are switched, and two novel graph convolution operations are proposed for feature propagation. Experimental results on real-world academic citation networks and quantum chemistry graphs show that our approach achieves or matches the state-of-the-art performance in four graph learning tasks, including semi-supervised node classification, multi-task graph classification, graph regression, and link prediction.