[Paper Review] Directed Graph Convolutional Network

Zekun Tong, Yuxuan Liang+3 more|arXiv (Cornell University)|Apr 29, 2020

Advanced Graph Neural Networks35 references65 citations

TL;DR

DGCN extends spectral-based GCNs to directed graphs by leveraging first- and second-order proximity, improving semi-supervised node classification on directed datasets.

ABSTRACT

Graph Convolutional Networks (GCNs) have been widely used due to their outstanding performance in processing graph-structured data. However, the undirected graphs limit their application scope. In this paper, we extend spectral-based graph convolution to directed graphs by using first- and second-order proximity, which can not only retain the connection properties of the directed graph, but also expand the receptive field of the convolution operation. A new GCN model, called DGCN, is then designed to learn representations on the directed graph, leveraging both the first- and second-order proximity information. We empirically show the fact that GCNs working only with DGCNs can encode more useful information from graph and help achieve better performance when generalized to other models. Moreover, extensive experiments on citation networks and co-purchase datasets demonstrate the superiority of our model against the state-of-the-art methods.

Motivation & Objective

• Extend spectral-based graph convolution to directed graphs without losing directionality.
• Introduce first- and second-order proximity to expand the receptive field.
• Develop a fusion mechanism to integrate multiple proximity-based convolutions.
• Demonstrate efficiency and effectiveness on real-world directed datasets.
• Provide insights into time/space complexity and generalization to other GNN models.

Proposed method

• Define first- and second-order proximity for directed graphs.
• Construct three proximity-based adjacency representations: first-order (A_F), second-order in-degree (A_S_in), and second-order out-degree (A_S_out).
• Apply spectral-style graph convolution to each proximity matrix with shared weights.
• Fuse the three propagated signals via a concatenation-based fusion function Gamma (e.g., Z = Concat(Z_F, alpha Z_S_in, beta Z_S_out)).
• Use a two-layer network with a final softmax for semi-supervised node classification.
• Provide training with cross-entropy on labeled nodes and full-batch computation for experiments.

Experimental results

Research questions

• RQ1 Can directed-graph spectral convolution be effectively realized without symmetrizing the graph?
• RQ2 Do first-order and second-order proximities capture complementary information to improve performance on directed graphs?
• RQ3 Does a fusion of multiple proximity-based convolutions yield better representations than using a single proximity?
• RQ4 How does DGCN perform versus state-of-the-art spectral- and spatial-based GNNs on directed/cited networks and co-purchase networks?

Key findings

• DGCN achieves competitive accuracy across seven datasets, often outperforming baselines like ChebNet, GCN, SGC, GraphSage, and GAT.
• Using both first- and second-order proximity (DGCN with both) generally improves results over using only first-order proximity.
• DGCN shows strong performance on directed datasets (Cora-Full, Cora-ML, CiteSeer, Amazon-Photo, Amazon-Computers) and remains robust on undirected ones (DBLP, PubMed).
• A two-layer DGCN with a fusion mechanism yields notable gains and demonstrates feature and label efficiency compared to baselines.
• The approach preserves directed information through second-order proximity while expanding the receptive field without excessive parameter growth.