Higher-order Graph Convolutional Networks

TL;DR

This paper introduces Motif Convolutional Networks, a novel graph attention model that captures higher-order node interactions using motif-based adjacency matrices, leading to improved semi-supervised node classification performance.

Contribution

It proposes a motif-based graph attention model that generalizes existing methods by incorporating higher-order neighborhoods with an attention mechanism.

Findings

Achieves state-of-the-art results on semi-supervised node classification

Effectively captures higher-order node interactions

Demonstrates the benefit of motif-based adjacency in graph neural networks

Abstract

Following the success of deep convolutional networks in various vision and speech related tasks, researchers have started investigating generalizations of the well-known technique for graph-structured data. A recently-proposed method called Graph Convolutional Networks has been able to achieve state-of-the-art results in the task of node classification. However, since the proposed method relies on localized first-order approximations of spectral graph convolutions, it is unable to capture higher-order interactions between nodes in the graph. In this work, we propose a motif-based graph attention model, called Motif Convolutional Networks (MCNs), which generalizes past approaches by using weighted multi-hop motif adjacency matrices to capture higher-order neighborhoods. A novel attention mechanism is used to allow each individual node to select the most relevant neighborhood to apply its filter. Experiments show that our proposed method is able to achieve state-of-the-art results on the semi-supervised node classification task.