Graph convolutional networks: a comprehensive review

Si Zhang,Jiejun Xu,Ross Maciejewski,Hanghang Tong

doi:10.1186/s40649-019-0069-y

Abstract

Graphs naturally appear in numerous application domains, ranging from social analysis, bioinformatics to computer vision. The unique capability of graphs enables capturing the structural relations among data, and thus allows to harvest more insights compared to analyzing data in isolation. However, it is often very challenging to solve the learning problems on graphs, because (1) many types of data are not originally structured as graphs, such as images and text data, and (2) for graph-structured data, the underlying connectivity patterns are often complex and diverse. On the other hand, the representation learning has achieved great successes in many areas. Thereby, a potential solution is to learn the representation of graphs in a low-dimensional Euclidean space, such that the graph properties can be preserved. Although tremendous efforts have been made to address the graph representation learning problem, many of them still suffer from their shallow learning mechanisms. Deep learning models on graphs (e.g., graph neural networks) have recently emerged in machine learning and other related areas, and demonstrated the superior performance in various problems. In this survey, despite numerous types of graph neural networks, we conduct a comprehensive review specifically on the emerging field of graph convolutional networks, which is one of the most prominent graph deep learning models. First, we group the existing graph convolutional network models into two categories based on the types of convolutions and highlight some graph convolutional network models in details. Then, we categorize different graph convolutional networks according to the areas of their applications. Finally, we present several open challenges in this area and discuss potential directions for future research.

Highlights

Graphs naturally arise in many real-world applications, including social analysis [1], fraud detection [2, 3], traffic prediction [4], computer vision [5], and many more
Cui et al discuss the differences between the traditional graph embedding and the recent network embedding methods [15]
The main contributions of this survey are summarized as follows: 1. We introduce two taxonomies to group the existing graph convolutional network models (Fig. 1)

Summary

Introduction

Graphs naturally arise in many real-world applications, including social analysis [1], fraud detection [2, 3], traffic prediction [4], computer vision [5], and many more. Since graph convolutional network is a very hot and fast developing research area, these existing surveys may not cover the most up-to-date models. In this survey, we focus on reviewing the existing literature of the graph convolutional networks and cover the recent progress. In “Spectral graph convolutional networks” and “Spatial graph convolutional networks” sections, we categorize the existing models into the spectralbased methods and the spatial-based methods by the types of graph filtering with some detailed examples. In “Challenges and future researches” section, we discuss some challenges of the existing graph convolutional network models and provide some directions for the future work. We denote the transpose of a matrix A as AT

Graphs and graph signals

Graph Fourier transform

Challenges and future researches