Directed Graph Convolutional Network

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.

[1]  Si Zhang,et al.  Graph convolutional networks: a comprehensive review , 2019, Computational Social Networks.

[2]  Philip S. Yu,et al.  A Comprehensive Survey on Graph Neural Networks , 2019, IEEE Transactions on Neural Networks and Learning Systems.

[3]  Stephan Günnemann,et al.  Pitfalls of Graph Neural Network Evaluation , 2018, ArXiv.

[4]  Jure Leskovec,et al.  Knowledge-aware Graph Neural Networks with Label Smoothness Regularization for Recommender Systems , 2019, KDD.

[5]  Lise Getoor,et al.  Query-driven Active Surveying for Collective Classification , 2012 .

[6]  Qimai Li,et al.  Label Efficient Semi-Supervised Learning via Graph Filtering , 2019, 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

[7]  Max Welling,et al.  Semi-Supervised Classification with Graph Convolutional Networks , 2016, ICLR.

[8]  Lise Getoor,et al.  Collective Classification in Network Data , 2008, AI Mag..

[9]  Jure Leskovec,et al.  GNNExplainer: Generating Explanations for Graph Neural Networks , 2019, NeurIPS.

[10]  Jie Chen,et al.  EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphs , 2020, AAAI.

[11]  Stephan Günnemann,et al.  Predict then Propagate: Graph Neural Networks meet Personalized PageRank , 2018, ICLR.

[12]  Stephan Günnemann,et al.  Personalized Embedding Propagation: Combining Neural Networks on Graphs with Personalized PageRank , 2018, ArXiv.

[13]  Tiago Pereira,et al.  Spectra of Laplacian Matrices of Weighted Graphs: Structural Genericity Properties , 2017, SIAM J. Appl. Math..

[14]  Yong Yu,et al.  SVDFeature: a toolkit for feature-based collaborative filtering , 2012, J. Mach. Learn. Res..

[15]  Kilian Q. Weinberger,et al.  Simplifying Graph Convolutional Networks , 2019, ICML.

[16]  Pierre Vandergheynst,et al.  Wavelets on Graphs via Spectral Graph Theory , 2009, ArXiv.

[17]  Chong Wang,et al.  Attention-based Graph Neural Network for Semi-supervised Learning , 2018, ArXiv.

[18]  Abhinav Gupta,et al.  Zero-Shot Recognition via Semantic Embeddings and Knowledge Graphs , 2018, 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition.

[19]  Jure Leskovec,et al.  Inductive Representation Learning on Large Graphs , 2017, NIPS.

[20]  Stephan Günnemann,et al.  Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking , 2017, ICLR.

[21]  Mingzhe Wang,et al.  LINE: Large-scale Information Network Embedding , 2015, WWW.

[22]  Ruoyu Li,et al.  Adaptive Graph Convolutional Neural Networks , 2018, AAAI.

[23]  Wenwu Zhu,et al.  Structural Deep Network Embedding , 2016, KDD.

[24]  Yuan Luo,et al.  Graph Convolutional Networks for Text Classification , 2018, AAAI.

[25]  Jure Leskovec,et al.  How Powerful are Graph Neural Networks? , 2018, ICLR.

[26]  Mark S. Granovetter.  T H E S T R E N G T H O F WEAK TIES: A NETWORK THEORY REVISITED , 1983 .

[27]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[28]  Joonseok Lee,et al.  N-GCN: Multi-scale Graph Convolution for Semi-supervised Node Classification , 2018, UAI.

[29]  Yoshua Bengio,et al.  Understanding the difficulty of training deep feedforward neural networks , 2010, AISTATS.

[30]  Geoffrey E. Hinton,et al.  Visualizing Data using t-SNE , 2008 .

[31]  Zhizhen Zhao,et al.  LanczosNet: Multi-Scale Deep Graph Convolutional Networks , 2019, ICLR.

[32]  Xavier Bresson,et al.  Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering , 2016, NIPS.

[33]  Stephanie M. Reich,et al.  Friending, IMing, and hanging out face-to-face: overlap in adolescents' online and offline social networks. , 2012, Developmental psychology.

[34]  Pietro Liò,et al.  Graph Attention Networks , 2017, ICLR.