Digraph Inception Convolutional Networks

Graph Convolutional Networks (GCNs) have shown promising results in modeling graph-structured data. However, they have difficulty with processing digraphs because of two reasons: 1) transforming directed to undirected graph to guarantee the symmetry of graph Laplacian is not reasonable since it not only misleads message passing scheme to aggregate incorrect weights but also deprives the unique characteristics of digraph structure; 2) due to the fixed receptive field in each layer, GCNs fail to obtain multi-scale features that can boost their performance. In this paper, we theoretically extend spectral-based graph convolution to digraphs and derive a simplified form using personalized PageRank. Specifically, we present the Digraph Inception Convolutional Networks (DiGCN) which utilizes digraph convolution and k-order proximity to achieve larger receptive fields and learn multi-scale features in digraphs. We empirically show that DiGCN can encode more structural information from digraphs than GCNs and help achieve better performance when generalized to other models. Moreover, experiments on various benchmarks demonstrate its superiority against the state-of-the-art methods.

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

[2]  Tingyang Xu,et al.  DropEdge: Towards Deep Graph Convolutional Networks on Node Classification , 2020, ICLR.

[3]  Xiaogang Wang,et al.  Person Re-identification with Deep Similarity-Guided Graph Neural Network , 2018, ECCV.

[4]  Pietro Liò,et al.  Deep Graph Infomax , 2018, ICLR.

[5]  Sergey Brin,et al.  Reprint of: The anatomy of a large-scale hypertextual web search engine , 2012, Comput. Networks.

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

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

[8]  Rajeev Motwani,et al.  The PageRank Citation Ranking : Bringing Order to the Web , 1999, WWW 1999.

[9]  David S. Rosenblum,et al.  Directed Graph Convolutional Network , 2020, ArXiv.

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

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

[12]  Aleksandar Bojchevski,et al.  Is PageRank All You Need for Scalable Graph Neural Networks ? , 2019 .

[13]  Bryan Hooi,et al.  NodeAug: Semi-Supervised Node Classification with Data Augmentation , 2020, KDD.

[14]  Davide Eynard,et al.  SIGN: Scalable Inception Graph Neural Networks , 2020, ArXiv.

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

[16]  Yu Zheng,et al.  Predicting Citywide Crowd Flows in Irregular Regions Using Multi-View Graph Convolutional Networks , 2019, IEEE Transactions on Knowledge and Data Engineering.

[17]  Andrew Lim,et al.  On Isometry Robustness of Deep 3D Point Cloud Models Under Adversarial Attacks , 2020, 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

[18]  F. Chung.  Laplacians and the Cheeger Inequality for Directed Graphs , 2005 .

[19]  Yann Dauphin,et al.  Convolutional Sequence to Sequence Learning , 2017, ICML.

[20]  Ken-ichi Kawarabayashi,et al.  Representation Learning on Graphs with Jumping Knowledge Networks , 2018, ICML.

[21]  Bernard Ghanem,et al.  DeepGCNs: Can GCNs Go As Deep As CNNs? , 2019, 2019 IEEE/CVF International Conference on Computer Vision (ICCV).

[22]  Seyed-Ahmad Ahmadi,et al.  V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation , 2016, 2016 Fourth International Conference on 3D Vision (3DV).

[23]  Matthias Fey,et al.  Just Jump: Dynamic Neighborhood Aggregation in Graph Neural Networks , 2019, ArXiv.

[24]  Bryan Hooi,et al.  GraphCrop: Subgraph Cropping for Graph Classification , 2020, ArXiv.

[25]  Pasquale Minervini,et al.  Convolutional 2D Knowledge Graph Embeddings , 2017, AAAI.

[26]  Sergey Ioffe,et al.  Rethinking the Inception Architecture for Computer Vision , 2015, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[27]  Yongdong Zhang,et al.  LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation , 2020, SIGIR.

[28]  Hao Wang,et al.  Rethinking Knowledge Graph Propagation for Zero-Shot Learning , 2018, 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

[29]  Yangyong Zhu,et al.  GraphInception: Convolutional Neural Networks for Collective Classification in Heterogeneous Information Networks , 2019, IEEE Transactions on Knowledge and Data Engineering.

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

[31]  Matteo Barigozzi,et al.  NETS: Network Estimation for Time Series , 2018 .

[32]  Yi Ma,et al.  Spectral-based Graph Convolutional Network for Directed Graphs , 2019, ArXiv.

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

[35]  Xi Chen,et al.  Long-tail Relation Extraction via Knowledge Graph Embeddings and Graph Convolution Networks , 2019, NAACL.

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

[37]  Thomas Hofmann,et al.  Semi-supervised Learning on Directed Graphs , 2004, NIPS.

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

[39]  G. P. Barker,et al.  Algebraic Perron-Frobenius theory , 1975 .

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

[41]  Yu Zheng,et al.  GeoMAN: Multi-level Attention Networks for Geo-sensory Time Series Prediction , 2018, IJCAI.

[42]  Yuwei Wu,et al.  Campus3D: A Photogrammetry Point Cloud Benchmark for Hierarchical Understanding of Outdoor Scene , 2020, ACM Multimedia.

[43]  Kristina Lerman,et al.  MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing , 2019, ICML.

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

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

[46]  Ashish Goel,et al.  Fast Incremental and Personalized PageRank , 2010, Proc. VLDB Endow..

[47]  Michael M. Bronstein,et al.  MOTIFNET: A MOTIF-BASED GRAPH CONVOLUTIONAL NETWORK FOR DIRECTED GRAPHS , 2018, 2018 IEEE Data Science Workshop (DSW).

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