{"type":"ScholarlyArticle","title":"MR-GCN: Multi-Relational Graph Convolutional Networks based on Generalized Tensor Product","authors":[{"name":"Zhichao Huang","slug":"zhichao-huang","given":"Zhichao","family":"Huang","affiliation":"Harbin Institute of Technology , Shenzhen , Shenzhen 518055 , China; Shenzhen Key Laboratory of Internet Information Collaboration , Shenzhen 518055 , China"},{"name":"Xutao Li","slug":"xutao-li","given":"Xutao","family":"Li","affiliation":"Harbin Institute of Technology , Shenzhen , Shenzhen 518055 , China; Shenzhen Key Laboratory of Internet Information Collaboration , Shenzhen 518055 , China"},{"name":"Yunming Ye","slug":"yunming-ye","given":"Yunming","family":"Ye","affiliation":"Harbin Institute of Technology , Shenzhen , Shenzhen 518055 , China; Shenzhen Key Laboratory of Internet Information Collaboration , Shenzhen 518055 , China"},{"name":"Michael K. Ng","slug":"michael-k-ng","given":"Michael K.","family":"Ng","affiliation":"Department of Mathematics , The University of Hong Kong , Pokfulam , Hong Kong , China"}],"abstract":"Graph Convolutional Networks (GCNs) have been extensively studied in recent years. Most of existing GCN approaches are designed for the homogenous graphs with a single type of relation. However, heterogeneous graphs of multiple types of relations are also ubiquitous and there is a lack of methodologies to tackle such graphs. Some previous studies address the issue by performing conventional GCN on each single relation and then blending their results. However, as the convolutional kernels neglect the correlations across relations, the strategy is sub-optimal. In this paper, we propose the Multi-Relational Graph Convolutional Network (MR-GCN) framework by developing a novel convolution operator on multi-relational graphs. In particular, our multi-dimension convolution operator extends the graph spectral analysis into the eigen-decomposition of a Laplacian tensor. And the eigen-decomposition is formulated with a generalized tensor product, which can correspond to any unitary transform instead of limited merely to Fourier transform. We conduct comprehensive experiments on four real-world multi-relational graphs to solve the semi-supervised node classification task, and the results show the superiority of MR-GCN against the state-of-the-art competitors.","doi":"10.24963/ijcai.2020/175","url":"https://ijcai.org/proceedings/2020/175","pdf":"https://ijcai.org/proceedings/2020/0175.pdf","markdown":"https://ijcai.org/proceedings/2020/175.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/175","volume":{"slug":"2020","title":"Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2020","url":"https://ijcai.org/proceedings/2020/","year":2020,"location":"Yokohama","dates":"January 2021 (postponed from 11-17 July 2020)","editors":"Christian Bessiere","isbn":"978-0-9992411-6-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2020"},"section":"Data Mining","track":"Main track","number":175,"pages":{"first":1258,"last":1264},"keywords":["Machine Learning: Deep Learning: Convolutional networks","Data Mining: Classification, Semi-Supervised Learning","Machine Learning: Tensor and Matrix Methods","Data Mining: Mining Graphs, Semi Structured Data, Complex Data"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/24927/file_24927.m3u8","length_sec":279,"provider":"hls"}],"references":[{"position":1,"raw":"[Bruna et al., 2013] Joan Bruna, Wojciech Zaremba, Arthur Szlam, and Yann LeCun. Spectral networks and lo- cally connected networks on graphs. arXiv preprint arXiv:1312.6203, 2013.","title":"Spectral networks and locally connected networks on graphs","authors":"Bruna","year":"2013","venue":null,"doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Defferrard et al., 2016] Michaël Defferrard, Xavier Bres- son, and Pierre Vandergheynst. Convolutional neural networks on graphs with fast localized spectral filtering. In Advances in Neural Information Processing Systems, pages 3844-3852, 2016.","title":"Convolutional neural networks on graphs with fast localized spectral filtering","authors":"Michaël Defferrard, Xavier Bresson, Pierre Vandergheynst","year":"2016","venue":"Advances in Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Grover and Leskovec, 2016] Aditya Grover and Jure Leskovec. node2vec: Scalable feature learning for networks. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pages 855-864, 2016.","title":"node2vec: Scalable feature learning for networks","authors":"Leskovec Grover, Aditya Grover, Jure Leskovec","year":"2016","venue":"Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery & Data Mining","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Hamilton et al., 2017] Will Hamilton, Zhitao Ying, and Jure Leskovec. Inductive representation learning on large graphs. In Advances in Neural Information Processing Systems, pages 1024-1034, 2017.","title":"Inductive representation learning on large graphs","authors":"Hamilton","year":"2017","venue":"Advances in Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Henaff et al., 2015] Mikael Henaff, Joan Bruna, and Yann LeCun. Deep convolutional networks on graph-structured data. arXiv preprint arXiv:1506.05163, 2015.","title":"Deep convolutional networks on graph-structured data","authors":"Mikael Henaff, Joan Bruna, Yann Lecun","year":"2015","venue":null,"doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Jain, 1979] Anil K Jain. A sinusoidal family of unitary transforms. IEEE Transactions on Pattern Analysis and Machine Intelligence, (4):356-365, 1979.","title":"A sinusoidal family of unitary transforms","authors":"K Anil, Jain","year":"1979","venue":"IEEE Transactions on Pattern Analysis and Machine Intelligence","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Jørgensen et al., 2018] Peter Bjørn Jørgensen, Karsten Wedel Jacobsen, and Mikkel N Schmidt. Neural message passing with edge updates for predicting properties of molecules and materials. arXiv preprint arXiv:1806.03146, 2018.","title":"Neural message passing with edge updates for predicting properties of molecules and materials","authors":"Jørgensen","year":"2018","venue":null,"doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Khan and Blumenstock, 2019] Muhammad Raza Khan and Joshua E. Blumenstock. Multi-gcn: Graph convolutional networks for multi-view networks, with applications to global poverty. In Thirty-Third AAAI Conference on Ar- tificial Intelligence, pages 606-613, 2019.","title":"Multi-gcn: Graph convolutional networks for multi-view networks, with applications to global poverty","authors":"Blumenstock ; Khan, Raza Muhammad, Joshua E Khan, Blumenstock","year":"2019","venue":"Thirty-Third AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Kilmer and Martin, 2011] Misha E Kilmer and Carla D Martin. Factorization strategies for third-order tensors. Linear Algebra and its Applications, 435(3):641-658, 2011.","title":"Factorization strategies for third-order tensors","authors":"Misha E Kilmer, Carla D Martin","year":"2011","venue":"Linear Algebra and its Applications","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Kipf and Welling, 2016] Thomas N Kipf and Max Welling. Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907, 2016.","title":"Semi-supervised classification with graph convolutional networks","authors":"N Thomas, Max Kipf, Welling","year":"2016","venue":null,"doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Li et al., 2013] Xutao Li, Michael K Ng, and Yunming Ye. Multicomm: Finding community structure in multi- dimensional networks. IEEE Transactions on Knowledge and Data Engineering, 26(4):929-941, 2013.","title":"Multicomm: Finding community structure in multidimensional networks","authors":"Li","year":"2013","venue":"IEEE Transactions on Knowledge and Data Engineering","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Li et al., 2017] Xutao Li, Yunming Ye, and Xiaofei Xu. Low-rank tensor completion with total variation for visual data inpainting. In Thirty-First AAAI Conference on Arti- ficial Intelligence, pages 2210-2216, 2017.","title":"Low-rank tensor completion with total variation for visual data inpainting","authors":"Li","year":"2017","venue":"Thirty-First AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Ma et al., 2019] Yao Ma, Suhang Wang, Chara C Aggarwal, Dawei Yin, and Jiliang Tang. Multi-dimensional graph convolutional networks. In Proceedings of the 2019 SIAM International Conference on Data Mining, pages 657-665, 2019.","title":"Multi-dimensional graph convolutional networks","authors":"Yao Ma, Suhang Wang, Chara C Aggarwal, Dawei Yin, Jiliang Tang","year":"2019","venue":"Proceedings of the 2019 SIAM International Conference on Data Mining","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Monti et al., 2017] Federico Monti, Davide Boscaini, Jonathan Masci, Emanuele Rodola, Jan Svoboda, and Michael M Bronstein. Geometric deep learning on graphs and manifolds using mixture model cnns. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 5115-5124, 2017.","title":"Geometric deep learning on graphs and manifolds using mixture model cnns","authors":"Federico Monti, Davide Boscaini, Jonathan Masci, Emanuele Rodola, Jan Svoboda, Michael M Bronstein","year":"2017","venue":"Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Ng et al., 2011] Michaek Kwok-Po Ng, Xutao Li, and Yun- ming Ye. Multirank: co-ranking for objects and relations in multi-relational data. In Proceedings of the 17th ACM SIGKDD International Conference on Knowledge Discov- ery & Data Mining, pages 1217-1225, 2011.","title":"Multirank: co-ranking for objects and relations in multi-relational data","authors":"Ng","year":"2011","venue":"Proceedings of the 17th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Perozzi et al., 2014] Bryan Perozzi, Rami Al-Rfou, and Steven Skiena. Deepwalk: Online learning of social repre- sentations. In Proceedings of the 20th ACM SIGKDD In- ternational Conference on Knowledge Discovery & Data Mining, pages 701-710, 2014.","title":"Deepwalk: Online learning of social representations","authors":"Bryan Perozzi, Rami Al-Rfou, Steven Skiena","year":"2014","venue":"Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Schlichtkrull et al., 2018] Michael Schlichtkrull, Thomas N Kipf, Peter Bloem, Rianne Van Den Berg, Ivan Titov, and Max Welling. Modeling relational data with graph convo- lutional networks. In European Semantic Web Conference, pages 593-607, 2018.","title":"Modeling relational data with graph convolutional networks","authors":"Michael Schlichtkrull, Thomas N Kipf, Peter Bloem, Rianne Van Den, Ivan Berg, Max Titov, Welling","year":"2018","venue":"European Semantic Web Conference","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Song et al., 2019] Guangjing Song, Michael K Ng, and Xiongjun Zhang. Robust tensor completion using trans- formed tensor svd. arXiv preprint arXiv:1907.01113, 2019.","title":"Robust tensor completion using transformed tensor svd","authors":"Song","year":"2019","venue":null,"doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Sun et al., 2019] Yiwei Sun, Suhang Wang, Tsung-Yu Hsieh, Xianfeng Tang, and Vasant Honavar. Megan: A generative adversarial network for multi-view network embedding. In Twenty-Eighth International Joint Confer- ence on Artificial Intelligence, pages 3527-3533, 2019.","title":"Megan: A generative adversarial network for multi-view network embedding","authors":"Yiwei Sun, Suhang Wang, Tsung-Yu Hsieh, Xianfeng Tang, Vasant Honavar","year":"2019","venue":"Twenty-Eighth International Joint Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":"/proceedings/2019/489"},{"position":20,"raw":"[Tang et al., 2015] Jian Tang, Meng Qu, Mingzhe Wang, Ming Zhang, Jun Yan, and Qiaozhu Mei. Line: Large- scale information network embedding. In The World Wide Web Conference, pages 1067-1077, 2015.","title":"Line: Largescale information network embedding","authors":"Jian Tang, Meng Qu, Mingzhe Wang, Ming Zhang, Jun Yan, Qiaozhu Mei","year":"2015","venue":"The World Wide Web Conference","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Wang et al., 2019] Xiao Wang, Houye Ji, Chuan Shi, Bai Wang, Yanfang Ye, Peng Cui, and Philip S Yu. Hetero- geneous graph attention network. In The World Wide Web Conference, pages 2022-2032, 2019.","title":"Heterogeneous graph attention network","authors":"Xiao Wang, Houye Ji, Chuan Shi, Bai Wang, Yanfang Ye, Peng Cui, Philip S Yu","year":"2019","venue":"The World Wide Web Conference","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Yang et al., 2016] Zhilin Yang, William W Cohen, and Rus- lan Salakhutdinov. Revisiting semi-supervised learning with graph embeddings. In International Conference on Machine Learning, pages 40-48, 2016.","title":"Revisiting semi-supervised learning with graph embeddings","authors":"Zhilin Yang, William W Cohen, Ruslan Salakhutdinov","year":"2016","venue":"International Conference on Machine Learning","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Ying et al., 2018] Rex Ying, Ruining He, Kaifeng Chen, Pong Eksombatchai, William L Hamilton, and Jure Leskovec. Graph convolutional neural networks for web- scale recommender systems. In Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pages 974-983, 2018.","title":"Graph convolutional neural networks for webscale recommender systems","authors":"Rex Ying, Ruining He, Kaifeng Chen, Pong Eksombatchai, William L Hamilton, Jure Leskovec","year":"2018","venue":"Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Yun et al., 2019] Seongjun Yun, Minbyul Jeong, Raehyun Kim, Jaewoo Kang, and Hyunwoo J Kim. Graph trans- former networks. In Advances in Neural Information Pro- cessing Systems, pages 11960-11970, 2019.","title":"Graph transformer networks","authors":"Yun","year":"2019","venue":"Advances in Neural Information Processing Systems","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}