近年來由於圖神經網路的長足發展，推薦系統技術也跟著取得了顯著的效能進步，但前人研究提出普通的圖神經網路(GNN)、圖卷積網路(GCN) 其訊息傳遞機制是扁平的，因此無法捕獲到使用者-項目二分圖上的層次結構，但這種層次結構在真實情境中卻可能隱含了豐富的訊息，比如某些使用者可能因為相似的喜好而可以自成一個使用者群集，某些項目也可能因為受眾相似而形成一個項目群集，而某幾個群集又可以因為更抽象的特徵而形成更高一層的群集，依此類推。這種分層表示能夠為推薦系統提供額外的依據，有利於幫同一群集中的使用者更加精準地推薦項目。本研究提出了一個新穎的推薦系統演算法，階層式二分圖卷積網路(HierBGCN)，主要設計了BiDiffPool層，能夠對二分圖進行可微分的池化操作，逐層減少節點數，同時保持二分圖的性質。 堆疊BiDiffPool層，即可以階層式的方式將每層的使用者-項目二分圖進行群集而得到多層的粗化圖，並在每一層的圖上使用 GCN 獲取高階鄰居資訊。最後再將每一層的資訊進行融合，得到使用者及項目的最終表示，藉以捕獲到豐富的層次訊息，並進行端到端的訓練。 在實驗結果中，本研究提出的HierBGCN比過去專用於同質圖的階層式GNN效果更好，因為HierBGCN是專為二分圖所設計的方法，能夠在圖池化過程中保留二分圖的性質，此外HierBGCN在推薦系統效能上有顯著的進步，在各項指標都比過去最佳的扁平GCN推薦模型來的高，驗證了學習圖的層次結構表示確實能夠提升推薦任務的準確性。

In recent years, due to the rapid development of Graph Neural Network(GNN), recommendation system technology has also made significant performance improvement. However, previous studies have announced that the message passing mechanism of classical GNNs is inherently flat, so it is unable to capture hierarchical representations of graphs, but the hierarchical structure of graph may provide a rich of information for the recommendation system.
In this work, we proposes a novel recommendation system model, Hierarchical Bipartite Graph Convolutional Network (HierBGCN), in which we mainly designs the BiDiffPool layer, which can perform differentiable pooling operations on the bipartite graph, reducing the number of nodes layer by layer, while maintaining the property of the bipartite graph. By stacking multiple BiDiffPool layers, the user-item bipartite graphs of each layer can be clustered in a hierarchical manner to obtain a multi-layered coarsened graph, and GNN can be used on each layer of graphs to capture high-order neighbor information. Then the information of each layer is aggregated to obtain the final representation of the user and the item to capture the rich information in the hierarchical structure. Finally, the model is trained in an end-to-end manner. In the experimental results, the proposed HierBGCN is better than the previous classical hierarchical GNN designed for homogeneous graphs in the performance of the recommendation system, because HierBGCN is specially designed for bipartite graphs, which can maintain the properties of bipartite graphs during graph pooling. In addition, HierBGCN has also made significant improvement than the best flat GNN recommendation model in previous, which verifies that the learning of hierarchical structure of graph can actually improve the performance of the recommendation task.

[1]Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. Neural machine translationby jointly learning to align and translate. 2014.
[2]YixinCao,XiangWang,XiangnanHe,ZikunHu,andTat­SengChua. Unifyingknowl­edgegraphlearningandrecommendation: Towardsabetterunderstandingofuserpref­erences. volume abs/1902.06236, 2019.
[3]Chong Chen, Min Zhang, Yongfeng Zhang, Yiqun Liu, and Shaoping Ma. Efficientneural matrix factorization without sampling for recommendation. volume 38, NewYork, NY, USA, January 2020. Association for Computing Machinery.
[4]HongyangGaoandShuiwangJi. Graphu­nets. InInternationalConferenceonMachineLearning, pages 2083–2092, 2019.
[5]Xavier Glorot and Yoshua Bengio. Understanding the difficulty of training deep feed­forwardneuralnetworks. InYeeWhyeTehandMikeTitterington,editors,Proceedingsof the Thirteenth International Conference on Artificial Intelligence and Statistics, vol­ume 9 ofProceedings of Machine Learning Research, pages 249–256, Chia LagunaResort, Sardinia, Italy, 13–15 May 2010. PMLR.
[6]Ian J. Goodfellow, Jean Pouget­Abadie, Mehdi Mirza, Bing Xu, David Warde­Farley,Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial networks.2014.
[7]William L. Hamilton, Rex Ying, and Jure Leskovec. Inductive representation learn­ing on large graphs. InProceedings of the 31st International Conference on NeuralInformation Processing Systems, NIPS’17, page 1025–1035, 2017.
[8]Chaoyang He, Tian Xie, Yu Rong, Wen­bing Huang, Junzhou Huang, Xiang Ren, andCyrusShahabi. Adversarialrepresentationlearningonlarge­scalebipartitegraphs. vol­ume abs/1906.11994, 2019.
[9]Xiangnan He, Kuan Deng, Xiang Wang, Yan Li, Yongdong Zhang, and Meng Wang.Lightgcn: Simplifying and powering graph convolution network for recommendation.volume abs/2002.02126, 2020.
[10]Xiangnan He, Lizi Liao, Hanwang Zhang, Liqiang Nie, Xia Hu, and Tat­Seng Chua.Neural collaborative filtering. InProceedings of the 26th International Conference onWorld Wide Web, WWW ’17, page 173–182, Republic and Canton of Geneva, CHE,2017. International World Wide Web Conferences Steering Committee.
[11]Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization. vol­ume abs/1412.6980, 2015.
[12]Thomas N. Kipf and Max Welling. Semi­Supervised Classification with Graph Con­volutional Networks. InProceedings of the 5th International Conference on LearningRepresentations, ICLR ’17, 2017.36
doi:10.6844/ncku.latex.template.2019.Z00
[13]Yehuda Koren, Robert Bell, and Chris Volinsky. Matrix factorization techniques forrecommender systems. volume 42, pages 30–37, Aug 2009.
[14]Junhyun Lee, Inyeop Lee, and Jaewoo Kang. Self­attention graph pooling. InProceed­ings of the 36th International Conference on Machine Learning, 09–15 Jun 2019.
[15]Chong Li, Kunyang Jia, Dan Shen, C.J. Richard Shi, and Hongxia Yang. Hierarchi­cal representation learning for bipartite graphs. InProceedings of the Twenty­EighthInternational Joint Conference on Artificial Intelligence, IJCAI­19, pages 2873–2879.International Joint Conferences on Artificial Intelligence Organization, 7 2019.
[16]ZhaoLi,XinShen,YuhangJiao,XumingPan,PengchengZou,XianlingMeng,Cheng­wei Yao, and Jiajun Bu. Hierarchical bipartite graph neural networks: Towards large­scale e­commerce applications. In2020 IEEE 36th International Conference on DataEngineering (ICDE), pages 1677–1688, 2020.
[17]Marcel Nassar. Hierarchical bipartite graph convolution networks. volumeabs/1812.03813, 2018.
[18]Shirui Pan, Ruiqi Hu, Guodong Long, Jing Jiang, Lina Yao, and Chengqi Zhang. Ad­versariallyregularizedgraphautoencoderforgraphembedding. InJeromeLang,editor,Proceedings of the 27th International Joint Conference on Artificial Intelligence, IJCAI2018, pages 2609–2615, United States of America, 2018. Association for the Advance­ment of Artificial Intelligence (AAAI). International Joint Conference on ArtificialIntelligence 2018, IJCAI 2018 ; Conference date: 13­07­2018 Through 19­07­2018.
[19]Luca Pasa, Nicolò Navarin, Wolfgang Erb, and Alessandro Sperduti. Simple graphconvolutional networks. volume abs/2106.05809, 2021.
[20]EkagraRanjan,SoumyaSanyal,andParthaPratimTalukdar. ASAP:Adaptivestructureaware pooling for learning hierarchical graph representations. 2019.
[21]Steffen Rendle, Christoph Freudenthaler, Zeno Gantner, and Lars Schmidt­Thieme.Bpr: Bayesian personalized ranking from implicit feedback. InProceedings of theTwenty­Fifth Conference on Uncertainty in Artificial Intelligence, UAI ’09, page 452–461, Arlington, Virginia, USA, 2009. AUAI Press.
[22]Olaf Ronneberger, Philipp Fischer, and Thomas Brox. U­net: Convolutional networksfor biomedical image segmentation. volume abs/1505.04597, 2015.
[23]XiaoyuanSuandTaghiM.Khoshgoftaar. Asurveyofcollaborativefilteringtechniques.volume 421425, 2009.
[24]Rianne van den Berg, Thomas N. Kipf, and Max Welling. Graph convolutional matrixcompletion. 2017.
[25]Aäron van den Oord, Yazhe Li, and Oriol Vinyals. Representation learning with con­trastive predictive coding. volume abs/1807.03748, 2018.
[26]Petar Veličković, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Liò,and Yoshua Bengio. Graph Attention Networks. 2018. accepted as poster.37
doi:10.6844/ncku.latex.template.2019.Z00
[27]Xiang Wang, Xiangnan He, Meng Wang, Fuli Feng, and Tat­Seng Chua. Neural graphcollaborative filtering. InProceedings of the 42nd International ACM SIGIR Confer­enceon ResearchandDevelopment in InformationRetrieval,SIGIR’19,page165–174,New York, NY, USA, 2019. Association for Computing Machinery.
[28]JiancanWu,XiangWang,FuliFeng,XiangnanHe,LiangChen,JianxunLian,andXingXie. Self­supervised graph learning for recommendation. volume abs/2010.10783,2020.
[29]Shiwen Wu, Wentao Zhang, Fei Sun, and Bin Cui. Graph neural networks in recom­mender systems: A survey.CoRR, abs/2011.02260, 2020.
[30]Jheng­Hong Yang, Chih­Ming Chen, Chuan­Ju Wang, and Ming­Feng Tsai. Hop­rec:High­order proximity for implicit recommendation. InProceedings of the 12th ACMConference on Recommender Systems, RecSys ’18, page 140–144. Association forComputing Machinery, 2018.
[31]Tiansheng Yao, Xinyang Yi, Derek Zhiyuan Cheng, Felix X. Yu, Aditya KrishnaMenon, Lichan Hong, Ed H. Chi, Steve Tjoa, Jieqi Kang, and Evan Ettinger. Self­supervised learning for deep models in recommendations.CoRR, abs/2007.12865,2020.
[32]Rex Ying, Ruining He, Kaifeng Chen, Pong Eksombatchai, William L. Hamilton, andJure Leskovec. Graph convolutional neural networks for web­scale recommender sys­tems. volume abs/1806.01973, 2018.
[33]Zhitao Ying, Jiaxuan You, Christopher Morris, Xiang Ren, Will Hamilton, and JureLeskovec. Hierarchical graph representation learning with differentiable pooling. InS. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa­Bianchi, and R. Garnett,editors,Advances in Neural Information Processing Systems, volume 31. Curran Asso­ciates, Inc., 2018.
[34]Muhan Zhang and Yixin Chen. Inductive graph pattern learning for recommender sys­tems based on a graph neural network. volume abs/1904.12058, 2019.
[35]Jie Zhou, Ganqu Cui, Shengding Hu, Zhengyan Zhang, Cheng Yang, Zhiyuan Liu,Lifeng Wang, Changcheng Li, and Maosong Sun. Graph neural networks: A review ofmethods and applications.AI Open, 1:57–81, 2020.38