{"type":"ScholarlyArticle","title":"Quaternion Collaborative Filtering for Recommendation","authors":[{"name":"Shuai Zhang","slug":"shuai-zhang","given":"Shuai","family":"Zhang","affiliation":"University of New South Wales"},{"name":"Lina Yao","slug":"lina-yao","given":"Lina","family":"Yao","affiliation":"University of New South Wales"},{"name":"Lucas Vinh Tran","slug":"lucas-vinh-tran","given":"Lucas","family":"Vinh Tran","affiliation":"Nanyang Technological University"},{"name":"Aston Zhang","slug":"aston-zhang","given":"Aston","family":"Zhang","affiliation":"Amazon Inc."},{"name":"Yi Tay","slug":"yi-tay","given":"Yi","family":"Tay","affiliation":"Nanyang Technological University"}],"abstract":"This paper proposes Quaternion Collaborative Filtering (QCF), a novel representation learning method for recommendation. Our proposed QCF relies on and exploits computation with Quaternion algebra, benefiting from the expressiveness and rich representation learning capability of Hamilton products. Quaternion representations, based on hypercomplex numbers, enable rich inter-latent dependencies between imaginary components. This encourages intricate relations to be captured when learning user-item interactions, serving as a strong inductive bias  as compared with the real-space inner product. All in all, we conduct extensive experiments on six real-world datasets, demonstrating the effectiveness of Quaternion algebra in recommender systems. The results exhibit that QCF outperforms a wide spectrum of strong neural baselines on all datasets. Ablative experiments confirm the effectiveness of Hamilton-based composition over multi-embedding composition in real space.","doi":"10.24963/ijcai.2019/599","url":"https://ijcai.org/proceedings/2019/599","pdf":"https://ijcai.org/proceedings/2019/0599.pdf","markdown":"https://ijcai.org/proceedings/2019/599.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/599","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Machine Learning M-Z","track":"Main track","number":599,"pages":{"first":4313,"last":4319},"keywords":["Machine Learning: Recommender Systems","Machine Learning: Deep Learning"],"videos":[],"references":[{"position":1,"raw":"[Baez, 2002] John Baez. The octonions. Bulletin of the American Mathematical Society, 39(2):145-205, 2002.","title":"The octonions","authors":"John Baez","year":"2002","venue":"Bulletin of the American Mathematical Society","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Chen et al., 2017] Xu Chen, Yongfeng Zhang, Qingyao Ai, Hongteng Xu, Junchi Yan, and Zheng Qin. Personalized key frame recommendation. In SIGIR, pages 315-324. ACM, 2017.","title":"Personalized key frame recommendation","authors":"Yongfeng Xu Chen, Qingyao Zhang, Hongteng Ai, Junchi Xu, Zheng Yan, Qin","year":"2017","venue":"SIGIR","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Danihelka et al., 2016] Ivo Danihelka, Greg Wayne, Be- nigno Uria, Nal Kalchbrenner, and Alex Graves. As- sociative long short-term memory. arXiv preprint arXiv:1602.03032, 2016.","title":"Associative long short-term memory","authors":"Ivo Danihelka, Greg Wayne, Benigno Uria, Nal Kalchbrenner, Alex Graves","year":"2016","venue":null,"doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Dziugaite and Roy, 2015] Gintare Karolina Dziugaite and Daniel M Roy. Neural network matrix factorization. arXiv preprint arXiv:1511.06443, 2015.","title":"Neural network matrix factorization","authors":"Karolina Gintare, Daniel M Dziugaite, Roy","year":"2015","venue":null,"doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Gaudet and Maida, 2018] Chase J Gaudet and Anthony S Maida. Deep quaternion networks. In 2018 IJCNN, pages 1-8. IEEE, 2018.","title":"Deep quaternion networks","authors":"J Chase, Anthony S Gaudet, Maida","year":"2018","venue":"IJCNN","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Hayashi and Shimbo, 2017] Katsuhiko Hayashi and Masashi Shimbo. On the equivalence of holographic and complex embeddings for link prediction. arXiv preprint arXiv:1702.05563, 2017.","title":"On the equivalence of holographic and complex embeddings for link prediction","authors":"Katsuhiko Hayashi, Masashi Shimbo","year":"2017","venue":null,"doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[He et al., 2016] Xiangnan He, Hanwang Zhang, Min-Yen Kan, and Tat-Seng Chua. Fast matrix factorization for on- line recommendation with implicit feedback. In SIGIR, 2016.","title":"Fast matrix factorization for online recommendation with implicit feedback","authors":"He","year":"2016","venue":"SIGIR","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[He et al., 2017] Xiangnan He, Lizi Liao, Hanwang Zhang, Liqiang Nie, Xia Hu, and Tat-Seng Chua. Neural collabo- rative filtering. In WWW, 2017.","title":"Neural collaborative filtering","authors":"He","year":"2017","venue":"WWW","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Hidasi et al., 2015] Balázs Hidasi, Alexandros Karat- zoglou, Linas Baltrunas, and Domonkos Tikk. Session- based recommendations with recurrent neural networks. arXiv preprint arXiv:1511.06939, 2015.","title":"Sessionbased recommendations with recurrent neural networks","authors":"Balázs Hidasi, Alexandros Karatzoglou, Linas Baltrunas, Domonkos Tikk","year":"2015","venue":null,"doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Hsieh et al., 2017] Cheng-Kang Hsieh, Longqi Yang, Yin Cui, Tsung-Yi Lin, Serge Belongie, and Deborah Estrin. Collaborative metric learning. In WWW, 2017.","title":"Collaborative metric learning","authors":"Cheng-Kang Hsieh, Longqi Yang, Yin Cui, Tsung-Yi Lin, Serge Belongie, Deborah Estrin","year":"2017","venue":"WWW","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Koren et al., 2009] Yehuda Koren, Robert Bell, and Chris Volinsky. Matrix factorization techniques for recom- mender systems. Computer, (8):30-37, 2009.","title":"Matrix factorization techniques for recommender systems","authors":"Koren","year":"2009","venue":"Computer","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Koren, 2008] Yehuda Koren. Factorization meets the neigh- borhood: a multifaceted collaborative filtering model. In KDD, 2008.","title":"Factorization meets the neighborhood: a multifaceted collaborative filtering model","authors":"Koren ;, Yehuda Koren","year":"2008","venue":"KDD","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"Parcollet et al., ] Titouan Parcollet, Ying Zhang, Mohamed Morchid, Chiheb Trabelsi, Georges Linarès, Renato De Mori, and Yoshua Bengio. Quaternion convolutional neural networks for end-to-end automatic speech recogni- tion. arXiv preprint arXiv:1806.07789.","title":"Quaternion convolutional neural networks for end-to-end automatic speech recognition","authors":"Parcollet","year":null,"venue":null,"doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Parcollet et al., 2016] Titouan Parcollet, Mohamed Morchid, Pierre-Michel Bousquet, Richard Dufour, Georges Linarès, and Renato De Mori. Quaternion neural networks for spoken language understanding. In 2016 IEEE SLT Workshop, pages 362-368. IEEE, 2016.","title":"Quaternion neural networks for spoken language understanding","authors":"Parcollet","year":"2016","venue":"IEEE SLT Workshop","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Parcollet et al., 2018a] Titouan Parcollet, Mohamed Morchid, and Georges Linarès. Quaternion convolutional neural networks for heterogeneous image processing. CoRR, abs/1811.02656, 2018.","title":"Titouan Parcollet, Mohamed Morchid, and Georges Linarès. Quaternion convolutional neural networks for heterogeneous image processing","authors":"Parcollet","year":"2018","venue":null,"doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Parcollet et al., 2018b] Titouan Parcollet, Mirco Ravanelli, Mohamed Morchid, Georges Linarès, and Renato De Mori. Speech recognition with quaternion neural net- works. CoRR, abs/1811.09678, 2018.","title":"Speech recognition with quaternion neural networks","authors":"Parcollet","year":"2018","venue":null,"doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Parcollet et al., 2019] Titouan Parcollet, Mirco Ravanelli, Mohamed Morchid, Georges Linarès, Chiheb Trabelsi, Renato De Mori, and Yoshua Bengio. Quaternion recur- rent neural networks. In ICLR, 2019.","title":"Quaternion recurrent neural networks","authors":"Parcollet","year":"2019","venue":"ICLR","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Rendle et al., 2009] Steffen Rendle, Christoph Freuden- thaler, Zeno Gantner, and Lars Schmidt-Thieme. Bpr: Bayesian personalized ranking from implicit feedback. In UAI, 2009.","title":"Bpr: Bayesian personalized ranking from implicit feedback","authors":"Steffen Rendle, Christoph Freudenthaler, Zeno Gantner, Lars Schmidt-Thieme","year":"2009","venue":"UAI","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Ruder, 2016] Sebastian Ruder. An overview of gradi- ent descent optimization algorithms. arXiv preprint arXiv:1609.04747, 2016.","title":"An overview of gradient descent optimization algorithms","authors":"Sebastian Ruder","year":"2016","venue":null,"doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Sedhain et al., 2015] Suvash Sedhain, Aditya Krishna Menon, Scott Sanner, and Lexing Xie. Autorec: Au- toencoders meet collaborative filtering. In WWW, 2015.","title":"Autorec: Autoencoders meet collaborative filtering","authors":"Sedhain","year":"2015","venue":"WWW","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Tay et al., 2018a] Yi Tay, Luu Anh Tuan, and Siu Cheung Hui. Latent relational metric learning via memory-based attention for collaborative ranking. In WWW 2018, 2018.","title":"Latent relational metric learning via memory-based attention for collaborative ranking","authors":"Tay","year":"2018","venue":"WWW 2018","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Tay et al., 2018b] Yi Tay, Anh Tuan Luu, and Siu Cheung Hui. Hermitian co-attention networks for text matching in asymmetrical domains. 2018.","title":"Hermitian co-attention networks for text matching in asymmetrical domains","authors":"Tay","year":"2018","venue":null,"doi":null,"url":null,"internal_url":"/proceedings/2018/615"},{"position":23,"raw":"[Trabelsi et al., 2017] Chiheb Trabelsi, Olexa Bilaniuk, Dmitriy Serdyuk, and et al. Deep complex networks. CoRR, abs/1705.09792, 2017.","title":"Deep complex networks","authors":"Trabelsi","year":"2017","venue":null,"doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Trouillon et al., 2016] Théo Trouillon, Johannes Welbl, Se- bastian Riedel, Éric Gaussier, and Guillaume Bouchard. Complex embeddings for simple link prediction. In ICML, 2016.","title":"Complex embeddings for simple link prediction","authors":"Théo Trouillon, Johannes Welbl, Sebastian Riedel, Éric Gaussier, Guillaume Bouchard","year":"2016","venue":"ICML","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Van den Oord et al., 2013] Aaron Van den Oord, Sander Dieleman, and Benjamin Schrauwen. Deep content-based music recommendation. In NIPS, pages 2643-2651, 2013.","title":"Deep content-based music recommendation","authors":"Oord Van Den","year":"2013","venue":"NIPS","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Witten and Shragge, 2006] Ben Witten and Jeff Shragge. Quaternion-based signal processing. In SEG Technical Program Expanded Abstracts 2006, pages 2862-2866. So- ciety of Exploration Geophysicists, 2006.","title":"Quaternion-based signal processing","authors":"Ben Witten, Jeff Shragge","year":"2006","venue":"SEG Technical Program Expanded Abstracts 2006","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Wu et al., 2017] Chao-Yuan Wu, Amr Ahmed, Alex Beu- tel, Alexander J Smola, and How Jing. Recurrent recom- mender networks. In WSDM. ACM, 2017.","title":"Recurrent recommender networks","authors":"Chao-Yuan, Amr Wu, Alex Ahmed, Alexander J Beutel, How Smola, Jing","year":"2017","venue":"WSDM","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Zhang et al., 2017a] Shuai Zhang, Lina Yao, and Aixin Sun. Deep learning based recommender system: A survey and new perspectives. arXiv preprint arXiv:1707.07435, 2017.","title":"Deep learning based recommender system: A survey and new perspectives","authors":"Zhang","year":"2017","venue":null,"doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Zhang et al., 2017b] Yongfeng Zhang, Qingyao Ai, Xu Chen, and W Bruce Croft. Joint representation learning for top-n recommendation with heterogeneous information sources. In CIKM, 2017.","title":"Joint representation learning for top-n recommendation with heterogeneous information sources","authors":"Zhang","year":"2017","venue":"CIKM","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Zhou et al., 2011] Ke Zhou, Shuang-Hong Yang, and Hongyuan Zha. Functional matrix factorizations for cold- start recommendation. In SIGIR, 2011.","title":"Functional matrix factorizations for coldstart recommendation","authors":"Ke Zhou, Shuang-Hong Yang, Hongyuan Zha","year":"2011","venue":"SIGIR","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}