{"type":"ScholarlyArticle","title":"Improved Bounded Matrix Completion for Large-Scale Recommender Systems","authors":[{"name":"Huang Fang","slug":"huang-fang","given":"Huang","family":"Fang","affiliation":"Departments of Statistics and Computer Science"},{"name":"Zhang Zhen","slug":"zhang-zhen","given":"Zhang","family":"Zhen","affiliation":"Departments of Statistics and Computer Science"},{"name":"Yiqun Shao","slug":"yiqun-shao","given":"Yiqun","family":"Shao","affiliation":"Department of Mathematics University of California , Davis"},{"name":"Cho-Jui Hsieh","slug":"cho-jui-hsieh","given":"Cho-Jui","family":"Hsieh","affiliation":"Departments of Statistics and Computer Science"}],"abstract":"Matrix completion is a widely used technique for personalized recommender system. In this paper, we focus on the idea of Bounded Matrix Completion (BMC) which imposes bounded constraint into the original matrix completion problem. It has been shown that BMC works well for several real world datasets, and an efficient coordinate descent solver called BMA has been proposed in~\\cite{bma}. However, we observe that the BMA algorithm sometimes fails to converge to a stationary point, resulting in a  relatively poor accuracy in those cases. To overcome this issue, we propose our new approach for solving BMC under the ADMM framework. The proposed algorithm is gauranteed to converge to stationary points. Experimental results on real world datasets show that our algorithm can reach a lower objective value, obtain a higher predict accuracy rate and have better scalability compared with BMA. We also present that our method outperforms the state-of-art standard matrix factorization in most cases.","doi":"10.24963/ijcai.2017/229","url":"https://ijcai.org/proceedings/2017/229","pdf":"https://ijcai.org/proceedings/2017/0229.pdf","markdown":"https://ijcai.org/proceedings/2017/229.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/229","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Machine Learning A-R","track":"Main track","number":229,"pages":{"first":1654,"last":1660},"keywords":["Machine Learning: Data Mining","Machine Learning: Machine Learning","Constraints and Satisfiability: Constraint Optimisation"],"videos":[],"references":[{"position":1,"raw":"[Boyd et al., 2011] S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein. Distributed optimization and statistical learning via the alternating direction method of multipli- ers. Found. Trends Mach. Learn., pages 1-122, January 2011.","title":"Distributed optimization and statistical learning via the alternating direction method of multipliers","authors":"S Boyd, N Parikh, E Chu, B Peleato, J Eckstein","year":"2011","venue":"Found. Trends Mach. Learn","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Cabral et al., 2013] Ricardo Cabral, Fernando De la Torre, Joo P. Costeira, and Alexandre Bernardino. Unifying nu- clear norm and bilinear factorization approaches for low- rank matrix decomposition. In Computer Vision (ICCV), 2013 IEEE International Conference on, December 2013.","title":"Unifying nuclear norm and bilinear factorization approaches for lowrank matrix decomposition","authors":"Ricardo Cabral, Fernando De La Torre, Joo P Costeira, Alexandre Bernardino","year":"2013","venue":"IEEE International Conference on","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Candes and Recht., 2009] E. J. Candes and B. Recht. Exact matrix completion via convex optimization. Foundations of Computational mathematics, 9(6):717-772, 2009.","title":"Exact matrix completion via convex optimization","authors":"E J Candes, B Recht","year":"2009","venue":"Foundations of Computational mathematics","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Chiang et al., 2015] Kai-Yang Chiang, Cho-Jui Hsieh, and Inderjit S Dhillon. Matrix completion with noisy side in- formation. In Advances in Neural Information Processing Systems, pages 3447-3455, 2015.","title":"Matrix completion with noisy side information","authors":"Kai-Yang Chiang, Cho-Jui Hsieh, Inderjit S Dhillon","year":"2015","venue":"Advances in Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Du et al., 2014] Simon S. Du, Y. Liu, B. Chen, and L. Li. Maxios: Large scale nonnegative matrix factorization for collaborative filtering. In In Conference on Neural In- formation Processing Systems (NIPS) 2014, workshop on Distributed Machine Learning and Matrix Computations., 2014.","title":"Maxios: Large scale nonnegative matrix factorization for collaborative filtering","authors":"Simon S Du, Y Liu, B Chen, L Li","year":"2014","venue":"Conference on Neural Information Processing Systems (NIPS) 2014, workshop on Distributed Machine Learning and Matrix Computations","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Funk, 2006] Simon Funk. Stochastic gradient descent, http://sifter.org/∼ simon/journal/20061211.html, 2006.","title":"Stochastic gradient descent","authors":"Simon Funk","year":"2006","venue":null,"doi":null,"url":"http://sifter.org/∼simon/journal/20061211.html","internal_url":null},{"position":7,"raw":"[Gemulla et al., 2011] Rainer Gemulla, Erik Nijkamp, Pe- ter J Haas, and Yannis Sismanis. Large-scale matrix fac- torization with distributed stochastic gradient descent. In Proceedings of the 17th ACM SIGKDD international con- ference on Knowledge discovery and data mining, pages 69-77. ACM, 2011.","title":"Large-scale matrix factorization with distributed stochastic gradient descent","authors":"Rainer Gemulla, Erik Nijkamp, Peter J Haas, Yannis Sismanis","year":"2011","venue":"Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Halko et al., 2011] Nathan Halko, Per-Gunnar Martinsson, and Joel A Tropp. Finding structure with randomness: Probabilistic algorithms for constructing approximate ma- trix decompositions. SIAM review, 53(2):217-288, 2011.","title":"Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions","authors":"Halko","year":"2011","venue":"SIAM review","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Hsieh and Olsen, 2014] Cho-Jui Hsieh and Peder A Olsen. Nuclear norm minimization via active subspace selection. In ICML, 2014.","title":"Nuclear norm minimization via active subspace selection","authors":"Cho-Jui Hsieh, Peder A Olsen","year":"2014","venue":"ICML","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Hsieh et al., 2015] Cho-Jui Hsieh, Nagarajan Natarajan, and Inderjit Dhillon. Pu learning for matrix completion. In International Conference on Machine Learning, pages 2445-2453, 2015.","title":"Pu learning for matrix completion","authors":"Cho-Jui Hsieh, Nagarajan Natarajan, Inderjit Dhillon","year":"2015","venue":"International Conference on Machine Learning","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Koren et al., 2009a] Y. Koren, R. Bell, and C. Volinsky. Ma- trix factorization techniques for recommender systems. IEEE Computer, pages 42-49, 2009.","title":"Matrix factorization techniques for recommender systems","authors":"Koren","year":"2009","venue":"IEEE Computer","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Koren et al., 2009b] Yehuda Koren, Robert Bell, and Chris Volinsky. Matrix factorization techniques for recom- mender systems. Computer, 2009.","title":"Matrix factorization techniques for recommender systems","authors":"Koren","year":"2009","venue":"Computer","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Koren, 2008] Yehuda Koren. Factorization meets the neigh- borhood: a multifaceted collaborative filtering model. In In Proc. of the 14th ACM SIGKDD conference, pages 426- 434, 2008.","title":"Factorization meets the neighborhood: a multifaceted collaborative filtering model","authors":"Koren ;, Yehuda Koren","year":"2008","venue":"Proc. of the 14th ACM SIGKDD conference","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Larsen, 1998] Rasmus Munk Larsen. Lanczos bidiagonal- ization with partial reorthogonalization, 1998.","title":"Lanczos bidiagonalization with partial reorthogonalization","authors":"Rasmus Munk Larsen","year":"1998","venue":null,"doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Lin et al., 2011] Z. Lin, M. Chen, L. q. Wu, and Y. Ma. Lin- earized alternating direction method with adaptive penalty for low rank representation. In Neural Information Pro- cessing Systems (NIPS), 2011.","title":"Linearized alternating direction method with adaptive penalty for low rank representation","authors":"Z Lin, M Chen, L Q Wu, Y Ma","year":"2011","venue":"Neural Information Processing Systems (NIPS)","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Mazumder et al., 2010] Rahul Mazumder, Trevor Hastie, and Robert Tibshirani. Spectral regularization algorithms for learning large incomplete matrices. Journal of machine learning research, 11(Aug):2287-2322, 2010.","title":"Spectral regularization algorithms for learning large incomplete matrices","authors":"Rahul Mazumder, Trevor Hastie, Robert Tibshirani","year":"2010","venue":"Journal of machine learning research","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[R. Kannan and Park., 2012] M. Ishteva R. Kannan and H. Park. Bounded matrix low rank approximation. In ICDM 2012 IEEE 12th International Conference on, pages 10-13, December 2012.","title":"Bounded matrix low rank approximation","authors":"M Ishteva, R Kannan, H Park","year":"2012","venue":"ICDM 2012 IEEE 12th International Conference on","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Rao et al., 2015] Nikhil Rao, Hsiang-Fu Yu, Pradeep Ravikumar, and Inderjit S. Dhillon. Collaborative filtering with graph information: Consistency and scalable meth- ods. In Neural Information Processing Systems (NIPS), December 2015.","title":"Collaborative filtering with graph information: Consistency and scalable methods","authors":"Nikhil Rao, Hsiang-Fu Yu, Pradeep Ravikumar, Inderjit S Dhillon","year":"2015","venue":"Neural Information Processing Systems (NIPS)","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Yu et al., 2012] Hsiang-Fu Yu, Cho-Jui Hsieh, Si Si, and In- derjit S. Dhillon. Scalable coordinate descent approaches to parallel matrix factorization for recommender systems. In IEEE International Conference of Data Mining, 2012.","title":"Scalable coordinate descent approaches to parallel matrix factorization for recommender systems","authors":"Hsiang-Fu Yu, Cho-Jui Hsieh, Si Si, Inderjit S Dhillon","year":"2012","venue":"IEEE International Conference of Data Mining","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Yun et al., 2014] Hyokun Yun, Hsiang-Fu Yu, Cho-Jui Hsieh, SVN Vishwanathan, and Inderjit Dhillon. No- mad: Non-locking, stochastic multi-machine algorithm for asynchronous and decentralized matrix completion. Pro- ceedings of the VLDB Endowment, 7(11):975-986, 2014.","title":"Nomad: Non-locking, stochastic multi-machine algorithm for asynchronous and decentralized matrix completion","authors":"Hyokun Yun, Hsiang-Fu Yu, Cho-Jui Hsieh, Svn Vishwanathan, Inderjit Dhillon","year":"2014","venue":"Proceedings of the VLDB Endowment","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}