Huafeng Liu
Abstract
Low-rank matrix approximation (LRMA) has attracted more and more attention in the community of recommendation. Even though LRMA-based recommendation methods (including Global LRMA and Local LRMA) obtain promising results, they suffer from the complicated structure of the large-scale and sparse rating matrix, especially when the underlying system includes a large set of items with various types and a huge amount of users with diverse interests. Thus, they have to predefine the important parameters, such as the rank of the rating matrix and the number of submatrices. Moreover, most existing Local LRMA methods are usually designed in a two-phase separated framework and do not consider the missing mechanisms of rating matrix. In this article, a non-parametric unified Bayesian graphical model is proposed for Adaptive Local low-rank Matrix Approximation (ALoMA). ALoMA has ability to simultaneously identify rating submatrices, determine the optimal rank for each submatrix, and learn the submatrix-specific user/item latent factors. Meanwhile, the missing mechanism is adopted to characterize the whole rating matrix. These four parts are seamlessly integrated and enhance each other in a unified framework. Specifically, the user-item rating matrix is adaptively divided into proper number of submatrices in ALoMA by exploiting the Chinese Restaurant Process. For each submatrix, by considering both global/local structure information and missing mechanisms, the latent user/item factors are identified in an optimal latent space by adopting automatic relevance determination technique. We theoretically analyze the model’s generalization error bounds and give an approximation guarantee. Furthermore, an efficient Gibbs sampling-based algorithm is designed to infer the proposed model. A series of experiments have been conducted on six real-world datasets (Epinions, Douban, Dianping, Yelp, Movielens (10M), and Netflix). The results demonstrate that ALoMA outperforms the state-of-the-art LRMA-based methods and can easily provide interpretable recommendation results.
- Michal Aharon, Michal Elad, and Alfred Bruckstein. 2006. SVD: An algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans. Sign. Process. 54, 11 (2006), 4311--4322.Google Scholar
Digital Library
- Chris Anderson. 2006. The Long Tail: Why the Future of Business Is Selling Less of More. Hyperion.Google Scholar
- Christophe Andrieu, Nando De Freitas, Arnaud Doucet, and Michael I. Jordan. 2003. An introduction to mcmc for machine learning. Mach. Learn. 50, 1--2 (2003), 5--43.Google ScholarCross Ref
- Alex Beutel, Amr Ahmed, and Alex Smola. 2015. ACCAMS: Additive co-clustering to approximate matrices succinctly. In Proceedings of the International Conference on World Wide Web. 119--129.Google ScholarDigital Library
- Alex Beutel, Kenton Murray, Christos Faloutsos, and Alexander J. Smola. 2014. Cobafi: Collaborative Bayesian filtering. In Proceedings of the International Conference on World Wide Web. ACM, 97--108.Google Scholar
- Bence Bolgar and Peter Antal. 2016. Bayesian matrix factorization with non-random missing data using informative gaussian process priors and soft evidences. In Proceedings of the International Conference on Probabilistic Graphical Models. 25--36.Google Scholar
- Emmanuel J. Candes and Yaniv Plan. 2011. Matrix completion with noise. Proc. IEEE 98, 6 (2011), 925--936.Google ScholarCross Ref
- Emmanuel J. Candès and Benjamin Recht. 2009. Exact matrix completion via convex optimization. Found. Comput. Math. 9, 6 (2009), 717.Google ScholarCross Ref
- Chao Chen, Dongsheng Li, Qin Lv, Junchi Yan, Stephen M. Chu, and Li Shang. 2016. MPMA: Mixture probabilistic matrix approximation for collaborative filtering. In Proceedings of the International Joint Conference on Artificial Intelligent. 1382--1388.Google Scholar
- Chao Chen, Dongsheng Li, Qin Lv, Junchi Yan, Li Shang, and Stephen M. Chu. 2017. GLOMA: Embedding global information in local matrix approximation models for collaborative filtering. In Proceedings of the AAAI Conference on Artificial Intelligence. 1295--1301.Google Scholar
- Chao Chen, Dongsheng Li, Yingying Zhao, Qin Lv, and Li Shang. 2015. WEMAREC: Accurate and scalable recommendation through weighted and ensemble matrix approximation. In Proceedings of the ACM SIGIR Conference on Research and Development in Information Retrieval. ACM, 303--312.Google ScholarDigital Library
- Loc Do and Hady Wirawan Lauw. 2016. Probabilistic models for contextual agreement in preferences. ACM Trans. Inf. Syst. 34, 4, Article 21 (June 2016), 33 pages.Google ScholarDigital Library
- Thomas L. Griffiths, Michael I. Jordan, Joshua B. Tenenbaum, and David M. Blei. 2004. Hierarchical topic models and the nested chinese restaurant process. In Proceedings of the International Conference on Neural Information Processing Systems. 17--24.Google Scholar
- Jonathan L. Herlocker, Joseph A. Konstan, Loren G. Terveen, and John T. Riedl. 2004. Evaluating collaborative filtering recommender systems. ACM Trans. Inf. Syst. 22, 1 (Jan. 2004), 5--53.Google ScholarDigital Library
- José Miguel Hernández-Lobato, Neil Houlsby, and Zoubin Ghahramani. 2014. Probabilistic matrix factorization with non-random missing data. In Proceedings of the International Conference on Machine Learning. 1512--1520.Google Scholar
- Yehuda Koren, Robert Bell, and Chris Volinsky. 2009. Matrix factorization techniques for recommender systems. Computer 42, 8 (2009), 30--37.Google ScholarDigital Library
- Joonseok Lee, Seungyeon Kim, Guy Lebanon, and Yoram Singer. 2013. Local low-rank matrix approximation. In Proceedings of the International Conference on Machine Learning. 82--90.Google Scholar
- Dongsheng Li, Chao Chen, Wei Liu, Tun Lu, Ning Gu, and Stephen Chu. 2017. Mixture-rank matrix approximation for collaborative filtering. In Proceedings of the International Conference on Neural Information Processing Systems. 477--485.Google Scholar
- Dongsheng Li, Chao Chen, Qin Lv, Junchi Yan, Li Shang, and Stephen Chu. 2016. Low-rank matrix approximation with stability. In Proceedings of the International Conference on Machine Learning. 295--303.Google Scholar
- Hui Li, Dingming Wu, Wweibing Tang, and Ninos Mamoulis. 2015. Overlapping community regularization for rating prediction in social recommender systems. In Proceedings of ACM Conference on Recommender Systems. 27--34.Google ScholarDigital Library
- Roderick J. A. Little and Donald B. Rubin. 2014. Statistical Analysis with Missing Data (2nd ed.). Vol. 333. John Wiley 8 Sons.Google Scholar
- Hao Ma, Dengyong Zhou, Chao Liu, Michael R. Lyu, and Irwin King. 2011. Recommender systems with social regularization. In Proceedings of ACM Conference on Web Search and Web Data Mining. ACM, 287--296.Google ScholarDigital Library
- Lester W. Mackey, Michael I. Jordan, and Ameet Talwalkar. 2011. Divide-and-conquer matrix factorization. In Proceedings of the International Conference on Neural Information Processing Systems. 1134--1142.Google Scholar
- Benjamin Marlin, Richard S. Zemel, Sam Roweis, and Malcolm Slaney. 2012. Collaborative Filtering and the Missing at Random Assumption. 2012.Google Scholar
- Benjamin M. Marlin and Richard S. Zemel. 2009. Collaborative prediction and ranking with non-random missing data. In Proceedings of the ACM Conference on Recommender Systems. 5--12.Google Scholar
- Paolo Massa and Paolo Avesani. 2007. Trust-aware recommender systems. In Proceedings of ACM Conference on Recommender Systems. 17--24.Google ScholarDigital Library
- Radford M. Neal. 1996. Bayesian Learning for Neural Networks. Springer. 456--456 pages.Google Scholar
- Shohei Ohsawa, Yachiko Obara, and Takayuki Osogami. 2016. Gated probabilistic matrix factorization: Learning users’ attention from missing values. In Proceedings of the International Joint Conference on Artificial Intelligence. AAAI Press, 1888--1894.Google Scholar
- Ruslan Salakhutdinov and Andriy Mnih. 2007. Probabilistic matrix factorization. In Proceedings of International Conference on Machine Learning. 880--887.Google Scholar
- Ruslan Salakhutdinov and Andriy Mnih. 2008. Bayesian probabilistic matrix factorization using Markov chain monte carlo. In Proceedings of the International Conference on Machine Learning. 880--887.Google ScholarDigital Library
- Lei Shi, Wayne Xin Zhao, and Yi-Dong Shen. 2017. Local representative-based matrix factorization for cold-start recommendation. ACM Transation on Information System 36, 2, Article 22 (Aug. 2017), 28 pages.Google Scholar
- Ruoyu Sun and Zhi-Quan Luo. 2016. Guaranteed matrix completion via non-convex factorization. IEEE Trans. Inf. Theory 62, 11 (2016), 6535--6579.Google ScholarDigital Library
- Keqiang Wang, Wayne Xin Zhao, Hongwei Peng, and Xiaoling Wang. 2016. Bayesian probabilistic multi-topic matrix factorization for rating prediction. In Proceedings of the International Joint Conference on Artificial Intelligent. 3910--3916.Google Scholar
- David P. Wipf and Bhaskar D. Rao. 2007. An empirical Bayesian strategy for solving the simultaneous sparse approximation problem. IEEE Trans. Sign. Process. 55, 7 (2007), 3704--3716.Google ScholarCross Ref
- Yao Wu, Xudong Liu, Min Xie, Martin Ester, and Qing Yang. 2016. CCCF: Improving collaborative filtering via scalable user-item co-clustering. In Proceedings of the International Conference on Web Search and Data Mining. ACM, 73--82.Google ScholarDigital Library
- Menghao Zhang, Binbin Hu, Chuan Shi, and Bai Wang. 2017. Local low-rank matrix approximation with preference selection of anchor points. In Proceedings of the International Conference on World Wide Web. 1395--1403.Google ScholarDigital Library
- Yongfeng Zhang, Min Zhang, Yiqun Liu, and Shaoping Ma. 2013. Improve collaborative filtering through bordered block diagonal form matrices. In Proceedings of the ACM SIGIR Conference on Research and Development in Information Retrieval. ACM, 313--322.Google ScholarDigital Library
Index Terms
- Adaptive Local Low-rank Matrix Approximation for Recommendation
Recommendations
Bayesian Additive Matrix Approximation for Social Recommendation
Social relations between users have been proven to be a good type of auxiliary information to improve the recommendation performance. However, it is a challenging issue to sufficiently exploit the social relations and correctly determine the user ...
A novel learning-to-rank based hybrid method for book recommendation
WI '17: Proceedings of the International Conference on Web IntelligenceRecommendation system is able to recommend items that are likely to be preferred by the user. Hybrid recommender systems combine the advantages of the collaborative filtering and content-based filtering for improved recommendation. Hybrid recommendation ...
A multi-attribute probabilistic matrix factorization model for personalized recommendation
Recommendation systems can interpret personal preferences and recommend the most relevant choices to the benefit of countless users. Attempts to improve the performance of recommendation systems have hence been the focus of much research in an era of ...
Comments