Dynamic-K Recommendation with Personalized Decision Boundary

  • Yan GaoEmail author
  • Jiafeng Guo
  • Yanyan Lan
  • Huaming Liao
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10390)


In this paper, we investigate the recommendation task in the most common scenario with implicit feedback (e.g., clicks, purchases). State-of-the-art methods in this direction usually cast the problem as to learn a personalized ranking on a set of items (e.g., webpages, products). The top-N results are then provided to users as recommendations, where the N is usually a fixed number pre-defined by the system according to some heuristic criteria (e.g., page size, screen size). There is one major assumption underlying this fixed-number recommendation scheme, i.e., there are always sufficient relevant items to users’ preferences. Unfortunately, this assumption may not always hold in real-world scenarios. In some applications, there might be very limited candidate items to recommend, and some users may have very high relevance requirement in recommendation. In this way, even the top-1 ranked item may not be relevant to a user’s preference. Therefore, we argue that it is critical to provide a dynamic-K recommendation, where the K should be different with respect to the candidate item set and the target user. We formulate this dynamic-K recommendation task as a joint learning problem with both ranking and classification objectives. The ranking objective is the same as existing methods, i.e., to create a ranking list of items according to users’ interests. The classification objective is unique in this work, which aims to learn a personalized decision boundary to differentiate the relevant items from irrelevant items. Based on these ideas, we extend two state-of-the-art ranking-based recommendation methods, i.e., BPRMF and HRM, to the corresponding dynamic-K versions, namely DK-BPRMF and DK-HRM. Our experimental results on two datasets show that the dynamic-K models are more effective than the original fixed-N recommendation methods.


Implicit feedback Dynamic-K recommendation 



The work was funded by 973 Program of China under Grant No. 2014CB340401, the National Key RD Program of China under Grant No. 2016QY02D0405, the National Natural Science Foundation of China (NSFC) under Grants No. 61232010, 61472401, 61433014, 61425016, and 61203298, the Key Research Program of the CAS under Grant No. KGZD-EW-T03-2, and the Youth Innovation Promotion Association CAS under Grants No. 20144310 and 2016102.


  1. 1.
    Adomavicius, G., Tuzhilin, A.: Toward the next generation of recommender systems: a survey of the state-of-the-art and possible extensions. IEEE Trans. Knowl. Data Eng. 17(6), 734–749 (2005)CrossRefGoogle Scholar
  2. 2.
    Aiolli, F.: Convex auc optimization for top-n recommendation with implicit feedback. In: Proceedings of the 8th ACM Conference on Recommender Systems, pp. 293–296. ACM (2014)Google Scholar
  3. 3.
    Feipeng, Z., Yuhong, G.: Improving top-n recommendation with heterogeneous loss. J. Artif. Intell. Res. (2016)Google Scholar
  4. 4.
    Gopalan, P., Hofman, J.M., Blei, D.M.: Scalable recommendation with poisson factorization. arXiv preprint arXiv:1311.1704 (2013)
  5. 5.
    Johnson, C.C.: Logistic matrix factorization for implicit feedback data. In: Advances in Neural Information Processing Systems 27 (2014)Google Scholar
  6. 6.
    Karatzoglou, A., Baltrunas, L., Shi, Y.: Learning to rank for recommender systems. In: Proceedings of the 7th ACM Conference on Recommender Systems, pp. 493–494. ACM (2013)Google Scholar
  7. 7.
    Mnih, A., Teh, Y.W.: Learning item trees for probabilistic modelling of implicit feedback. arXiv preprint arXiv:1109.5894 (2011)
  8. 8.
    Oard, D.W., Kim, J., et al.: Implicit feedback for recommender systems. In: Proceedings of the AAAI Workshop on Recommender Systems, pp. 81–83 (1998)Google Scholar
  9. 9.
    Park, D., Neeman, J., Zhang, J., Sanghavi, S., Dhillon, I.S.: Preference completion: Large-scale collaborative ranking from pairwise comparisons. Statistics 1050, 16 (2015)Google Scholar
  10. 10.
    Rendle, S., Freudenthaler, C., Gantner, Z., Schmidt-Thieme, L.: Bpr: Bayesian personalized ranking from implicit feedback. In: Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence, pp. 452–461. AUAI Press (2009)Google Scholar
  11. 11.
    Ricci, F., Rokach, L., Shapira, B.: Introduction to Recommender Systems Handbook. Springer, Heidelberg (2011)Google Scholar
  12. 12.
    Sculley, D.: Combined regression and ranking. In: Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 979–988. ACM (2010)Google Scholar
  13. 13.
    Shalev-Shwartz, S., Singer, Y., Srebro, N.: Pegasos: Primal estimated sub-gradient solver for svm. In: Proceedings of the 24th International Conference on Machine Learning, pp. 807–814. ACM (2007)Google Scholar
  14. 14.
    Shi, Y., Karatzoglou, A., Baltrunas, L., Larson, M., Hanjalic, A., Oliver, N.: Tfmap: optimizing map for top-n context-aware recommendation. In: Proceedings of the 35th International ACM SIGIR Conference on Research and Development in Information Retrieval, pp. 155–164. ACM (2012)Google Scholar
  15. 15.
    Shi, Y., Karatzoglou, A., Baltrunas, L., Larson, M., Oliver, N., Hanjalic, A.: Climf: learning to maximize reciprocal rank with collaborative less-is-more filtering. In: Proceedings of the Sixth ACM Conference on Recommender Systems, pp. 139–146. ACM (2012)Google Scholar
  16. 16.
    Wang, P., Guo, J., Lan, Y., Xu, J., Wan, S., Cheng, X.: Learning hierarchical representation model for next basket recommendation. In: Proceedings of the 38th International ACM SIGIR Conference on Research and Development in Information Retrieval, pp. 403–412. ACM (2015)Google Scholar
  17. 17.
    Weimer, M., Karatzoglou, A., Le, Q.V., Smola, A.: Maximum margin matrix factorization for collaborative ranking. In: Advances in Neural Information Processing Systems, pp. 1–8 (2007)Google Scholar
  18. 18.
    Yun, H., Raman, P., Vishwanathan, S.: Ranking via robust binary classification. In: Advances in Neural Information Processing Systems, pp. 2582–2590 (2014)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Yan Gao
    • 1
    Email author
  • Jiafeng Guo
    • 1
  • Yanyan Lan
    • 1
  • Huaming Liao
    • 1
  1. 1.CAS Key Lab of Network Data Science and Technology Institute of Computing TechnologyChinese Academy of SciencesBeijingChina

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