Social Recommendation Terms: Probabilistic Explanation Optimization

  • Jie Liu
  • Lin Zhang
  • Victor S. Sheng
  • Yuanjun Laili
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10228)


The Probabilistic Matrix Factorization (PMF) model has been widely studied for recommender systems, which outperform previous models with a solid probabilistic explanation. To further improve its accuracy by using social information, researchers attempt to combine the PMF model with social network graphs by adding social terms. However, existing works on social terms do not provide theoretical explanations to make the models well understood. The lack of explanations limits further improvement of prediction accuracy. Hence, in this paper we provide our explanation and propose a unified covariance framework to solve this problem. Our explanation, including regularization terms, factorization terms and an ensemble of them, reveals how most social terms work from a probabilistic view. Our framework shows that those terms could be optimized in a direct way compatible to PMF. We find out that accuracy improvements for existing works on regularization terms rely more on personalized properties, and that social information for factorization terms is helpful but not always necessary.


Probabilistic matrix factorization Regularization terms Factorization terms Social networks 



This work is partially supported by National Nature Science Foundation of China (No. 61374199, National High-tech R&D Program (No. 2015AA042101),) and Beijing Natural Science Foundation (No. 4142031).


  1. 1.
    Chua, F.C.T., Lauw, H.W., Lim, E.-P.: Generative models for item adoptions using social correlation. IEEE Trans. Knowl. Data Eng. 25(9), 2036–2048 (2013)CrossRefGoogle Scholar
  2. 2.
    Salakhutdinov, R., Mnih, A.: Probabilistic matrix factorization. In: Proceedings of the NIPS, pp. 1257–1264, 2007Google Scholar
  3. 3.
    Salakhutdinov, R. Mnih, A.: Bayesian probabilistic matrix factorization using Markov chain Monte Carlo. In: Proceedings of the ICML, pp. 880–887 (2008)Google Scholar
  4. 4.
    Jamali, M., Ester, M.: A matrix factorization technique with trust propagation for recommendation in social networks. In: Proceedings of the RecSys, pp. 135–142 (2010)Google Scholar
  5. 5.
    Ma, H., Zhou, D., Liu, C., Lyu, M.R., King, I.: Recommender systems with social regularization. In: Proceedings of the WSDM, pp. 287–296 (2011)Google Scholar
  6. 6.
    Ma, H.: An experimental study on implicit social recommendation. In: Proceedings of the SIGIR, pp. 73–82 (2013)Google Scholar
  7. 7.
    Yang, X., Steck, H., Liu, Y.: Circle-based recommendation in online social networks. In: Proceedings of the SIGKDD, pp. 1267–1275 (2012)Google Scholar
  8. 8.
    Forsati, R., Mahdavi, M., Shamsfard, M., Sarwat, M.: Matrix factorization with explicit trust and distrust side information for improved social recommendation. ACM Trans. Inform. Syst. 32(4) (2014)Google Scholar
  9. 9.
    Ma, H., Lyu, Ml.R., King, I.: Learning to recommend with trust and distrust relationships. In: Proceedings of the RecSys, pp. 189–196 (2009)Google Scholar
  10. 10.
    Fazeli, S., Loni, B., Bellogin, A., Drachsler, H., Sloep, P.: Implicit vs. explicit trust in social matrix factorization. In: Proceedings of the RecSys, pp. 317–320 (2014)Google Scholar
  11. 11.
    Xia, F., Liu, H., Asabere, N.Y., Wang, W., Yang, Z.: Multi-category item recommendation using neighborhood associations in trust networks. In: Proceedings of the WWW, pp. 403–404 (2014)Google Scholar
  12. 12.
    Ma, H., Yang, H., Lyu, Ml.R., King, I.: SoRec: social recommendation using probabilistic matrix factorization. In: Proceedings of the CIKM, pp. 931–940 (2008)Google Scholar
  13. 13.
    Yang, B., Yu, L., Liu, D., Liu, J.: Social collaborative filtering by trust. In: Proceedings of the IJCAI, pp. 2747–2753 (2013)Google Scholar
  14. 14.
    Zhang, Y., Lai, G., Zhang, M., Zhang, Y., Liu, Y., Ma, S.: Explicit factor models for explainable recommendation based on phrase-level sentiment analysis. In: Proceedings of the SIGIR, pp. 83–92 (2014)Google Scholar
  15. 15.
    Jiang, M., Cui, P., Liu, R., Yang, Q., Wang, F., Zhu, W., Yang, S.: Social contextual recommendation. In: Proceedings of the CIKM, pp. 45–54 (2012)Google Scholar
  16. 16.
    Wang, T., Jin, X., Ding, X., Ye, X.: User interests imbalance exploration in social recommendation: a fitness adaptation. In: Proceedings of the CIKM, pp. 281–290 (2014)Google Scholar
  17. 17.
    Jiang, Y., Liu, J., Zhang, X., Li, Z., Lu. H.: TCRec: product recommendation via exploiting social-trust network and product category information. In: Proceedings of the WWW, pp. 233–234 (2013)Google Scholar
  18. 18.
    Yao, W., He, J., Huang, G., Zhang, Y.: Modeling dual role preferences for trust-aware recommendation. In: Proceedings of the SIGIR, pp. 975–978 (2014)Google Scholar
  19. 19.
    Zhao, T., Li, C., Li, M., Ding, Q., Li, L.: Social recommendation incorporating topic mining and social trust analysis. In: Proceedings of the CIKM, pp. 1643–1648 (2013)Google Scholar
  20. 20.
    Yuan, Q., Chen, L., Zhao, S.: Factorization vs. regularization: integrating heterogeneous social relationships in top-n recommendation. In: Proceedings of the RecSys, pp. 245–252 (2011)Google Scholar
  21. 21.
    Guo, L., Ma, J., Chen, Z.: Learning to recommend with multi-faceted trust in social networks. In: Proceedings of the WWW, pp. 205–206 (2013)Google Scholar
  22. 22.
    Feng, H., Qian, X.: Recommendation via user’s personality and social contextual. In: Proceedings of the CIKM, pp. 1521–1524 (2013)Google Scholar
  23. 23.
    Tang, J., Hu, X., Gao, H., Liu, H.: Exploiting local and global social context for recommendation. In: Proceedings of the AAAI, pp. 2712–2718 (2013)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Jie Liu
    • 1
    • 2
  • Lin Zhang
    • 1
    • 2
  • Victor S. Sheng
    • 3
  • Yuanjun Laili
    • 1
    • 2
  1. 1.School of Automation Science and Electrical EngineeringBeihang UniversityBeijingChina
  2. 2.Engineering Research Center of Complex Product Advanced Manufacturing SystemMinistry of EducationBeijingChina
  3. 3.Department of Computer ScienceUniversity of Central ArkansasConwayUSA

Personalised recommendations