SCIENCE CHINA Information Sciences, Volume 62 , Issue 11 : 212105(2019) https://doi.org/10.1007/s11432-018-9915-8

## Recommendation over time: a probabilistic model of time-aware recommender systems

• AcceptedMay 17, 2019
• PublishedOct 9, 2019
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### Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant Nos. 61672049, 61732001).

### References

[1] Koren Y. Collaborative filtering with temporal dynamics. In: Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2009. 447--456. Google Scholar

[2] Baltrunas L, Amatriain X. Towards time-dependant recommendation based on implicit feedback. In: Proceedings of Workshop on Context-aware Recommender Systems, New York, 2009. 423--424. Google Scholar

[3] Xiang L, Yang Q. Time-dependent models in collaborative filtering based recommender system. In: Proceedings of the 2009 IEEE/WIC/ACM International Joint Conference on Web Intelligence and Intelligent Agent Technology, Milan, 2009. 450--457. Google Scholar

[4] Agarwal D, Chen B C, Elango P. Fast Online learning through offline initialization for time-sensitive recommendation. In: Proceedings of ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2010. 703--712. Google Scholar

[5] Koenigstein N, Dror G, Koren Y. Yahoo music recommendations: modeling music ratings with temporal dynamics and item taxonomy. In: Proceedings of the 5th ACM Conference on Recommender Systems, 2011. 165--172. Google Scholar

[6] Ramirez-Garcia X, Garcia-Valdez M. A pre-filtering based context-aware recommender system using fuzzy rules. In: Design of Intelligent Systems Based on Fuzzy Logic, Neural Networks and Nature-Inspired Optimization. Berlin: Springer, 2015. 497--505. Google Scholar

[7] Suksawatchon J, Darapisut S, Suksawatchon U. The constant time of predictive algorithm for music recommendation with time context. In: Proceedings of International Joint Conference on Computer Science and Software Engineering, 2015. 63--68. Google Scholar

[8] Bogina V, Kuflik T, Mokryn O. Learning item temporal dynamics for predicting buying sessions. In: Proceedings of the 21st Annual Meeting of the Intelligent Interfaces, Sonoma, 2016. 251--255. Google Scholar

[9] Xiong L, Chen X, Huang T K, et al. Temporal collaborative filtering with Bayesian probabilistic tensor factorization. In: Proceedings of the SIAM International Conference on Data Mining, 2010. 211--222. Google Scholar

[10] Dunlavy D M, Kolda T G, Acar E. Temporal Link Prediction Using Matrix and Tensor Factorizations. ACM Trans Knowl Discov Data, 2011, 5: 1-27 CrossRef Google Scholar

[11] Bhargava P, Phan T, Zhou J Y, et al. Who, what, when, and where: multi-dimensional collaborative recommendations using tensor factorization on sparse user-generated data. In: Proceedings of International World Wide Web Conferences Steering Committee, 2015. 130--140. Google Scholar

[12] Géry M, Haddad H. Evaluation of web usage mining approaches for user's next request prediction. In: Proceedings of the 5th ACM International Workshop on Web Information and Data Management, New Orleans, 2003. 74--81. Google Scholar

[13] Huang Y M, Huang T C, Wang K T, et al. A Markov-based recommendation model for exploring the transfer of learning on the web. J Educ Tech Soc, 2009, 12: 144--162. Google Scholar

[14] Awad M A, Khalil I. Prediction of User's Web-Browsing Behavior: Application of Markov Model.. IEEE Trans Syst Man Cybern B, 2012, 42: 1131-1142 CrossRef PubMed Google Scholar

[15] Hariri N, Mobasher B, Burke R. Context-aware music recommendation based on latenttopic sequential patterns. In: Proceedings of ACM Conference on Recommender Systems, 2012. 131--138. Google Scholar

[16] Chen W, Niu Z D, Zhao X Y. A hybrid recommendation algorithm adapted in e-learning environments. World Wide Web, 2014, 17: 271-284 CrossRef Google Scholar

[17] Zhang J D, Chow C Y. Point-of-interest recommendations in location-based social networks. SIGSPATIAL Special, 2016, 7: 26-33 CrossRef Google Scholar

[18] Chen J, Wang C K, Wang J M. A personalized interest-forgetting Markov model for recommendations. In: Proceedings of the 29th AAAI Conference on Artificial Intelligence, 2015. 16--22. Google Scholar

[19] Gopalachari M V, Sammulal P. Hybrid recommender system with conceptualization and temporal preferences. In: Proceedings of the 2nd International Conference on Computer and Communication Technologies, 2015. 811--819. Google Scholar

[20] Sahoo N, Singh P V, Mukhopadhyay T. A Hidden Markov Model for Collaborative Filtering. MIS Q, 2012, 36: 1329-1356 CrossRef Google Scholar

[21] Sanchez F, Alduan M, Alvarez F. Recommender System for Sport Videos Based on User Audiovisual Consumption. IEEE Trans Multimedia, 2012, 14: 1546-1557 CrossRef Google Scholar

[22] Alanazi A, Bain M. A people-to-people content-based reciprocal recommender using hidden markov models. In: Proceedings of the 7th ACM Conference on Recommender Systems, 2013. 303--306. Google Scholar

[23] Gu W R, Dong S B, Zeng Z Z. Increasing recommended effectiveness with markov chains and purchase intervals. Neural Comput Applic, 2014, 25: 1153-1162 CrossRef Google Scholar

[24] Zhang H, Ni W, Li X. Modeling the Heterogeneous Duration of User Interest in Time-Dependent Recommendation: A Hidden Semi-Markov Approach. IEEE Trans Syst Man Cybern Syst, 2018, 48: 177-194 CrossRef Google Scholar

[25] Zhang H, Ni W, Li X, et al. A hidden semi-Markov approach for time-dependent recommendation. In: Proceedings of Pacific Asia Conference on Information Systems, 2016. Google Scholar

[26] Le D T, Fang Y, Lauw H W. Modeling sequential preferences with dynamic user and context factors. In: Proceedings of Joint European Conference on Machine Learning and Knowledge Discovery in Databases, Riva del Garda, 2016. 145--161. Google Scholar

[27] Alanazi A, Bain M. A scalable people-to-people hybrid reciprocal recommender using hidden Markov models. In: Proceedings of the 2nd International Workshop on Machine Learning Methods for Recommender Systems, 2016. Google Scholar

[28] Lu Z, Agarwal D, Dhillon I S. A spatio-temporal approach to collaborative filtering. In: Proceedings of the 3rd ACM Conference on Recommender Systems, New York, 2009. 13--20. Google Scholar

[29] Paisley J, Gerrish S, Blei D. Dynamic modeling with the collaborative Kalman filter. In: Proceedings of 5th Annual NYAS Machine Learning Symposium, 2010. Google Scholar

[30] Sun J Z, Varshney K R, Subbian K. Dynamic matrix factorization: a state space approach. In: Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing, 2012. 1897--1900. Google Scholar

[31] Sun J Z, Parthasarathy D, Varshney K R. Collaborative Kalman Filtering for Dynamic Matrix Factorization. IEEE Trans Signal Process, 2014, 62: 3499-3509 CrossRef ADS Google Scholar

[32] Gultekin S, Paisley J. A collaborative Kalman filter for time-evolving dyadic processes. In: Proceedings of IEEE International Conference on Data Mining, Shenzhen, 2014. 140--149. Google Scholar

[33] Ding Y, Li X. Time weight collaborative filtering. In: Proceedings of the ACM International Conference on Information and Knowledge Management, 2005. 485--492. Google Scholar

[34] Liu N N, Zhao M, Xiang E, et al. Online evolutionary collaborative filtering. In: Proceedings of the 4th ACM Conference on Recommender Systems, Barcelona, 2010. 95--102. Google Scholar

[35] Chandramouli B, Levandoski J J, Eldawy A, et al. StreamRec: a real-time recommender system. In: Proceedings of the 2011 ACM SIGMOD International Conference on Management of Data, 2011. 6--8. Google Scholar

[36] Huang Y X, Cui B, Zhang W Y, et al. TencentRec: real-time stream recommendation in practice. In: Proceedings of the 2015 ACM SIGMOD International Conference on Management of Data, 2015. 227--238. Google Scholar

[37] Su H Y, Lin X F, Yan B, et al. The collaborative filtering algorithm with time weight based on mapReduce. In: Proceedings of International Conference on Big Data Computing and Communications, 2015. 386--395. Google Scholar

[38] Rezaeimehr F, Moradi P, Ahmadian S. TCARS: Time- and Community-Aware Recommendation System. Future Generation Comput Syst, 2018, 78: 419-429 CrossRef Google Scholar

[39] Yu H, Li Z Y. A collaborative filtering method based on the forgetting curve. In: Proceedings of the 2010 International Conference on Web Information Systems and Mining, Sanya, 2010. 183--187. Google Scholar

[40] Shi Y C. An improved collaborative filtering recommendation method based on timestamp. In: Proceedings of International Conference on Advanced Communication Technology, 2014. 1180--1184. Google Scholar

[41] Xiang L, Yuan Q, Zhao S W, et al. Temporal recommendation on graphs via long- and short-term preference fusion. In: Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2010. 723--731. Google Scholar

[42] Ding Y, Wang D, Li G. Exploiting long-term and short-term preferences and RFID trajectories in shop recommendation. Softw Pract Exper, 2017, 47: 849-865 CrossRef Google Scholar

[43] Yu J, Liu F F. A short-term user interest model for personalized recommendation. In: Proceedings of IEEE International Conference on Information Management and Engineering, Chengdu, 2010. 219--222. Google Scholar

[44] Li L, Zheng L, Yang F. Modeling and broadening temporal user interest in personalized news recommendation. Expert Syst Appl, 2014, 41: 3168-3177 CrossRef Google Scholar

[45] Basile P, Caputo A, Gemmis M D, et al. Modeling short-term preferences in time-aware recommender systems. In: Proceedings of Workshop on Deep Content Analytics Techniques for Personalized and Intelligent Services, 2015. 44--54. Google Scholar

[46] Daneshmand S M, Javari A, Abtahi S E. A Time-Aware Recommender System Based on Dependency Network of Items. Comput J, 2015, 58: 1955-1966 CrossRef Google Scholar

[47] Azadjalal M M, Moradi P, Abdollahpouri A. A trust-aware recommendation method based on Pareto dominance and confidence concepts. Knowledge-Based Syst, 2017, 116: 130-143 CrossRef Google Scholar

[48] Chang S Y, Zhang Y, Tang J L, et al. Streaming recommender systems. In: Proceedings of the 26th International Conference on World Wide Web, Perth, 2017. 381--389. Google Scholar

[49] Tan Y K, Xu X X, Liu Y. Improved recurrent neural networks for session-based recommendations. In: Proceedings of the 1st Workshop on Deep Learning for Recommender Systems, 2016. 17--22. Google Scholar

[50] Devooght R, Bersini H. Long and short-term recommendations with recurrent neural networks. In: Proceedings of Conference on User Modeling, Adaptation and Personalization, 2017. 13--21. Google Scholar

[51] Wu C Y, Ahmed A, Beutel A, et al. Recurrent recommender networks. In: Proceedings of the Tenth ACM International Conference on Web Search and Data Mining, Cambridge, 2017. 495--503. Google Scholar

[52] Villatel K, Smirnova E, Mary J, et al. Recurrent neural networks for long and short-term sequential recommendation. 2018,. arXiv Google Scholar

[53] Hidasi B, Karatzoglou A. Recurrent neural networks with top-k gains for session-based recommendations. In: Proceedings of the 27th ACM International Conference on Information and Knowledge Management, Torino, 2018. 843--852. Google Scholar

[54] Durrett R. Essentials of Stochastic Processes. New York: Springer, 2012. 139--183. Google Scholar

[55] Rabiner L R. A tutorial on hidden Markov models and selected applications in speech recognition. Proc IEEE, 1989, 77: 257-286 CrossRef Google Scholar

[56] Harper F M, Konstan J A. The MovieLens Datasets. ACM Trans Interact Intell Syst, 2016, 5: 1-19 CrossRef Google Scholar

[57] Tang J L, Gao H J, Liu H. Mtrust: discerning multi-faceted trust in a connected world. In: Proceedings of the 5th ACM International Conference on Web Search and Data Mining, 2012. 93--102. Google Scholar

[58] Tang J L, Liu H, Gao H J, et al. Etrust: Understanding trust evolution in an online world. In: Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2012. 253--261. Google Scholar

[59] Massa P, Avesani P. Trust-aware recommender systems. In: Proceedings of the 2007 ACM Conference on Recommender Systems, New York, 2007. 17--24. Google Scholar

[60] Jalili M, Ahmadian S, Izadi M. Evaluating Collaborative Filtering Recommender Algorithms: A Survey. IEEE Access, 2018, 6: 74003-74024 CrossRef Google Scholar

• Figure 1

Online learning and cold-start performance. (a) MLK; (b) Ep.

• Figure 2

Time convergence. (a) MLM; (b) EpEx.

•

Algorithm 1 Update

function Update($({\rm~user,~item},~T,~l)$);

${\rm~RecRating(user).push((user,~item},~T,~l))$;

${\rm~RecRating(item).push((user,~item},~T,~l))$;

ConvertRating(user);

UpdateParameter(user);

ConvertRating(item);

UpdateParameter(item);

function ConvertRating(${\rm~user}$);

while ${\rm~RecRating(user).size}()>M$ do

$({\rm~user,item}_1,~t_1,~l_1)~\leftarrow~{\rm~RecRating(user).front}()$;

Update $\phi_{{\rm~user},~j}$ by (17);

${\rm~RecRating(user).pop}()$;

$({\rm~user,~item}_2,~t_2,~l_2)~\leftarrow~{\rm~RecRating(user).front}()$;

if $\tau_{\rm~user}<t_2$ then

$\tau_{\rm~user}~\leftarrow~t_2$;

for $j=1,\ldots,~J$

$f_{{\rm~user},~t,~j}~\leftarrow~x_{{\rm~user},~t,~j}$;

end for

end if

end while

function UpdateParameter(${\rm~user}$);

for $t~\in~{\rm~TM(RR(user))}$

Prepare $E_{{\rm~user},~t,~j}$ by (12);

end for

Initial $\alpha_{\tau_{\rm~user},~j}$ as (eqn_alpha_1);

for $t~\in~{\rm~TM(RR(user))}$, forward

Calculate $\alpha_{t,~j}$ by (eqn_alpha_2);

end for

Initial $\beta_{T,~j}$ as (eqn_beta_1);

for $t~\in~{\rm~TM(RR(user))}$, backward

Calculate $\beta_{t,~i}$ by (eqn_beta_2);

end for

for $t~\in~{\rm~TM(RR(user))}$

Calculate $\gamma_{t,~i}$ and $\xi_{t,~i,~j}$ by (eqn_gamma) and (eqn_xi);

end for

Update $\pi_i$, $A_{i,~j}$, and $p_{j,~k}$ by (13)–(16);

• Table 1   Hyperparameters, random variables and parameters
 Symbol Meaning $J$ Number of user types $K$ Number of item types $M$ Max number of recent ratings $\lambda_1$ Regularization for $\pi$ and $\omega$ $\lambda_2$ Regularization for $A$ and $B$ $X_{{\rm~user},t}$ The type ${\rm~user}$ belongs to at time $t$ $Y_{{\rm~item},t}$ The type item belongs to at time $t$ $R_{{\rm~user,item},t}$ The rating that ${\rm~user}$ give to item at time $t$ $p_{j,k}$ Probability that type $j$ user likes type $k$ item $A_{i,j}$ Jump rate matrix for users $B_{k,m}$ Jump rate matrix for items $\pi_j$ Global prior distribution for users $\omega_k$ Global prior distribution for items $f_{{\rm~user},t,j}$ Approximation of user variable distribution $g_{{\rm~item},t,k}$ Approximation of item variable distribution
• Table 2   Additional persistent variables
 Variable name Data type Meaning $\tau_{\rm~user}$ Number Time of the first recent rating of ${\rm~user}$ $\tau_{\rm~item}$ Number Time of the first recent rating of item $\phi_{{\rm~user},j}$ Number Local prior for users $\psi_{{\rm~item},k}$ Number Local prior for items $x_{{\rm~user},t,j}$ Number $P(X_{{\rm~user},t}=j|{\rm~Rating})$ $y_{{\rm~item},t,k}$ Number $P(Y_{{\rm~item},t}=k|{\rm~Rating})$ ${\rm~RecRating(user)}$ Queue Recent rating for ${\rm~user}$ ${\rm~RecRating(item)}$ Queue Recent rating for item
•

Algorithm 2 Prediction

function Predict($({\rm~user,item},t)$);

$({\rm~user,item}_1,T_1,l_1)~\leftarrow~{\rm~RecRating(user).back}()$;

for $j=1,\dots,~J$

$\hat{x}_{{\rm~user},t,j}~\leftarrow~\sum_{i=1}^J~x_{{\rm~user},T_1,i}\exp(A(t-T_1))_{i,j}$;

end for

$({\rm~user}_2,{\rm~item},T_2,l_2)~\leftarrow~{\rm~RecRating(item).back}()$;

for $k=1,\dots,~K$

$\hat{y}_{{\rm~item},t,k}~\leftarrow~\sum_{m=1}^K~y_{{\rm~item},T_2,l}\exp(B(t-T_2))_{m,k}$;

end for

for $n=1,\dots,~N$

$\hat{r}_n~\leftarrow~\sum\nolimits_{j~=~1}^J~{\sum\nolimits_{k~=~1}^K~{\hat{x}_{{\rm~user},t,j}~\hat{y}_{{\rm~item},t,k}~\Pr(n-1;N-1,p_{j,k})~}~}~$;

end for

return $\hat{r}$;

• Table 3   The experiment datasets with different sizes
 Dataset User Item Rating Density(%) MLK (MovieLens100k) [56] 944 1683 100000 6.29 MLM (MovieLens1M) 6040 3706 1000209 4.47 Ep (Epinions) [57,58] 2874 2624 122361 1.62 EpEx (Epinions extended) [59] 11201 109520 5449415 0.44
• Table 4   The scores of precision
 Setting Classical Time-ordered Dataset MLK MLM Ep EpEx MLK MLM Ep EpEx SRec 0.698 0.728 0.796 0.953 0.662 0.703 0.788 0.943 TCARS 0.717 0.750 0.783 0.951 0.702 0.724 0.746 0.940 GRU4Rec 0.652 0.654 0.715 0.936 0.613 0.622 0.705 0.939 RRN 0.665 0.730 0.740 0.938 0.684 0.702 0.734 0.936 RT 0.717 0.745 0.831 0.954 0.730 0.717 0.792 0.945
• Table 5   Normalized discounted cumulative gain
 Setting Classical Time-ordered Dataset MLK MLM Ep EpEx MLK MLM Ep EpEx SRec 0.924 0.933 0.945 0.984 0.938 0.933 0.954 0.979 TCARS 0.931 0.941 0.936 0.979 0.939 0.940 0.938 0.978 GRU4Rec 0.903 0.904 0.905 0.974 0.916 0.908 0.923 0.976 RRN 0.914 0.932 0.915 0.971 0.933 0.933 0.927 0.976 RT 0.930 0.938 0.956 0.984 0.946 0.939 0.954 0.980
• Table 6   Mean reciprocal rank
 Setting Classical Time-ordered Dataset MLK MLM Ep EpEx MLK MLM Ep EpEx SRec 0.855 0.897 0.919 0.980 0.850 0.872 0.897 0.971 TCARS 0.854 0.910 0.880 0.955 0.794 0.876 0.831 0.964 GRU4Rec 0.797 0.839 0.835 0.969 0.765 0.837 0.815 0.966 RRN 0.828 0.892 0.843 0.953 0.833 0.875 0.843 0.964 RT 0.867 0.903 0.939 0.978 0.853 0.884 0.898 0.970

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