Abstract：Most ranking-oriented collaborative filtering (CF) algorithms have two limitations. Firstly, they only consider the accordance of user preferences but ignore the degrees and popularities of user preferences when computing user similarities. Secondly, an intermediate step is necessary to formulate the value function, for preference prediction and aggregation in greedy algorithms to derive recommendation lists. To address these problems, we propose a Degree-Popularity weighting scheme integrating TF-IDF to weight the degrees and popularities of user pairwise relative preferences, and compute similarities between users based on weighted Kendall Tau rank correlation coefficient. Preference aggregations and predictions are directly formulated and the recommendation lists are consequently derived by applying the Schulze method. We conduct extensive experiments on two movie datasets under NDCG evaluation, implying advantageous results in comparison with the state-of-the-art CF algorithms.
 Su X, Khoshgoftaar TM. A survey of collaborative filtering techniques[J]. Adv. in Artif. Intell. 2009,2009:2-2.  Hu Y, Koren Y, Volinsky C. Collaborative Filtering for Implicit Feedback Datasets[C]//Proceedings of the 2008 Eighth IEEE International Conference on Data Mining: IEEE Computer Society; 2008: 263-272.  Liu NN, Yang Q. EigenRank: a ranking-oriented approach to collaborative filtering[C]//Proceedings of the 31st annual international ACM SIGIR conference on research and development in information retrieval. Singapore, Singapore: ACM; 2008: 83-90.  Sarwar B, Karypis G, Konstan J, Riedl J. Item-based collaborative filtering recommendation algorithms[C]//Proceedings of the 10th international conference on World Wide Web. Hong Kong, Hong Kong: ACM; 2001: 285-295.  刘建国, 周涛, 汪秉宏. 个性化推荐系统的研究进展[J]. 自然科学进展,2008,19:15.  Adomavicius G, Tuzhilin A. Toward the next generation of recommender systems: a survey of the state-of-the-art and possible extensions[J]. Knowledge and Data Engineering, IEEE Transactions, 2005,17:734-749.  Weimer, Markus, Karatzoglou, et al. COFIRANK-Maximum Margin Matrix Factorization for Collaborative Ranking[C]//Proceedings of NIPS; 2007.  Shi Y, Larson M, Hanjalic A. List-wise learning to rank with matrix factorization for collaborative filtering[C]//Proceedings of the fourth ACM conference on recommender systems. Barcelona, Spain: ACM; 2010: 269-272.  Cohen W W, Schapire R E, Singer Y. Learning to order things[J]. Artif. Int. Res. 1999,10:243-270.  Wang S, Sun J, Gao B J, et al. Adapting Vector Space Model to Ranking-based Collaborative Filtering[C]//Proceedings of CIKM; 2012.  Gunawardana A, Shani G. A Survey of Accuracy Evaluation Metrics of Recommendation Tasks[J]. Mach. Learn. Res. 2009,10:2935-2962.  Valizadegan H J R, Zhang R, Mao J. Learning to Rank by Optimizing NDCG Measure[C]//Proceedings of the Conference on Neural Information Processing Systems (NIPS); 2009.