Top-N Recommendation on Graphs

Recommender systems play an increasingly important role in online applications to help users find what they need or prefer. Collaborative filtering algorithms that generate predictions by analyzing the user-item rating matrix perform poorly when the matrix is sparse. To alleviate this problem, this paper proposes a simple recommendation algorithm that fully exploits the similarity information among users and items and intrinsic structural information of the user-item matrix. The proposed method constructs a new representation which preserves affinity and structure information in the user-item rating matrix and then performs recommendation task. To capture proximity information about users and items, two graphs are constructed. Manifold learning idea is used to constrain the new representation to be smooth on these graphs, so as to enforce users and item proximities. Our model is formulated as a convex optimization problem, for which we need to solve the well known Sylvester equation only. We carry out extensive empirical evaluations on six benchmark datasets to show the effectiveness of this approach.

[1]  Gediminas Adomavicius,et al.  Toward the next generation of recommender systems: a survey of the state-of-the-art and possible extensions , 2005, IEEE Transactions on Knowledge and Data Engineering.

[2]  Parikshit Ram,et al.  Efficient retrieval of recommendations in a matrix factorization framework , 2012, CIKM.

[3]  Yifan Hu,et al.  Collaborative Filtering for Implicit Feedback Datasets , 2008, 2008 Eighth IEEE International Conference on Data Mining.

[4]  Roberto Turrin,et al.  Performance of recommender algorithms on top-n recommendation tasks , 2010, RecSys '10.

[5]  George Karypis,et al.  Item-based top-N recommendation algorithms , 2004, TOIS.

[6]  Xiaojun Wu,et al.  Graph Regularized Nonnegative Matrix Factorization for Data Representation , 2017, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[7]  S T Roweis,et al.  Nonlinear dimensionality reduction by locally linear embedding. , 2000, Science.

[8]  John Riedl,et al.  An Algorithmic Framework for Performing Collaborative Filtering , 1999, SIGIR Forum.

[9]  Zhao Kang,et al.  Top-N Recommender System via Matrix Completion , 2016, AAAI.

[10]  Xiaofei He,et al.  Locality Preserving Projections , 2003, NIPS.

[11]  Zhao Kang,et al.  Robust Subspace Clustering via Tighter Rank Approximation , 2015, CIKM.

[12]  John Riedl,et al.  Item-based collaborative filtering recommendation algorithms , 2001, WWW '01.

[13]  Feiping Nie,et al.  A New Simplex Sparse Learning Model to Measure Data Similarity for Clustering , 2015, IJCAI.

[14]  Neil Yorke-Smith,et al.  A Novel Bayesian Similarity Measure for Recommender Systems , 2013, IJCAI.

[15]  Diego Fernández,et al.  Comparison of collaborative filtering algorithms , 2011, ACM Trans. Web.

[16]  Chris H. Q. Ding,et al.  Collaborative Filtering: Weighted Nonnegative Matrix Factorization Incorporating User and Item Graphs , 2010, SDM.

[17]  Thomas S. Huang,et al.  Graph Regularized Nonnegative Matrix Factorization for Data Representation. , 2011, IEEE transactions on pattern analysis and machine intelligence.

[18]  George Karypis,et al.  SLIM: Sparse Linear Methods for Top-N Recommender Systems , 2011, 2011 IEEE 11th International Conference on Data Mining.

[19]  Hui Tian,et al.  A new user similarity model to improve the accuracy of collaborative filtering , 2014, Knowl. Based Syst..

[20]  Peter Benner,et al.  On the ADI method for Sylvester equations , 2009, J. Comput. Appl. Math..

[21]  Lars Schmidt-Thieme,et al.  BPR: Bayesian Personalized Ranking from Implicit Feedback , 2009, UAI.

[22]  Zhao Kang,et al.  Top-N Recommendation with Novel Rank Approximation , 2016, SDM.