Collaborative Filtering: Weighted Nonnegative Matrix Factorization Incorporating User and Item Graphs

Collaborative filtering is an important topic in data mining and has been widely used in recommendation system. In this paper, we proposed a unified model for collaborative filtering based on graph regularized weighted nonnegative matrix factorization. In our model, two graphs are constructed on users and items, which exploit the internal information (e.g. neighborhood information in the user-item rating matrix) and external information (e.g. content information such as user’s occupation and item’s genre, or other kind of knowledge such as social trust network). The proposed method not only inherits the advantages of model-based method, but also owns the merits of memory-based method which considers the neighborhood information. Moreover, it has the ability to make use of content information and any additional information regarding user-user such as social trust network. Due to the use of these internal and external information, the proposed method is able to find more interpretable lowdimensional representations for users and items, which is helpful for improving the recommendation accuracy. Experimental results on benchmark collaborative filtering data sets demonstrate that the proposed methods outperform the state of the art collaborative filtering methods a lot.

[1]  Fan Chung,et al.  Spectral Graph Theory , 1996 .

[2]  Y. Shoham,et al.  Ecom Syst Content-based, Collaborative Recommendation , 1997 .

[3]  John Riedl,et al.  An algorithmic framework for performing collaborative filtering , 1999, SIGIR '99.

[4]  Eric Horvitz,et al.  Collaborative Filtering by Personality Diagnosis: A Hybrid Memory and Model-Based Approach , 2000, UAI.

[5]  H. Sebastian Seung,et al.  Algorithms for Non-negative Matrix Factorization , 2000, NIPS.

[6]  David M. Pennock,et al.  Probabilistic Models for Unified Collaborative and Content-Based Recommendation in Sparse-Data Environments , 2001, UAI.

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

[8]  Raymond J. Mooney,et al.  Content-boosted collaborative filtering for improved recommendations , 2002, AAAI/IAAI.

[9]  Bernhard Schölkopf,et al.  Learning with Local and Global Consistency , 2003, NIPS.

[10]  Alexander J. Smola,et al.  Kernels and Regularization on Graphs , 2003, COLT.

[11]  Tommi S. Jaakkola,et al.  Weighted Low-Rank Approximations , 2003, ICML.

[12]  Luo Si,et al.  Flexible Mixture Model for Collaborative Filtering , 2003, ICML.

[13]  Thomas Hofmann,et al.  Unifying collaborative and content-based filtering , 2004, ICML.

[14]  Thomas Hofmann,et al.  Latent semantic models for collaborative filtering , 2004, TOIS.

[15]  Luo Si,et al.  An automatic weighting scheme for collaborative filtering , 2004, SIGIR '04.

[16]  Tommi S. Jaakkola,et al.  Maximum-Margin Matrix Factorization , 2004, NIPS.

[17]  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.

[18]  Bernhard Schölkopf,et al.  Learning from labeled and unlabeled data on a directed graph , 2005, ICML.

[19]  Jun Wang,et al.  Unifying user-based and item-based collaborative filtering approaches by similarity fusion , 2006, SIGIR.

[20]  Mikhail Belkin,et al.  Manifold Regularization: A Geometric Framework for Learning from Labeled and Unlabeled Examples , 2006, J. Mach. Learn. Res..

[21]  Fei Wang,et al.  Recommendation on Item Graphs , 2006, Sixth International Conference on Data Mining (ICDM'06).

[22]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[23]  Chris H. Q. Ding,et al.  Orthogonal nonnegative matrix t-factorizations for clustering , 2006, KDD '06.

[24]  Fillia Makedon,et al.  Learning from Incomplete Ratings Using Non-negative Matrix Factorization , 2006, SDM.

[25]  Punam Bedi,et al.  Trust Based Recommender System for Semantic Web , 2007, IJCAI.

[26]  Stephen Lin,et al.  Graph Embedding and Extensions: A General Framework for Dimensionality Reduction , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[27]  Gang Chen,et al.  Collaborative Filtering Using Orthogonal Nonnegative Matrix Tri-factorization , 2007, Seventh IEEE International Conference on Data Mining Workshops (ICDMW 2007).

[28]  Ruslan Salakhutdinov,et al.  Probabilistic Matrix Factorization , 2007, NIPS.

[29]  Jiawei Han,et al.  Non-negative Matrix Factorization on Manifold , 2008, 2008 Eighth IEEE International Conference on Data Mining.

[30]  Fei Wang,et al.  Semi-Supervised Clustering via Matrix Factorization , 2008, SDM.

[31]  Michael R. Lyu,et al.  SoRec: social recommendation using probabilistic matrix factorization , 2008, CIKM '08.

[32]  Quanquan Gu,et al.  Transductive Classification via Dual Regularization , 2009, ECML/PKDD.

[33]  Quanquan Gu,et al.  Local Relevance Weighted Maximum Margin Criterion for Text Classification , 2009, SDM.

[34]  Quanquan Gu,et al.  Co-clustering on manifolds , 2009, KDD.

[35]  Quanquan Gu,et al.  Local Learning Regularized Nonnegative Matrix Factorization , 2009, IJCAI.

[36]  Chris H. Q. Ding,et al.  Convex and Semi-Nonnegative Matrix Factorizations , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.