Abstract: Model-based collaborative filtering algorithms usually express user's preferences and item's attributes by latent factors through matrix factorization,but the traditional matrix factorization algorithm is difficult to deal with the serious data sparsity and data variability problems in the recommendation system.To solve the above problem,a matrix factorization algorithm based on bordered block diagonal matrix is proposed.Firstly,the original sparse matrix is transformed into bordered block diagonal matrix by a graph partitioning algorithm based on community discovery,which merges users with the same preference and items with similar characteristics into the same diagonal block,and then splices the diagonal blocks and the bordered into several sub-diagonal matrices which have higher densities.The experimental results show that,by decomposing the sub-diagonal matrices in parallel can not only improve the precision of prediction,but also improve the interpretability of the recommendation results.At the same time,each sub-diagonal matrix can be decomposed independently and in parallel,which can improve the efficiency of the algorithm.

Key words: Collaborative filtering, Community discovery, Matrix factorization, Recommendation system