结合非负矩阵填充及子集划分的协同推荐算法

Collaborative Filtering Algorithm Integrating Non-negative Matrix Completion and Subgroups Partitioning

针对协同过滤推荐中评分矩阵极度稀疏问题,以及很多应用对数据存在非负约束要求,提出一种结合矩阵填充及用户-兴趣子集划分的协同推荐算法.首先提出非负约束下的低秩矩阵填充模型(Non-negative Constrained Low Rank Matrix Completion,LR-NM F),以及有效求解该模型的迭代算法.该算法不仅可以利用重构矩阵填充原始矩阵中的缺失项,而且可以得到评分矩阵的非负分解表示.在此基础上,提出一种结合LR-NMF的基于群组的协同推荐方法.利用矩阵非负分解结果,通过块模型近似算法划分用户-兴趣子集或物品-特征子集,最终产生top-N协同推荐列表.实验结果表明,提出的方法不仅有效填充评分矩阵的缺失项,而且推荐精度优于其它协同推荐算法.在大规模稀疏数据集中,仍然具有很好的性能.

In the recommender system, the user-item rating matrix is very sparse, and the non-negative constraints of the data are required. Therefore, this paper puts forward a collaborative recommendation method based on matrix completion and user-interest subsets division. Firstly, a low rank matrix filling model with non-negative constraints （ Non-negative Constrained Low Rank Matrix Comple- tion, LR-NMF ） is presented and then an iterative algorithm for solving the model is proposed. The algorithm not only uses the reconstruction matrix to fill the missing items in the original matrix, but also obtain the non-negative decomposition expression of the scoring matrix. On this basis, a group based collaborative recommendation method combined with LR-NMF is proposed. By using non- negative matrix decomposition results, we divide the user-interest subset or item-feature subset into groups,resulting in top-N collaborative recommendation list. Empirical results reveal that the proposed method not only effectively fills the missing items of the scoring matrix ,but also outperforms other collaborative recommendation algorithms. Even in large-scale sparse data sets ,it still has very good performance.