Abstract: It is extremely hard for the existing collaborative filtering algorithms to handle the problems of data sparsity and computation scalability in a recommendation system. This paper proposes a novel approach called CF-cluMA (Collaborative Filtering based on clustered Matrix Approximation) for collaborative filtering with the goal to tackle the problems. The CF-cluMA approach comprises two components. The first component is to partition the global user-item rating matrix into local dense block matrices by co-clustering its rows (users) and columns (items). The second one is to approximate the global user-item rating matrix by singular value decomposition (SVD) on the local dense blocks with Schimidt orthogonalization. The experiments on the EachMovie dataset demonstrate that the proposed CF-cluMA approach outperforms state-of-the-art collaborative filtering methods in terms of recommendation accuracy and computation complexity. This research has great managerial implications for recommendation systems in E-commerce.

Key words: spectral clustering, matrix approximation, collaborative filtering, data sparsity, computation scalability

摘要： 由于推荐系统中存在巨量的用户和商品,现有的协同过滤方法很难处理用户-商品推荐中的数据稀疏性和计算可扩展性问题。本文提出了一种基于聚类矩阵近似的协同过滤推荐方法CF-cluMA。一方面,CF-cluMA方法通过对用户和商品进行分别聚类,并利用聚类后的用户-商品分块评分矩阵来刻画用户对于商品兴趣的局部性特点,以降低用户-商品评分矩阵的全局稀疏性。另一方面,CF-cluMA方法通过对局部稠密分块矩阵实施奇异值分解,并利用施密特变换近似全局用户-商品评分矩阵来预测用户对未知商品评分,以降低协同过滤算法的复杂性。在EachMovie电影评分真实数据集上的实验表明,相比于已有的基于矩阵近似的协同过滤推荐方法,本文所提出的CF-cluMA方法能够有效提升推荐系统的准确性并降低推荐系统的计算复杂性。本文的研究对于电子商务推荐系统具有重要的管理启示。

关键词: 谱聚类, 矩阵近似, 协同过滤, 数据稀疏性, 可扩展性