Recommendation system has attracted large amount of attention in the field of E-commerce research. Traditional MF (Matrix Factorization) methods take a global view on the user-item rating matrix to derive latent user vectors and latent item vectors for rating prediction. However, there is an inherent structure in the user-item rating matrix and a local correspondence between user clusters and item clusters as the users induce the items and the items imply the users in a recommendation system. Motivated by this observation, this paper proposes a novel rating prediction approach called RP-LGMC (Rating Prediction based on Local and Global information with Matrix Clustering) based on matrix factorization by making use of the local correspondence between user clusters and item clusters. The RP-LGMC approach consists of three components. The first component is to partition the user-item rating matrix into small blocks by the sparse subspace clustering (SCC) algorithm with co-clustering its rows (users) and columns (items) simultaneously. The second component is local distillation to extract those dense and stable blocks by thresholding block density and standard deviation. The third component is to predict the ratings with residual approximation on the local blocks and SVD++ on the global blocks of the original user-item matrix$R$. The RP-LGMC approach can not only reduce the data sparsity but also increase the computation scalability. Experiments on the MovieLens-25 M dataset demonstrate that the proposed RP-LGMC approach performs better than most state-of-the-art methods in terms of recommendation accuracy and has lower computation complexity than the SVD++ algorithm.

推荐系统在电子商务研究领域引起了广泛的关注。传统的MF（矩阵分解）方法对用户项评级矩阵具有全局视图，以导出潜在用户矢量和潜在项目矢量以进行评级预测。但是，在用户项目评分矩阵中存在固有的结构，并且当用户诱导项目并且项目暗示用户在推荐系统中时，用户群集和项目群集之间存在局部对应关系。基于这种观察，本文提出了一种新的评级预测方法，称为RP-LGMC（基于矩阵聚类的基于本地和全局信息的评级预测），它利用用户聚类和项目聚类之间的局部对应关系进行矩阵分解。RP-LGMC方法包含三个组件。第一个组件是通过稀疏子空间聚类（SCC）算法将用户项评分矩阵划分为小块，同时将其行（用户）和列（项）共同聚类。第二个成分是局部蒸馏，以通过限制块密度和标准偏差来提取那些致密且稳定的块。第三个组成部分是使用原始用户项目矩阵的局部块和SVD ++的残余近似值预测收视率$\mathrm{[R}$。RP-LGMC方法不仅可以减少数据稀疏性，而且可以提高计算的可扩展性。在MovieLens-25 M数据集上进行的实验表明，与SVD ++算法相比，建议的RP-LGMC方法在推荐精度方面表现优于大多数最新技术，并且具有较低的计算复杂度。