关键词: 评分矩阵, 低秩矩阵恢复, 秩1矩阵, 用户聚类数, 奇异值分解

Abstract: Rating matrix is high-dimensional, sparse and low rank. The low rank matrix recovery is the important method for   rating matrix of research. For these algorithms, different scoring matrix rank will obtain different recovery precision. But there is no theory to study the score matrix rank, thus affecting the application of these algorithms. This paper analyzes the relationship between clustering number of user and rank of rating matrix, and then it presents the method of computing the cluster number of user, and on this basis, it proposes a number of clusters based on rank 1 matrix recovery（Clusters Number Rank-1 Matrix Completion, CN-R1MC） algorithm to recover rating matrix. Through a plurality of recommendation system data sets on the experiments, the cluster number of user can approximate rank of rating matrix better, which has an important role in improving recovery accuracy for the rating matrix. The proposed algorithm has good application value.

Key words: rating matrix, low-rank matrix completion, rank-one matrix, number of user clustering, singular value decomposition