Destructure-and-restructure matrix approximation

Abstract

A matrix approximation is used to predict the missing values of a matrix, which has many applications in recommender systems. After predicting the missing values of a user-item rating matrix, we can recommend unrated items to a user according to their approximated values. This paper proposes a new approximation scheme for large and sparse global matrices, which is called a destructure-and-restructure matrix approximation. The basic idea is to first destructure a global matrix into many local matrices, and then restructure it from local matrix approximations. However, distance computation is a challenging issue in matrix destructure because no prior knowledge about the most appropriate feature vectors and distance measures are available. To deal with this issue, we propose a novel scheme that does not require any distance computation for local matrix construction, which is based on the application of convergence probabilities of a graph random walk. At first, a user-item bipartite graph is built from the global matrix. After performing random walk on the bipartite graph, we select several user-item pairs as anchors. Then, another random walk with restart is applied to construct local matrices from anchors. For each local matrix, we propose a weighted matrix factorization that is based on the rating distribution of the training data. In the restructure process, we first compute the approximation credibility of each local matrix, and we then finally obtain the global matrix approximation weighted from credible local approximations. Our experiments on five real-world datasets show that the proposed solution outperforms the state-of-the-art schemes in terms of lower prediction errors and higher coverage ratios.