Understanding and improving relational matrix factorization in recommender systems

Matrix factorization techniques such as the singular value decomposition (SVD) have had great success in recommender systems. We present a new perspective of SVD for constructing a latent space from the training data, which is justified by the theory of hypergraph model. We show that the vectors representing the items in the latent space can be grouped into (approximately) orthogonal clusters which correspond to the vertex clusters in the co-rating hypergraph, and the lengths of the vectors are indicators of the representativeness of the items. These properties are used for making top-N recommendations in a two-phase algorithm. In this work, we provide a new explanation for the significantly better performance of the asymmetric SVD approaches and a novel algorithm for better diversity in top-N recommendations.