Relation Regularized Matrix Factorization

In many applications, the data, such as web pages and research papers, contain relation (link) structure among entities in addition to textual content information. Matrix factorization (MF) methods, such as latent semantic indexing (LSI), have been successfully used to map either content information or relation information into a lower-dimensional latent space for subsequent processing. However, how to simultaneously model both the relation information and the content information effectively with an MF framework is still an open research problem. In this paper, we propose a novel MF method called relation regularized matrix factorization (RRMF) for relational data analysis. By using relation information to regularize the content MF procedure, RRMF seamlessly integrates both the relation information and the content information into a principled framework. We propose a linear-time learning algorithm with convergence guarantee to learn the parameters of RRMF. Extensive experiments on real data sets show that RRMF can achieve state-of-the-art performance.

Wu-Jun Li, Dit-Yan Yeung