MatMat: Matrix Factorization by Matrix Fitting

Matrix factorization is a widely adopted recommender system technique that fits scalar rating values by dot products of user feature vectors and item feature vectors. However, the formulation of matrix factorization as a scalar fitting problem is not friendly to side information incorporation or multi-task learning. In this paper, we replace the scalar values of the user rating matrix by matrices, and fit the matrix values by matrix products of user feature matrix and item feature matrix. Our framework is friendly to multitask learning and side information incorporation. We use popularity data as side information in our paper in particular to enhance the performance of matrix factorization techniques. In the experiment section, we prove the competence of our method compared with other approaches using both accuracy and fairness metrics. Our framework is an ideal substitute for tensor factorization in context-aware recommendation and many other scenarios.