  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.
