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.

翻译：矩阵因子化是一种广泛采用的建议系统技术,适合用户特质矢量和物品特质矢量的圆点产品标值的标度评级值。然而,将矩阵因子化作为标度适切问题,不利于信息集成或多任务学习。在本文中,我们用矩阵取代用户的标度矩阵的标度值,用用户特质矩阵和项目特质矩阵的矩阵产品来匹配矩阵值。我们的框架有利于多任务学习和侧信息集成。我们尤其利用本文中的普及数据作为侧面信息,以提高矩阵因子化技术的性能。在试验部分,我们证明我们的方法与使用准确性和公平性度衡量法的其他方法相比是胜任的。我们的框架是背景认知建议和许多其他假设中用于强因子化的典型替代物。