Incorporating Hierarchical Information into the Matrix Factorization Model for Collaborative Filtering

Matrix factorization (MF) is one of the well-known methods in collaborative filtering to build accurate and efficient recommender systems. While in all the previous studies about MF items are considered to be of the same type, in some applications, items are divided into different groups, related to each other in a defined hierarchy (e.g. artists, albums and tracks). This paper proposes Hierarchical Matrix Factorization (HMF), a method that incorporates such relations into MF, to model the item vectors. This method is applicable in the situations that item groups form a general-to-specific hierarchy with child-to-parent (many-to-one or many-to-many) relationship between successive layers. This study evaluates the accuracy of the proposed method in comparison to basic MF on the Yahoo! Music dataset by examining three different hierarchical models. The results in all the cases demonstrate the superiority of HMF. In addition to the effectiveness of HMF in improving the prediction accuracy in the mentioned scenarios, this model is very efficient and scalable. Furthermore, it can be readily integrated with the other variations of MF.