Balanced hierarchical max margin matrix factorization for recommendation system

Matrix factorization (MF) is one of the most important regression analysis methods used in recommendation systems. Max margin matrix factorization (MMMF) is a variant of MF which transforms the regression analysis problem into a single multi-class classification problem, and then learns a multi-class max margin classifier to achieve to a better error rate. One drawback of multi-class MMMF is its bias towards class with small sample size. Therefore, hierarchical MMMF (HMF) which uses some two-class MMMF problems in a hierarchical manner for multi-class classification was proposed. Each two-class MMMF of HMF is learned on the basis of thresholded training data which is too imbalanced for some two-class MMMFs. Meanwhile, all training data is used in each two-class MMMF. In the test phase of HMF, an imbalanced tree is used to estimate rating. Each node of this tree is a learned two-class MMMF. In this paper, we propose a balanced HMF, which constructs a balanced tree with minimum depth. Each node of this tree is a learned two-class MMMF on the basis of a part of data which is selected such that to be more balanced than that of the traditional HMF. Moreover, each part of data in our proposed balanced HMF does not have overlap with all previous parts of data. Therefore, the overall training data used in each step of balanced HMF is smaller than that of in the traditional HMF. Experimental results on real datasets show that training time, test time and error rate of our proposed balanced HMF is better than those of the traditional HMF.