Recommender systems, which can significantly help users find their interested items from the information era, has attracted an increasing attention from both the scientific and application society. One of the widest applied recommendation methods is the Matrix Factorization (MF). However, most of MF based approaches focus on the user-item rating matrix, but ignoring the ingredients which may have significant influence on users’ preferences on items. In this paper, we propose a multi-linear interactive MF algorithm (MLIMF) to model the interactions between the users and each event associated with their final decisions. Our model considers not only the user-item rating information but also the pairwise interactions based on some empirically supported factors. In addition, we compared the proposed model with three typical other methods: user-based collaborative filtering (UCF), item-based collaborative filtering (ICF) and regularized MF (RMF). Experimental results on two real-world datasets, MovieLens 1M and MovieLens 100k, show that our method performs much better than other three methods in the accuracy of recommendation. This work may shed some light on the in-depth understanding of modeling user online behaviors and the consequent decisions. 
Multi-linear interactive matrix factorization