An efficient non-negative matrix-factorization-based approach to collaborative filtering for recommender systems

Matrix-factorization (MF)-based approaches prove to be highly accurate and scalable in addressing collaborative filtering (CF) problems. During the MF process, the non-negativity, which ensures good representativeness of the learnt model, is critically important. However, current non-negative MF (NMF) models are mostly designed for problems in computer vision, while CF problems differ from them due to their extreme sparsity of the target rating-matrix. Currently available NMF-based CF models are based on matrix manipulation and lack practicability for industrial use. In this work, we focus on developing an NMF-based CF model with a single-element-based approach. The idea is to investigate the non-negative update process depending on each involved feature rather than on the whole feature matrices. With the non-negative single-element-based update rules, we subsequently integrate the Tikhonov regularizing terms, and propose the regularized single-element-based NMF (RSNMF) model. RSNMF is especially suitable for solving CF problems subject to the constraint of non-negativity. The experiments on large industrial datasets show high accuracy and low-computational complexity achieved by RSNMF.