Robust and Accurate Representation Learning for High-dimensional and Sparse Matrices in Recommender Systems

How to accurately represent a high-dimensional and sparse (HiDS) user-item rating matrix is a crucial issue in implementing a recommender system. A latent factor (LF) model is one of the most popular and successful approaches to address this issue. It is developed by minimizing the errors between the observed entries and the estimated ones on an HiDS matrix. Current studies commonly employ L2-norm to minimize the errors because it has a smooth gradient, making a resultant LF model can accurately represent an HiDS matrix. As is well known, however, L2-norm is very sensitive to the outlier data or called unreliable ratings in the context of the recommender system. Unfortunately, the unreliable ratings often exist in an HiDS matrix due to some malicious users. To address this issue, this paper proposes a Smooth L1-norm-oriented Latent Factor (SL1-LF) model. Its main idea is to employ smooth L1-norm rather than L2-norm to minimize the errors, making it have both high robustness and accuracy in representing an HiDS matrix. Experimental results on four HiDS matrices generated by industrial recommender systems demonstrate that the proposed SL1-LF model is robust to the outlier data and has significantly higher prediction accuracy than state-of-the-art models for the missing data of an HiDS matrix.