One-class Matrix Factorization: Point-Wise Regression-Based or Pair-Wise Ranking-Based?

One-class matrix factorization (MF) is an important technique for recommender systems with implicit feedback. In one widely used setting, a regression function is fit in a point-wise manner on observed and some unobserved (user, item) entries. Recently, in AAAI 2019, Chen et al. [2] proposed a pair-wise ranking-based approach for observed (user, item) entries to be compared against unobserved ones. They concluded that the pair-wise setting performs consistently better than the more traditional point-wise setting. However, after some detailed investigation, we explain by mathematical derivations that their method may perform only similar to the point-wise ones. We also identified some problems when reproducing their experimental results. After considering suitable settings, we rigorously compare point-wise and pair-wise one-class MFs, and show that the pair-wise method is actually not better. Therefore, for one-class MF, the more traditional and mature point-wise setting should still be considered. Our findings contradict the conclusions in [2] and serve as a call for caution when researchers are comparing between two machine learning methods.