Robust matrix factorization for collaborative filtering in recommender systems

Recently, matrix factorization has produced state-of-the-art results in recommender systems. However, given the typical sparsity of ratings, the often large problem scale, and the large number of free parameters that are often implied, developing robust and efficient models remains a challenge. Previous works rely on dense and/or sparse factor matrices to estimate unavailable user ratings. In this work we develop a new formulation for recommender systems that is based on projective non-negative matrix factorization, but relaxes the non-negativity constraint. Driven by a simple yet instructive intuition, the proposed formulation delivers promising and stable results that depend on a minimal number of parameters. Experiments that we conducted on two popular recommender system datasets demonstrate the efficiency and promise of our proposed method. We make available our code and datasets at https://github.com/christosbampis/PCMF_release.