Learning Discrete Matrix Factorization Models

Matrix factorization is among the most popular approaches for matrix completion, with recent advances including gradient-based and deep-learning-based methods. Even though many applications involve matrices with discrete values, most of the existing matrix factorization models focus on the continuous domain. Discretization is applied as an additional step, often using a heuristic mapping that results in sub-optimal solutions, which either do not take into account the structure of the matrix or introduce significant quantization errors. In this letter, we propose a novel method that allows gradient-based and deep-learning-based methods to jointly learn both the matrix factorization model and a discretization operator. By introducing a loss function that accounts for the reconstruction error with respect to the discrete predictions, we obtain a discrete matrix completion algorithm with high reconstruction accuracy. Experiments using well-known datasets show the improvement obtained by the proposed algorithm over the state of the art.