  We consider a novel algorithm, for the completion of partially observed
low-rank matrices in a structured setting where each entry can be chosen from a
finite discrete alphabet set, such as in common recommender systems. The
proposed low-rank matrix completion (MC) method is an improved variation of
state-of-the-art (SotA) discrete aware matrix completion method which we
previously proposed, in which discreteness is enforced by an $\ell_0$-norm
regularizer, not by replaced with the $\ell_1$-norm, but instead approximated
by a continuous and differentiable function normalized via fractional
programming (FP) under a proximal gradient (PG) framework. Simulation results
demonstrate the superior performance of the new method compared to the SotA
techniques as well as the earlier $\ell_1$-norm-based discrete-aware matrix
completion approach.
