Discrete Aware Matrix Completion via Convexized $\ell_0$-Norm Approximation
This work addresses matrix completion for discrete data in applications like recommender systems, but it is incremental as it builds on a previously proposed method.
The paper tackles the problem of low-rank matrix completion with entries from a finite discrete alphabet, such as in recommender systems, by proposing an improved method that approximates an ℓ0-norm regularizer via fractional programming under a proximal gradient framework, resulting in superior performance compared to state-of-the-art techniques.
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.