Discrete Aware Matrix Completion via Convexized $\ell_0$-Norm Approximation

TL;DR

This paper introduces a novel matrix completion algorithm for discrete low-rank matrices, improving accuracy by using a convexized $\

Contribution

It presents an enhanced discrete-aware matrix completion method that employs a convexified $\

Findings

Outperforms state-of-the-art discrete matrix completion methods

Uses a differentiable approximation of $\

Demonstrates superior accuracy in simulations

Abstract

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.