Discrete-Aware Matrix Completion via Proximal Gradient

TL;DR

This paper introduces a new algorithm for completing low-rank matrices with entries from a finite discrete set, leveraging proximal gradient optimization to enforce discrete constraints.

Contribution

The paper proposes a novel proximal gradient-based method specifically designed for discrete-aware matrix completion, incorporating a regularization term for discrete alphabet enforcement.

Findings

Effective completion of discrete low-rank matrices demonstrated.

Algorithm outperforms existing methods in accuracy and efficiency.

Applicable to various discrete data recovery tasks.

Abstract

We present a novel algorithm for the completion of low-rank matrices whose entries are limited to a finite discrete alphabet. The proposed method is based on the recently-emerged proximal gradient (PG) framework of optimization theory, which is applied here to solve a regularized formulation of the completion problem that includes a term enforcing the discrete-alphabet membership of the matrix entries.