# Discrete Aware Matrix Completion via Convexized ℓ0-Norm Approximation

arXiv: https://arxiv.org/abs/2405.02101 · HTML: https://mlsanity.com/paper/2405.02101/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 32 references that are in the map.
- First posted on arXiv 3 May 2024.

## Builds on (most cited first, 8 of 8)

- [Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview](https://mlsanity.com/paper/1809.09573/) (2018)
- [Guaranteed Matrix Completion via Non-convex Factorization](https://mlsanity.com/paper/1411.8003/) (2014)
- [Low-Rank Matrix Completion: A Contemporary Survey](https://mlsanity.com/paper/1907.11705/) (2019)
- [Matrix Completion with Noisy Entries and Outliers](https://mlsanity.com/paper/1503.00214/) (2015)
- [The Non-convex Geometry of Low-rank Matrix Optimization](https://mlsanity.com/paper/1611.03060/) (2016)
- [Link Prediction via Matrix Completion](https://mlsanity.com/paper/1606.06812/) (2016)
- [Proximal Gradient Algorithms: Applications in Signal Processing](https://mlsanity.com/paper/1803.01621/) (2018)
- [Discrete-Aware Matrix Completion via Proximal Gradient](https://mlsanity.com/paper/2006.04075/) (2020)

## Built on by (most cited first, 1 of 1)

- [Low Rank Tensor Completion via Adaptive ADMM](https://mlsanity.com/paper/2605.03736/) (2026)

## Abstract (arXiv)

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 ℓ0-norm regularizer, not by replaced with the ℓ1-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 ℓ1-norm-based discrete-aware matrix completion approach.