# A framework to generate sparsity-inducing regularizers for enhanced low-rank matrix completion

arXiv: https://arxiv.org/abs/2310.04954 · HTML: https://mlsanity.com/paper/2310.04954/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 27 references that are in the map.
- First posted on arXiv 8 Oct 2023.

## Builds on (most cited first, 5 of 5)

- [Nonconvex Nonsmooth Low-Rank Minimization via Iteratively Reweighted Nuclear Norm](https://mlsanity.com/paper/1510.06895/) (2015)
- [Bilinear Factor Matrix Norm Minimization for Robust PCA: Algorithms and Applications](https://mlsanity.com/paper/1810.05186/) (2018)
- [Generalized Nonconvex Nonsmooth Low-Rank Minimization](https://mlsanity.com/paper/1404.7306/) (2014)
- [Generalized Singular Value Thresholding](https://mlsanity.com/paper/1412.2231/) (2014)
- [Enhanced Low-Rank Matrix Approximation](https://mlsanity.com/paper/1511.01966/) (2015)

## Abstract (arXiv)

Applying half-quadratic optimization to loss functions can yield the corresponding regularizers, while these regularizers are usually not sparsity-inducing regularizers (SIRs). To solve this problem, we devise a framework to generate an SIR with closed-form proximity operator. Besides, we specify our framework using several commonly-used loss functions, and produce the corresponding SIRs, which are then adopted as nonconvex rank surrogates for low-rank matrix completion. Furthermore, algorithms based on the alternating direction method of multipliers are developed. Extensive numerical results show the effectiveness of our methods in terms of recovery performance and runtime.