A framework to generate sparsity-inducing regularizers for enhanced low-rank matrix completion
Optimization and Control
2023-10-10 v1 Information Retrieval
Machine Learning
Audio and Speech Processing
Image and Video Processing
Abstract
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.
Cite
@article{arxiv.2310.04954,
title = {A framework to generate sparsity-inducing regularizers for enhanced low-rank matrix completion},
author = {Zhi-Yong Wang and Hing Cheung So},
journal= {arXiv preprint arXiv:2310.04954},
year = {2023}
}