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

TL;DR

This paper introduces a novel framework for generating sparsity-inducing regularizers with closed-form proximity operators, specifically designed to improve low-rank matrix completion tasks.

Contribution

The authors propose a new framework to create sparsity-inducing regularizers from loss functions, enhancing low-rank matrix completion with nonconvex rank surrogates.

Findings

Effective recovery performance demonstrated

Reduced runtime in experiments

Framework applicable to common loss functions

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.