Low Rank Regularization: A Review

TL;DR

This paper provides a comprehensive review of low rank regularization, bridging theoretical advances and practical applications across various fields, highlighting the advantages of non-convex regularizers over traditional convex methods.

Contribution

It systematically summarizes traditional models, applications, regularizers, and optimization methods, emphasizing the effectiveness of non-convex regularizers in practical problems.

Findings

Non-convex regularizers outperform nuclear norm in practical tasks.

Traditional models are effectively applied to issues like image denoising.

Extensive experiments validate the advantages of non-convex approaches.

Abstract

Low rank regularization, in essence, involves introducing a low rank or approximately low rank assumption for matrix we aim to learn, which has achieved great success in many fields including machine learning, data mining and computer version. Over the last decade, much progress has been made in theories and practical applications. Nevertheless, the intersection between them is very slight. In order to construct a bridge between practical applications and theoretical research, in this paper we provide a comprehensive survey for low rank regularization. We first review several traditional machine learning models using low rank regularization, and then show their (or their variants) applications in solving practical issues, such as non-rigid structure from motion and image denoising. Subsequently, we summarize the regularizers and optimization methods that achieve great success in traditional machine learning tasks but are rarely seen in solving practical issues. Finally, we provide a discussion and comparison for some representative regularizers including convex and non-convex relaxations. Extensive experimental results demonstrate that non-convex regularizers can provide a large advantage over the nuclear norm, the regularizer widely used in solving practical issues.