Low Rank Regularization: A Review
This is an incremental work that bridges theoretical research and practical applications of low rank regularization for researchers in machine learning and related domains.
This paper provides a comprehensive survey of low rank regularization, reviewing its applications in fields like machine learning and computer vision, and demonstrates through experiments that non-convex regularizers offer significant advantages over the widely used nuclear norm.
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.