A Comprehensive Survey for Low Rank Regularization

08/14/2018
by   Zhanxuan Hu, et al.
0

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.

READ FULL TEXT

page 10

page 12

research
01/15/2014

Low-Rank Modeling and Its Applications in Image Analysis

Low-rank modeling generally refers to a class of methods that solve prob...
research
12/03/2015

Weighted Schatten p-Norm Minimization for Image Denoising and Background Subtraction

Low rank matrix approximation (LRMA), which aims to recover the underlyi...
research
09/14/2018

Efficient Rank Minimization via Solving Non-convexPenalties by Iterative Shrinkage-Thresholding Algorithm

Rank minimization (RM) is a wildly investigated task of finding solution...
research
10/27/2020

Learning Low-Rank Document Embeddings with Weighted Nuclear Norm Regularization

Recently, neural embeddings of documents have shown success in various l...
research
05/21/2021

Lecture notes on non-convex algorithms for low-rank matrix recovery

Low-rank matrix recovery problems are inverse problems which naturally a...
research
05/24/2018

Simple and practical algorithms for ℓ_p-norm low-rank approximation

We propose practical algorithms for entrywise ℓ_p-norm low-rank approxim...
research
09/30/2022

TT-NF: Tensor Train Neural Fields

Learning neural fields has been an active topic in deep learning researc...

Please sign up or login with your details

Forgot password? Click here to reset