A Survey on Nonconvex Regularization-Based Sparse and Low-Rank Recovery in Signal Processing, Statistics, and Machine Learning

In the past decade, sparse and low-rank recovery has drawn much attention in many areas such as signal/image processing, statistics, bioinformatics, and machine learning. To achieve sparsity and/or low-rankness inducing, the \ell _{1} norm and nuclear norm are of the most popular regularization pe...

Full description

Saved in:
Bibliographic Details
Published in:IEEE access 2018, Vol.6, p.69883-69906
Main Authors: Wen, Fei, Chu, Lei, Liu, Peilin, Qiu, Robert C.
Format: Article
Language:English
Subjects:
Algorithms
Bioinformatics
compressive sensing
Computational geometry
Convergence
Convexity
Covariance matrices
Covariance matrix
covariance matrix estimation
Estimation
Image processing
low-rank
Machine learning
matrix completion
nonconvex
Optimization
Principal component analysis
Principal components analysis
Recovery
regression
Regression analysis
Regularization
Signal processing
Sparse
Sparse matrices
Statistics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In the past decade, sparse and low-rank recovery has drawn much attention in many areas such as signal/image processing, statistics, bioinformatics, and machine learning. To achieve sparsity and/or low-rankness inducing, the \ell _{1} norm and nuclear norm are of the most popular regularization penalties due to their convexity. While the \ell _{1} and nuclear norm are convenient as the related convex optimization problems are usually tractable, it has been shown in many applications that a nonconvex penalty can yield significantly better performance. In recent, nonconvex regularization-based sparse and low-rank recovery is of considerable interest and it in fact is a main driver of the recent progress in nonconvex and nonsmooth optimization. This paper gives an overview of this topic in various fields in signal processing, statistics, and machine learning, including compressive sensing, sparse regression and variable selection, sparse signals separation, sparse principal component analysis (PCA), large covariance and inverse covariance matrices estimation, matrix completion, and robust PCA. We present recent developments of nonconvex regularization based sparse and low-rank recovery in these fields, addressing the issues of penalty selection, applications and the convergence of nonconvex algorithms. Code is available at https://github.com/FWen/ncreg.git .
ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2018.2880454