Nonconvex Regularized Robust PCA Using the Proximal Block Coordinate Descent Algorithm

This work addresses the robust principal component analysis (PCA) problem using generalized nonoconvex regularization for low-rank and sparsity promotion. While the popular nuclear and \ell _1-norm penalties have a bias problem, nonconvex regularization can alleviate the bias problem and can be expe...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on signal processing 2019-10, Vol.67 (20), p.5402-5416
Main Authors: Wen, Fei, Ying, Rendong, Liu, Peilin, Truong, Trieu-Kien
Format: Article
Language:English
Subjects:
Algorithms
Approximation algorithms
Bias
block coordinate descent
Convergence
Descent
Fines & penalties
low-rank
Mathematical analysis
Matrix converters
nonconvex optimization
Nonlinear programming
Optimization
Principal component analysis
Principal components analysis
Regression analysis
Regularization
Robust principal component analysis
Robustness (mathematics)
Signal processing algorithms
sparse
Sparse matrices
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:This work addresses the robust principal component analysis (PCA) problem using generalized nonoconvex regularization for low-rank and sparsity promotion. While the popular nuclear and \ell _1-norm penalties have a bias problem, nonconvex regularization can alleviate the bias problem and can be expected to achieve better performance. In this paper, a proximal block coordinate descent (BCD) algorithm is used to efficiently solve the nonconvex regularized robust PCA problem. It is globally convergent under weak conditions. Further, for a popular class of penalties having discontinuous threshoding functions, we establish the convergence to a restricted strictly local minimizer and, also, a local linear convergence rate for the proximal BCD algorithm. Moreover, convergence to a local minimizer has been derived for hard-thresholding. Our result is the first on nonconvex robust PCA with established convergence to strictly local minimizer with local linear convergence rate. Numerical experiments have been provided to demonstrate the performance of the new algorithm.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2019.2940121