Robust Matrix Completion via Maximum Correntropy Criterion and Half-Quadratic Optimization

Yicong He, Fei Wang, Yingsong Li, Jing Qin, Badong Chen

Research output: Journal article publicationJournal articleAcademic researchpeer-review

39 Citations (Scopus)

Abstract

Robust matrix completion aims to recover a low-rank matrix from a subset of noisy entries perturbed by complex noises. Traditional matrix completion algorithms are always based on l_2-norm minimization and are sensitive to non-Gaussian noise with outliers. In this paper, we propose a novel robust and fast matrix completion method based on the maximum correntropy criterion (MCC). The correntropy-based error measure is utilized instead of the l_2-based error norm to improve robustness against noise. By using the half-quadratic optimization technique, the correntropy-based optimization can be transformed into a weighted matrix factorization problem. Two efficient algorithms are then derived: an alternating minimization-based algorithm and an alternating gradient descent-based algorithm. These algorithms do not require the singular value decomposition (SVD) to be calculated for each iteration. Furthermore, an adaptive kernel width selection strategy is proposed to accelerate the convergence speed as well as improve the performance. A comparison with existing robust matrix completion algorithms is provided by simulations and shows that the new methods can achieve better performance than the existing state-of-the-art algorithms.

Original languageEnglish
Article number8894529
Pages (from-to)181-195
Number of pages15
JournalIEEE Transactions on Signal Processing
Volume68
DOIs
Publication statusPublished - Nov 2019

Keywords

  • correntropy
  • Matrix completion
  • matrix factorization
  • robust methods

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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