Matrix completion by Truncated Nuclear Norm Regularization

Debing Zhang, Yao Hu, Jieping Ye, Xuelong Li, Xiaofei He

Research output: Chapter in Book/Report/Conference proceedingConference contribution

70 Scopus citations

Abstract

Estimating missing values in visual data is a challenging problem in computer vision, which can be considered as a low rank matrix approximation problem. Most of the recent studies use the nuclear norm as a convex relaxation of the rank operator. However, by minimizing the nuclear norm, all the singular values are simultaneously minimized, and thus the rank can not be well approximated in practice. In this paper, we propose a novel matrix completion algorithm based on the Truncated Nuclear Norm Regularization (TNNR) by only minimizing the smallest N-r singular values, where N is the number of singular values and r is the rank of the matrix. In this way, the rank of the matrix can be better approximated than the nuclear norm. We further develop an efficient iterative procedure to solve the optimization problem by using the alternating direction method of multipliers and the accelerated proximal gradient line search method. Experimental results in a wide range of applications demonstrate the effectiveness of our proposed approach.

Original languageEnglish (US)
Title of host publication2012 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2012
Pages2192-2199
Number of pages8
DOIs
StatePublished - Oct 1 2012
Event2012 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2012 - Providence, RI, United States
Duration: Jun 16 2012Jun 21 2012

Publication series

NameProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
ISSN (Print)1063-6919

Other

Other2012 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2012
CountryUnited States
CityProvidence, RI
Period6/16/126/21/12

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition

Cite this

Zhang, D., Hu, Y., Ye, J., Li, X., & He, X. (2012). Matrix completion by Truncated Nuclear Norm Regularization. In 2012 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2012 (pp. 2192-2199). [6247927] (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition). https://doi.org/10.1109/CVPR.2012.6247927