TY - GEN
T1 - Matrix completion by Truncated Nuclear Norm Regularization
AU - Zhang, Debing
AU - Hu, Yao
AU - Ye, Jieping
AU - Li, Xuelong
AU - He, Xiaofei
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84866667614&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84866667614&partnerID=8YFLogxK
U2 - 10.1109/CVPR.2012.6247927
DO - 10.1109/CVPR.2012.6247927
M3 - Conference contribution
AN - SCOPUS:84866667614
SN - 9781467312264
T3 - Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
SP - 2192
EP - 2199
BT - 2012 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2012
T2 - 2012 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2012
Y2 - 16 June 2012 through 21 June 2012
ER -