NDLI: Matrix completion via capped nuclear norm

Content Provider	IET Digital Library
Author	Zhang, Fanlong Yang, Zhangjing Chen, Yu Yang, Jian Yang, Guowei
Abstract	Matrix completion is to recover a low-rank matrix from a subset of its entries. One of the solution strategies is based on nuclear norm minimisation. However, since the nuclear norm is defined as the sum of all singular values, each of which is treated equally, the rank function may not be well approximated in practice. To overcome this drawback, this study presents a matrix completion method based on capped nuclear norm (MC-CNN). The capped nuclear norm can reflect the rank function more directly and accurately than the nuclear norm, Schatten p-norm (to the power p) and truncated nuclear norm. The relation between the capped nuclear norm and the truncated nuclear norm is revealed for the first time. Difference of convex functions’ programming is employed to solve MC-CNN. In the proposed algorithm, a key sub-problem, i.e. a matrix completion problem with linear regularisation term, is solved by using the active subspace selection method. In addition, the algorithm convergence is discussed. Experimental results show encouraging results of the proposed algorithm in comparison with the state-of-the-art matrix completion methods on both synthetic and real visual datasets.
Starting Page	959
Ending Page	966
Page Count	8
ISSN	17519659
Volume Number	12
e-ISSN	17519667
Issue Number	Issue 6, Jun (2018)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-ipr/12/6
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-ipr.2017.0515
Journal	IET Image Processing
Publisher Date	2018-01-22
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Active Subspace Selection Method Algebra Algorithm Convergence Berkeley Segmentation Dataset Capped Nuclear Norm Computer Vision And Image Processing Technique Convergence Convex Function Programming Image Segmentation Linear Regularisation Term Low-rank Matrix Recovery Matrix Completion MC-CNN Nuclear Norm Minimisation Optical, Image And Video Signal Processing Rank Function Real Visual Datasets Schatten P-norm Singular Value Singular Value Decomposition Synthetic Visual Datasets Truncated Nuclear Norm
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering Computer Vision and Pattern Recognition Software

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