Document Type
Journal Article
Department/Unit
Department of Mathematics
Title
Folded-concave penalization approaches to tensor completion
Language
English
Abstract
© 2014 Elsevier B.V.The existing studies involving matrix or tensor completion problems are commonly under the nuclear norm penalization framework due to the computational efficiency of the resulting convex optimization problem. Folded-concave penalization methods have demonstrated surprising developments in sparse learning problems due to their nice practical and theoretical properties. To share the same light of folded-concave penalization methods, we propose a new tensor completion model via folded-concave penalty for estimating missing values in tensor data. Two typical folded-concave penalties, the minmax concave plus (MCP) penalty and the smoothly clipped absolute deviation (SCAD) penalty, are employed in the new model. To solve the resulting nonconvex optimization problem, we develop a local linear approximation augmented Lagrange multiplier (LLA-ALM) algorithm which combines a two-step LLA strategy to search a local optimum of the proposed model efficiently. Finally, we provide numerical experiments with phase transitions, synthetic data sets, real image and video data sets to exhibit the superiority of the proposed model over the nuclear norm penalization method in terms of the accuracy and robustness.
Keywords
Folded-concave penalization, Local linear approximation, Nuclear norm, Sparse learning, Tensor completion
Publication Date
2015
Source Publication Title
Neurocomputing
Volume
152
Start Page
261
End Page
273
Publisher
Elsevier
DOI
10.1016/j.neucom.2014.10.069
Link to Publisher's Edition
http://dx.doi.org/10.1016/j.neucom.2014.10.069
ISSN (print)
09252312
Recommended Citation
Cao, Wenfei, Yao Wang, Can Yang, Xiangyu Chang, Zhi Han, and Zongben Xu. "Folded-concave penalization approaches to tensor completion." Neurocomputing 152 (2015): 261-273.