UM
A Regularized Variable Projection Algorithm for Separable Nonlinear Least-Squares Problems
Chen G.-Y.1; Gan M.1; Chen C.L.P.4; Li H.-X.2
2019-02-01
Source PublicationIEEE Transactions on Automatic Control
ISSN15582523 00189286
Volume64Issue:2Pages:526-537
AbstractSeparable nonlinear least-squares (SNLLS) problems arise frequently in many research fields, such as system identification and machine learning. The variable projection (VP) method is a very powerful tool for solving such problems. In this paper, we consider the regularization of ill-conditioned SNLLS problems based on the VP method. Selecting an appropriate regularization parameter is difficult because of the nonlinear optimization procedure. We propose to determine the regularization parameter using the weighted generalized cross-validation method at every iteration. This makes the original objective function changing during the optimization procedure. To circumvent this problem, we use an inequation to produce a consistent demand of decreasing at successive iterations. The approximation of the Jacobian of the regularized problem is also discussed. The proposed regularized VP algorithm is tested by the parameter estimation problem of several statistical models. Numerical results demonstrate the effectiveness of the proposed algorithm.
KeywordData fitting regularization separable nonlinear least squares (SNLLS) variable projection (VP) weighted generalized cross validation (WGCV)
DOI10.1109/TAC.2018.2838045
URLView the original
Language英語
Fulltext Access
Citation statistics
Cited Times [WOS]:46   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Affiliation1.Fuzhou University
2.City University of Hong Kong
3.Central South University China
4.Universidade de Macau
5.Institute of Automation Chinese Academy of Sciences
6.Ministry of Education China
7.Dalian Maritime University
Recommended Citation
GB/T 7714
Chen G.-Y.,Gan M.,Chen C.L.P.,et al. A Regularized Variable Projection Algorithm for Separable Nonlinear Least-Squares Problems[J]. IEEE Transactions on Automatic Control,2019,64(2):526-537.
APA Chen G.-Y.,Gan M.,Chen C.L.P.,&Li H.-X..(2019).A Regularized Variable Projection Algorithm for Separable Nonlinear Least-Squares Problems.IEEE Transactions on Automatic Control,64(2),526-537.
MLA Chen G.-Y.,et al."A Regularized Variable Projection Algorithm for Separable Nonlinear Least-Squares Problems".IEEE Transactions on Automatic Control 64.2(2019):526-537.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Chen G.-Y.]'s Articles
[Gan M.]'s Articles
[Chen C.L.P.]'s Articles
Baidu academic
Similar articles in Baidu academic
[Chen G.-Y.]'s Articles
[Gan M.]'s Articles
[Chen C.L.P.]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Chen G.-Y.]'s Articles
[Gan M.]'s Articles
[Chen C.L.P.]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.
 

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.