Modified Gram-Schmidt Method-Based Variable Projection Algorithm for Separable Nonlinear Models - Details

author：

Chen, Guang-Yong (Chen, Guang-Yong.) ^[1] | Gan, Min (Gan, Min.) ^[2] | Ding, Feng (Ding, Feng.) ^[3] | Chen, C. L. Philip (Chen, C. L. Philip.) ^[4]

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Abstract：

Separable　nonlinear　models　are　very　common　in　various　research　fields,　such　as　machine　learning　and　system　identification.　The　variable　projection　(VP)　approach　is　efficient　for　the　optimization　of　such　models.　In　this　paper,　we　study　various　VP　algorithms　based　on　different　matrix　decompositions.　Compared　with　the　previous　method,　we　use　the　analytical　expression　of　the　Jacobian　matrix　instead　of　finite　differences.　This　improves　the　efficiency　of　the　VP　algorithms.　In　particular,　based　on　the　modified　Gram-Schmidt　(MGS)　method,　a　more　robust　implementation　of　the　VP　algorithm　is　introduced　for　separable　nonlinear　least-squares　problems.　In　numerical　experiments,　we　compare　the　performance　of　five　different　implementations　of　the　VP　algorithm.　Numerical　results　show　the　efficiency　and　robustness　of　the　proposed　MGS　method-based　VP　algorithm.　©　2012　IEEE.

Keyword：

Efficiency Jacobian matrices Least squares approximations Nonlinear systems Numerical methods Parameter estimation

Community：

[ 1 ] [Chen, Guang-Yong]College of Mathematics and Computer Science, Fuzhou University, Fuzhou; 350116, China
[ 2 ] [Chen, Guang-Yong]Fujian Provincial Key Laboratory of Network Computing and Intelligent Information Processing, Fuzhou University, Fuzhou; 350116, China
[ 3 ] [Chen, Guang-Yong]Key Laboratory of Spatial Data Mining and Information Sharing, Ministry of Education, Fuzhou; 350116, China
[ 4 ] [Chen, Guang-Yong]Center for Discrete Mathematics and Theoretical Computer Science, Fuzhou University, Fuzhou; 350116, China
[ 5 ] [Gan, Min]College of Mathematics and Computer Science, Fuzhou University, Fuzhou; 350116, China
[ 6 ] [Gan, Min]Fujian Provincial Key Laboratory of Network Computing and Intelligent Information Processing, Fuzhou University, Fuzhou; 350116, China
[ 7 ] [Gan, Min]Key Laboratory of Spatial Data Mining and Information Sharing, Ministry of Education, Fuzhou; 350116, China
[ 8 ] [Gan, Min]Center for Discrete Mathematics and Theoretical Computer Science, Fuzhou University, Fuzhou; 350116, China
[ 9 ] [Ding, Feng]College of Automation and Electronic Engineering, Qingdao University of Science and Technology, Qingdao; 266042, China
[ 10 ] [Ding, Feng]School of Internet of Things Engineering, Jiangnan University, Wuxi; 214122, China
[ 11 ] [Chen, C. L. Philip]Department of Computer and Information Science, Faculty of Science and Technology, University of Macau, 99999, China
[ 12 ] [Chen, C. L. Philip]Navigation College, Dalian Maritime University, Dalian; 116026, China
[ 13 ] [Chen, C. L. Philip]State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing; 100080, China

Reprint 's Address：

[gan, min]fujian provincial key laboratory of network computing and intelligent information processing, fuzhou university, fuzhou; 350116, china;;[gan, min]college of mathematics and computer science, fuzhou university, fuzhou; 350116, china;;[gan, min]center for discrete mathematics and theoretical computer science, fuzhou university, fuzhou; 350116, china;;[gan, min]key laboratory of spatial data mining and information sharing, ministry of education, fuzhou; 350116, china

Email：

aganmin@aliyun.com

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Source ：

IEEE Transactions on Neural Networks and Learning Systems

ISSN： 2162-237X

Year： 2019

Issue： 8

Volume： 30

Page： 2410-2418

8 . 7 9 3

JCR@2019

1 0 . 2 0 0

JCR@2023

ESI HC Threshold：162

JCR Journal Grade：1

CAS Journal Grade：1

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WoS CC Cited Count：

SCOPUS Cited Count：

ESI Highly Cited Papers on the List： 0 Unfold All

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Chinese Cited Count：

30 Days PV： 3

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