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Effective Algorithms for Solving Trace Minimization Problem in Multivariate Statistics
Joint Authors
Li, Jiao-fen
Wen, Ya-qiong
Zhou, Xue-lin
Wang, Kai
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-24, 24 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-08-10
Country of Publication
Egypt
No. of Pages
24
Main Subjects
Abstract EN
This paper develops two novel and fast Riemannian second-order approaches for solving a class of matrix trace minimization problems with orthogonality constraints, which is widely applied in multivariate statistical analysis.
The existing majorization method is guaranteed to converge but its convergence rate is at best linear.
A hybrid Riemannian Newton-type algorithm with both global and quadratic convergence is proposed firstly.
A Riemannian trust-region method based on the proposed Newton method is further provided.
Some numerical tests and application to the least squares fitting of the DEDICOM model and the orthonormal INDSCAL model are given to demonstrate the efficiency of the proposed methods.
Comparisons with some latest Riemannian gradient-type methods and some existing Riemannian second-order algorithms in the MATLAB toolbox Manopt are also presented.
American Psychological Association (APA)
Li, Jiao-fen& Wen, Ya-qiong& Zhou, Xue-lin& Wang, Kai. 2020. Effective Algorithms for Solving Trace Minimization Problem in Multivariate Statistics. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-24.
https://search.emarefa.net/detail/BIM-1194155
Modern Language Association (MLA)
Li, Jiao-fen…[et al.]. Effective Algorithms for Solving Trace Minimization Problem in Multivariate Statistics. Mathematical Problems in Engineering No. 2020 (2020), pp.1-24.
https://search.emarefa.net/detail/BIM-1194155
American Medical Association (AMA)
Li, Jiao-fen& Wen, Ya-qiong& Zhou, Xue-lin& Wang, Kai. Effective Algorithms for Solving Trace Minimization Problem in Multivariate Statistics. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-24.
https://search.emarefa.net/detail/BIM-1194155
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1194155