ε -Algorithm Accelerated Fixed-Point Iteration for the Three-Way GIPSCAL Problem in Asymmetric MDS

Yuefeng Qin (), Chen Mao and Jiaofen Li
Additional contact information
Yuefeng Qin: School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin 541004, China
Chen Mao: School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin 541004, China
Jiaofen Li: School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin 541004, China

Mathematics, 2025, vol. 13, issue 16, 1-30

Abstract: The Generalized Inner Product SCALing (GIPSCAL) model is a specialized tool for analyzing square asymmetric tables within asymmetric multidimensional scaling (MDS), with applications in sociology (e.g., social mobility tables) and marketing (e.g., brand switching data). This paper presents the development of an efficient numerical algorithm for solving the three-way GIPSCAL problem. We focus on vector ε -algorithm-accelerated fixed-point iterations, detailing the underlying acceleration principles. Extensive numerical experiments show that the proposed method achieves acceleration performance comparable to polynomial extrapolation and Anderson acceleration. Furthermore, compared to continuous-time projected gradient flow methods and first- and second-order Riemannian optimization algorithms from the Manopt toolbox, our approach demonstrates superior computational efficiency and scalability.

Keywords: multidimensional scaling; three-way asymmetric data; generalized inner product scaling; ε-algorithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/16/2680/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/16/2680/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:16:p:2680-:d:1728744

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().