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

Author

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  • 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
    Center for Applied Mathematics of Guangxi (GUET), Guilin 541004, China)

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.

Suggested Citation

  • Yuefeng Qin & Chen Mao & Jiaofen Li, 2025. "ε -Algorithm Accelerated Fixed-Point Iteration for the Three-Way GIPSCAL Problem in Asymmetric MDS," Mathematics, MDPI, vol. 13(16), pages 1-30, August.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:16:p:2680-:d:1728744
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