Work

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

Year: 2025

Type: article

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.

Source: Mathematics

DOI: 10.3390/math13162680

Authors: Yuefeng Qin, Chen Mao, Jiaofen Li

Institution: Guilin University of Electronic Technology

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funders: National Natural Science Foundation of China, Guilin University of Electronic Technology