Efficient Iterative Methods for Direct INDSCAL with Missing Values in Metric Multidimensional Scaling

Time: 2026-04-23 21:01:00

Title: Efficient Iterative Methods for Direct INDSCAL with Missing Values in Metric Multidimensional Scaling
Speaker: Prof. Jiaofen Li (Invited by Prof. Xiaoshan Chen)
Guilin University of Electronic Technology
Time: April 23, 11:00–12:00
Venue: Room 401, East Building, School of Mathematical Sciences

Speaker Biography:
    Jiaofen Li is a professor and doctoral supervisor at Guilin University of Electronic Technology. She has conducted academic visits to Southern Illinois University (USA), the University of Macau, and others. Her research interests lie in numerical algebra and its applications. She has led four projects funded by the National Natural Science Foundation of China, and her research achievements have been recognized with the second and third prizes of the Guangxi Natural Science Award. In recent years, as first author or corresponding author, she has published more than 30 SCI papers in renowned domestic and international journals, including IMA Journal of Numerical Analysis, Journal of Scientific Computing, Advances in Computational Mathematics, BIT Numerical Mathematics, Statistics and Computing, and Computational Optimization and Applications.

Abstract:
    The classical INdividual Differences SCALing (INDSCAL) model is a standard framework for simultaneous metric multidimensional scaling (MDS) of multiple dissimilarity matrices. Its direct INDSCAL variant works directly with squared dissimilarities on the product manifold O0(n, r) x D(r)m and naturally accommodates missing entries via indicator-weighted residuals. While this formulation and its Riemannian structure are well documented in the literature, comparatively little attention has been given to simple, first-order algorithms tailored to this setting with missing data. In this talk, we revisit direct INDSCAL fitting with missing values from a Riemannian optimization perspective and develop a streamlined Riemannian gradient method equipped with a Zhang–Hager-type nonmonotone line search. The proposed scheme avoids both Riemannian Hessian evaluations and vector transport operations, admits global convergence guarantees under standard assumptions, and has low per-iteration cost. Extensive numerical experiments on synthetic datasets with systematically controlled missing rates and on two real data sets show that the proposed method delivers solution quality comparable to that of classical projected gradient flows, several first- and second-order solvers from the Manopt toolbox, and three representative Riemannian conjugate-gradient algorithms, while often achieving lower runtime and stable performance across a range of missing-data patterns. These results indicate that the proposed first-order scheme is a practical and efficient alternative for medium- to large-scale direct INDSCAL problems with incomplete dissimilarity information.