勷勤数学•专家报告

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

报  告  人： 李姣芬 教授  (邀请人：陈小山)

                                                  桂林电子科技大学

时      间： 4月23日  11：00-12:00

地     点：数科院东楼401

报告人简介:

          李姣芬，桂林电子科技大学教授，博士生导师。曾访问美国南伊利诺伊大学、澳门大学等，研究方向数值代数及其应用。主持国家自然科学基金项目4项，研究成果获广西自然科学奖二等奖和三等奖。 近年来以第一作者或通讯作者在IMA Journal of Numerical Analysis, Journal of Scientific Computing, Advances in Computational Mathematics, BIT Numerical Mathematics, Statistics and Computing, Computational Optimization and Applications 等国内外权威期刊发表SCI论文30余篇。

摘      要：

         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.

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