A Riemannian Inexact-Newton Method for Solving the Orthogonal INDSCAL Problem in Multidimensional Scaling

A Riemannian Inexact-Newton Method for Solving the Orthogonal INDSCAL Problem in Multidimensional Scaling | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A Riemannian Inexact-Newton Method for Solving the Orthogonal INDSCAL Problem in Multidimensional Scaling Xue-lin Zhou, Chao-qian Li, Jiao-fen Li This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4910274/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The well-known individual differences scaling (INDSCAL) model is intended for simultaneous metric multidimensional scaling (MDS) of several doubly centered matrices of squared dissimilarities. In this work, the problem of fitting the orthogonal INDSCAL model to the data is reformulated and studied as a matrix optimization problem on the product manifold of orthonormal and diagonal matrices. A Riemannian inexact Newton method is proposed to address the underlying problem, with the global and quadratic convergence of the proposed method established under some mild assumptions. Furthermore, the positive definiteness condition of the Riemannian Hessian of the objective function at a solution is derived. Some numerical experiments are provided to illustrate the efficiency of the proposed method. Mathematics subject classification: 15A24; 15A57; 65F10; 65F30 Computational Mathematics Numerical Analysis Applied Statistics Multidimensional scaling Individual differences scaling Riemannian optimization Inexact Newton method Full Text Additional Declarations The authors declare no competing interests. Supplementary Files Matlabcodes.rar Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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