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

The classical INdividual Differences SCALing (INDSCAL) model is widely used for simultaneous metric multidimensional scaling (MDS) of multiple doubly centered squared dissimilarity matrices. An alternative approach, called for short direct INDSCAL, is proposed for analyzing directly the input matrices of squared dissimilarities. An important consequence is that missing values can be easily handled. In this study, we reformulate the fitting of the direct INDSCAL model with missing values as a Riemannian optimization problem defined on a product manifold consisting of Stiefel sub-manifold of zero column-sums matrices and non-negative diagonal matrices. To address this problem, we propose a simple and efficient Riemannian gradient algorithm incorporating the Zhang-Hager nonmonotone line search strategy. The global convergence of the method is established. Extensive numerical experiments are provided to illustrate the computational effectiveness of the proposed approach and to benchmark its performance against several state-of-the-art methods. Mathematics subject classification:15A24, 15A57, 65C60, 65F30