Multidimensional scaling using majorization: SMACOF in R

Abstract

In this paper we present the methodology of multidimensional scaling problems (MDS) solved by means of the majorization algorithm. The objective function to be minimized is known as stress and functions which majorize stress are elaborated. This strategy to solve MDS problems is called SMACOF and it is implemented in an R package of the same name which is presented in this article. We extend the basic SMACOF theory in terms of configuration constraints, three-way data, unfolding models, and projection of the resulting configurations onto spheres and other quadratic surfaces. Various examples are presented to show the possibilities of the SMACOF approach offered by the corresponding package.