Multidimensional Scaling Using Majorization: SMACOF in R

By Jan de Leeuw, Patrick Mair. 2008

610 citations recorded by the source corpus.

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.

Subfields: Analytical Chemistry, Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/b8d16d3bcbd3e64c825d3dea94d718485fa51f1c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Analytical Chemistry

1. A. Enders
2. J. Uscinski
3. Justin Stoler
4. Casey A. Klofstad

In Applied Mathematics

1. A. Enders
2. Pieter Vermeesch
3. J. Uscinski
4. Eduardo Garzanti
5. Alberto Resentini
6. Justin Stoler
7. Casey A. Klofstad

In Computational Theory and Mathematics

1. A. Enders
2. J. Uscinski
3. Justin Stoler
4. Casey A. Klofstad

Citations in the corpus

• An R package for statistical provenance analysis (2016, background): “Another example is the introduction of weighted MDS (de Leeuw and Mair, 2009) to handle, say, datasets containing samples of widely different sizes.”
• The different forms of COVID-19 misinformation and their consequences (2020, methodology): “We use the “smacof” package in the R statistical computing environment to execute this analysis (De Leeuw & Mair, 2009).”