Published by the Foundation for Open Access Statistics Editors-in-chief: Bettina Grün, Torsten Hothorn, Rebecca Killick, Edzer Pebesma, Achim Zeileis    ISSN 1548-7660; CODEN JSSOBK
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Authors: Patrick J. F. Groenen, Michel van de Velden
Title: Multidimensional Scaling by Majorization: A Review
Abstract: A major breakthrough in the visualization of dissimilarities between pairs of objects was the formulation of the least-squares multidimensional scaling (MDS) model as defined by the Stress function. This function is quite flexible in that it allows possibly nonlinear transformations of the dissimilarities to be represented by distances between points in a low dimensional space. To obtain the visualization, the Stress function should be minimized over the coordinates of the points and the over the transformation. In a series of papers, Jan de Leeuw has made a significant contribution to majorization methods for the minimization of Stress in least-squares MDS. In this paper, we present a review of the majorization algorithm for MDS as implemented in the smacof package and related approaches. We present several illustrative examples and special cases.

Page views:: 3230. Submitted: 2016-03-24. Published: 2016-09-12.
Paper: Multidimensional Scaling by Majorization: A Review     Download PDF (Downloads: 2591)
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DOI: 10.18637/jss.v073.i08

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Paper: Creative Commons Attribution 3.0 Unported License
Code: GNU General Public License (at least one of version 2 or version 3) or a GPL-compatible license.