Selecting the Optimal Multidimensional Scaling Procedure for Metric Data With R Environment

Marek Walesiak , Andrzej Dudek

Abstract

In multidimensional scaling (MDS) carried out on the basis of a metric data matrix (interval, ratio), the main decision problems relate to the selection of the method of normalization of the values of the variables, the selection of distance measure and the selection of MDS model. The article proposes a solution that allows choosing the optimal multidimensional scaling procedure according to the normalization methods, distance measures and MDS model applied. The study includes 18 normalization methods, 5 distance measures and 3 types of MDS models (ratio, interval and spline). It uses two criteria for selecting the optimal multidimensional scaling procedure: Kruskal’s Stress-1 fit measure and Hirschman-Herfindahl HHI index calculated based on Stress per point values. The results are illustrated by an empirical example.
Author Marek Walesiak (EMaT / DEaCS)
Marek Walesiak,,
- Department of Econometrics and Computer Science
, Andrzej Dudek (EMaT / DEaCS)
Andrzej Dudek,,
- Department of Econometrics and Computer Science
Journal seriesStatistics in Transition. New Series, ISSN 1234-7655, e-ISSN 2450-0291, (B 15 pkt)
Issue year2017
Vol18
No3
Pages521-540
Publication size in sheets0.95
Keywords in Englishmultidimensional scaling, normalization of variables, distance measures, HHI index, R program
ASJC Classification1804 Statistics, Probability and Uncertainty; 2613 Statistics and Probability
DOIDOI:10.21307/stattrans-2016-084
URL http://stat.gov.pl/en/sit-en/issues-and-articles-sit/urrentissuse/
Languageen angielski
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Walesiak_Dudek_Selecting_the_Optimal_Multidimensional_Scaling.pdf 1,18 MB
Score (nominal)15
Score sourcejournalList
ScoreMinisterial score = 15.0, 27-11-2019, ArticleFromJournal
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2017 = 0.385
Citation count*12 (2019-12-05)
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
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