findOptimalIscalInterval: Selecting the optimal I-Scal multidimensional scaling...

In mdsOpt: Searching for Optimal MDS Procedure for Metric, Nonmetric and Interval-Valued Data

Selecting the optimal I-Scal multidimensional scaling procedure for interval-valued data

Description

Selecting the optimal multidimensional scaling procedure - I-Scal (by varying all combinations of normalization and optimization methods)

Usage

findOptimalIscalInterval(table,critical_stress=
(max(as.numeric(gsub(",",".",table[,"I-STRESS"],fixed=TRUE)))+
min(as.numeric(gsub(",",".",table[,"I-STRESS"],fixed=TRUE))))/2,
critical_HHI=NA)

Arguments

table	result from optSmacofSym_nMDS. Data frame ordered by increasing value of I-Stress fit measure with columns: Normalization method Optimization method I-STRESS HHI spb
critical_stress	threshold value of I-Stress fit measure. Default - mid-range of I-Stress fit measures calculated for all MDS procedures
critical_HHI	threshold value of Hirschman-Herfindahl HHI index. Only one parameter critical_stress or critical_HHI can be set, and the function finds the optimal value among the procedures for which the selected measure is lower or equal treshold value

Value

Nr	number of row in table with optimal multidimensional scaling procedure
Normalization_method	normalization method used for optimal multidimensional scaling procedure
Opt_method	optimization method in I-Scal procedure: "MM" - the majorization minimization algortihm,"BFGS" - Broyden–Fletcher–Goldfarb–Shanno algorithm
I_STRESS	value I-Stress fit measure for optimal multidimensional scaling procedure
HHI_spb	Herfindahl-Hirschman HHI index, calculated based on stress per box, for optimal multidimensional scaling procedure

Author(s)

Marek Walesiak [e-mail]

Department of Econometrics and Computer Science, Wroclaw University of Economics and Business, Poland

Andrzej Dudek [e-mail]

Department of Financial Investments and Risk Management, Wroclaw University of Economics and Business, Poland

References

Borg, I., Groenen, P.J.F. (2005), Modern Multidimensional Scaling. Theory and Applications, 2nd Edition, Springer Science+Business Media, New York. ISBN: 978-0387-25150-9. Available at: https://link.springer.com/book/10.1007/0-387-28981-X.

Borg, I., Groenen, P.J.F., Mair, P. (2013), Applied Multidimensional Scaling, Springer, Heidelberg, New York, Dordrecht, London. Available at: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/978-3-642-31848-1")}.

Groenen, P.J.F. Winsberg, S., Rodriguez, O., Diday, E. (2006), I-Scal: Multidimensional scaling of interval dissimilarities, Computational Statistics & Data Analysis, 51(1), 360–378. Available at: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.csda.2006.04.003")}.

Herfindahl, O.C. (1950), Concentration in the Steel Industry, Doctoral thesis, Columbia University.

Hirschman, A.O. (1964), The Paternity of an Index, The American Economic Review, Vol. 54, 761-762.

Walesiak, M. (2014), Przegląd formuł normalizacji wartości zmiennych oraz ich własności w statystycznej analizie wielowymiarowej [Data Normalization in Multivariate Data Analysis. An Overview and Properties], Przegląd Statystyczny, tom 61, z. 4, 363-372

Walesiak, M. (2016), Visualization of Linear Ordering Results for Metric Data with the Application of Multidimensional Scaling, Ekonometria, 2(52), 9-21. Available at: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.15611/ekt.2016.2.01")}.

Walesiak, M., Dudek, A. (2017), Selecting the Optimal Multidimensional Scaling Procedure for Metric Data with R Environment, STATISTICS IN TRANSITION new series, September, Vol. 18, No. 3, pp. 521-540. Available at: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.59170/stattrans-2017-027")}.

Walesiak, M., Dehnel, G. (2020), The Measurement of Social Cohesion at Province Level in Poland Using Metric and Interval-Valued Data, Sustainability, 12(18), 7664, 1-19. Available at: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.3390/su12187664")}.

Walesiak, M., Dehnel, G., Dudek, A. (2025), Visualisation of linear ordering results using multidimensional scaling – problems and an overview of studies, Argumenta Oeconomica, No 1 (54), 187-203. Available at: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.15611/aoe.2025.1.12")}.

Walesiak, M., Dehnel, G. (2026), Assessment of the implementation of SDG 4 goal by EU countries in the light of the 2030 Agenda using a hybrid approach in linear ordering, PLoS ONE 21(6): e0333545. Available at: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1371/journal.pone.0333545")}.

See Also

data.Normalization, interval_normalization

Examples

  
  library(clusterSim)
  library(mdsOpt)
  data(data_symbolic_interval_polish_voivodships)
  x<-data_symbolic_interval_polish_voivodships
  metnor<-c("n1","n2","n3","n5","n5a","n8","n9","n9a","n11","n12a")
  methods<-c("MM","BFGS")
  w<-optIscalInterval(x,dataType="simple",normalizations=metnor,optMethods=methods,outDec=".")
  print(findOptimalIscalInterval(w))
  

mdsOpt documentation built on Oct. 2, 2026, 5:09 p.m.