Title:	Searching for Optimal MDS Procedure for Metric and Interval-Valued Data
Version:	0.7-7
Date:	2025-06-26
Depends:	R (≥ 3.6.0), smacof, clusterSim, symbolicDA
Imports:	animation, plotrix, spdep
Suggests:	testthat, R.rsp
VignetteBuilder:	R.rsp
Description:	Selecting the optimal multidimensional scaling (MDS) procedure for metric data via metric MDS (ratio, interval, mspline) and nonmetric MDS (ordinal). Selecting the optimal multidimensional scaling (MDS) procedure for interval-valued data via metric MDS (ratio, interval, mspline).Selecting the optimal multidimensional scaling procedure for interval-valued data by varying all combinations of normalization and optimization methods.Selecting the optimal MDS procedure for statistical data referring to the evaluation of tourist attractiveness of Lower Silesian counties. (Borg, I., Groenen, P.J.F., Mair, P. (2013) <doi:10.1007/978-3-642-31848-1>, Walesiak, M. (2016) <doi:10.15611/ekt.2016.2.01>, Walesiak, M. (2017) <doi:10.15611/ekt.2017.3.01>).
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Encoding:	UTF-8
NeedsCompilation:	no
Packaged:	2025-06-27 09:59:17 UTC; andrzej
Author:	Marek Walesiak [aut], Andrzej Dudek [aut, cre]
Maintainer:	Andrzej Dudek <andrzej.dudek@ue.wroc.pl>
Repository:	CRAN
Date/Publication:	2025-06-27 12:10:02 UTC

The evaluation of tourist attractiveness of Lower Silesian counties

Description

The empirical study uses the statistical data presented in the article (Gryszel, Walesiak, 2014) and referring to the attractiveness level of 31 objects (29 Lower Silesian counties, pattern and antipattern object) The evaluation of tourist attractiveness of Lower Silesian counties was performed using 16 metric variables (measured on a ratio scale): x1 – beds in hotels per 1 km2 of a county area, x2 – number of nights spent daily by resident tourists per 1000 inhabitants of a county, x3 – number of nights spent daily by foreign tourists per 1000 inhabitants of a county, x4 – gas pollution emission in tons per 1 km2 of a county area, x5 – number of criminal offences and crimes against life and health per 1000 inhabitants of a county, x6 – number of property crimes per 1000 inhabitants of a county, x7 – number of historical buildings per 100 km2 of a county area, x8 – x9 – x10 – number of events as well as cultural and tourist ventures in a county, x11 – number of natural monuments calculated per 1 km2 of a county area, x12 – number of tourist economy entities per 1000 inhabitants of a county (natural and legal persons), x13 – expenditure of municipalities and counties on tourism, culture and national heritage protection as well as physical culture per 1 inhabitant of a county in PLN, x14 – viewers in cinemas per 1000 inhabitants of a county, x15 – museum visitors per 1000 inhabitants of a county, x16 – number of construction permits (hotels and accommodation buildings, commercial and service buildings, transport and communication buildings, civil and water engineering constructions) issued in a county in the years 2011-2012 per 1 km2 of a county area. The statistical data were collected in 2012 and come from the Local Data Bank of the Central Statistical Office of Poland, the data for x7 variable only were obtained from the regional conservation officer.

Format

data.frame: 31 objects (29 counties, pattern and antipattern object), 16 variables. The coordinates of a pattern object cover the most preferred preference variable (stimulants, destimulants, nominants) values. The coordinates of an anti-pattern object cover the least preferred preference variable values.

Source

Gryszel, P., Walesiak, M., (2014), Zastosowanie uogólnionej miary odległości GDM w ocenie atrakcyjności turystycznej powiatów Dolnego Śląska [The Application of the General Distance Measure (GDM) in the Evaluation of Lower Silesian Districts’ Attractiveness], Folia Turistica, 31, 127-147.

Examples

  library(mdsOpt)
  metnor<-c("n1","n2","n3","n5","n5a","n8","n9","n9a","n11","n12a")
  metscale<-c("ratio","interval")
  metdist<-c("euclidean","GDM1")
  data(data_lower_silesian)
  res<-optSmacofSym_mMDS(data_lower_silesian,normalizations=metnor,
  distances=metdist,mdsmodels=metscale)
  print(findOptimalSmacofSym(res))
  

draw series of isoquants

Description

function draw series of isoquants (a contour line drawn through the set of points at which the same quantity of output is produced while changing the quantities of two or more inputs)

Usage

drawIsoquants(x,y=NULL,number=6,steps=NULL)

Arguments

Value

This is a plotting function, thus does not return any value

Author(s)

Marek Walesiak marek.walesiak@ue.wroc.pl, Andrzej Dudek andrzej.dudek@ue.wroc.pl

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

References

Walesiak, M., (2016), Visualization of Linear Ordering Results for Metric Data with the Application of Multidimensional Scaling, Ekonometria, 2(52), 9-21. Available at: doi:10.15611/ekt.2016.2.01.

Walesiak, M. (2017), The application of multidimensional scaling to measure and assess changes in the level of social cohesion of the Lower Silesia region in the period 2005-2015, Ekonometria, 3(57), 9-25. Available at: doi:10.15611/ekt.2017.3.01.

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.

Examples

#Example 1
library(mdsOpt)
library(smacof)
library(clusterSim)
data(data_lower_silesian)
z<-data.Normalization(data_lower_silesian, type="n1")
d<-dist.GDM(z, method="GDM1")
res <- smacofSym(delta=d,ndim=2,type="interval")
print("Objects configuration", quote=FALSE)
plot(res, plot.type="confplot")
r1<-res$conf[nrow(z),1]
r2<-res$conf[nrow(z),2]
r3<-res$conf[nrow(z)-1,1]
r4<-res$conf[nrow(z)-1,2]
arrows(r1,r2,r3,r4,length=0.1,col="black")
res_up<-as.matrix(dist(res$conf,method="euclidean"))
drawIsoquants(res$conf[nrow(z)-1,],steps=max(res_up)/6)
# or 
# drawIsoquants(res$conf[nrow(z)-1,],steps=c(0.3,0.2),number=8)

#Example 2
library(mdsOpt)
library(smacof)
library(clusterSim)
data(data_lower_silesian)
z<-data.Normalization(data_lower_silesian, type="n1")
d<-dist.GDM(z, method="GDM1")
res<-smacofSym(delta=d,ndim=2,type="interval")
res1<-res$conf
#write.table(res1,"conf_2d.csv",dec=",",sep=";",col.names=NA,row.names=TRUE)
alfa<- 1.05*pi
a<- cos(alfa)
b<- -sin(alfa)
c<- sin(alfa)
d<- cos(alfa)
D<-array(c(a,b,c,d), c(2,2))
#res1<-read.csv2("conf_2d.csv", header=TRUE, row.names=1)
res1<-as.matrix(res1)
res2<-res1
plot(res2, xlab="Dimension 1",ylab="Dimension 2",main="",asp=1)
points(res2[1:31,],pch=1,font=2)
text(res2[c(1:31),],pos=3,cex=0.7,row.names(z[c(1:31),]))
r1<-res2[nrow(z),1]
r2<-res2[nrow(z),2]
r3<-res2[nrow(z)-1,1]
r4<-res2[nrow(z)-1,2]
arrows(r1,r2,r3,r4,length=0.1,col="black")
res_up<-as.matrix(dist(res2,method="euclidean"))
drawIsoquants(res2[nrow(z)-1,],steps=max(res_up)/6)

Selecting the optimal multidimensional scaling (MDS) procedure

Description

Selecting the optimal multidimensional scaling procedure - metric MDS (by varying all combinations of normalization methods, distance measures, and metric MDS models) and nonmetric MDS (by varying all combinations of normalization methods and distance measures)

Usage

findOptimalSmacofSym(table,
critical_stress=(max(as.numeric(gsub(",",".",table[,"STRESS 1"],fixed=TRUE)))+
min(as.numeric(gsub(",",".",table[,"STRESS 1"],fixed=TRUE))))/2,
critical_HHI=NA)

Arguments

Value

Author(s)

Marek Walesiak marek.walesiak@ue.wroc.pl, Andrzej Dudek andrzej.dudek@ue.wroc.pl

Department of Econometrics and Computer Science, 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: doi:10.1007/978-3-642-31848-1.

De Leeuw, J., Mair, P. (2015), Shepard Diagram, Wiley StatsRef: Statistics Reference Online, John Wiley & Sons Ltd.

Dudek, A., Walesiak, M. (2020), The Choice of Variable Normalization Method in Cluster Analysis, pp. 325-340, [In:] K. S. Soliman (Ed.), Education Excellence and Innovation Management: A 2025 Vision to Sustain Economic Development during Global Challenges, Proceedings of the 35th International Business Information Management Association Conference (IBIMA), 1-2 April 2020, Seville, Spain. ISBN: 978-0-9998551-4-1.

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. Available at: doi:10.5604/01.3001.0016.1740.

Walesiak, M. (2016a), Wybór grup metod normalizacji wartości zmiennych w skalowaniu wielowymiarowym [The Choice of Groups of Variable Normalization Methods in Multidimensional Scaling], Przegląd Statystyczny, tom 63, z. 1, 7-18. Available at: doi:10.5604/01.3001.0014.1145.

Walesiak, M. (2016b), Visualization of Linear Ordering Results for Metric Data with the Application of Multidimensional Scaling, Ekonometria, 2(52), 9-21. Available at: 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.

Walesiak, M., Dudek, A. (2020), Searching for an Optimal MDS Procedure for Metric and Interval-Valued Data using mdsOpt R package, pp. 307-324, [In:] K. S. Soliman (Ed.), Education Excellence and Innovation Management: A 2025 Vision to Sustain Economic Development during Global Challenges, Proceedings of the 35th International Business Information Management Association Conference (IBIMA), 1-2 April 2020, Seville, Spain. ISBN: 978-0-9998551-4-1.

See Also

data.Normalization, dist.GDM, dist, smacofSym

Examples

  
  library(mdsOpt)
  metnor<-c("n1","n2","n3","n5","n5a","n8","n9","n9a","n11","n12a")
  metscale<-c("ratio","interval")
  metdist<-c("euclidean","manhattan","maximum","seuclidean","GDM1")
  data(data_lower_silesian)
  res<-optSmacofSym_mMDS(data_lower_silesian,normalizations=metnor,
  distances=metdist,mdsmodels=metscale,outDec=".")
  print(findOptimalSmacofSym(res))
  

Selecting the optimal multidimensional scaling procedure for interval-valued data

Description

Selecting the optimal multidimensional scaling procedure by varying all combinations of normalization methods, distance measures for interval-valued data, and metric MDS models/

Usage

optSmacofSymInterval(x,dataType="simple",normalizations=NULL,
distances=NULL,mdsmodels=NULL,spline.degrees=c(2),outputCsv="",
outputCsv2="",y=NULL,outDec=",",
stressDigits=6,HHIDigits=2,...)

Arguments

Details

Parameter normalizations may be the subset of the following values:

"n1","n2","n3","n3a","n4","n5","n5a","n6","n6a",

"n7","n8","n9","n9a","n10","n11","n12","n12a","n13"

(e.g. normalizations=c("n1","n2","n3","n5","n5a",

"n8","n9","n9a","n11","n12a"))

if normalizations is set to "n0" no normalization is applied

Parameter distances may be the subset of the following values:

"H_q1","H_q2","U_2_q1","U_2_q2" (In following order: Hausdorff distance with q=1, Euclidean Hausdorff distance with q=2, Ichino-Yaguchi distance with q=1; Euclidean Ichino-Yaguchi distance with q=2)

(e.g. distances=c("H_q1","U_2_q1"))

Parameter mdsmodels may be the subset of the following values (metric MDS):

"ratio","interval","mspline" (e.g. c("ratio","interval"))

Value

Data frame ordered by increasing value of Stress-1 fit measure with columns:

Author(s)

Marek Walesiak marek.walesiak@ue.wroc.pl, Andrzej Dudek andrzej.dudek@ue.wroc.pl

Department of Econometrics and Computer Science, 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: doi:10.1007/978-3-642-31848-1.

De Leeuw, J., Mair, P. (2015), Shepard Diagram, Wiley StatsRef: Statistics Reference Online, John Wiley & Sons Ltd.

Dudek, A., Walesiak, M. (2020), The Choice of Variable Normalization Method in Cluster Analysis, pp. 325-340, [In:] K. S. Soliman (Ed.), Education Excellence and Innovation Management: A 2025 Vision to Sustain Economic Development during Global Challenges, Proceedings of the 35th International Business Information Management Association Conference (IBIMA), 1-2 April 2020, Seville, Spain. ISBN: 978-0-9998551-4-1.

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. Available at: doi:10.5604/01.3001.0016.1740.

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.

Walesiak, M., Dudek, A. (2020), Searching for an Optimal MDS Procedure for Metric and Interval-Valued Data using mdsOpt R package, pp. 307-324, [In:] K. S. Soliman (Ed.), Education Excellence and Innovation Management: A 2025 Vision to Sustain Economic Development during Global Challenges, Proceedings of the 35th International Business Information Management Association Conference (IBIMA), 1-2 April 2020, Seville, Spain. ISBN: 978-0-9998551-4-1.

See Also

data.Normalization, interval_normalization, dist.Symbolic, smacofSym

Examples

  
 library(mdsOpt)
 library(clusterSim)
 data(data_symbolic_interval_polish_voivodships)
 metnor<-c("n1","n2","n3","n5","n5a","n8","n9","n9a","n11","n12a")
 metscale<-c("ratio","interval","mspline")
 metdist<-c("H_q1","H_q2","U_2_q1","U_2_q2")
 res<-optSmacofSymInterval(data_symbolic_interval_polish_voivodships,dataType="simple",
 normalizations=metnor,distances=metdist,mdsmodels=metscale,spline.degrees=c(2,3),outDec=".")
 stress<-as.numeric(gsub(",",".",res[,"STRESS 1"],fixed=TRUE))
 hhi<-as.numeric(gsub(",",".",res[,"HHI spp"],fixed=TRUE))
 t<-findOptimalSmacofSym(res)
 cs<-(min(stress)+max(stress))/2 # critical stress
 plot(stress[-t$Nr],hhi[-t$Nr], xlab="Stress-1", ylab="HHI",type="n",font.lab=3)
 text(stress[-t$Nr],hhi[-t$Nr],labels=(1:nrow(res))[-t$Nr])
 abline(v=cs,col="red")
 points(stress[t$Nr],hhi[t$Nr], cex=5,col="red")
 text(stress[t$Nr],hhi[t$Nr],labels=(1:nrow(res))[t$Nr],col="red")
 print(t)
 

Selecting the optimal multidimensional scaling procedure - metric MDS

Description

Selecting the optimal multidimensional scaling procedure by varying all combinations of normalization methods, distance measures, and metric MDS models

Usage

optSmacofSym_mMDS(x,normalizations=NULL,distances=NULL,
mdsmodels=NULL,weights=NULL,spline.degrees=c(2),
outputCsv="",outputCsv2="",outDec=",",
stressDigits=6,HHIDigits=2,...)

Arguments

Details

Parameter normalizations may be the subset of the following values:

"n1","n2","n3","n3a","n4","n5","n5a","n6","n6a",

"n7","n8","n9","n9a","n10","n11","n12","n12a","n13"

(e.g. normalizations=c("n1","n2","n3","n5","n5a",

"n8","n9","n9a","n11","n12a"))

if normalizations is set to "n0" no normalization is applied

Parameter distances may be the subset of the following values:

"euclidean","manhattan","maximum","seuclidean","GDM1"

(e.g. distances=c("euclidean","manhattan"))

Parameter mdsmodels may be the subset of the following values (metric MDS):

"ratio","interval","mspline" (e.g. c("ratio","interval"))

Value

Data frame ordered by increasing value of Stress-1 fit measure with columns:

Author(s)

Marek Walesiak marek.walesiak@ue.wroc.pl, Andrzej Dudek andrzej.dudek@ue.wroc.pl

Department of Econometrics and Computer Science, 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: doi:10.1007/978-3-642-31848-1.

De Leeuw, J., Mair, P. (2015), Shepard Diagram, Wiley StatsRef: Statistics Reference Online, John Wiley & Sons Ltd.

Dudek, A., Walesiak, M. (2020), The Choice of Variable Normalization Method in Cluster Analysis, pp. 325-340, [In:] K. S. Soliman (Ed.), Education Excellence and Innovation Management: A 2025 Vision to Sustain Economic Development during Global Challenges, Proceedings of the 35th International Business Information Management Association Conference (IBIMA), 1-2 April 2020, Seville, Spain. ISBN: 978-0-9998551-4-1.

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. Available at: doi:10.5604/01.3001.0016.1740.

Walesiak, M. (2016a), Wybór grup metod normalizacji wartości zmiennych w skalowaniu wielowymiarowym [The Choice of Groups of Variable Normalization Methods in Multidimensional Scaling], Przegląd Statystyczny, tom 63, z. 1, 7-18. Available at: doi:10.5604/01.3001.0014.1145.

Walesiak, M. (2016b), Visualization of Linear Ordering Results for Metric Data with the Application of Multidimensional Scaling, Ekonometria, 2(52), 9-21. Available at: 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.

Walesiak, M., Dudek, A. (2020), Searching for an Optimal MDS Procedure for Metric and Interval-Valued Data using mdsOpt R package, pp. 307-324, [In:] K. S. Soliman (Ed.), Education Excellence and Innovation Management: A 2025 Vision to Sustain Economic Development during Global Challenges, Proceedings of the 35th International Business Information Management Association Conference (IBIMA), 1-2 April 2020, Seville, Spain. ISBN: 978-0-9998551-4-1.

See Also

data.Normalization, dist.GDM, dist, smacofSym

Examples

  
  library(mdsOpt)
  metnor<-c("n1","n2","n3","n5","n5a","n8","n9","n9a","n11","n12a")
  metscale<-c("ratio","interval","mspline")
  metdist<-c("euclidean","manhattan","seuclidean","maximum","GDM1")
  data(data_lower_silesian)
  res<-optSmacofSym_mMDS(data_lower_silesian,,normalizations=metnor,distances=metdist,
    mdsmodels=metscale, spline.degrees=c(2:3),outDec=".")
  stress<-as.numeric(gsub(",",".",res[,"STRESS 1"],fixed=TRUE))
  hhi<-as.numeric(gsub(",",".",res[,"HHI spp"],fixed=TRUE))
  cs<-(min(stress)+max(stress))/2 # critical stress
  t<-findOptimalSmacofSym(res,critical_stress=cs)
  print(t)
  plot(stress[-t$Nr],hhi[-t$Nr], xlab="Stress-1", ylab="HHI",type="n",font.lab=3)
  text(stress[-t$Nr],hhi[-t$Nr],labels=(1:nrow(res))[-t$Nr])
  abline(v=cs,col="red")
  points(stress[t$Nr],hhi[t$Nr], cex=5,col="red")
  text(stress[t$Nr],hhi[t$Nr],labels=(1:nrow(res))[t$Nr],col="red")
  

Selecting the optimal multidimensional scaling procedure - nonmetric MDS

Description

Selecting the optimal multidimensional scaling procedure by varying all combinations of normalization methods and distance measures

Usage

optSmacofSym_nMDS(x,normalizations=NULL,distances=NULL,
mdsmodels=c("ordinal"),weights=NULL,
outputCsv="",outputCsv2="",outDec=",",
stressDigits=6,HHIDigits=2,...)

Arguments

Details

Parameter normalizations may be the subset of the following values:

"n1","n2","n3","n3a","n4","n5","n5a","n6","n6a",

"n7","n8","n9","n9a","n10","n11","n12","n12a","n13"

(e.g. normalizations=c("n1","n2","n3","n5","n5a",

"n8","n9","n9a","n11","n12a"))

if normalizations is set to "n0" no normalization is applied

Parameter distances may be the subset of the following values:

"euclidean", "manhattan","maximum","seuclidean","GDM1"

(e.g. distances=c("euclidean","manhattan"))

Parameter mdsmodels "ordinal" MDS model (nonmetric MDS)

Value

Data frame ordered by increasing value of Stress-1 fit measure with columns:

Author(s)

Marek Walesiak marek.walesiak@ue.wroc.pl, Andrzej Dudek andrzej.dudek@ue.wroc.pl

Department of Econometrics and Computer Science, 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: doi:10.1007/978-3-642-31848-1.

De Leeuw, J., Mair, P. (2015), Shepard Diagram, Wiley StatsRef: Statistics Reference Online, John Wiley & Sons Ltd.

Dudek, A., Walesiak, M. (2020), The Choice of Variable Normalization Method in Cluster Analysis, pp. 325-340, [In:] K. S. Soliman (Ed.), Education Excellence and Innovation Management: A 2025 Vision to Sustain Economic Development during Global Challenges, Proceedings of the 35th International Business Information Management Association Conference (IBIMA), 1-2 April 2020, Seville, Spain. ISBN: 978-0-9998551-4-1.

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. Available at: doi:10.5604/01.3001.0016.1740.

Walesiak, M. (2016a), Wybór grup metod normalizacji wartości zmiennych w skalowaniu wielowymiarowym [The Choice of Groups of Variable Normalization Methods in Multidimensional Scaling], Przegląd Statystyczny, tom 63, z. 1, 7-18. Available at: doi:10.5604/01.3001.0014.1145.

Walesiak, M. (2016b), Visualization of Linear Ordering Results for Metric Data with the Application of Multidimensional Scaling, Ekonometria, 2(52), 9-21. Available at: 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.

Walesiak, M., Dudek, A. (2020), Searching for an Optimal MDS Procedure for Metric and Interval-Valued Data using mdsOpt R package, pp. 307-324, [In:] K. S. Soliman (Ed.), Education Excellence and Innovation Management: A 2025 Vision to Sustain Economic Development during Global Challenges, Proceedings of the 35th International Business Information Management Association Conference (IBIMA), 1-2 April 2020, Seville, Spain. ISBN: 978-0-9998551-4-1.

See Also

data.Normalization, dist.GDM, dist, smacofSym

Examples

  
  library(mdsOpt)
  metnor<-c("n1","n2","n3","n5","n5a","n8","n9","n9a","n11","n12a")
  metscale<-"ordinal"
  metdist<-c("euclidean","manhattan","maximum","seuclidean","GDM1")
  data(data_lower_silesian)
  res<-optSmacofSym_nMDS(data_lower_silesian,normalizations=metnor,
  distances=metdist,mdsmodels=metscale)
  stress<-as.numeric(gsub(",",".",res[,"STRESS 1"],fixed=TRUE))
  hhi<-as.numeric(gsub(",",".",res[,"HHI spp"],fixed=TRUE))
  cs<-(min(stress)+max(stress))/2 # critical stress
  t<-findOptimalSmacofSym(res,critical_stress=cs)
  print(t)
  plot(stress[-t$Nr],hhi[-t$Nr], xlab="Stress-1", ylab="HHI",type="n",font.lab=3)
  text(stress[-t$Nr],hhi[-t$Nr],labels=(1:nrow(res))[-t$Nr])
  abline(v=cs,col="red")
  points(stress[t$Nr],hhi[t$Nr], cex=5,col="red")
  text(stress[t$Nr],hhi[t$Nr],labels=(1:nrow(res))[t$Nr],col="red")
  

Cretaes video by FFmpeg with animation of dataset rotated

Description

This function opens a graphics device to record the images produced in the code expr, then uses FFmpeg to convert these images to a video.

Usage

rotation2dAnimation(conf2d,
ani.interval=0.2,
ani.nmax=361,
ani.width=500,
ani.height=500,
ani.video.name="mds_rotate.mp4",
angle.start=-pi,
angle.stop=pi,
angle.step=pi/180)

Arguments

Details

This function uses system to call FFmpeg to convert the images to a single video. The command line used in this function is: ffmpeg -y -r <1/interval> -i <img.name>%d.<ani.type> other.opts video.name

where interval comes from ani.options('interval'), and ani.type is from ani.options('ani.type'). For more details on the numerous options of FFmpeg, please see the reference.

Some linux systems may use the alternate software 'avconv' instead of 'ffmpeg'. The package will attempt to determine which command is present and set ani.options('ffmpeg') to an appropriate default value. This can be overridden by passing in the ffmpeg argument.

Value

An integer indicating failure (-1) or success (0) of the converting (refer to system).

Author(s)

Marek Walesiak marek.walesiak@ue.wroc.pl, Andrzej Dudek andrzej.dudek@ue.wroc.pl

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

References

Walesiak, M. (2016), Visualization of Linear Ordering Results for Metric Data with the Application of Multidimensional Scaling, Ekonometria, 2(52), 9-21. Available at: doi:10.15611/ekt.2016.2.01.

Walesiak, M. (2017), The application of multidimensional scaling to measure and assess changes in the level of social cohesion of the Lower Silesia region in the period 2005-2015, Ekonometria, 3(57), 9-25. Available at: doi:10.15611/ekt.2017.3.01.

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.

https://yihui.org/animation/example/savevideo/

http://ffmpeg.org/documentation.html

See Also

Other utilities: im.convert, saveGIF, saveHTML, saveLatex, saveSWF

Examples

  
    library(mdsOpt)
    library(smacof)
    library(animation)
    library(spdep)
    library(clusterSim)
    data(data_lower_silesian)
    z<-data.Normalization(data_lower_silesian, type="n1")
    d<-dist.GDM(z, method="GDM1")
    res<-smacofSym(delta=d,ndim=2,type="interval")
    konf<-as.matrix(res$conf)
    #Uncomment only if ffmpeg is properly installed for animation package 
    #see:  https://yihui.org/animation/example/savevideo/ 
    #oopts = if (.Platform$OS.type == "windows") {
    # ani.options(ffmpeg = "D:/Installer/ffmpeg/bin/ffmpeg.exe")
    #}
    #rotation2dAnimation(conf2d=konf,angle.start=-0,angle.stop=2*pi)