Help for package mdsOpt

Title:

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

Version:

0.8-1

Date:

2026-10-02

Depends:

R (≥ 3.6.0), smacof, clusterSim, symbolicDA

Imports:

animation, plotrix, spdep

Suggests:

testthat, R.rsp, ggplot2, ggrepel

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>, Dehnel, G., Walesiak, M. (2019) <doi:10.21307/stattrans-2019-014>, Walesiak, M. (2016) <doi:10.15611/ekt.2016.2.01>, Walesiak, M. (2017) <doi:10.15611/ekt.2017.3.01>), Walesiak, M., Dehnel, G. (2020) <doi:10.3390/su12187664>, Walesiak, M., Dehnel, G., Dudek, A. (2025) <doi:10.15611/aoe.2025.1.12>, Walesiak, M., Dehnel, G. (2026) <doi:10.1371/journal.pone.0333545>.

License:

GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]

Encoding:

UTF-8

NeedsCompilation:

yes

Packaged:

2026-10-02 14:43:05 UTC; andrzej

Author:

Marek Walesiak

[aut], Andrzej Dudek

[aut, cre]

Maintainer:

Andrzej Dudek <andrzej.dudek@ue.wroc.pl>

Repository:

CRAN

Date/Publication:

2026-10-02 16:00:08 UTC

Multidimensional Scaling of Interval-Valued Dissimilarities

Description

Internal function for multidimensional scaling of interval-valued dissimilarities using either the hypersphere or hyperbox model. Optimization can be performed using the majorization-minimization algorithm or the BFGS quasi-Newton method.

Usage

.IMDS(
  IDM,
  p = 2,
  eps = 1e-5,
  maxit = 1000,
  model = c("sphere", "box"),
  opt.method = c("MM", "BFGS"),
  ini = "auto",
  report = 100,
  grad.num = FALSE,
  rel = 0,
  dil = 1
)

Arguments

IDM

Interval-valued dissimilarity matrix represented as a three-dimensional array. IDM[1,,] contains the lower dissimilarity matrix and IDM[2,,] contains the upper dissimilarity matrix.

p

Number of dimensions of the multidimensional scaling configuration.

eps

Convergence criterion used by the majorization-minimization algorithm.

maxit

Maximum number of optimization iterations.

model

Character string specifying the symbolic representation. "sphere" uses the hypersphere model and "box" uses the hyperbox model.

opt.method

Optimization method. "MM" uses the majorization-minimization algorithm and "BFGS" uses the BFGS quasi-Newton method.

ini

Initial configuration. If "auto", the coordinates obtained from classical multidimensional scaling of the midpoint dissimilarity matrix are used as the initial centers and initial radii are generated automatically. Alternatively, a list containing an initial coordinate matrix and an initial radius vector or matrix can be supplied.

report

Frequency with which optimization progress is reported.

grad.num

Logical value indicating whether a numerical gradient should be used for BFGS optimization. If FALSE, the analytical gradient is used.

rel

Control parameter for the relaxed update used by the majorization-minimization procedure. A nonzero value enables the relaxed update. This argument is not used for BFGS optimization.

dil

Control parameter for optimal dilation of the configuration in the majorization-minimization procedure. A nonzero value enables dilation. This argument is not used for BFGS optimization.

Details

The function performs multidimensional scaling for interval-valued dissimilarities.

Two representations are available. In the hypersphere model each object is represented by a center and a radius. In the hyperbox model each object is represented by a center and dimension-specific half-ranges.

The stress criterion can be minimized either by the majorization-minimization method or by the BFGS optimization method.

This is an internal function used by higher-level procedures in the mdsOpt package and is not normally intended to be called directly by users.

Value

An object containing the fitted interval multidimensional scaling configuration. Depending on the selected model, components can include:

X: Matrix of coordinates of the object centers with p columns.
r: Radius vector for the hypersphere model.
R: Radius or half-range matrix for the hyperbox model.
str: Value of the stress criterion for the fitted configuration.
IDM: Original interval-valued dissimilarity matrix.
EIDM: Interval-valued dissimilarities implied by the fitted configuration.

References

Nash, J. C. (1990). Compact Numerical Methods for Computers: Linear Algebra and Function Minimisation. Adam Hilger.

Borg, I., Groenen, P. J. F., and Mair, P. (2013). Applied Multidimensional Scaling. Springer.

Compute Interval Distances for the Hyperbox Model

Description

Internal function for computing interval-valued distances between objects represented by hyperboxes.

Usage

.idistBox(X, R)

Arguments

X

A numeric matrix containing the coordinates of the centers of the hyperboxes. Rows correspond to objects and columns to dimensions.

R

A numeric matrix containing the half-ranges (radii) of the hyperboxes. It must have the same dimensions as X.

Details

The function computes interval-valued dissimilarities between pairs of hyperboxes defined by their centers X and their half-ranges R.

It is an internal utility used by the interval-valued multidimensional scaling procedures in the mdsOpt package and is not normally called directly by users.

Value

A three-dimensional array representing an interval-valued dissimilarity matrix. The first layer contains the lower bounds of the pairwise distances and the second layer contains the upper bounds.

Plot an Interval Multidimensional Scaling Configuration

Description

Internal plotting function for visualizing the results of interval-valued multidimensional scaling.

Usage

.plot.imds(x,
  xylim = "auto",
  clab = 1:nrow(X),
  lab.cex = 1,
  lab.col = "black",
  ...
)

Arguments

x

An object containing the result of interval multidimensional scaling, typically produced by an internal IMDS optimization procedure. The object should contain the coordinates and interval representation required for plotting the fitted configuration.

xylim

Controls the limits of the plotting area. If set to "auto", the plotting limits are determined automatically from the data. Alternatively, plotting limits can be supplied explicitly.

clab

Labels used for the plotted objects. By default, consecutive integer labels from 1 to nrow(X) are used.

lab.cex

Numeric value controlling the size of the object labels. The default is 1.

lab.col

Color used for the object labels. The default is "black".

...

Additional graphical parameters passed to the underlying plotting functions.

Details

The function provides a graphical representation of an interval-valued multidimensional scaling configuration.

Objects are displayed together with their corresponding labels. The plot limits can be determined automatically or supplied by the user, while label size and color can be controlled using lab.cex and lab.col, respectively.

This is an internal plotting utility used by functions in the mdsOpt package and is not normally intended to be called directly by users.

Value

The function is called primarily for its graphical side effect.

It produces a plot of the interval multidimensional scaling configuration and does not return a meaningful value.

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

x

two dimensional point (center)

y

optional - second point, used for calculations of step size if steps is null

number

number of isoquants

steps

distance between following isoquants starting from x, if length of this arguments is lower than number argument last item is repeated

Value

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

Author(s)

Marek Walesiak marek.walesiak@ue.wroc.pl

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

Andrzej Dudek andrzej.dudek@ue.wroc.pl

Department of Financial Investments and Risk Management, 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. Available at: doi:10.59170/stattrans-2017-027.

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: 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: doi:10.1371/journal.pone.0333545.

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 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 marek.walesiak@ue.wroc.pl

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

Andrzej Dudek andrzej.dudek@ue.wroc.pl

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: 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: 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: doi:10.15611/ekt.2016.2.01.

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: doi:10.3390/su12187664.

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))

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

table

result from optSmacofSym_nMDS or optSmacofSym_mMDS. Data frame ordered by increasing value of Stress-1 fit measure or HHI index with columns:

Normalization method

Distance measure

MDS model

Spline degree

STRESS 1

HHI spp

critical_stress

threshold value of Kruskal's Stress-1 fit measure. Default - mid-range of Kruskal's Stress-1 fit measures calculated for all MDS procedures

critical_HHI

Value

Nr

number of row in table with optimal multidimensional scaling procedure

Normalization_method

normalization method used for optimal multidimensional scaling procedure

MDS_model

MDS model used for optimal multidimensional scaling procedure

Spline_degree

Additional spline.degree value for optimal procedure, if mspline model is used for simulation. For other models there is no value for this field

Distance_measure

distance measure used for optimal multidimensional scaling procedure

STRESS_1

value of Kruskal Stress-1 fit measure for optimal multidimensional scaling procedure

HHI_spp

Hirschman-Herfindahl HHI index, calculated based on stress per point, for optimal multidimensional scaling procedure

Author(s)

Marek Walesiak marek.walesiak@ue.wroc.pl

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

Andrzej Dudek andrzej.dudek@ue.wroc.pl

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

References

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. (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. (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.

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))

Calculation of I-stress per box indices for multidimensional scaling procedure for interval-valued data

Description

Calculation of I-stress per box indices for multidimensional scaling procedure for interval-valued data

Usage

ispb(EIDM,idiss)

Arguments

EIDM

the interval-valued dissimilarity matrix IDM (an object of class "array": IDM[1,,]: the lower dissmilarity matrix; IDM[2,,]: the upper dissmilarity matrix) in reduced space

idiss

the primary interval-valued dissimilarity matrix

Value

The vector of i-stress per box percentage values

Author(s)

Marek Walesiak marek.walesiak@ue.wroc.pl

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

Andrzej Dudek andrzej.dudek@ue.wroc.pl

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

References

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.

Examples


library(mdsOpt)
library(clusterSim)
data(data_symbolic_interval_polish_voivodships)
x1<-data_symbolic_interval_polish_voivodships[,,1]
y1<-data_symbolic_interval_polish_voivodships[,,2]
norm_type="n2" 
normalized<-interval_normalization(x=x1,y=y1,dataType="separate_tables",type=norm_type)
x<-normalized$simple[,,1]
y<-normalized$simple[,,2]
my.idiss<-.idistBox(X=(x+y)/2,R=(y-x)/2)
#Apply the hyperbox model via the MM algorithm
cmat<-(my.idiss[2, , ] + my.idiss[1, , ])/2
iniX<-cmdscale(as.dist(cmat), k = 2)
n=dim(my.idiss)[2]
iniR<-matrix(rep(1,n * 2), nrow = n, ncol = 2)
res.mm_box<-.IMDS(IDM=my.idiss, p=2,model="box",opt.method="MM", ini=list(iniX,iniR))
.plot.imds(res.mm_box)
title(main="box_MM")
#windows()
spb<-ispb(res.mm_box$EIDM,my.idiss)
w<-sort(spb,decreasing=TRUE)
print(spb)
names(w)<-order(spb,decreasing = TRUE)
plot(w, xlab="Object", ylab="spb in percents")
text(w,pos=1,names(w))

Selecting the optimal multidimensional scaling procedure for interval-valued data

Description

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

Usage

optIscalInterval(x,dataType="simple",normalizations=NULL,
optMethods=NULL,outputCsv="",outputCsv2="",y=NULL,outDec=",",
stressDigits=6,HHIDigits=2,...)

Arguments

x

interval-valued data table or matrix or dataset

dataType

Type of symbolic data table passed to function:

'sda' - full symbolicDA format object;

'simple' - three dimensional array with lower and upper bound of intervals in third dimension;

'separate_tables' - lower bound of intervals in x, upper bound of intervals in y (formula y=... needed in argument list);

'rows' - lower and upper bound of intervals in neighbouring rows;

'columns' - lower and upper bound of intervals in neighbouring columns

normalizations

optional, vector of normalization methods that should be used in procedure

optMethods

optional, vector of optimization methods

outputCsv

optional, name of csv file with results

outputCsv2

optional, name of csv (comma as decimal point sign) file with results

y

matrix or dataset with upper bounds of intervals if argument dataType is equal to "separate_tables"

outDec

decimal sign used in returned table

stressDigits

Number of decimal digits for displaying I-Stress value

HHIDigits

Number of decimal digits for displaying HHI spb value

...

arguments passed to smds I-scal implementation (function .IMDS), like p, maxit, eps and others

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 optMethods may be the subset of the following values (.IMDS):

("MM","BFGS")

Function .IMDS is a clone of IMDS function from former smds package

Value

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

Normalization method

normalization method used for p-th multidimensional scaling procedure

Opt method

Optimization method used .IMDS I-Scal implememtatiomn

Spline degree

Additional spline.degree value if mspline model is used for simulation, for other models there is no value in this cell

I-STRESS

value of I-Stress fit measure for p-th multidimensional scaling procedure

HHI spb

Hirschman-Herfindahl HHI index calculated based on stress per boc for p-th multidimensional scaling procedure

Author(s)

Marek Walesiak marek.walesiak@ue.wroc.pl

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

Andrzej Dudek andrzej.dudek@ue.wroc.pl

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

References

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.

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. (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.

Examples

  
  library(mdsOpt)
  library(ggplot2)
  library(ggrepel)
  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")
  res<-optIscalInterval(x,dataType="simple",normalizations=metnor,optMethods=methods,outDec=".")
  Istress<-as.numeric(gsub(",",".",res[,"I-STRESS"],fixed=TRUE))
  hhi<-as.numeric(gsub(",",".",res[,"HHI spb"],fixed=TRUE))
  t<-findOptimalIscalInterval(res)
  cs<-(min(Istress)+max(Istress))/2 # critical I-stress
  print(t)
  # write.table(res,file="smds_HHI.csv",sep=";",dec=",",row.names=TRUE,col.names=NA)
  # plot 'old way'
  plot(Istress[-t$Nr],hhi[-t$Nr], xlab="I-Stress", ylab="HHI",type="n",font.lab=3)
  text(Istress[-t$Nr],hhi[-t$Nr],labels=(1:nrow(res))[-t$Nr])
  abline(v=cs,col="red")
  points(Istress[t$Nr],hhi[t$Nr], cex=5,col="red")
  text(Istress[t$Nr],hhi[t$Nr],labels=(1:nrow(res))[t$Nr],col="red")
  #or plot ggplot2 
  plot_data <- data.frame(
   object = seq_len(nrow(res)),
   stress = Istress,
   hhi = hhi,
   optimal = seq_len(nrow(res)) == t$Nr
  )
  plot_data <- plot_data[
   is.finite(plot_data$stress) &
     is.finite(plot_data$hhi),
  ]
  p <- ggplot(
   plot_data,
   aes(
     x = stress,
     y = hhi
   )
  ) +

  # critical stress line
  geom_vline(
   xintercept = cs,
   colour = "red",
   linewidth = 0.7
  ) +

  # ordinary points
  geom_point(
   data = subset(
     plot_data,
     !optimal
   ),
   shape = 16,
   size = 2.2
  ) +

  # labels for ordinary points
  geom_text_repel(
   data = subset(
     plot_data,
     !optimal
   ),
   aes(
     label = object
   ),
   size = 3.5,
   box.padding = 0.45,
   point.padding = 0.30,
   force = 2,
   max.overlaps = Inf,
   min.segment.length = 0,
   seed = 123
  ) +

  # optimal solution highlighted by a large red circle
  geom_point(
   data = subset(
     plot_data,
     optimal
   ),
   shape = 16,
   size = 3,
   stroke = 1.2,
   colour = "red"
  ) +

  # label for optimal solution
  geom_text_repel(
   data = subset(
     plot_data,
     optimal
   ),
   aes(
     label = object
   ),
   colour = "red",
   fontface = "bold",
   size = 4,
   box.padding = 0.7,
   point.padding = 0.8,
   force = 3,
   max.overlaps = Inf,
   min.segment.length = 0,
   seed = 123
  ) +

  labs(
   x = "I Stress",
   y = "HHI spb"
  ) +

  theme_classic(
   base_size = 12
  ) +

  theme(
   axis.title = element_text(
     face = "italic"
   )
  )
  print(p)

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

x

interval-valued data table or matrix or dataset

dataType

Type of symbolic data table passed to function:

'sda' - full symbolicDA format object;

'simple' - three dimensional array with lower and upper bound of intervals in third dimension;

'separate_tables' - lower bound of intervals in x, upper bound of intervals in y;

'rows' - lower and upper bound of intervals in neighbouring rows;

'columns' - lower and upper bound of intervals in neighbouring columns

normalizations

optional, vector of normalization methods that should be used in procedure

distances

optional, vector of distance measures (Hausdorf, Ichino-Yaguchi) that should be used in procedure

mdsmodels

optional, vector of multidimensional models (ratio, interval, mspline) that should be used in procedure

spline.degrees

optional, vector (e.g. 2:4) of spline.degree parameter values that should be used in procedure for mspline model

outputCsv

optional, name of csv file with results

outputCsv2

optional, name of csv (comma as decimal point sign) file with results

y

matrix or dataset with upper bounds of intervals if argument dataType is equal to "separate_tables"

outDec

decimal sign used in returned table

stressDigits

Number of decimal digits for displaying Stress 1 value

HHIDigits

Number of decimal digits for displaying HHI spp value

...

arguments passed to smacofSym, like ndim, itmax, eps and others

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:

Normalization method

normalization method used for p-th multidimensional scaling procedure

MDS model

MDS model used for p-th multidimensional scaling procedure

Spline degree

Additional spline.degree value if mspline model is used for simulation, for other models there is no value in this cell

Distance measure

distance measures for interval-valued data used for p-th multidimensional scaling procedure

STRESS 1

value of Kruskal Stress-1 fit measure for p-th multidimensional scaling procedure

HHI spp

Hirschman-Herfindahl HHI index calculated based on stress per point for p-th multidimensional scaling procedure

Author(s)

Marek Walesiak marek.walesiak@ue.wroc.pl

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

Andrzej Dudek andrzej.dudek@ue.wroc.pl

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

References

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.

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.

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

x

matrix or dataset

normalizations

optional, vector of normalization methods that should be used in procedure

distances

optional, vector of distance measures (manhattan, Euclidean, Chebyshew, squared Euclidean, GDM1) that should be used in procedure

mdsmodels

optional, vector of multidimensional models (ratio, interval, mspline) that should be used in procedure

spline.degrees

optional, vector (e.g. 2:4) of spline.degree parameter values that should be used in procedure for mspline model

weights

optional, variable weights used in distance calculation. Each weight takes value from interval [0; 1] and sum of weights equals one

outputCsv

optional, name of csv file with results

outputCsv2

optional, name of csv (comma as decimal point sign) file with results

outDec

decimal sign used in returned table

stressDigits

Number of decimal digits for displaying Stress 1 value

HHIDigits

Number of decimal digits for displaying HHI spp value

...

arguments passed to smacofSym, like ndim, itmax, eps and others

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:

Normalization method

normalization method used for p-th multidimensional scaling procedure

MDS model

MDS model used for p-th multidimensional scaling procedure

Spline degree

Additional spline.degree value if mspline model is used for simulation, for other models there is no value in this cell

Distance measure

distance measure used for p-th multidimensional scaling procedure

STRESS 1

value of Kruskal Stress-1 fit measure for p-th multidimensional scaling procedure

HHI spp

Hirschman-Herfindahl HHI index calculated based on stress per point for p-th multidimensional scaling procedure

Author(s)

Marek Walesiak marek.walesiak@ue.wroc.pl

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

Andrzej Dudek andrzej.dudek@ue.wroc.pl

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

References

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.

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. (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.

Examples

  
  library(mdsOpt)
  library(ggplot2)
  library(ggrepel)
  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 'old way'
  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")
  #or plot ggplot2
  plot_data <- data.frame(
     object = seq_len(nrow(res)),
     stress = stress,
     hhi = hhi,
     optimal = seq_len(nrow(res)) == t$Nr
   )
   plot_data <- plot_data[
     is.finite(plot_data$stress) &
       is.finite(plot_data$hhi),
   ]
   p <- ggplot(
     plot_data,
     aes(
       x = stress,
       y = hhi
     )
   ) +
   
   # critical stress line
   geom_vline(
     xintercept = cs,
     colour = "red",
     linewidth = 0.7
   ) +
   
   # ordinary points
   geom_point(
     data = subset(
       plot_data,
       !optimal
     ),
     shape = 16,
     size = 2.2
   ) +
   
   # labels for ordinary points
   geom_text_repel(
     data = subset(
       plot_data,
       !optimal
     ),
     aes(
       label = object
     ),
     size = 3.5,
     box.padding = 0.45,
     point.padding = 0.30,
     force = 2,
     max.overlaps = Inf,
     min.segment.length = 0,
     seed = 123
   ) +
   
   # optimal solution highlighted by a large red circle
   geom_point(
     data = subset(
       plot_data,
       optimal
     ),
     shape = 16,
     size = 3,
     stroke = 1.2,
     colour = "red"
   ) +
   
   # label for optimal solution
   geom_text_repel(
     data = subset(
       plot_data,
       optimal
     ),
     aes(
       label = object
     ),
     colour = "red",
     fontface = "bold",
     size = 4,
     box.padding = 0.7,
     point.padding = 0.8,
     force = 3,
     max.overlaps = Inf,
     min.segment.length = 0,
     seed = 123
   ) +
   
   labs(
     x = "Stress-1",
     y = "HHI"
   ) +
   
   theme_classic(
     base_size = 12
   ) +
   
   theme(
     axis.title = element_text(
       face = "italic"
     )
   )
   print(p)

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

x

matrix or dataset

normalizations

optional, vector of normalization methods that should be used in procedure

distances

optional, vector of distance measures (manhattan, Euclidean, Chebyshew, squared Euclidean, GDM1) that should be used in procedure

mdsmodels

"ordinal" (nonmetric MDS)

weights

optional, variable weights used in distance calculation. Each weight takes value from interval [0; 1] and sum of weights equals one

outputCsv

optional, name of csv file with results

outputCsv2

optional, name of csv (comma as decimal point sign) file with results

outDec

decimal sign used in returned table

stressDigits

Number of decimal digits for displaying Stress 1 value

HHIDigits

Number of decimal digits for displaying HHI spp value

...

arguments passed to smacofSym

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:

Normalization method

normalization method used for p-th multidimensional scaling procedure

MDS model

"ordinal" MDS model (nonmetric MDS) for p-th multidimensional scaling procedure

Distance measure

distance measure used for p-th multidimensional scaling procedure

STRESS 1

value of Kruskal Stress-1 fit measure for p-th multidimensional scaling procedure

HHI spp

Hirschman-Herfindahl HHI index calculated based on stress per point for p-th multidimensional scaling procedure

Author(s)

Marek Walesiak marek.walesiak@ue.wroc.pl

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

Andrzej Dudek andrzej.dudek@ue.wroc.pl

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

References

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.

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. (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.

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

conf2d

two dimensional dataset ot matrix

ani.video.name

the file name of the output video (e.g. ‘animation.mp4’ or ‘animation.avi’)

ani.interval

interval betwwen animation frames

ani.nmax

maximal number of frames

ani.width

width of movie

ani.height

height of movie

angle.start

starting angle for animation

angle.stop

end angle for animation

angle.step

step of animation in radians

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

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

Andrzej Dudek andrzej.dudek@ue.wroc.pl

Department of Financial Investments and Risk Management, 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.

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

https://ffmpeg.org/documentation.html

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)

Package {mdsOpt}

Multidimensional Scaling of Interval-Valued Dissimilarities

Description

Usage

Arguments

Details

Value

References

See Also

Compute Interval Distances for the Hyperbox Model

Description

Usage

Arguments

Details

Value

See Also

Plot an Interval Multidimensional Scaling Configuration

Description

Usage

Arguments

Details

Value

See Also

The evaluation of tourist attractiveness of Lower Silesian counties

Description

Format

Source

Examples

draw series of isoquants

Description

Usage

Arguments

Value

Author(s)

References

Examples

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

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Selecting the optimal multidimensional scaling (MDS) procedure

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Calculation of I-stress per box indices for multidimensional scaling procedure for interval-valued data

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Selecting the optimal multidimensional scaling procedure for interval-valued data

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Selecting the optimal multidimensional scaling procedure for interval-valued data

Description

Usage

Arguments

Details

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