iscal.sda: Multidimensional scaling for symbolic interval data - IScal...

Description Usage Arguments Details Value Author(s) References See Also Examples


Multidimensional scaling for symbolic interval data - IScal algorithm





symbolic interval data: a 3-dimensional table, first dimension represents object number, second dimension - variable number, and third dimension contains lower- and upper-bounds of intervals (Simple form of symbolic data table)


Dimensionality of reduced space


if TRUE x are treated as raw data and min-max dist matrix is calulated. See details


IScal, which was proposed by Groenen et. al. (2006), is an adaptation of well-known nonmetric multidimensional scaling for symbolic data. It is an iterative algorithm that uses I-STRESS objective function. This function is normalized within the range [0; 1] and can be interpreted like classical STRESS values. IScal, like Interscal and SymScal, requires interval-valued dissimilarity matrix. Such dissmilarity matrix can be obtained from symbolic data matrix (that contains only interval-valued variables), judgements obtained from experts, respondents. See Lechevallier Y. (2001) for details on calculating interval-valued distance. See file ../doc/Symbolic_MDS.pdf for further details



coordinates of rectangles


final STRESSSym value


Andrzej Dudek

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


Billard L., Diday E. (red.) (2006), Symbolic Data Analysis, Conceptual Statistics and Data Mining, John Wiley & Sons, Chichester.

Bock H.H., Diday E. (eds.) (2000), Analysis of symbolic data. Explanatory methods for extracting statistical information from complex data, Springer-Verlag, Berlin.

Diday E., Noirhomme-Fraiture M. (red.) (2008), Symbolic Data Analysis with SODAS Software, John Wiley & Sons, Chichester.

Groenen P.J.F, Winsberg S., Rodriguez O., Diday E. (2006), I-Scal: multidimensional scaling of interval dissimilarities, Computational Statistics and Data Analysis, 51, pp. 360-378. Available at:

Lechevallier Y. (ed.), Scientific report for unsupervised classification, validation and cluster analysis, Analysis System of Symbolic Official Data - Project Number IST-2000-25161, project report.

See Also



# Example will be available in next version of package, thank You for your patience :-)

Example output

Loading required package: clusterSim
Loading required package: cluster
Loading required package: MASS
Loading required package: XML

Attaching package: 'symbolicDA'

The following object is masked from 'package:clusterSim':


Warning messages:
1: In rgl.init(initValue, onlyNULL) : RGL: unable to open X11 display
2: 'rgl_init' failed, running with rgl.useNULL = TRUE 
3: .onUnload failed in unloadNamespace() for 'rgl', details:
  call: fun(...)
  error: object 'rgl_quit' not found 

symbolicDA documentation built on Aug. 8, 2019, 5:03 p.m.