interval_normalization {clusterSim}R Documentation

Types of normalization formulas for interval-valued symbolic variables


Types of normalization formulas for interval-valued symbolic variables





matrix dataset or symbolic table object


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 bounds of intervals in x, upper bounds in y;

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

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


type of normalization:

n0 - without normalization

n1 - standardization ((x-mean)/sd)

n2 - positional standardization ((x-median)/mad)

n3 - unitization ((x-mean)/range)

n3a - positional unitization ((x-median)/range)

n4 - unitization with zero minimum ((x-min)/range)

n5 - normalization in range <-1,1> ((x-mean)/max(abs(x-mean)))

n5a - positional normalization in range <-1,1> ((x-median)/max(abs(x-median)))

n6 - quotient transformation (x/sd)

n6a - positional quotient transformation (x/mad)

n7 - quotient transformation (x/range)

n8 - quotient transformation (x/max)

n9 - quotient transformation (x/mean)

n9a - positional quotient transformation (x/median)

n10 - quotient transformation (x/sum)

n11 - quotient transformation (x/sqrt(SSQ))

n12 - normalization ((x-mean)/sqrt(sum((x-mean)^2)))

n12a - positional normalization ((x-median)/sqrt(sum((x-median)^2)))

n13 - normalization with zero being the central point ((x-midrange)/(range/2))


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


arguments passed to sum, mean, min sd, mad and other aggregation functions. In particular: na.rm - a logical value indicating whether NA values should be stripped before the computation


Normalized data


Marek Walesiak, Andrzej Dudek

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


Jajuga, K., Walesiak, M. (2000), Standardisation of data set under different measurement scales, In: R. Decker, W. Gaul (Eds.), Classification and information processing at the turn of the millennium, Springer-Verlag, Berlin, Heidelberg, 105-112. Available at: doi: 10.1007/978-3-642-57280-7_11.

Milligan, G.W., Cooper, M.C. (1988), A study of standardization of variables in cluster analysis, "Journal of Classification", vol. 5, 181-204. Available at: doi: 10.1007/BF01897163.

Walesiak, M. (2014), Przeglad formul normalizacji wartosci zmiennych oraz ich wlasnosci w statystycznej analizie wielowymiarowej [Data normalization in multivariate data analysis. An overview and properties], "Przeglad Statystyczny" ("Statistical Review"), vol. 61, no. 4, 363-372. Available at:

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:

See Also




[Package clusterSim version 0.49-2 Index]