interval_normalization: Types of normalization formulas for interval-valued symbolic...

In clusterSim: Searching for Optimal Clustering Procedure for a Data Set

Types of normalization formulas for interval-valued symbolic variables

Description

Types of normalization formulas for interval-valued symbolic variables

Usage

interval_normalization(x,dataType="simple",type="n0",y=NULL,...)

Arguments

x	matrix dataset or symbolic table object
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 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	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))

y	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

Value

Normalized data

Author(s)

Marek Walesiak [e-mail], Andrzej Dudek [e-mail]

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

References

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: \Sexpr[results=rd]{tools:::Rd_expr_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: \Sexpr[results=rd]{tools:::Rd_expr_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: \Sexpr[results=rd]{tools:::Rd_expr_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. Available at: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.59170/stattrans-2017-027")}.

See Also

data.Normalization

Examples

library(clusterSim)
data(data_symbolic_interval_polish_voivodships)
n<-interval_normalization(data_symbolic_interval_polish_voivodships,dataType="simple",type="n2")
plotInterval(n$simple)

clusterSim documentation built on Sept. 30, 2024, 9:15 a.m.