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

interval_normalization {clusterSim} | R Documentation

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

Department of Econometrics and Computer Science, University of Economics, Wroclaw, Poland http://keii.ue.wroc.pl/clusterSim/

### 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: 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: http://keii.ue.wroc.pl/pracownicy/mw/2014_Walesiak_Przeglad_Statystyczny_z_4.pdf.

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: http://stat.gov.pl/en/sit-en/issues-and-articles-sit/.

### 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)

[Package clusterSim version 0.49-2 Index]