data.Normalization {clusterSim}

Types of variable (column) and object (row) normalization formulas

Description

Types of variable (column) and object (row) normalization formulas

Usage

data.Normalization (x,type="n0",normalization="column",...)

Arguments

x

vector, matrix or dataset

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))

normalization

"column" - normalization by variable, "row" - normalization by object

...

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

Details

See file ../doc/dataNormalization_details.pdf for further details

Thanks Wolfgang Lederer (<[e-mail]>) for reporting n4/vector error

Value

Normalized data The numeric shifts and scalings used (if any) are returned as attributes "normalized:shift" and "normalized:scale"

Author(s)

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

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

References

Anderberg, M.R. (1973), Cluster analysis for applications, Academic Press, New York, San Francisco, London. ISBN 9780120576500.

Gatnar, E., Walesiak, M. (Eds.) (2004), Metody statystycznej analizy wielowymiarowej w badaniach marketingowych [Multivariate statistical analysis methods in marketing research], Wydawnictwo AE, Wroclaw, 35-38. Available at: http://keii.ue.wroc.pl/pracownicy/mw/2004_Gatnar_Walesiak_Metody_SAW_w_badaniach_marketingowych.pdf.

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.

Mlodak, A. (2006), Analiza taksonomiczna w statystyce regionalnej, Difin, Warszawa. ISBN 83-7251-605-7.

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.

See Also

cluster.Sim

Examples

library(clusterSim)
data(data_ratio)
z1 <- data.Normalization(data_ratio,type="n1",normalization="column",na.rm=FALSE)
z2 <- data.Normalization(data_ratio,type="n10",normalization="row",na.rm=FALSE)