clusterSim (version 0.51-5)

replication.Mod: Modification of replication analysis for cluster validation

Description

Modification of replication analysis for cluster validation

Usage

replication.Mod(x, v="m", u=2, centrotypes="centroids", 
	normalization=NULL, distance=NULL, method="kmeans", 
	S=10, fixedAsample=NULL)

Value

A

3-dimensional array containing data matrices for A sample of objects in each simulation (first dimension represents simulation number, second - object number, third - variable number)

B

3-dimensional array containing data matrices for B sample of objects in each simulation (first dimension represents simulation number, second - object number, third - variable number)

centroid

3-dimensional array containing centroids of u clusters for A sample of objects in each simulation (first dimension represents simulation number, second - cluster number, third - variable number)

medoid

3-dimensional array containing matrices of observations on u representative objects (medoids) for A sample of objects in each simulation (first dimension represents simulation number, second - cluster number, third - variable number)

clusteringA

2-dimensional array containing cluster numbers for A sample of objects in each simulation (first dimension represents simulation number, second - object number)

clusteringB

2-dimensional array containing cluster numbers for B sample of objects in each simulation (first dimension represents simulation number, second - object number)

clusteringBB

2-dimensional array containing cluster numbers for B sample of objects in each simulation according to 4 step of replication analysis procedure (first dimension represents simulation number, second - object number)

cRand

value of mean corrected Rand index for S simulations

Arguments

x

data matrix

v

type of data: metric ("r" - ratio, "i" - interval, "m" - mixed), nonmetric ("o" - ordinal, "n" - multi-state nominal, "b" - binary)

u

number of clusters given arbitrary

centrotypes

"centroids" or "medoids"

normalization

optional, normalization formulas for metric data (normalization by variable):

for ratio data: "n0" - without normalization, "n6" - (x/sd), "n6a" - (x/mad), "n7" - (x/range), "n8" - (x/max), "n9" - (x/mean), "n9a" - (x/median), "n10" - (x/sum), "n11" - x/sqrt(SSQ)

for interval or mixed data: "n0" - without normalization, "n1" - (x-mean)/sd, "n2" - (x-median)/mad, "n3" - (x-mean)/range, "n3a" - positional unitization (x-median)/range, "n4" - (x-min)/range, "n5" - (x-mean)/max[abs(x-mean)], "n5a" - (x-median)/max[abs(x-median)], "n12" - normalization (x - mean)/(sum(x - mean)^2)^0.5, "n12a" - positional normalization (x - median)/(sum(x - median)^2)^0.5, "n13" - normalization with zero being the central point ((x-midrange)/(range/2))

distance

distance measures

NULL for "kmeans" method (based on data matrix),

for ratio data: "d1" - Manhattan, "d2" - Euclidean, "d3" - Chebychev (max), "d4" - squared Euclidean, "d5" - GDM1, "d6" - Canberra, "d7" - Bray-Curtis

for interval or mixed (ratio & interval) data: "d1", "d2", "d3", "d4", "d5"

for ordinal data: "d8" - GDM2

for multi-state nominal: "d9" - Sokal & Michener

for binary data: "b1" = Jaccard; "b2" = Sokal & Michener; "b3" = Sokal & Sneath (1); "b4" = Rogers & Tanimoto; "b5" = Czekanowski; "b6" = Gower & Legendre (1); "b7" = Ochiai; "b8" = Sokal & Sneath (2); "b9" = Phi of Pearson; "b10" = Gower & Legendre (2)

method

clustering method: "kmeans" (default), "single", "complete", "average", "mcquitty", "median", "centroid", "ward.D", "ward.D2", "pam", "diana"

S

the number of simulations used to compute mean corrected Rand index

fixedAsample

if NULL A sample is generated randomly, otherwise this parameter contains object numbers arbitrarily assigned to A sample

Author

Marek Walesiak , Andrzej Dudek

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

Details

See file ../doc/replication.Mod_details.pdf for further details

References

Breckenridge, J.N. (2000), Validating cluster analysis: consistent replication and symmetry, "Multivariate Behavioral Research", 35 (2), 261-285. Available at: tools:::Rd_expr_doi("10.1207/S15327906MBR3502_5").

Gordon, A.D. (1999), Classification, Chapman and Hall/CRC, London. ISBN 9781584880134.

Hubert, L., Arabie, P. (1985), Comparing partitions, "Journal of Classification", no. 1, 193-218. Available at: tools:::Rd_expr_doi("10.1007/BF01908075").

Milligan, G.W. (1996), Clustering validation: results and implications for applied analyses, In P. Arabie, L.J. Hubert, G. de Soete (Eds.), Clustering and classification, World Scientific, Singapore, 341-375. ISBN 9789810212872.

Walesiak, M. (2008), Ocena stabilnosci wynikow klasyfikacji z wykorzystaniem analizy replikacji, In: J. Pociecha (Ed.), Modelowanie i prognozowanie zjawisk spoleczno-gospodarczych, Wydawnictwo AE, Krakow, 67-72.

See Also

cluster.Sim, hclust, kmeans, dist, dist.BC, dist.SM, dist.GDM,

data.Normalization

Examples

library(clusterSim)
data(data_ratio)
w <- replication.Mod(data_ratio, u=5, S=10)
print(w)

library(clusterSim)
data(data_binary)
replication.Mod(data_binary,"b", u=2, "medoids", NULL,"b1", "pam", fixedAsample=c(1,3,6,7))