clusterSim (version 0.51-5)

index.Gap: Calculates Tibshirani, Walther and Hastie gap index

Description

Calculates Tibshirani, Walther and Hastie gap index

Usage

index.Gap (x, clall, reference.distribution="unif", B=10, 
	method="pam",d=NULL,centrotypes="centroids")

Value

Gap

Tibshirani, Walther and Hastie gap index for u clusters

diffu

necessary value for choosing correct number of clusters via gap statistic Gap(u)-[Gap(u+1)-s(u+1)]

Arguments

x

data

clall

Two vectors of integers indicating the cluster to which each object is allocated in partition of n objects into u, and u+1 clusters

reference.distribution

"unif" - generate each reference variable uniformly over the range of the observed values for that variable or "pc" - generate the reference variables from a uniform distribution over a box aligned with the principal components of the data. In detail, if \(X=\{x_{ij}\}\) is our n x m data matrix, assume that the columns have mean 0 and compute the singular value decomposition $X=UDV^T$. We transform via $X'=XV$ and then draw uniform features Z' over the ranges of the columns of X' , as in method a) above. Finally we back-transform via $Z=Z'V^T$ to give reference data Z

B

the number of simulations used to compute the gap statistic

method

the cluster analysis method to be used. This should be one of: "ward.D", "ward.D2", "single", "complete", "average", "mcquitty", "median", "centroid", "pam", "k-means","diana"

d

optional distance matrix, used for calculations if centrotypes="medoids"

centrotypes

"centroids" or "medoids"

Author

Marek Walesiak , Andrzej Dudek

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

Details

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

Thanks to dr Michael P. Fay from National Institute of Allergy and Infectious Diseases for finding "one column error".

References

Tibshirani, R., Walther, G., Hastie, T. (2001), Estimating the number of clusters in a data set via the gap statistic, "Journal of the Royal Statistical Society", ser. B, vol. 63, part 2, 411-423. Available at: tools:::Rd_expr_doi("10.1111/1467-9868.00293").

See Also

index.G1, index.G2, index.G3, index.C, index.S, index.H, index.KL, index.DB

Examples

# Example 1
library(clusterSim)
data(data_ratio)
cl1<-pam(data_ratio,4)
cl2<-pam(data_ratio,5)
clall<-cbind(cl1$clustering,cl2$clustering)
g<-index.Gap(data_ratio, clall, reference.distribution="unif", B=10,
   method="pam")
print(g)

# Example 2
library(clusterSim)
means <- matrix(c(0,2,4,0,3,6), 3, 2)
cov <- matrix(c(1,-0.9,-0.9,1), 2, 2)
x <- cluster.Gen(numObjects=40, means=means, cov=cov, model=2)
x <- x$data
md <- dist(x, method="euclidean")^2
# nc - number_of_clusters
min_nc=1
max_nc=5
min <- 0
clopt <- NULL
res <- array(0, c(max_nc-min_nc+1, 2))
res[,1] <- min_nc:max_nc
found <- FALSE
for (nc in min_nc:max_nc){
  cl1 <- pam(md, nc, diss=TRUE)
  cl2 <- pam(md, nc+1, diss=TRUE)
  clall <- cbind(cl1$clustering, cl2$clustering)
  gap <- index.Gap(x,clall,B=20,method="pam",centrotypes="centroids")
  res[nc-min_nc+1, 2] <- diffu <- gap$diffu
  if ((res[nc-min_nc+1, 2] >=0) && (!found)){
    nc1 <- nc
    min <- diffu
    clopt <- cl1$cluster
    found <- TRUE
  }
}
if (found){
print(paste("Minimal nc where diffu>=0 is",nc1,"for diffu=",round(min,4)),quote=FALSE)
}else{
print("I have not found clustering with diffu>=0", quote=FALSE)
}
plot(res,type="p",pch=0,xlab="Number of clusters",ylab="diffu",xaxt="n")
abline(h=0, untf=FALSE)
axis(1, c(min_nc:max_nc))

# Example 3
library(clusterSim)
means <- matrix(c(0,2,4,0,3,6), 3, 2)
cov <- matrix(c(1,-0.9,-0.9,1), 2, 2)
x <- cluster.Gen(numObjects=40, means=means, cov=cov, model=2)
x <- x$data
md <- dist(x, method="euclidean")^2
# nc - number_of_clusters
min_nc=1
max_nc=5
min <- 0
clopt <- NULL
res <- array(0, c(max_nc-min_nc+1, 2))
res[,1] <- min_nc:max_nc
found <- FALSE
for (nc in min_nc:max_nc){
  cl1 <- pam(md, nc, diss=TRUE)
  cl2 <- pam(md, nc+1, diss=TRUE)
  clall <- cbind(cl1$clustering, cl2$clustering)
  gap <- index.Gap(x,clall,B=20,method="pam",d=md,centrotypes="medoids")
  res[nc-min_nc+1, 2] <- diffu <- gap$diffu
  if ((res[nc-min_nc+1, 2] >=0) && (!found)){
    nc1 <- nc
    min <- diffu
    clopt <- cl1$cluster
    found <- TRUE
  }
}
if (found){
print(paste("Minimal nc where diffu>=0 is",nc1,"for diffu=",round(min,4)),quote=FALSE)
}else{
print("I have not found clustering with diffu>=0",quote=FALSE)
}
plot(res, type="p", pch=0, xlab="Number of clusters", ylab="diffu", xaxt="n")
abline(h=0, untf=FALSE)
axis(1, c(min_nc:max_nc))