# index.GAP: Calculates Tibshirani, Walther and Hastie gap index In clusterSim: Searching for Optimal Clustering Procedure for a Data Set

 index.Gap R Documentation

## 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")```

### 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"

### 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".

### 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)]

### 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

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: doi: 10.1111/1467-9868.00293.

`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))
```

clusterSim documentation built on May 25, 2022, 9:09 a.m.