R: Calculates Tibshirani, Walther and Hastie gap index

index.Gap {clusterSim} | 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.

### 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))

[Package clusterSim version 0.49-2 Index]