R: Calculates Krzanowski-Lai index

index.KL {clusterSim} | R Documentation

## Calculates Krzanowski-Lai index

### Description

Calculates Krzanowski-Lai index

### Usage

    index.KL (x,clall,d=NULL,centrotypes="centroids")

### Arguments

`x` | data
`clall` | Three vectors of integers indicating the cluster to which each object is allocated in partition of n objects into u-1, u, and u+1 clusters
`d` | optional distance matrix, used for calculations if centrotypes="medoids"
`centrotypes` | "centroids" or "medoids"

### Details

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

### Value

Krzanowski-Lai index

### 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

Krzanowski, W.J., Lai, Y.T. (1988), A criterion for determining the number of groups in a data set using sum of squares clustering, "Biometrics", 44, 23-34.

Milligan, G.W., Cooper, M.C. (1985), An examination of procedures of determining the number of cluster in a data set, "Psychometrika", vol. 50, no. 2, 159-179. Available at: doi: 10.1007/BF02294245.

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.Gap`, `index.DB`

### Examples

    # Example 1
    library(clusterSim)
    data(data_ratio)
    cl1<-pam(data_ratio,4)
    cl2<-pam(data_ratio,5)
    cl3<-pam(data_ratio,6)
    clall<-cbind(cl1$clustering,cl2$clustering,cl3$clustering)
    index.KL(data_ratio,clall)

    # Example 2
    library(clusterSim)
    data(data_ratio)
    md <- dist(data_ratio, method="manhattan")
    # nc - number_of_clusters
    min_nc=2
    max_nc=15
    res <- array(0, c(max_nc-min_nc+1, 2))
    res[,1] <- min_nc:max_nc
    clusters <- NULL
    for (nc in min_nc:max_nc)
    {
      if(nc-1==1){
        clustering1<-rep(1,nrow(data_ratio))
      }
      else{
        clustering1 <- pam(md, nc-1, diss=TRUE)$clustering
      }
      clustering2 <- pam(md, nc, diss=TRUE)$clustering
      clustering3 <- pam(md, nc+1, diss=TRUE)$clustering
      clall<- cbind(clustering1, clustering2, clustering3)
      res[nc-min_nc+1,2] <- KL <- index.KL(data_ratio,clall,centrotypes="centroids")
      clusters <- rbind(clusters, clustering2)
    }
    print(paste("max KL for",(min_nc:max_nc)[which.max(res[,2])],"clusters=",max(res[,2])))
    print("clustering for max KL")
    print(clusters[which.max(res[,2]),])
    #write.table(res,file="KL_res.csv",sep=";",dec=",",row.names=TRUE,col.names=FALSE)
    plot(res,type="p",pch=0,xlab="Number of clusters",ylab="KL",xaxt="n")
    axis(1, c(min_nc:max_nc))

    # Example 3
    library(clusterSim)
    data(data_ratio)
    md <- dist(data_ratio, method="manhattan")
    # nc - number_of_clusters
    min_nc=2
    max_nc=15
    res <- array(0, c(max_nc-min_nc+1, 2))
    res[,1] <- min_nc:max_nc
    clusters <- NULL
    for (nc in min_nc:max_nc)
    {
      if(nc-1==1){
        clustering1<-rep(1,nrow(data_ratio))
      }
      else{
        clustering1 <- pam(md, nc-1, diss=TRUE)$clustering
      }
      clustering2 <- pam(md, nc, diss=TRUE)$clustering
      clustering3 <- pam(md, nc+1, diss=TRUE)$clustering
      clall<- cbind(clustering1, clustering2, clustering3)
      res[nc-min_nc+1,2] <- KL <- index.KL(data_ratio,clall,d=md,centrotypes="medoids")
      clusters <- rbind(clusters, clustering2)
    }
    print(paste("max KL for",(min_nc:max_nc)[which.max(res[,2])],"clusters=",max(res[,2])))
    print("clustering for max KL")
    print(clusters[which.max(res[,2]),])
    #write.table(res,file="KL_res.csv",sep=";",dec=",",row.names=TRUE,col.names=FALSE)
    plot(res,type="p",pch=0,xlab="Number of clusters",ylab="KL",xaxt="n")
    axis(1, c(min_nc:max_nc))

[Package clusterSim version 0.49-2 Index]