INCA index

Description

INCAindex helps to estimate the number of clusters in a dataset.

Usage

INCAindex(d, pert_clus)

Arguments

Value

Returns an object of class incaix which is a list containing the following components:

Note

For a correct geometrical interpretation it is convenient to verify whether the distance matrix d is Euclidean. It admits the associated methods summary and plot. The first simply returns the percentage of well-classified units and the second offers a barchart with the percentages of well classified units for each group in the given partition.

Author(s)

Itziar Irigoien itziar.irigoien@ehu.es; Konputazio Zientziak eta Adimen Artifiziala, Euskal Herriko Unibertsitatea (UPV-EHU), Donostia, Spain.

Conchita Arenas carenas@ub.edu; Departament d'Estadistica, Universitat de Barcelona, Barcelona, Spain.

References

Arenas, C. and Cuadras, C.M. (2002). Some recent statistical methods based on distances. Contributions to Science, 2, 183–191.

Irigoien, I. and Arenas, C. (2008). INCA: New statistic for estimating the number of clusters and identifying atypical units. Statistics in Medicine, 27(15), 2948–2973.

See Also

estW, INCAtest

Examples

#generate 3 clusters, each of them with 20 objects in dimension 5.
mu1 <- sample(1:10, 5, replace=TRUE)
x1 <- matrix(rnorm(20*5, mean = mu1, sd = 1),ncol=5, byrow=TRUE)
mu2 <- sample(1:10, 5, replace=TRUE)
x2 <- matrix(rnorm(20*5, mean = mu2, sd = 1),ncol=5, byrow=TRUE)
mu3 <- sample(1:10, 5, replace=TRUE)
x3 <- matrix(rnorm(20*5, mean = mu3, sd = 1),ncol=5, byrow=TRUE)
x <- rbind(x1,x2,x3)

# Euclidean distance between units.
d <- dist(x)

# given the right partition, calculate the percentage of well classified objects.
partition <- c(rep(1,20), rep(2,20), rep(3,20))
INCAindex(d, partition)


# In order to estimate the number of cluster in data, try several 
#  partitions and compare the results
library(cluster)
T <- rep(NA, 5)
for (l in 2:5){
	part <- pam(d,l)$clustering
	T[l] <- INCAindex(d,part)$Total
}

plot(T, type="b",xlab="Number of clusters", ylab="INCA", xlim=c(1.5, 5.5))

Results

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> library(ICGE)
Loading required package: MASS
Loading required package: cluster
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/ICGE/INCAindex.Rd_%03d_medium.png", width=480, height=480)
> ### Name: INCAindex
> ### Title: INCA index
> ### Aliases: INCAindex print.incaix summary.incaix plot.incaix
> ### Keywords: multivariate cluster
> 
> ### ** Examples
> 
> #generate 3 clusters, each of them with 20 objects in dimension 5.
> mu1 <- sample(1:10, 5, replace=TRUE)
> x1 <- matrix(rnorm(20*5, mean = mu1, sd = 1),ncol=5, byrow=TRUE)
> mu2 <- sample(1:10, 5, replace=TRUE)
> x2 <- matrix(rnorm(20*5, mean = mu2, sd = 1),ncol=5, byrow=TRUE)
> mu3 <- sample(1:10, 5, replace=TRUE)
> x3 <- matrix(rnorm(20*5, mean = mu3, sd = 1),ncol=5, byrow=TRUE)
> x <- rbind(x1,x2,x3)
> 
> # Euclidean distance between units.
> d <- dist(x)
> 
> # given the right partition, calculate the percentage of well classified objects.
> partition <- c(rep(1,20), rep(2,20), rep(3,20))
> INCAindex(d, partition)

 ---INCA index---

      number    well       %
Group units   classified  well class. 
  1      20      20        1 
  2      20      20        1 
  3      20      20        1 

 INCA index : 1 
 ---------------------------------------------
> 
> 
> # In order to estimate the number of cluster in data, try several 
> #  partitions and compare the results
> library(cluster)
> T <- rep(NA, 5)
> for (l in 2:5){
+ 	part <- pam(d,l)$clustering
+ 	T[l] <- INCAindex(d,part)$Total
+ }
> 
> plot(T, type="b",xlab="Number of clusters", ylab="INCA", xlim=c(1.5, 5.5))
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>