ICGE (version 0.4.2)

estW: INCA Statistic

Description

Assume that n units are divided into k clusters C1,...,Ck, and consider a fixed unit x0. Function estW calculates the INCA statistic \(W(x0)\) and the related \(U_i\) statistics.

Usage

estW(d, dx0, pert = "onegroup")

Value

The function returns an object of class incaest which is a list containing the following components:

Wvalue

is the INCA statistic \(W(x_0)\).

Uvalue

is a vector containing the statistics \(U_i\).

Arguments

d

a distance matrix or a dist object with distance information between units.

dx0

an n-vector containing the distances d0j between x0 and unit j.

pert

an n-vector that indicates which group each unit belongs to. Note that the expected values of pert are consecutive integers bigger or equal than 1 (for instance 1,2,3,4..., k). The default value indicates the presence of only one group in data.

Author

Itziar Irigoien ; Konputazio Zientziak eta Adimen Artifiziala, Euskal Herriko Unibertsitatea (UPV/EHU), Donostia, Spain.

Conchita Arenas ; 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

vgeo, proxi , deltas

Examples

data(iris)
d <- dist(iris[,1:4])

# characteristics of a specific flower (likely group 1)
x0 <- c(5.3, 3.6, 1.1, 0.1) 
# distances between  flower x0 and the rest of flowers in iris
dx0 <- rep(0,150)
for (i in 1:150){
	dif <-x0-iris[i,1:4]
	dx0[i] <- sqrt(sum(dif*dif))
}
estW(d, dx0, iris[,5])