# [R] Help with Mahalanobis

Jose Claudio Faria joseclaudio.faria at terra.com.br
Fri Jul 8 19:57:15 CEST 2005

```Dear R list,

I'm trying to calculate Mahalanobis distances for 'Species' of 'iris' data
as obtained below:

Squared Distance to Species From Species:

Setosa Versicolor Virginica
Setosa 	           0   89.86419 179.38471
Versicolor  89.86419          0  17.20107
Virginica  179.38471   17.20107         0

These distances were obtained with proc 'CANDISC' of SAS, please,
see Output 21.1.2: Iris Data: Squared Mahalanobis Distances from
http://www.id.unizh.ch/software/unix/statmath/sas/sasdoc/stat/chap21/sect19.htm

From these distances my intention is to make a cluster analysis as below, using
the package 'mclust':

In prior mail, my basic question was: how to obtain this matrix with R
from 'iris' data?

Well, I think that the basic soluction to calculate this distances is:

#
# --- Begin R script 1 ---
#
x   = as.matrix(iris[,1:4])
tra = iris[,5]

man = manova(x ~ tra)

# Mahalanobis
E    = summary(man)\$SS #Matrix E
S    = as.matrix(E\$Residuals)/man\$df.residual
InvS = solve(S)
ms = matrix(unlist(by(x, tra, mean)), byrow=T, ncol=ncol(x))
colnames(ms) = names(iris[1:4])
rownames(ms) = c('Set', 'Ver', 'Vir')
D2.12 = (ms[1,] - ms[2,])%*%InvS%*%(ms[1,] - ms[2,])
print(D2.12)
D2.13 = (ms[1,] - ms[3,])%*%InvS%*%(ms[1,] - ms[3,])
print(D2.13)
D2.23 = (ms[2,] - ms[3,])%*%InvS%*%(ms[2,] - ms[3,])
print(D2.23)
#
# --- End R script 1 ---
#

Well, I would like to generalize a soluction to obtain
the matrices like 'Mah' (below) or a complete matrix like in the
Output 21.1.2. Somebody could help me?

#
# --- Begin R script 2 ---
#

Mah = c(        0,
89.86419,        0,
179.38471, 17.20107, 0)

n = 3
D = matrix(0, n, n)

nam = c('Set', 'Ver', 'Vir')
rownames(D) = nam
colnames(D) = nam

k = 0
for (i in 1:n) {
for (j in 1:i) {
k      = k+1
D[i,j] = Mah[k]
D[j,i] = Mah[k]
}
}

D=sqrt(D) #D2 -> D

library(mclust)
dendroS = hclust(as.dist(D), method='single')
dendroC = hclust(as.dist(D), method='complete')

win.graph(w = 3.5, h = 6)
split.screen(c(2, 1))
screen(1)
plot(dendroS, main='Single', sub='', xlab='', ylab='', col='blue')

screen(2)
plot(dendroC, main='Complete', sub='', xlab='', col='red')
#
# --- End R script 2 ---
#

I always need of this type of analysis and I'm not founding how to make it in
the CRAN documentation (Archives, packages: mclust, cluster, fpc and mva).

Regards,
--
Jose Claudio Faria
Brasil/Bahia/UESC/DCET