# [R] Help with Mahalanobis

Jose Claudio Faria joseclaudio.faria at terra.com.br
Sun Jul 10 18:24:07 CEST 2005

```Well, as I did not get a satisfactory reply to the original question I tried to
make a basic function that, I find, solve the question.

I think it is not the better function, but it is working.

So, perhaps it can be useful to other people.

#
# Calculate the matrix of Mahalanobis Distances between groups
# from data.frames
#
# by: José Cláudio Faria
# date: 10/7/05 13:23:48
#

D2Mah = function(y, x) {

stopifnot(is.data.frame(y), !missing(x))
stopifnot(dim(y)[1] != dim(x)[1])
y    = as.matrix(y)
x    = as.factor(x)
man  = manova(y ~ x)
E    = summary(man)\$SS[2] #Matrix E
S    = as.matrix(E\$Residuals)/man\$df.residual
InvS = solve(S)
mds  = matrix(unlist(by(y, x, mean)), byrow=T, ncol=ncol(y))

colnames(mds) = names(y)
Objects       = levels(x)
rownames(mds) = Objects

library(gtools)
nObjects = nrow(mds)
comb     = combinations(nObjects, 2)

tmpD2 = numeric()
for (i in 1:dim(comb)[1]){
a = comb[i,1]
b = comb[i,2]
tmpD2[i] = (mds[a,] - mds[b,])%*%InvS%*%(mds[a,] - mds[b,])
}

# Thanks Gabor for the below
tmpMah = matrix(0, nObjects, nObjects, dimnames=list(Objects, Objects))
tmpMah[lower.tri(tmpMah)] = tmpD2
D2 = tmpMah + t(tmpMah)
return(D2)
}

#
# To try
#
D2M = D2Mah(iris[,1:4], iris[,5])
print(D2M)

Thanks all for the complementary aid (specially to Gabor).

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