# [R] Help with Mahalanobis

Gabor Grothendieck ggrothendieck at gmail.com
Mon Jul 11 01:08:50 CEST 2005

```And here is one more simplification using the buildin mahalanobis
function:

D2Mah3 = function(y, x) {

stopifnot(is.data.frame(y), !missing(x))
stopifnot(dim(y) != dim(x))
y    = as.matrix(y)
x    = as.factor(x)
man  = manova(y ~ x)
E    = summary(man)\$SS #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))

nObjects = nrow(mds)

### changed part is next two statements
f <- function(a,b) mapply(function(a,b)
mahalanobis(mds[a,],mds[b,],InvS,TRUE), a, b)

D2 <- outer(seq(nObjects), seq(nObjects), f)
}

#
# test
#
D2M3 = D2Mah3(iris[,1:4], iris[,5])

On 7/10/05, Gabor Grothendieck <ggrothendieck at gmail.com> wrote:
> I think you could simplify this by replacing everything after the
> nObjects = nrow(mds) line with just these two statements.
>
>  f <- function(a,b) mapply(function(a,b)
>    (mds[a,] - mds[b,])%*%InvS%*%(mds[a,] - mds[b,]), a,b)
>
>  D2 <- outer(seq(nObjects), seq(nObjects), f)
>
> This also eliminates dependence on gtools and the complexity
> of dealing with triangular matrices.
>
> Regards.
>
> Here it is in full:
>
> D2Mah2 = function(y, x) {
>
>  stopifnot(is.data.frame(y), !missing(x))
>  stopifnot(dim(y) != dim(x))
>  y    = as.matrix(y)
>  x    = as.factor(x)
>  man  = manova(y ~ x)
>  E    = summary(man)\$SS #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))
>
>  library(gtools)
>  nObjects = nrow(mds)
>
>  ### changed part is next two statements
>  f <- function(a,b) mapply(function(a,b)
>    (mds[a,] - mds[b,])%*%InvS%*%(mds[a,] - mds[b,]), a,b)
>
>  D2 <- outer(seq(nObjects), seq(nObjects), f)
> }
>
> #
> # test
> #
> D2M2 = D2Mah2(iris[,1:4], iris[,5])
> print(D2M2)
>
>
>
>
> On 7/10/05, Jose Claudio Faria <joseclaudio.faria at terra.com.br> wrote:
> > 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) != dim(x))
> >   y    = as.matrix(y)
> >   x    = as.factor(x)
> >   man  = manova(y ~ x)
> >   E    = summary(man)\$SS #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)){
> >     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
> > mails:
> >  joseclaudio.faria at terra.com.br
> >  jc_faria at uesc.br
> >  jc_faria at uol.com.br
> > tel: 73-3634.2779
> >
> > ______________________________________________
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