# [R] Help with Mahalanobis

Jose Claudio Faria joseclaudio.faria at terra.com.br
Mon Jul 11 01:13:05 CEST 2005

```Indeed, it is very nice Gabor (as always)!

So, a doubt: how to preserve the 'rowname' and 'colname' of D2, like in the
first function? I think it is useful to posterior analyzes (as cluster, for
example).

Regards,

# A small correction (reference to gtools was eliminated)
D2Mah2 = 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))
nObjects = nrow(mds)
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)

Gabor Grothendieck 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)[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))
>
>   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)[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
>>mails:
>> joseclaudio.faria at terra.com.br
>> jc_faria at uesc.br
>> jc_faria at uol.com.br
>>tel: 73-3634.2779
>>
>>______________________________________________
>>R-help at stat.math.ethz.ch mailing list
>>https://stat.ethz.ch/mailman/listinfo/r-help
>>
>
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--
Jose Claudio Faria
Brasil/Bahia/UESC/DCET