[R] Help with Mahalanobis

[Jose Claudio Faria]

I think we now have a very good R function here.
Thanks for all Gabor!

JCFaria

Gabor Grothendieck wrote:
> This one adds the labels:
> 
> 
> D2Mah4 = 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$df.residual
>  InvS = solve(S)
>  mds  = matrix(unlist(by(y, x, mean)), byrow=T, ncol=ncol(y))
> 
>  f <- function(a,b) mapply(function(a,b)
>    mahalanobis(mds[a,],mds[b,],InvS,TRUE), a, b)
>  seq. <- seq(length = nrow(mds))
>  names(seq.) <- levels(x)
>  D2 <- outer(seq., seq., f)
> }
> 
> #
> # test
> #
> D2M4 = D2Mah4(iris[,1:4], iris[,5])
> print(D2M4)
> 
> 
> 
> On 7/10/05, Jose Claudio Faria <joseclaudio.faria at terra.com.br> wrote:
> 
>>Indeed, it is very nice Gabor (as always)!
>>
>>So, a doubt: how to preserve the 'rowname' and 'colname' of D2, like in the
>>first function? I think it is useful to posterior analyzes (as cluster, for
>>example).
>>
>>Regards,
>>
>># A small correction (reference to gtools was eliminated)
>>D2Mah2 = function(y, x) {
>>  stopifnot(is.data.frame(y), !missing(x))
>>  stopifnot(dim(y)[1] != dim(x)[1])
>>  y    = as.matrix(y)
>>  x    = as.factor(x)
>>  man  = manova(y ~ x)
>>  E    = summary(man)$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
>>>>Estatistica Experimental/Prof. Adjunto
>>>>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
>>>>PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
>>>>
>>>
>>>
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>>>
>>
>>
>>--
>>Jose Claudio Faria
>>Brasil/Bahia/UESC/DCET
>>Estatistica Experimental/Prof. Adjunto
>>mails:
>> joseclaudio.faria at terra.com.br
>> jc_faria at uesc.br
>> jc_faria at uol.com.br
>>tel: 73-3634.2779