Hi everyone. My problem is about multivariate analysis. Given a multivariate data X, of dimension (n by p), n is the number of observations while p is the number of variables. I wanted a sample of size p+1 that will have its product of the eigen values of the covariance matrix to be the minimum among all the possible samples (n combination (p+1)). I have written a syntax with worked well, but the problem is that it does not work when the dimension of X is large (when n is greater than 25). I think the problem is memory size, is there anyway I can maximize the memory.
Here is the syntax that I used.
 
> bestunits <- function(x){
+ n <- nrow(x)
+ p <- ncol(x)
+ h <- p+1
+ nchoosek <- function(n,h){
+ factorial(n)/(factorial(h+1)*factorial(n-h-1))}
+ vec11 <- matrix(nrow=nchoosek(n,h), ncol=p)
+ vec12 <- matrix(nrow=nchoosek(n,h), ncol=h)
+ for (i in 1:nchoosek(n,h)){
+ flag <- sample(1:n, h, replace=FALSE)
+ z <- x[flag,]
+ y <- eigen(var(z), only.values=TRUE)$values
+ vec11[i,] <- y
+ vec12[i,] <- flag
+ }
+ product <- apply(vec11,1,prod)
+ best <- which.min(product)
+ sample <- vec12[best,]
+ bestsample <- x[sample,]
+ return(bestsample)
+ }
Thanks
Oyeyemi, Gafar Matanmi
Department of Statistics
University of Ilorin
Ilorin, Nigeria


      
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