[R] Help: Strange MDS behavior

[Youngser Park]

Hi!
I have a dissimilarity matrix X and try to compare it with X' = 
dist(cmdscsale(X,k)).
If I increase k, I should expect that the error (or fit) should 
monotonically decrease, right.

Here is a sample code;

   library(mva)
   set.seed(12345)
   x <- as.matrix(dist(matrix(rnorm(100),ncol=10,byrow=T)))
#  x[1,2]<-x[2,1]<-1000  ## <<--** 1
#  x[5,6]<-x[6,5]<-1000  ## <<--** 2
   fit <- NULL
   for(k in 1:9)
    {
    mds <- cmdscale(x,k,add=T)
    xprime <- as.matrix(dist(mds$points))
    fit[k] <- sum((x-xprime)^2)/sum(x^2)
    }
   plot(fit)

When I run this example, it gives a nice "good" plot. However, with 
those two commented lines added, the plot is opposite, that is, the fit 
is increasing as k grows!

I really don't understand this behavior. The reason why I added those 
two lines is because my real input data is not an Euclidean distance 
matrix, but a dissimilarity matrix calculated from my own metric.

So, does this mean that the matrix X *must* be an Euclidean distance 
matrix in this example?
Thanks in advance.

- Youngser