[R] Help: Strange MDS behavior

Youngser Park youngser at jhu.edu
Thu Nov 13 19:52:49 CET 2003

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

Here is a sample code;

   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)

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

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