[R] Difference between prcomp and cmdscale

[Prof Brian Ripley]

On Thu, 14 Jun 2007, michael watson (IAH-C) wrote:

> I'm looking for someone to explain the difference between these
> procedures.  The function prcomp() does principal components anaylsis,
> and the function cmdscale() does classical multi-dimensional scaling
> (also called principal coordinates analysis).
>
> My confusion stems from the fact that they give very similar results:
>
> my.d <- matrix(rnorm(50), ncol=5)
> rownames(my.d) <- paste("c", 1:10, sep="")
> # prcomp
> prc <- prcomp(my.d)
> # cmdscale
> mds <- cmdscale(dist(my.d))
> cor(prc$x[,1], mds[,1]) # produces 1 or -1
> cor(prc$x[,2], mds[,2]) # produces 1 or -1
>
> Presumably, under the defaults for these commands in R, they carry out
> the same (or very similar) procedures?

For Eucldean distance, the same.  The point being that classical MDS on 
Euclidean distances is just PCA on the reconstucted configuration, but 
that MDS is not restricted to a data matrix.

The relationship is explained in MASS, for example.

> Thanks
> Mick


-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
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