[R] Cluster graphs

[Prof Brian D Ripley]

On Thu, 30 Sep 1999, Stephen R. Laniel wrote:

> On 10/1/99, 9:42 AM +1000, Michael HART wrote:
> 
> > I have a number of items with "distances" of differences between each
> > other. What I want to do is to plot each item on a two dimensional plot
> > such that the positions on the plot indicate the approximate distance
> > between each item.
> 
> This doesn't seem like an especially R-related question, but I'll take a
> stab at it anyway.  To plot these distances, won't you need to resolve
> their positions first?  To resolve their positions, you could use a whole
> lot of methods (there's a seminal paper by Householder whose title I can't
> remember now -- it's a little paper, but dense).  The important thing to
> note is that a collection of distances doesn't uniquely specify a
> configuration; if I'm not mistaken, it only specifies configurations up to
> rigid motion.  You need to fix a coordinate system and define one of the
> points as an origin.

Yes, and also up to reflections.

> In any event, the whole problem seems beyond the scope of this list, unless
> I'm mistaken.

This problem is usually known as multidimensional scaling, I think because
influence of psychometricians.  There is an R function cmdscale in package
mva for `classical' MDS, where the distances really are Euclidean
distances, and functions sammon and isoMDS (to which it refers) for other
`distances' are in package MASS in the VR6 bundle on CRAN.

You will find a description of this in most Multivariate Analysis texts,
and in Venables & Ripley.

-- 
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)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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