[R] MDS size limitations

[Prof Brian Ripley]

On Thu, 21 Jun 2007, Steve Antos wrote:

> What are the limitations on size of matrix for MDS functions?

MDS works with a dissimilarity, not a matrix (neither conceptually nor in 
most R implementations, which typically use an object of class "dist").
It is better to think in terms of the number of objects 'n' and the number 
of dimensions of the representation (which I guess you mean as 2).

There are O(n^2) dissimilarities to be considered, and most of the 
algorithms appear to be slightly superlinear in that number. n=1000 runs 
in isoMDS in about a minute on my laptop, using about 75Mb of memory, and 
about 10 secs in sammon or cmdscale.  (Highly non-Euclidean 
dissimilarities are likely to be slower.)

Even 1000 objects is a lot to be considering for what is primarily a 
visualization technique.

Cruder forms of MDS such as Kohonen mapping are able to handle much larger 
datasets (but reveal less about them).

-- 
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 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595