Re: [R] MDS size limitations

From: Prof Brian Ripley <ripley_at_stats.ox.ac.uk>
Date: Thu, 21 Jun 2007 15:51:34 +0100 (BST)

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

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