Re: [R] MDS size limitations

From: Prof Brian Ripley <>
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,        
Professor of Applied Statistics,
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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