[R] Calculation time of isoMDS and the optimal number of dimensions

[Gavin Simpson]

On Tue, 2010-05-25 at 19:00 +0200, Joris Meys wrote:
> Dear all,
> 
> I'm running a set of nonparametric MDS analyses, using a wrapper for isoMDS,
> on a 800x800 distance matrix. I noticed that setting the parameter k to
> larger numbers seriously increases the calculation time. Actually, with k=10
> it calculates already longer than for k=2 and k=5 together. It's now
> calculating for 6 hours, and counting...

metaMDS will try 'trymax' random starts of isoMDS in an attempt to see
if convergent solutions are reached. The 10d computation is clearly much
more complex than fitting rank distances in 2 or even 5 d.

> There is quite a difference between the results using k=2 or k=5 when
> looking at the first 2 dimensions (logically...). I suspect the same when
> k=10. Yet, I start asking myself whether this makes sense if I'm only using
> the first 2 dimensions. And I can't think of a formal method to check in a
> nMDS framework how much dimensions are enough. Anybody an idea?

In nMDS the configuration counts, not the axes (as they are themselves
arbitrary directions --- having one or the other of a x or y
geographical coordinate isn't much use without the other coordinate if
you want to find your way to that location - you need both). It makes no
sense what so ever to compute a 10d nMDS solution if you only want a 2d
solution for later computations; there is no guarantee that the first
two "axes" of a 10d nMDS solution will be as good as those from the 2d
solution. If you only want a 2d solution, concentrate on finding the
best 2d solution you can using metaMDS.

> I use metaMDS from the vegan package, although it's not really meant to be
> used on these data.

Why do you say that? As long as you turn off a couple of the
"ecological" helper bits in metaMDS, all it is doing is handling random
starts of the isoMDS algorithm.

> 
> Cheers
> Joris
> 

HTH

G

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