R help - Feb 2007 - isoMDS - high stress value and strange configuration

Dear R users,

I have a specific question about isoMDS. Imagine the following (fake) 
distance table:

        hamburg bremen berlin munich cologne
hamburg       0    911    982    677     424
bremen      911      0    293    547     513
berlin      982    293      0    785     875
munich      677    547    785      0     375
cologne     424    513    875    375       0

Now if I try a non-metric multidimensional scaling on these 
dissimilarities using isoMDS (or metaMDS), the stress value is 6.34. 
Nevertheless, other programs (e.g. the Minissa routine implemented in 
UCINet) yield a stress value of 0.00, and the configuration looks 
completely different. I tried this with multiple distance matrices: 
One time UCINet computed a stress value of 0.21 while isoMDS produced 
a stress of 0.33, and again the configuration was completely 
different and apparently random (while the configuration in UCINet 
still made sense). Here is what I tried:

isoMDS(cities, y = cmdscale(cities, k = 2), k = 2, maxit = 50)

Please give me a hint on how to improve the results. I suppose the 
above command is not complete, or something is wrong with it, or 
maybe the input distances are not in the right format.

Btw, the problem does not occur when I use the real distances between 
these cities, not some other numbers, so apparently three-digit 
numbers should be fine as input values?

Thanks!

Phil

> I have a specific question about isoMDS. Imagine the following (fake) 
> distance table:
> 
>         hamburg bremen berlin munich cologne
> hamburg       0    911    982    677     424
> bremen      911      0    293    547     513
> berlin      982    293      0    785     875
> munich      677    547    785      0     375
> cologne     424    513    875    375       0
> 
> Now if I try a non-metric multidimensional scaling on these 
> dissimilarities using isoMDS (or metaMDS), the stress value is 6.34. 
> Nevertheless, other programs (e.g. the Minissa routine implemented in 
> UCINet) yield a stress value of 0.00, and the configuration looks 
> completely different. 
This indeed seems to be a case where NMDS is trapped in its starting
configuration. Metric scaling (cmdscale) produces a cute "horseshoe",
but the best NMDS solutions looks completely different. Any small change
from the initial solution leads into a worse configuration, and you need
a bigger change in the beginning. Using a random configuration seems to
help:
> isoMDS(dis, initMDS(dis))
initial  value 36.383132 
iter   5 value 28.671652
iter  10 value 16.711327
iter  15 value 6.392572
iter  20 value 3.007208
final  value 0.000000 
converged
$points
              [,1]      [,2]
hamburg  29.428121 -36.07858
bremen    2.740499  32.38745
berlin    1.984215  35.35429
munich  -16.910941 -14.13750
cologne -13.844187 -15.24468

$stress
[1] 1.56159e-14

In this case I generated the random configuration using function initMDS
of vegan, but you can do that quite well by any other way.

Another point (which does not matter here so much) is that isoMDS
multiplies stress by 100, so that your stress of 6 would corresponde
0.06 in some other software (assuming they use the same stress).

cheers, jari oksanen
-- 
Jari Oksanen <jarioksa at sun3.oulu.fi>