Newsgroups: comp.ai.neural-nets
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From: sopses@thor.cf.ac.uk (Susan Spenceley)
Subject: SUMMARY of 3d self-organising maps
Message-ID: <675.9505221614@thor.cf.ac.uk>
Sender: sopses@thor.cf.ac.uk (Susan Spenceley)
Organization: University of Wales College of Cardiff, Cardiff, Wales, UK
Date: Mon, 22 May 1995 17:14:26 +0100
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There have been several replies to my question about 3-d Kohonen
networks and some references. Here is a short summary

1) A. Bulsari has asked what might be gained out of 3-dimensional networks
and has suggested that a Kohonen network of the same dimension as the
input space might be the ideal situation  - since I seemed to be concerned
with neighbourliness of nodes. However the 2-d map is still the most
conveniant for a visual representation of the data.
2) Phillip Mitchem has pointed to some work on temporal self-organisation.
3) Dimitrij Surmeli to 3-d SOM work being done by Udo Seiffert in the area
of images

And as included in previous news articles

4) JJ Merelo mentioned an application in protein classification
5) Will Dwinnell asked why stop at 3-d and mentioned the dimensionality of
the problem and net optimality,
and 6) Michael Andrews about neurons n-dimensional space.

It seems that the 2-d network is conveniant for visually representing
arrangements of clusters although the nature of the input vectors MIGHT 
mean that they could be 'better' arranged in 3-dimensional space (or
indeed 1d space).

The way of evaluating a 3d arrangement isn't clear although in some
applications the physical neighbourliness does seem to have an intuitive
value that would be lost if the classes were re-arranged upon a 2-d  or 1-d 
surface. 

Networks greater than 3-d can't be visually represented so differ to the
1,2 or 3-d maps in this respect although the principles
of 2d maps could of course be extended beyond the 3d.

Would anyone using a 2-d map be willing to loose a dimension
and work only with 1-d maps? Perhaps some applications are facing
the necessity for higher dimensionality networks although theoretical
work seems to stop at 2d and despite the references that were supplied
there isn't much readily available on higher dimension networks.




 

-- 
Susan Spenceley

University of Wales, Department of Optometry and Vision Sciences
Cardiff, Wales, PO BOX 905, CF1 3XF.
