From: phi@cs.uwa.oz.au (Philip HINGSTON)
Subject: Re: Kohonen nets with other than rectangular output arrays
Organization: Dept. Computer Science, University of Western Australia.
Date: Thu, 7 Jan 1993 01:05:37 GMT

Before Christmas I posted a request for references on Kohonen networks
with neighbourhood graphs other than rectangular grids. I recieved a
number of very helpful replies as well as requests for copies of those
replies. Many thanks to those who responded with references. Rather than
responding individually to those who asked for copies, I include 2 replies
which subsumed the others.

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To: phi@cs.uwa.edu.au
Subject: Re: Kohonen nets with other than rectangular output arrays
Newsgroups: comp.ai.neural-nets
Organization: CS Dept, University of Texas at Austin
Cc: 

In article <phi.724924574@wambenger> you write:
>Hi, I guess the subject line says it. I have found some things
>discussing the choice between 1-d, 2-d, 3-d etc arrays of output
>neurons. What about other neighbourhood graphs? e.g. toroidal, trees etc
>Does anyone know of any references? Thanks, phi
>

Hi, the Fritzke paper discusses a variant of the kohonen map that adjusts
better to non-convex regions.  It's got a nice reference list.  The
Blackmore and Miikkulainen paper presents a different method for the same
purpose.  Contact risto@cs.utexas.edu to inquire, if the Fritzke paper
suits your interest.

Best of luck!

@string{ICANN-91 = "Proceedings of the International Conference on
		 Artificial Neural Networks {\rm (Espoo, Finland)}"}
@string{NORTH     = "North-Holland"}
@string{NORTH-ADDR = "Amsterdam; New York"}

@InProceedings{fritzke:grow,
  author = 	"Bernd Fritzke",
  title = 	"Let it Grow---{S}elf-Organizing Feature Maps with
		 Problem Dependent Cell Structure",
  booktitle = 	ICANN-91,
  pages = 	"403--408",
  publisher = 	NORTH,
  address = 	NORTH-ADDR,
  year = 	"1991"
}

@Unpublished{blackmore:incremental,
  author = 	"Justine Blackmore and Risto Miikkulainen",
  title = 	"Incremental Grid Growing: {E}ncoding High-Dimensional
		 Structure into a Two-Dimensional Feature Map",
  note = 	"submitted to ICNN-93",
  year = 	"1992"
}
-- 
Jonathan Abbey                               jonabbey@cs.utexas.edu
the university of texas at austin             --------------------
computer science/math/psychology    -- Oh, my.. life is just so.. you know.. --
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From: karit@idiap.ch (Kari Torkkola)
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To: phi@cs.uwa.edu.au (Philip HINGSTON)
Subject: Re: Kohonen nets with other than rectangular output a
Cc: karit@idiap.ch
Reply-To: karit@idiap.ch
Status: RO

In article <phi.724924574@wambenger>, you write:
|> Hi, I guess the subject line says it. I have found some things
|> discussing the choice between 1-d, 2-d, 3-d etc arrays of output
|> neurons. What about other neighbourhood graphs? e.g. toroidal, trees etc
|> Does anyone know of any references? Thanks, phi
|> 



You might want to look at the following articles:


@Article{Kangas90,
  author = 	"Jari Kangas and Teuvo Kohonen and Jorma Laaksonen",
  title = 	"Variants of Self-Organizing Maps",
  journal = 	"IEEE Transactions on Neural Networks",
  year = 	"1990",
  volume = 	"1",
  number = 	"1",
  pages = 	"93-99",
  month = 	"March",
}

@InProceedings{Martinetz91,
  author = "Thomas Martinetz and Klaus Schulten",
  title = "A Neural-Gas Network Learns Topologies",
  booktitle = "Artificial Neural Networks 
  	      (Proceedings of the Int. Conf. on 
  	      Artificial Neural Networks, ICANN91)",
  year = "1991",
  volume = "I",
  pages = "397-402",
  address =  "Espoo, Finland",
  month =    "June 24-28",
}

@InProceedings{Fritzke91,
  author = "Bernd Fritzke",
  title = "Let It Grow - Self-Organizing feature Maps with 
	   Problem Dependent cell Structure",
  booktitle = "Artificial Neural Networks 
  	      (Proceedings of the Int. Conf. on 
  	      Artificial Neural Networks, ICANN91)",
  year = "1991",
  volume = "I",
  pages = "403-408",
  address =  "Espoo, Finland",
  month =    "June 24-28",
}


Once I was using SOMs as the basis for speech recognition. Then 
I played myself with toroids and spherical surfaces, but they
affected the recognition accuracy (which was all I was interested in
at that point) very little, if at all (as expected). 


Yours,

Kari Torkkola,  research director, speech recognition
IDIAP (Institut Dalle Molle 
       d'Intelligence Artificielle Perceptive)
C.P. 609                                               tel:   +41-26-227664
CH-1920 Martigny                                       fax:   +41-26-227818
Switzerland                                            email: karit@idiap.ch
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