[arthur@mail4.ai.univie.ac.at: TR: Limitations of SOM]

[Jonathan Baxter]

Commenting on this paper:

> > Flexer A.: Limitations of self-organizing maps for vector quantization and
> >    multidimensional scaling, to appear in: Advances in Neural Information
> >    Processing Systems 9, edited by M.C. Mozer, M.I. Jordan, and T. Petsche,
> >    available in 1997.

Shimon Edelman said:

> 
> Seeing that comments are welcome... there seems to be a rather glaring
> gap in the references in this TR. Fukunaga proposed a similar
> combination of clustering and topology-preservation criteria in 1972,
> and there was a recent paper by Webb following up on that work. 
> 
> It would have been nice to see Baxter's idea of Canonical Vector
> Quantization discussed in this context.

If anyone is interested, there is a recent version (July 1996) of the Canonical
Quantization paper on my home page:

http://keating.anu.edu.au/~jon/papers/canonical.ps.gz

Title: The Canonical Distortion Measure for Vector Quantization and
Approximation.  
Author: Jonathan Baxter 
Abstract: 

To measure the quality of a set of vector quantization points a means
of measuring the distance between a random point and its quantization
is required. Common metrics such as the {\em Hamming} and {\em
Euclidean} metrics, while mathematically simple, are inappropriate for
comparing speech signals or images. In this paper it is shown how an
{\em environment} of functions on an input space $X$ induces a {\em
canonical distortion measure} (CDM) on X.  The depiction ``canonical''
is justified because it is shown that optimizing the reconstruction
error of X with respect to the CDM gives rise to optimal piecewise
constant approximations of the functions in the environment. The CDM
is calculated in closed form for several different function classes.
An algorithm for training neural networks to implement the CDM is
presented along with some encouraging experimental results.

-------------
Jonathan Baxter	
Department of Systems Engineering
Research School of Information Science and Technology
Australian National University
Canberra, A.C.T 0200
Australia 
Tel: +61 6 249 5182
Fax: +61 6 279 8088
E-mail: jon at syseng.anu.edu.au