Re: Kohonen networks and internals

[Robert.Land@t-online.de (robert_wilhelm_land)]

Robert Land wrote:
> It would be rather helpful to understand the SOFM's in a deeper way
> before starting to work with them.
> 
> Having an awful trouble in reading and understanding Kohonens book I
> would like to ask the list maintainers to permit me in asking and
> taking some chapters out of "Self-Organizing Maps" , 2nd edition into
> discussion - at least for this period of low traffic. It might help to
> maintain pdp++ by more users.




"Randall C. O'Reilly" wrote:
> This might be OK, but I do think that there are some better treatments
> of this material in the literature that might make that unnecessary.
> For example, the chapters in Hertz, Krough, & Palmer, though somewhat
> brief, are fairly clear.  Perhaps others on the list have other
> suggestions for good recent treatments?  BTW, I found the Kohonen
> presentation of his ideas not particularly easy to understand too.


Padraic Monaghan wrote:
> Hi, I found Kohonen's description of his stuff very accessible in the paper
> on the phonetic typewriter:
> 
> Kohonen, T. (1988).  The 'neural' phonetic typewriter. Computer,
> 21(3):11-22.




The phonetic typwriter is mentioned in SOM 2nd edition (quite at the
beginning) - I didn't have a closer look at it yet because I tried to
get a first impression of the book by reading rather briefly through
the first 3 chapters and then to decide if further literature is
required for a rather practical thinking person as I am.
Kohonen seems to be quite aware of the difficulties as he presents a
vast amount of books on page 277ff with very helpful advises and
intro's. Yet I have followed Randall's suggestion and ordered the book
of Hertz, Krough, & Palmer which can also be found at the nn FAQ_5 on
ftp.sas.com. Unfortunatly this and another book which deals deeply
with statstical analysis (Applied multivariate methods for data
analysis,ISBN: 0534237967) which I have ordered too can only be
delivered hopefuly before christmas. Surprising that I found a very
helpful german book introducing SOM's (in a better matter than any
other book or paper I had read so far) at my former university which
helps to step in without getting deperated about the maths required.
(I prefer more a "spiral" way of learning, going from the outer to the
inner)

What really _did_ surprise me was that not one person responded to my
inquiry on the neuralnet newsgroup. Either all are busy or they have
simular difficulties as I do - but rather want to ignore this.
Additionaly I made a inquiry on sci.maths on a awful context to read
from the previously mentioned FAQ for which I hope no one would blame
me presenting in this list:

"
Kohonen's learning law is an approximation to the k-means model, which
is an approximation to normal mixture estimation by maximum likelihood
assuming that the mixture components (clusters) all have spherical
covariance matrices and equal sampling probabilities. Hence if the
population contains clusters that are not equiprobable, k-means will
tend to produce sample clusters that are more nearly equiprobable than
the population clusters. Corrections for this bias can be obtained by
maximizing the likelihood without the assumption of equal sampling
probabilities Symons (1981). Such corrections are similar to
conscience but have the opposite effect. 
"

(The book of Symons seems to have run out)
I tryed to make some inquiries on "spherical covariance matrices"
which I had never heard of, but failed here too. So if anyone on this
list would be so kind and decompress this context in a understandably
matter - I would be very very thankful.




Robert