BOOK ANNOUNCEMENT

[villmann@informatik.uni-leipzig.d400.de]

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BOOK ANNOUNCEMENT


The following book is now avaible:

"Topologieerhaltung in selbstorganisierenden neuronalen Merkmalskarten"

author : Thomas Villmann

publisher : Verlag Harri Deutsch Frankfurt/M.

ISBN : 3 - 8171 - 1523 - 7

116 pages, 42 fig.


which is based on my PhD thesis.

The book describes the current state of research of measuring the 
topology preservation in Kohonen's self-organizing feature maps (SOFM).

After an introduction of SOFMs and considerations of their dynamics (
as an extension of the work done by H. Ritter et al.) actual measure of 
topology preservation are analyzed and the limits are shown.
Taking into account these consideration following an intuitive 
understanding of topology preservation a strong mathematical approach 
is developed which is based on the mathematical theory of (discrete) topology.
Using this theory a new measure, the so-called topographic function, is 
developed which measure the topology preservation according to its 
mathematical exact definition.
In the last chapter some applications of the topographic function
are presented. One of these is the estimation of growing self-organizing
feature maps with respect to their topology preservation. Thereby a growing
algorithm is presented which takes the principle components of the receptive
fields of the neurons for the growing step into account.


Please, note that the language of the book is German.

Sorry, other hardcopies of the PhD thesis are not avaible.


With best regards

Thomas Villmann

email: villmann at informatik.uni-leipzig.de