Winner-Relaxing and Winner-Enhancing Kohonen Maps:
Maximal Mutual Information from Enhancing the Winner
Jens Christian Claussen
The magnification behaviour of a
generalized family of self-organizing
feature maps,
the Winner Relaxing and Winner Enhancing
Kohonen algorithms
is analyzed by the magnification law in the
one-dimensional case, which can be obtained analytically.
The Winner-Enhancing case allows
to acheive a magnification exponent of one
and therefore provides optimal mapping in the sense of
information theory.
A numerical verification of the magnification law is
included,
and the ordering behaviour is analyzed.
Compared to the original Self-Organizing Map and
some other approaches, the generalized
Winner Enforcing Algorithm requires minimal extra computations
per learning step and is conveniently easy to implement.
9.7.2002.
Estimated to 8 pages (1 table and 5 figures included)
in journal format ($%&*§&-Word).
Currently available as Preprint.
Submitted to Complexity (Wiley Interscience)
for the Focus Issue on Complex Adaptive Systems,
Delmenhorst, March 2002, org. H. G. Schuster and K. Pawelzik.
This paper is not (yet) available online.
If you are interested,
please do not hesitate to
e-mail me
for a printed copy.