Winner-relaxing and winner-enhancing Kohonen maps: Maximal mutual information from enhancing the winner

Details Winner-relaxing and winner-enhancing Kohonen maps: Maximal mutual information from enhancing the winner Winner-relaxing and winner-enhancing Kohonen maps: Maximal mutual information from enhancing the winner

2006-09-20

arxiv.org/abs/cond-mat/0609513v1

Complexity 8(4), 15-22 (2003)

Physics

Condensed Matter

Statistical Mechanics

6 pages, 5 figures. For an extended version refer to cond-mat/0208414 (Neural Computation 17, 996-1009)

Scientific paper

10.1002/cplx.10084

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.

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