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

The magnification behavior 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 achieve 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 behavior 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.