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

AbstractThe 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. © 2003 Wiley Periodicals, Inc.