Magnification Laws of Winner-Relaxing and Winner-Enhancing Kohonen Feature Maps

Self-Organizing Maps are models for unsupervised representation formation of cortical receptor fields by stimuli-driven self-organization in laterally coupled winner-take-all feedforward structures. This paper discusses modifications of the original Kohonen model that were motivated by a potential function, in their ability to set up a neural mapping of maximal mutual information. Enhancing the winner update, instead of relaxing it, results in an algorithm that generates an infomax map corresponding to magnification exponent of one. Despite there may be more than one algorithm showing the same magnification exponent, the magnification law is an experimentally accessible quantity and therefore suitable for quantitative description of neural optimization principles.