On the stationary state of Kohonen's self-organizing sensory mapping
Biological Cybernetics
Introduction to the theory of neural computation
Introduction to the theory of neural computation
Neural computation and self-organizing maps: an introduction
Neural computation and self-organizing maps: an introduction
An analysis of the elastic net approach to the traveling salesman problem
Neural Computation
Asymptotic level density in topological feature maps
IEEE Transactions on Neural Networks
Magnification Control in Self-Organizing Maps and Neural Gas
Neural Computation
Winner-Relaxing Self-Organizing Maps
Neural Computation
International Journal of Remote Sensing
Magnification control in winner relaxing neural gas
Neurocomputing
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Whileas the Kohonen Self Organizing Map shows an asymptotic level density following a power law with a magnification exponent 2/3, it would be desired to have an exponent 1 in order to provide optimal mapping in the sense of information theory. In this paper, we study analytically and numerically the magnification behaviour of the Elastic Net algorithm as a model for self-organizing feature maps. In contrast to the Kohonen map the Elastic Net shows no power law, but for onedimensional maps nevertheless the density follows an universal magnification law, i.e. depends on the local stimulus density only and is independent on position and decouples from the stimulus density at other positions.