On the stationary state of Kohonen's self-organizing sensory mapping
Biological Cybernetics
Kernel-based equiprobabilistic topographic map formation
Neural Computation
Faithful Representations and Topographic Maps: From Distortion- to Information-Based Self-Organization
Neural Computation and Self-Organizing Maps; An Introduction
Neural Computation and Self-Organizing Maps; An Introduction
Kernel-based topographic map formation by local density modeling
Neural Computation
Asymptotic Level Density of the Elastic Net Self-Organizing Feature Map
ICANN '02 Proceedings of the International Conference on Artificial Neural Networks
Asymptotic level density in topological feature maps
IEEE Transactions on Neural Networks
Magnification Control in Self-Organizing Maps and Neural Gas
Neural Computation
Self-organizing maps with refractory period
ICANN'07 Proceedings of the 17th international conference on Artificial neural networks
Investigation of topographical stability of the concave and convex self-organizing map variant
ICANN'06 Proceedings of the 16th international conference on Artificial Neural Networks - Volume Part I
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A new family of self-organizing maps, the winner-relaxing Kohonen algorithm, is introduced as a generalization of a variant given by Kohonen in 1991. The magnification behavior is calculated analytically. For the original variant, a magnification exponent of 4/7 is derived; the generalized version allows steering the magnification in the wide range from exponent 1/2 to 1 in the one-dimensional case, thus providing optimal mapping in the sense of information theory. The winner-relaxing algorithm requires minimal extra computations per learning step and is conveniently easy to implement.