Extended Self Organizing Feature Map: A Tagged Potential Field Approach
Neural Processing Letters
Magnification Control in Self-Organizing Maps and Neural Gas
Neural Computation
Adaptive FIR neural model for centroid learning in self-organizing maps
IEEE Transactions on Neural Networks
A sequential algorithm for training the SOM prototypes based on higher-order recursive equations
Advances in Artificial Neural Systems
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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Two nonlinear models of weight adjustments of self-organizing maps are derived to obtain desirable densities of output units, one that approaches the probability distribution p(ξ) of the inputs and one that approaches a uniform distribution. If a convex model is used to adjust weights, the density of output units can be made to approach p(ξ) instead of the p(ξ)2/3 which results from the linear weight adjustment of Kohonen's self-organizing maps. If a concave model of weight adjustments is used, the density approaches a uniform distribution and the winner frequency distribution of output units is proportional to p(ξ). The former can provide more efficient data representations for vector quantization, while the latter can provide more meaningful measures for cluster analysis. Numerical demonstrations validate the mathematical derivations. The convergence of the concave model is faster than the linear and convex models while the convergence of the convex model is comparable to that of the linear model