On the rate of convergence in topology preserving neural networks

A formal analysis of the neighborhood interaction function selection in the topology preserving unsupervised neural network is presented in this paper. The definition of the neighborhood interaction function is motivated by anatomical evidence as opposed to what is currently used, which is a uniform neighborhood interaction set. By selecting a neighborhood interaction function with a neighborhood amplitude of interaction which is decreasing in spatial domain the topological order is always enforced and the rate of self-organization to final equilibrium state is improved. Several simulations are carried out to show the improvement in rate between using a neighborhood interaction function vs. using a neighborhood interaction set. An error measure functional is further defined to compare the two approaches quantitatively.