An analysis of Kohonen's self-organizing maps using a system of energy functions

In this paper a new method for analyzing Kohonen's self-organizing feature maps is presented. The method makes use of a system of energy functions, one energy function for each processing unit. It is shown that the training process is equivalent to minimizing each energy function subject to constraints. The analysis is used to prove the formation of topologically correct maps when the inherent dimensionality of the input patterns matches that of the network. The energy equations can be used to compute the steady-state weight values of the network. In addition, the analysis allows bounds on the training parameters to be determined. Finally, examples of energy landscapes are presented to graphically show the behavior of the network.