Improving the effectiveness of self-organizing map networks using a circular Kohonen layer

Kohonen's self-organizing map (SOM) network is one of the most important network architectures developed during the 1980's. The main function of SOM networks is to map the input data from an n-dimensional space to a lower dimensional (usually one or two-dimensional) plot while maintaining the original topological relations. A well known limitation of the Kohonen network is the `boundary effect' of nodes on or near the edge of the network. The boundary effect is responsible for retaining the undue influence of initial random weights assigned to the nodes of the network leading to ineffective topological representations. To overcome this limitation, we introduce and evaluate a modified, `circular' weight adjustment procedure. This procedure is applicable to a class of problems where the actual coordinates of the output map do not need to correspond to the original input topology. We tested the circular method with an example problem from the domain of group technology, typical of such class of problems.