Circular/wrap-around self-organizing map networks: an empirical study in clustering and classification

Kohonen's self-organizing map (SOM) network is one of the most important network architectures developed during the 1980s. 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 the undue influence of the initial random weights assigned to the nodes of the network, which can lead to incorrect topological representations. To overcome this limitation, we use a modified, 'circular', weight adjustment algorithm. Our procedure is most effective with the class of problems where the actual coordinates of the output map do not need to correspond to the original input topology. This class of problems includes applications requiring clustering or classification of input data. We tested our method with a well known example problem from the domain of Group Technology, which is typical of this class of problems. Test results show that the circular weight adjustment procedure has better convergence properties, and that the clusters formed using the circular approach are at least as good as, and in many cases superior to, the basic SOM method for these types of problems.