Circular/wrap-around self-organizing map networks: an empirical study in clustering and classification
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Circular=wrap-around self-organizing map networks: an empirical study in clustering and classi®cation MY Kiang1, UR Kulkarni2 and R St Louis2* 1
California State University and 2Arizona State University, Tempe, AZ, USA
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 in¯uence 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 modi®ed, `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 classi®cation 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. Keywords: neural networks; Kohonen SOM networks; cluster analysis; group technology
Introduction Kohonen's Self-Organizing networks1±4 have been successfully applied as a classi®cation tool to various problem domains, including speech recognition,5 image data compression,6 image or character recognition,7±9 robot control10,11 and medical diagnostics.12 One major drawback of the SOM networks is the `boundary effect' of nodes on or near the edges of the network. The boundary nodes have a truncated neighborhood, and hence have insuf®cient or sometimes no in¯uence on nodes that, in the application problem, may be their `natural neighbors' in the input topology. This has a tendency to prevent natural and meaningful contiguities between some nodes from appearing in the output map, leading to less effective clustering possibilities. One possible and seriously undesirable outcome of this phenomenon is that the network may be good at creating small local groups that accurately re¯ect the original relations among input data within a group, but may not be able to re¯ect their global relations. We have designed and tested a `circular' training algorithm that overcomes some of the ineffective topological representations caused by the boundary effect. Our algorithm treats the SOM as a continuous, boundaryless *Correspondence: RD St Louis, School of Accountancy and
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