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Commenced in January 2007 Frequency: Monthly Edition: International Publications Count: 29404

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Topology Preservation in SOM
The SOM has several beneficial features which make it a useful method for data mining. One of the most important features is the ability to preserve the topology in the projection. There are several measures that can be used to quantify the goodness of the map in order to obtain the optimal projection, including the average quantization error and many topological errors. Many researches have studied how the topology preservation should be measured. One option consists of using the topographic error which considers the ratio of data vectors for which the first and second best BMUs are not adjacent. In this work we present a study of the behaviour of the topographic error in different kinds of maps. We have found that this error devaluates the rectangular maps and we have studied the reasons why this happens. Finally, we suggest a new topological error to improve the deficiency of the topographic error.
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[1] J. Vesanto. "Using SOM in Data Mining," Thesis for the degree of Licentiate of Science in Technology. Espoo, Finland, 2000.
[2] G. Deboeck, T. Kohonen. "Visual Explorations in Finance with Self- Organizing Maps," Springer Finance. Springer-Verlag, London, 1998.
[3] K. Lagus. "Text Mining with the WEBSOM," Acta Polytechnica Scandinaviva, Mathematics and Computing Series No.110, Espoo. Finnish Academies of Technology, 2000.
[4] Dolnicar, S. The Use of Neural Networks in Marketing: Market Segmentation with Self-Organizing Feature Maps. Proceeding of the Workshop on Self-Organizing Maps (WSOM'97), 38-43 (1997).
[5] Kohonen, T., Oja, E., Simula, O., Visa, A., Kangas, J. Engineering application of the self-organizing map. Proceedings of the IEEE, Vol.84, No.10, 1358-1384 (1996)
[6] J Kohonen, T.: Self-Organizing Maps. Vol. 30. of Springer Series in Information Sciences, 3rd ed., Springer-Verlag, Berlin Heidelberg (2001)
[7] T. Kohonen, "Self-organized formation of topologically correct feature maps," Biological Cybernetics Vol. 43, 59-69 (1982).
[8] H. Ritter, T. Martinetz, K. Schultzen. "Neural Computation and Self- Organizing Maps: An Introduction," Reading, MA: Addison-Weley (1992)
[9] S. Kaski, "Data Exploration Using Self-Organizing Maps." PhD thesis, Helsinky University of Technology, Acta Polytechnica Scandinavica: Mathematics, Computing and Management in Engineering, 82. (1997).
[10] B. D. Ripley, "Pattern Recognition and Neural Networks." Cambridge University Press, Cambridge, Great Britain (1996).
[11] .J. Mao, A. K. Jain, "Artificial neural networks for feature extraction and multivariate data projection." IEEE Transaction on Neural Networks, Vol.6, 296-317 (1995)
[12] J. Vesanto, E. Alhoniemi, "Clustering of the Self-Organizing Map." IEEE Transactions on Neural Networks (2000).
[13] K. Obermayer, H. Ritter, K. Schultzen, "Development and spatial structure of cortical feature maps: A model study". Advances in Neural Information Proceedings Systems, Vol. 3, 11-17, San Mateo, CA (1991).
[14] M. Herrmann, "Self-Organizing Feature Map with Self-Organizing Neighborhood Widths." IEEE International Conference on Neural Networks (1995).
[15] A. Flexer, "Limitations of self-organizing maps for vector quantization and multidimensional scaling." Technical Report oefai-tr-96-23. The Australian Research Institute for Artificial Intelligence. (1997).
[16] G. J. Goodhill, T. J. Sejnowski. "Quantifying neighbourhood preservation in topographic mappings." Proceedings of the 3rd Joint Sympostium on Neural Computation. La Jolla. CA Vol. 6, 61-82 (1996).
[17] H.U. Bauer, K. R. Pawelzik, "Quantifying the Neighborhood Preservation of Self-Organizing Feature Maps." IEEE Transactions on Neural Networks, Vol. 3, No. 4, 570-579 (1992).
[18] J. C. Bezdek, N.R. Pal, "An index of topological preservation for feature extraction." Pattern Recognition, Vol. 28, No. 3, 381-391 (1995).
[19] K. Kiviluoto, "Topology Preservation in Self-Organizing Maps." Proceedings of International Conference on Neural Networks (ICNN), 294-299 (1996).
[20] SomToolbox, Helsinky University of Technology Available:
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