Abstract
The Self-Organizing Map (SOM), which projects a (high-dimensional) data manifold onto a lower-dimensional (usually 2-d) rigid lattice, is a commonly used manifold learning algorithm. However, a postprocessing – that is often done by interactive visualization schemes – is necessary to reveal the knowledge of the SOM. Thanks to the SOM property of producing (ideally) a topology preserving mapping, existing visualization schemes are often designed to show the similarities local to the lattice without considering the data topology. This can produce inadequate tools to investigate the detailed data structure and to what extent the topology is preserved during the SOM learning. A recent graph based SOM visualization, CONNvis [1], which exploits the underutilized knowledge of data topology, can be a suitable tool for such investigation. This paper discusses that CONNvis can represent the data topology on the SOM lattice despite the rigid grid structure, and hence can show the topology preservation of the SOM and the extent of topology violations.
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References
Taşdemir, K., Merényi, E.: Data topology visualization for the Self-Organizing Maps. In: Proc. 14th European Symposium on Artificial Neural Networks (ESANN 2006), Bruges, Belgium, D-Facto, April 26-28, pp. 277–282 (2006)
Cox, T.F., Cox, M.: Multidimensional Scaling. Chapman and Hall/CRC, Boca Raton (2001)
Tenenbaum, J.B., de Silva, V., Langford, J.: A global geometric framework for nonlinear dimensionality reduction. Science 290(5500), 2319–2323 (2000)
Roweis, S., Soul, L.: Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500), 2323–2326 (2000)
Kohonen, T.: Self-Organizing Maps, 2nd edn. Springer, Heidelberg (1997)
Yin, H.: Nonlinear multidimensional data projection and visualisation. In: Liu, J., Cheung, Y.-m., Yin, H. (eds.) IDEAL 2003. LNCS, vol. 2690, pp. 377–388. Springer, Heidelberg (2003)
Ultsch, A.: Self-organizing neural networks for visualization and classification. In: Lausen, O.B., Klar, R. (eds.) Information and Classification-Concepts, Methods and Applications, pp. 307–313. Springer, Berlin (1993)
Kraaijveld, M., Mao, J., Jain, A.: A nonlinear projection method based on Kohonen’s topology preserving maps. IEEE Trans. on Neural Networks 6(3), 548–559 (1995)
Cottrell, M., de Bodt, E.: A Kohonen map representation to avoid misleading interpretations. In: Proc. 4th European Symposium on Artificial Neural Networks (ESANN 1996), Bruges, Belgium, D-Facto, pp. 103–110 (1996)
Ultsch, A.: Maps for the visualization of high-dimensional data spaces. In: Proc. 4th Workshop on Self-Organizing Maps (WSOM 2003), vol. 3, pp. 225–230 (2003)
Kaski, S., Kohonen, T., Venna, J.: Tips for SOM processing and colourcoding of maps. In: Deboeck, T.K.G. (ed.) Visual Explorations in Finance Using Self-Organizing Maps, London (1998)
Himberg, J.: A SOM based cluster visualization and its application for false colouring. In: Proc. IEEE-INNS-ENNS International Joint Conf. on Neural Networks, Como, Italy, vol. 3, pp. 587–592 (2000)
Vesanto, J.: SOM-based data visualization methods. Intelligent Data Analysis 3(2), 111–126 (1999)
Taşdemir, K., Merényi, E.: Exploiting data topology in visualization and clustering of Self-Organizing Maps. IEEE Transactions on Neural Networks (submitted)
Merkl, D., Rauber, A.: Alternative ways for cluster visualization in Self-Organizing Maps. In: Proc. 1st Workshop on Self-Organizing Maps (WSOM 2005), Espoo, Finland, Helsinki University of Technology, June 4-6, pp. 106–111. Helsinki University of Technology, Neural Networks Research Centre, Espoo, Finland (1997)
Su, M.-C., Chang, H.-T.: A new model of self-organizing neural networks and its applications. IEEE Transactions on Neural Networks 12(1), 153–158 (2001)
Yin, H.: ViSOM- a novel method for multivariate data projection and structure visualization. IEEE Transactions on Neural Networks 13(1), 237–243 (2002)
Yin, H.: Resolution enhancement for the ViSOM. In: Proc. 4th Workshop on Self-Organizing Maps (WSOM 2003), pp. 208–212 (2003)
Merényi, E., Taşdemir, K., Farrand, W.: Intelligent information extraction to aid science decision making in autonomous space exploration. In: Proc. SPIE Defense and Security, Orlando, Florida, March 17-20 (2008)
Martinetz, T., Schulten, K.: Topology representing networks. Neural Networks 7(3), 507–522 (1993)
Ultsch, A.: Clustering with som: U*c. In: Proc. 5th Workshop on Self-Organizing Maps (WSOM 2005), Paris, France, September 5-8, 2005, pp. 75–82 (2005)
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Taşdemir, K. (2008). Exploring Topology Preservation of SOMs with a Graph Based Visualization. In: Fyfe, C., Kim, D., Lee, SY., Yin, H. (eds) Intelligent Data Engineering and Automated Learning – IDEAL 2008. IDEAL 2008. Lecture Notes in Computer Science, vol 5326. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88906-9_23
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DOI: https://doi.org/10.1007/978-3-540-88906-9_23
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