Abstract
In this paper, we propose a simple but powerful method to visualize connection weights by SOM. The conventional SOM has been well established and extensively used to visualize complex data. There have been a number of methods to visualize final connection weights. However, even sophisticated visualization techniques may be ineffective in dealing with ambiguous connection weights due to the complexity of the data set. To cope with this problem, we retrain a network with connection weights obtained by SOM. At this time, we do not optimize networks in terms of errors but we train networks to enhance the characteristics of connection weights at the price of optimality. This enhancement can be realized by smaller Gaussian width. Though these smaller Gaussian widths are not optimal ones in terms of errors, it may give some insights into the characteristics of connection weights. We applied the method to the famous Iris problem and a classification problem for OECD countries. In both problems, we can obtain U-matrices with more explicit boundaries for easy interpretation.
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References
Kohonen, T.: Self-Organization and Associative Memory. Springer, New York (1988)
Kohonen, T.: Self-Organizing Maps. Springer, Heidelberg (1995)
Goodhill, G.J., Sejnowski, T.J.: A unifying objective function for topographic mappings. Neural Computation 9, 1291–1303 (1997)
Luttrell, S.P.: A Bayesian analysis of self-organising maps. Neural Computation 6(5), 767–794 (1994)
Heskes, T.: Self-organizing maps, vector quantization, and mixture modeling. IEEE Transactions on Neural Networks 12(6), 1299–1305 (2001)
Bakker, B., Heskes, T.: Clustering ensembles of neural network models. Neural Networks 16, 261–269 (2003)
Utsugi, A.: Hyperparameter selection for self-organizing maps. Neural Computation 9(3), 623–635 (1997)
Utsugi, A.: Density estimation by mixture models with smoothing priors. Neural Computation 10, 2115–2135 (1998)
Kaski, S., Nikkilä, J., Kohonen, T.: Methods for interpreting a self-organized map in data analysis. In: Verleysen, M. (ed.) Proceedings of ESANN 1998, 6th European Symposium on Artificial Neural Networks, Bruges, April 22–24, 1998, pp. 185–190. D-Facto, Brussels, Belgium (1998)
Vesanto, J., Alhoniemi, E.: Clustering of the self-organizing map. IEEE-NN 11, 586 (2000)
Vesanto, J.: SOM-based data visualization methods. Intelligent-Data-Analysis 3, 111–126 (1999)
Bishop, C.M.: Neural networks for pattern recognition. Oxford University Press, Oxford (1995)
Dempster, A.P.N., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the em algorithm. Journal of the Royal Statistical Society (1), 1–38 (1977)
Kumagai, E., Funao, N.: Data Mining by R (in Japanese). 9-Ten Publishing Company (2007)
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Kamimura, R. (2009). Enhanced Visualization by Combing SOM and Mixture Models. In: Köppen, M., Kasabov, N., Coghill, G. (eds) Advances in Neuro-Information Processing. ICONIP 2008. Lecture Notes in Computer Science, vol 5507. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03040-6_33
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DOI: https://doi.org/10.1007/978-3-642-03040-6_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03039-0
Online ISBN: 978-3-642-03040-6
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