Abstract
In this paper we propose a new approach to combine unsupervised and supervised vector quantization for clustering and fuzzy classification using the framework of neural vector quantizers like self-organizing maps or neural gas. For this purpose the original cost functions are modified in such a way that both aspects, unsupervised vector quantization and supervised classification, are incorporated. The theoretical justification of the convergence of the new algorithm is given by an adequate redefinition of the underlying dissimilarity measure now interpreted as a dissimilarity in the data space combined with the class label space. This allows a gradient descent learning as known for the original algorithms. Thus a semi-supervised learning scheme is achieved. We apply this method for a spectra image cube of remote sensing data for landtype classification. The obtained fuzzy class visualizations allow a better understanding and interpretation of the spectra.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bauer, H.-U., Herrmann, M., Villmann, T.: Neural maps and topographic vector quantization. Neural Networks 12(4-5), 659–676 (1999)
Geweniger, T., Zühlke, D., Hammer, B., Villmann, T.: Median fuzzy c-means for clustering dissimilarity data. Neurocomputing 73(7-9), 1109–1116 (2010)
Hammer, B., Villmann, T.: Generalized relevance learning vector quantization. Neural Networks 15(8-9), 1059–1068 (2002)
Heskes, T.: Energy functions for self-organizing maps. In: Oja, E., Kaski, S. (eds.) Kohonen Maps, pp. 303–316. Elsevier, Amsterdam (1999)
Kästner, M., Villmann, T.: Functional relevance learning in generalized learning vector quantization. Machine Learning Reports 5(MLR-01-2011), 81–89 (2011), http://www.techfak.uni-bielefeld.de/~fschleif/mlr/mlr_01_2011.pdf ISSN:1865-3960
Kästner, M., Villmann, T.: Fuzzy supervised neural gas for semi-supervised vector quantization – theoretical aspects. Machine Learning Reports 5(MLR-02-2011), 1–16 (2011), http://www.techfak.uni-bielefeld.de/~fschleif/mlr/mlr__011.pdf ISSN:1865-3960
Kohonen, T.: Self-Organizing Maps. Springer Series in Information Sciences, vol. 30. Springer, Heidelberg (1995) (Second Extended Edition 1997)
Lee, J., Verleysen, M.: Generalization of the l p norm for time series and its application to self-organizing maps. In: Cottrell, M. (ed.) Proc. of Workshop on Self-Organizing Maps, WSOM 2005, Paris, Sorbonne, pp. 733–740 (2005)
Martinetz, T.M., Berkovich, S.G., Schulten, K.J.: ‘Neural-gas’ network for vector quantization and its application to time-series prediction. IEEE Trans. on Neural Networks 4(4), 558–569 (1993)
Midenet, S., Grumbach, A.: Learning associations by self-organizatiom: the LASSO model. Neurocomputing 6, 343–361 (1994)
Pekalska, E., Duin, R.: The Dissimilarity Representation for Pattern Recognition: Foundations and Applications. World Scientific (2006)
Sato, A., Yamada, K.: Generalized learning vector quantization. In: Touretzky, D.S., Mozer, M.C., Hasselmo, M.E. (eds.) Proceedings of the 1995 Conference on Advances in Neural Information Processing Systems, vol. 8, pp. 423–429. MIT Press, Cambridge (1996)
Schleif, F.-M., Villmann, T., Hammer, B., Schneider, P., Biehl, M.: Generalized Derivative Based Kernelized Learning Vector Quantization. In: Fyfe, C., Tino, P., Charles, D., Garcia-Osorio, C., Yin, H. (eds.) IDEAL 2010. LNCS, vol. 6283, pp. 21–28. Springer, Heidelberg (2010)
Schneider, P., Hammer, B., Biehl, M.: Adaptive relevance matrices in learning vector quantization. Neural Computation 21, 3532–3561 (2009)
Villmann, T., Der, R., Herrmann, M., Martinetz, T.: Topology Preservation in Self–Organizing Feature Maps: Exact Definition and Measurement. IEEE Transactions on Neural Networks 8(2), 256–266 (1997)
Villmann, T., Haase, S.: Divergence based vector quantization. Neural Computation 23(5), 1343–1392 (2011)
Villmann, T., Hammer, B., Schleif, F.-M., Geweniger, T., Herrmann, W.: Fuzzy classification by fuzzy labeled neural gas. Neural Networks 19, 772–779 (2006)
Villmann, T., Merényi, E., Hammer, B.: Neural maps in remote sensing image analysis. Neural Networks 16(3-4), 389–403 (2003)
Villmann, T., Schleif, F.-M.: Functional vector quantization by neural maps. In: Chanussot, J. (ed.) Proceedings of First Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS 2009), pp. 1–4. IEEE Press (2009) ISBN: 978-1-4244-4948-4
Villmann, T., Schleif, F.-M., Merenyi, E., Hammer, B.: Fuzzy Labeled Self-Organizing Map for Classification of Spectra. In: Sandoval, F., Prieto, A.G., Cabestany, J., Graña, M. (eds.) IWANN 2007. LNCS, vol. 4507, pp. 556–563. Springer, Heidelberg (2007)
Villmann, T., Seiffert, U., Schleif, F.-M., Brüß, C., Geweniger, T., Hammer, B.: Fuzzy Labeled Self-Organizing Map with Label-Adjusted Prototypes. In: Schwenker, F., Marinai, S. (eds.) ANNPR 2006. LNCS (LNAI), vol. 4087, pp. 46–56. Springer, Heidelberg (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kästner, M., Villmann, T. (2012). Fuzzy Supervised Self-Organizing Map for Semi-supervised Vector Quantization. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2012. Lecture Notes in Computer Science(), vol 7267. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29347-4_30
Download citation
DOI: https://doi.org/10.1007/978-3-642-29347-4_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-29346-7
Online ISBN: 978-3-642-29347-4
eBook Packages: Computer ScienceComputer Science (R0)