Abstract
We derive a novel derivative based version of kernelized Generalized Learning Vector Quantization (KGLVQ) as an effective, easy to interpret, prototype based and kernelized classifier. It is called D-KGLVQ and we provide generalization error bounds, experimental results on real world data, showing that D-KGLVQ is competitive with KGLVQ and the SVM on UCI data and additionally show that automatic parameter adaptation for the used kernels simplifies the learning.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bartlett, P., Mendelson, S.: Rademacher and Gaussian complexities: risk bounds and structural results. Journal of Machine Learning Research 3, 463–482 (2003)
Biehl, M., Hammer, B., Schleif, F.M., Schneider, P., Villmann, T.: Stationarity of matrix relevance learning vector quantization. Machine Learning Reports 3, 1–17 (2009) ISSN:1865-3960, http://www.uni-leipzig.de/~compint/mlr/mlr_01_2009.pdf
Bishop, C.: Pattern Recognition and Machine Learning. Springer, NY (2006)
Blake, C., Merz, C.: UCI repository of machine learning databases. Department of Information and Computer Science. University of California, Irvine (1998), http://www.ics.uci.edu/~mlearn/MLRepository.html
Crammer, K., Gilad-Bachrach, R., Navot, A., Tishby, A.: Margin analysis of the LVQ algorithm. In: Proc. NIPS 2002, pp. 462–469 (2002)
Hammer, B., Villmann, T.: Generalized relevance learning vector quantization. Neural Networks 15(8-9), 1059–1068 (2002)
Hammer, B., Villmann, T.: Mathematical aspects of neural networks. In: Verleysen, M. (ed.) Proc. of European Symposium on Artificial Neural Networks (ESANN 2003), d-side, Brussels, Belgium, pp. 59–72 (2003)
Kohonen, T.: Self-Organizing Maps. Springer Series in Information Sciences, vol. 30. Springer, Heidelberg (1995) (Second Extended Edition 1997)
Qin, A.K., Suganthan, P.N.: A novel kernel prototype-based learning algorithm. In: Proc. of ICPR’04, pp. 2621–2624 (2004)
Sato, A.S., Yamada, K.: Generalized learning vector quantization. In: Tesauro, G., Touretzky, D., Leen, T. (eds.) Advances in Neural Information Processing Systems, vol. 7, pp. 423–429. MIT Press, Cambridge (1995)
Schleif, F.M., Villmann, T., Kostrzewa, M., Hammer, B., Gammerman, A.: Cancer informatics by prototype-networks in mass spectrometry. Artificial Intelligence in Medicine 45, 215–228 (2009)
Schneider, P., Biehl, M., Hammer, B.: Adaptive relevance matrices in learning vector quantization. Neural Computation (to appear)
Seo, S., Obermayer, K.: Soft learning vector quantization. Neural Computation 15, 1589–1604 (2003)
Shawe-Taylor, J., Cristianini, N.: Kernel Methods for Pattern Analysis and Discovery. Cambridge University Press, Cambridge (2004)
Simmuteit, S., Schleif, F.M., Villmann, T., Elssner, T.: Tanimoto metric in tree-som for improved representation of mass spectrometry data with an underlying taxonomic structure. In: Proc. of ICMLA 2009, pp. 563–567. IEEE Press, Los Alamitos (2009)
Villmann, T., Schleif, F.M.: Functional vector quantization by neural maps. In: Proceedings of Whispers 2009, p. CD (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schleif, FM., Villmann, T., Hammer, B., Schneider, P., Biehl, M. (2010). Generalized Derivative Based Kernelized Learning Vector Quantization. In: Fyfe, C., Tino, P., Charles, D., Garcia-Osorio, C., Yin, H. (eds) Intelligent Data Engineering and Automated Learning – IDEAL 2010. IDEAL 2010. Lecture Notes in Computer Science, vol 6283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15381-5_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-15381-5_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15380-8
Online ISBN: 978-3-642-15381-5
eBook Packages: Computer ScienceComputer Science (R0)