Abstract
We consider pattern recognition problem when classes and their labels are linearly structured (or ordered). We propose the loss function based on the squared differences between the true and the predicted class labels. The optimal Bayes classifier is derived and then estimated by the recursive kernel estimator. Its consistency is established theoretically. Its RBF-like realization of the classifier is also proposed together with a recursive learning algorithm, which is well suited for on-line applications. The proposed approach was tested in real life example involving classification of moving vehicles.
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.
References
Bishop, C.: Neural Networks for Pattern Recognition. Oxford Univ. Press, Cambridge (1995)
Devroye, L., Györfi, L.: Nonparametric Density Estimation. The L 1 View. Wiley, New York (1985)
Devroye, L., Györfi, L., Lugosi, G.: Probabilistic Theory of Pattern Recognition. Springer, New York (1996)
Greblicki, W.: Learning to recognize patterns with a probabilistic teacher. Pattern Recognition 12, 159–164 (1980)
Györfi, L., Kohler, M., Krzyżak, A., Walk, H.: A Distribution-Free Theory of Nonparametric Regression. Springer, New York (2002)
Karayiannis, N.B., Randolph-Gips, M.M.: On the construction and training of reformulated radial basis function neural networks. IEEE Trans. on Neural Networks 14, 835–846 (2003)
Krzyżak, A., Skubalska-Rafajłowicz, E.: Combining space-filling curves and radial basis function networks. In: Rutkowski, L., Siekmann, J.H., Tadeusiewicz, R., Zadeh, L.A. (eds.) ICAISC 2004. LNCS (LNAI), vol. 3070, pp. 229–234. Springer, Heidelberg (2004)
Rafajłowicz, E., Skubalska-Rafajłowicz, E.: MAD loss in pattern recognition and RBF learning. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2008. LNCS (LNAI), vol. 5097, pp. 671–680. Springer, Heidelberg (2008)
Rafajłowicz, E.: Improving the efficiency of counting defects by learning RBF nets with MAD loss. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2008. LNCS (LNAI), vol. 5097, pp. 146–153. Springer, Heidelberg (2008)
Rafajłowicz, E.: RBF nets in faults localization. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds.) ICAISC 2006. LNCS (LNAI), vol. 4029, pp. 113–122. Springer, Heidelberg (2006)
Rafajłowicz, E., Krzyżak, A.: Pattern recognition with ordered labels. Nonlinear Analysis 71, 1437–1441 (2009)
Xu, L., Krzyżak, A., Yuille, A.: On radial basis function nets and kernel regression: statistical consistency, convergence, rates and receptive field size. Neural Networks 4, 609–628 (1994)
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
Krzyżak, A., Rafajłowicz, E. (2010). Pattern Recognition with Linearly Structured Labels Using Recursive Kernel Estimator. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2010. Lecture Notes in Computer Science(), vol 6113. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13208-7_53
Download citation
DOI: https://doi.org/10.1007/978-3-642-13208-7_53
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13207-0
Online ISBN: 978-3-642-13208-7
eBook Packages: Computer ScienceComputer Science (R0)