Abstract
The kernel-based feature extraction method is of importance in applications of artificial intelligence techniques to real-world problems. It extends the original data space to a higher dimensional feature space and tends to perform better in many non-linear classification problems than a linear approach. This work makes use of our previous research outcomes on the construction of wavelet kernel for kernel principal component analysis (KPCA). Using Monte Carlo simulation approach, we study noise effects of the performance of wavelet kernel PCA in spatial pattern data classification. We investigate how the classification accuracy change when feature dimension is changed. We also compare the classification accuracy obtained from the single-scale and multi-scale wavelet kernels to demonstrate the advantage of using multi-scale wavelet kernel in KPCA. Our study show that multi-scale wavelet kernel performs better than single-scale wavelet kernel in classification of data that we consider. It also demonstrates the usefulness of multi-scale wavelet kernels in application of feature extraction in kernel PCA.
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
Muller, K.R., Mika, S., Ratsch, G., Tsuda, K., Scholkopf, B.: An introduction to kernel-based learning alrorithms. IEEE Transactions on Netural Networks 12(2), 181–201 (2001)
Zhu, M.: Kernels and ensembles: perspectives on statistical learning. The American Statistician 62, 97–109 (2008)
Karatzoglou, A., Smola, A., Hornik, K., Zeileis, A.: Kernlab - an S4 package for kernel methods in R. Journal of Statistical Software 11(9), 1–20 (2004)
Vapnik, V.: The Nature of Statistical Learning Theory. Springer, NY (1995)
Vapnik, V.: Statistical Learning Theory. Wiley, New York (1998)
Chen, G.Y., Bhattacharya, P.: Function dot product kernels for support vector machine. In: 18th International Conference on Pattern Recognition (ICPR 2006), vol. 2, pp. 614–617 (2006)
Scholkopf, B., Smola, A.J., Muller, K.R.: Nonlinear component analysis as a kernel eigenvalue problem. Neur. Comput. 10, 1299–1319 (1998)
Takiguchi, T., Ariki, Y.: Robust Feature Extraction Using Kernel PCA. In: ICASSP 2006, pp. 509–512 (2006)
Scholkopf, B., Smola, A., Muller, K.R.: Nonlinear Component Analysis as a Kernel Eigenvalue Problem. Technical Report 44, Max-Planck-Institut fur biologische Kybernetik Arbeitsgruppe Bulthoff, Tubingen (1996)
Xie, S., Lawniczak, A.T., Krishnan, S., Liò, P.: Wavelet Kernel Principal Component Analysis in Noisy Multi-scale Data Classification. ISRN Computational Mathematics 2012, Article ID 197352, 13 Pages (2012), doi:10.5402/2012/197352
Xie, S., Lawniczak, A.T., Liò, P.: Feature Extraction Via Wavelet Kernel PCA for Data Classification. In: Proceedings of 2010 IEEE International Workshop on Machine Learning for Signal Processing, pp. 438–443 (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Xie, S., Lawniczak, A.T., Krishnan, S. (2013). Noise Effects on Spatial Pattern Data Classification Using Wavelet Kernel PCA. In: Guo, C., Hou, ZG., Zeng, Z. (eds) Advances in Neural Networks – ISNN 2013. ISNN 2013. Lecture Notes in Computer Science, vol 7951. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39065-4_34
Download citation
DOI: https://doi.org/10.1007/978-3-642-39065-4_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39064-7
Online ISBN: 978-3-642-39065-4
eBook Packages: Computer ScienceComputer Science (R0)