- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
ISRN Computational Mathematics
Volume 2012 (2012), Article ID 197352, 13 pages
Wavelet Kernel Principal Component Analysis in Noisy Multiscale Data Classification
1Department of Electrical and Computer Engineering, Ryerson University, Toronto, ON,
M5B 2K3, Canada
2Mathematics and Statistics Department, University of Guelph, Guelph, ON, Canada N1G 2W1
3Computer Laboratory, University of Cambridge, Cambridge CB3 0FD, UK
Received 3 May 2012; Accepted 13 June 2012
Academic Editors: L. Hajdu, L. S. Heath, R. A. Krohling, E. Weber, and W. G. Weng
Copyright © 2012 Shengkun Xie et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- I. T. Jolliffe, Principal Component Analysis, Springer Science, New York, NY, USA, 2004.
- B. Scholkopf, A. J. Smola, and K. R. Muller, “Nonlinear component analysis as a kernel eigenvalue problem,” Neural Computation, vol. 10, no. 5, pp. 1299–1319, 1998.
- B. Scholkopf and A. J. Smola, Learning with Kernels—Support Vector Machines, Regularization, Optimization and Beyond, The MIT Press, Cambridge, Mass, USA, 2002.
- R. Rosipal, M. Girolami, L. J. Trejo, and A. Cichocki, “Kernel PCA for feature extraction and de-noising in nonlinear regression,” Neural Computing & Applications, vol. 10, no. 3, pp. 231–243, 2001.
- T. Hastie, R. Tibshirani, and A. Buja, “Flexible discriminant analysis by optimal scoring,” Journal of the American statistical Association, vol. 89, pp. 1255–1270, 1994.
- K. R. Muller, S. Mika, G. Ratsch, K. Tsuda, and B. Scholkopf, “An introduction to kernel-based learning algorithms,” IEEE Transactions on Neural Networks, vol. 12, no. 2, pp. 181–201, 2001.
- M. Zhu, “Kernels and ensembles: perspectives on statistical learning,” The American Statistician, vol. 62, no. 2, pp. 97–109, 2008.
- A. Karatzoglou, A. Smola, K. Hornik, and A. Zeileis, “Kernlab—An S4 package for kernel methods in R,” Journal of Statistical Software, vol. 11, no. 9, pp. 1–20, 2004.
- V. Vapnik, The Nature of Statistical Learning Theory, Springer, New York, NY, USA, 1995.
- V. Vapnik, Statistical Learning Theory, Wiley, New York, NY, USA, 1998.
- L. Zhang, W. D. Zhou, and L. C. Jiao, “Wavelet Support Vector Machine,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 34, no. 1, pp. 34–39, 2004.
- T. Takiguchi and Y. Ariki, “Robust feature extraction using kernel PCA,” in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '06), pp. 509–512, Toulouse, France, May 2006.
- B. Scholkopf, A. Smola, and K. R. Muller, “Nonlinear component analysis as a kernel eigenvalue problem,” Technical Report 44, Max-Planck-Institut fur biologische Kybernetik Arbeitsgruppe Bulthoff, Tubingen, Germany, 1996.
- W. S. Chen, P. C. Yuen, J. Huang, and J. H. Lai, “Wavelet kernel construction for kernel discriminant analysis on face recognition,” in Proceedings of the Conference on Computer Vision and Pattern Recognition Workshops, p. 47, June 2006.
- W. F. Zhang, D. Q. Dai, and H. Yan, “Framelet Kernels with applications to support vector regression and regularization networks,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 40, no. 4, pp. 1128–1144, 2009.
- R. Opfer, “Multiscale kernels,” Technical Report, Institut fur Numerische und Angewandte Mathematik, Universitt Gottingen, 2004.
- A. Rakotomamonjy and S. Canu, “Frames, reproducing kernels, regularization and learning,” Journal of Machine Learning Research, vol. 6, pp. 1485–1515, 2005.
- P. Erästö and L. Holmström, “Bayesian multiscale smoothing for making inferences about features in scatterplots,” Journal of Computational and Graphical Statistics, vol. 14, no. 3, pp. 569–589, 2005.
- T. Phienthrakul and B. Kijsirikul, “Evolutionary strategies for multi-scale radial basis function kernels in support vector machines,” in Proceedings of the Conference on Genetic and Evolutionary Computation (GECCO '05), pp. 905–911, Washington, DC, USA, June 2005.
- N. Kingsbury, D. B. H. Tay, and M. Palaniswami, “Multi-scale kernel methods for classification,” in Proceedings of IEEE Workshop on Machine Learning for Signal Processing, pp. 43–48, September 2005.
- F. Wang, G. Tan, and Y. Fang, “Multiscale wavelet support vector regression for traffic flow prediction,” in Proceedings of the 3rd International Symposium on Intelligent Information Technology Application (IITA '09), vol. 3, pp. 319–322, November 2009.
- H. Cheng and J. Liu, “Super-resolution image reconstruction based on MWSVR estimation,” in Proceedings of the 7th World Congress on Intelligent Control and Automation (WCICA '08), pp. 5990–5994, June 2008.
- J. Wang and H. Peng, “Multi-scale wavelet support vector regression for soft sensor modeling,” in Proceedings of the International Conference on Neural Networks and Brain (ICNNB '05), vol. 1, pp. 284–287, October 2005.
- F. Han, D. Wang, C. Li, and X. Liao, “A multiresolution wavelet kernel for support vector regression,” in In Proceedings of the Third International Conference on Advances in Neural Networks (ISNN '06), vol. 1, pp. 1022–1029, 2006.
- F. Wu and Y. Zhao, “Least square support vector machine on gaussian wavelet kernel function set,” in Proceedings of the 3rd International Conference on Advances in Neural Networks (ISNN '06), vol. 3971 of Lecture Notes in Computer Science, pp. 936–941, 2006.
- S. Kadambe and P. Srinivasan, “Adaptive wavelets for signal classification and compression,” International Journal of Electronics and Communications, vol. 60, no. 1, pp. 45–55, 2006.
- I. Daubechies, Ten Lectures on Wavelets, SIAM, Philadelphia, Pa, USA, 1992.
- H. C. Shyu and Y. S. Sun, “Underwater acoustic signal analysis by multi-scaling and multi-translation wavelets,” in Wavelet Applications V, vol. 3391 of Proceedings of SPIE, pp. 628–636, Orlando, Fla, USA, April 1998.