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ISRN Computational Mathematics
Volume 2012 (2012), Article ID 197352, 13 pages
http://dx.doi.org/10.5402/2012/197352
Research Article

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, N1G 2W1, Canada
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.

Abstract

We introduce multiscale wavelet kernels to kernel principal component analysis (KPCA) to narrow down the search of parameters required in the calculation of a kernel matrix. This new methodology incorporates multiscale methods into KPCA for transforming multiscale data. In order to illustrate application of our proposed method and to investigate the robustness of the wavelet kernel in KPCA under different levels of the signal to noise ratio and different types of wavelet kernel, we study a set of two-class clustered simulation data. We show that WKPCA is an effective feature extraction method for transforming a variety of multidimensional clustered data into data with a higher level of linearity among the data attributes. That brings an improvement in the accuracy of simple linear classifiers. Based on the analysis of the simulation data sets, we observe that multiscale translation invariant wavelet kernels for KPCA has an enhanced performance in feature extraction. The application of the proposed method to real data is also addressed.