Wavelet and K-L Seperability Based Feature Extraction Method for Functional Data Classification

This paper proposes a novel feature extraction method, based on Discrete Wavelet Transform (DWT) and K-L Seperability (KLS), for the classification of Functional Data (FD). This method combines the decorrelation and reduction property of DWT and the additive independence property of KLS, which is helpful to extraction classification features of FD. It is an advanced approach of the popular wavelet based shrinkage method for functional data reduction and classification. A theory analysis is given in the paper to prove the consistent convergence property, and a simulation study is also done to compare the proposed method with the former shrinkage ones. The experiment results show that this method has advantages in improving classification efficiency, precision and robustness.

Authors:

• Jun Wan
• Zehua Chen
• Yingwu Chen
• Zhidong Bai

Keywords:

• classification
• functional data
• feature extraction
• K-Lseperability
• wavelet.

References:

[1] A. Berlinet, G. Biau, and L. Rouvière, "Functional supervised
classification with wavelets," Annales de l'ISUP, vol. 52, 2008, pp.
61-80.
[2] J. O. Ramsay and B. W. Silverman, Functional Data Analysis. Springer,
New York, 2005
[3] J. O. Ramsay and B. W. Silverman, Functional Data Analysis. Springer,
New York, 1997.
[4] Irene Epifanio, "Shape Descriptors for Classification of Functional
Data," Technometric, vol. 50, no. 3. 2008.
[5] G. Rosner and B. Vidakovic, "Wavelet functional ANOVA, Bayesian
false discovery rate, and longitudinal measurements of Oxygen,"
Pressure in Rats, Technical Report 1/2000, ISyE, Georgia Institute of
Technology, 2000
[6] P. N. Belhumeur, J. P. Hepana, and D. J. Kriegman, "Eigenfaces vs.
fisherfaces: Recognition using class specific linear projection," IEEE
Trans. Pattern Analysis and Machine Intelligence, vol.19 1997,
pp.711-720.
[7] P. Hall, D. S. Poskitt, and B. Presnell. "A functional data-analytic
approach to signal discrimination," Technometrics, vol. 43, 2001, pp.1-9.
[8] U. Amato, A. Antoniadis, and I. D. Feis, "Dimension reduction in
functional regression with applications," Computational Statistics and
Data Analysis, vol. 50, 2006, pp. 2422-2446.
[9] F. Ferraty and P. Vieu, Nonparameter Functional Data Analysis: Theory
and Practice, Springer, 2006.
[10] Marek Kurzynski and Edward Puchala, "The optimal feature extraction
procedure for statistical pattern recognition," ICCSA 2006, LNCS 3982,
pp. 1210-1215.
[11] C. Abraham, G. Biau, and B. Cadre, "On the kernel rule for function
classification," Annals of the Institute of Statistical Mathematics, vol. 58,
2006, pp. 619-633.
[12] S. Boucheron, O. Bousquet, and G. Lugosi, "Theory of classification: A
survey of some recent advances," ESAIM: Probability and Statistics, vol.
9, 2005, pp.323-375.
[13] T. Hastie, R. Tibshirani, and J. Friedman, "The elements of statistical
learning," Data mining, inference and prediction, Springer-Verlag, 2001
[14] S. G. Mallat, A Wavelet Tour of Signal Processing, San Diego: Academic
Press, 1998.
[15] U. K. Jung, M. K. Jeong, , J.C. Lu, "Wavelet-based Data Reduction and
Mining for Multiple Functional Data," International Journal of
Production Research, vol. 44, no. 14, 2006, pp. 2695-2710(16).
[16] C. R. Shalizi, "Methods and techniques of complex systems science: An
overview," T. S. Deisboeck and J. Y. Kresh, Complex Systems Science in
Biomedicine, Chapter 1, pp. 33-114, Springer, Singapore, 2006.
[17] L. Devroye, L. Gyorfi, and G. Lugosi, A Probabilistic Theory of Pattern
Recognition, Springer-Verlag, New-York, 1996.