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Wavelet and K-L Seperability Based Feature Extraction Method for Functional Data Classification
Abstract: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.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1062246Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1245
 A. Berlinet, G. Biau, and L. Rouvière, "Functional supervised classification with wavelets," Annales de l'ISUP, vol. 52, 2008, pp. 61-80.
 J. O. Ramsay and B. W. Silverman, Functional Data Analysis. Springer, New York, 2005
 J. O. Ramsay and B. W. Silverman, Functional Data Analysis. Springer, New York, 1997.
 Irene Epifanio, "Shape Descriptors for Classification of Functional Data," Technometric, vol. 50, no. 3. 2008.
 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
 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.
 P. Hall, D. S. Poskitt, and B. Presnell. "A functional data-analytic approach to signal discrimination," Technometrics, vol. 43, 2001, pp.1-9.
 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.
 F. Ferraty and P. Vieu, Nonparameter Functional Data Analysis: Theory and Practice, Springer, 2006.
 Marek Kurzynski and Edward Puchala, "The optimal feature extraction procedure for statistical pattern recognition," ICCSA 2006, LNCS 3982, pp. 1210-1215.
 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.
 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.
 T. Hastie, R. Tibshirani, and J. Friedman, "The elements of statistical learning," Data mining, inference and prediction, Springer-Verlag, 2001
 S. G. Mallat, A Wavelet Tour of Signal Processing, San Diego: Academic Press, 1998.
 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).
 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.
 L. Devroye, L. Gyorfi, and G. Lugosi, A Probabilistic Theory of Pattern Recognition, Springer-Verlag, New-York, 1996.