GA Based Optimal Feature Extraction Method for Functional Data Classification

Authors: Jun Wan, Zehua Chen, Yingwu Chen, Zhidong Bai

Abstract:

Classification is an interesting problem in functional data analysis (FDA), because many science and application problems end up with classification problems, such as recognition, prediction, control, decision making, management, etc. As the high dimension and high correlation in functional data (FD), it is a key problem to extract features from FD whereas keeping its global characters, which relates to the classification efficiency and precision to heavens. In this paper, a novel automatic method which combined Genetic Algorithm (GA) and classification algorithm to extract classification features is proposed. In this method, the optimal features and classification model are approached via evolutional study step by step. It is proved by theory analysis and experiment test that this method has advantages in improving classification efficiency, precision and robustness whereas using less features and the dimension of extracted classification features can be controlled.

Keywords: Classification, functional data, feature extraction, genetic algorithm, wavelet.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1081651

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] 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.
[4] P. Hall, D. S. Poskitt, and B. Presnell. "A functional data-analytic approach to signal discrimination," Technometrics, vol. 43, 2001, pp.1-9.
[5] 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.
[6] F. Ferraty and P. Vieu, Nonparameter Functional Data Analysis: Theory and Practice, Springer, 2006.
[7] J. O. Ramsay and B. W. Silverman, Functional Data Analysis. Springer, New York, 1997.
[8] Irene Epifanio, "Shape descriptors for classification of functional data," Technometric, vol. 50, no. 3. 2008.
[9] 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
[10] S.G. Mallat, A Wavelet Tour of Signal Processing, San Diego: Academic Press, 1998.
[11] Marek Kurzynski and Edward Puchala, "The optimal feature extraction procedure for statistical pattern recognition," ICCSA 2006, LNCS 3982, pp. 1210-1215.
[12] 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.
[13] 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.
[14] T. Hastie, R. Tibshirani, and J. Friedman, "The elements of statistical learning," Data mining, inference and prediction, Springer-Verlag, 2001
[15] L. Devroye, L. Gyorfi, and G. Lugosi, A Probabilistic Theory of Pattern Recognition, Springer-Verlag, New-York, 1996.