GA Based Optimal Feature Extraction Method for Functional Data Classification
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:62732", author = "Jun Wan and Zehua Chen and Yingwu Chen and Zhidong Bai", title = "GA Based Optimal Feature Extraction Method for Functional Data Classification", 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.", volume = "4", number = "2", pages = "306-7", }