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Erschienen in: International Journal of Machine Learning and Cybernetics 12/2018

23.05.2017 | Original Article

Generalized eigenvalue proximal support vector regressor for the simultaneous learning of a function and its derivatives

verfasst von: Reshma Khemchandani, Keshav Goyal, Suresh Chandra

Erschienen in: International Journal of Machine Learning and Cybernetics | Ausgabe 12/2018

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Abstract

Generalized eigenvalue proximal support vector regressor (GEPSVR) determines a pair of \(\epsilon\)-insensitive bounding regressors by solving a pair of generalized eigenvalue problem. On the lines of GEPSVR, in this paper we propose a novel regressor for the simultaneous learning of a function and its derivatives, termed as GEPSVR of a Function and its Derivatives. The proposed method is fast as it requires the solution of a pair of generalized eigenvalue problems as compared to the solution of a large Quadratic Programming Problem required in other existing approaches. The experiment results on several benchmark functions of more than one variable proves the efficacy of our proposed method.

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Literatur
1.
Zurück zum Zitat Antonio J, Martin H, Santos M, Lope J (2010) Orthogonal variant moments features in image analysis. Inf Sci 180:846–860MathSciNetCrossRef Antonio J, Martin H, Santos M, Lope J (2010) Orthogonal variant moments features in image analysis. Inf Sci 180:846–860MathSciNetCrossRef
2.
Zurück zum Zitat Burges C (1998) A tutorial on support vector machines for pattern recognition. Data Min Knowl Discov 2(2):121–167CrossRef Burges C (1998) A tutorial on support vector machines for pattern recognition. Data Min Knowl Discov 2(2):121–167CrossRef
4.
Zurück zum Zitat Ebrahimi T, Garcia G, Vesin J (2002) Joint time-frequency-space classification of EEG in a braincomputer interface appplication. J Appl Signal Process 1:713–729MATH Ebrahimi T, Garcia G, Vesin J (2002) Joint time-frequency-space classification of EEG in a braincomputer interface appplication. J Appl Signal Process 1:713–729MATH
5.
Zurück zum Zitat Guarracino MR, Cifarelli C, Seref O, Pardalos PM (2007) A classification method based on generalized eigenvalue problems. Optim Methods Softw 22(1):73–81MathSciNetCrossRef Guarracino MR, Cifarelli C, Seref O, Pardalos PM (2007) A classification method based on generalized eigenvalue problems. Optim Methods Softw 22(1):73–81MathSciNetCrossRef
6.
Zurück zum Zitat Khemchandani R, Chandra S (2006) Regularized least squares twin SVR for the simultaneous learning of a function and its derivative. In: IJCNN, pp 1192–1197 Khemchandani R, Chandra S (2006) Regularized least squares twin SVR for the simultaneous learning of a function and its derivative. In: IJCNN, pp 1192–1197
7.
Zurück zum Zitat Khemchandani R, Chandra S (2007) Twin support vector machines for pattern classification. IEEE Trans Pattern Anal Mach Intell 29:905–910CrossRef Khemchandani R, Chandra S (2007) Twin support vector machines for pattern classification. IEEE Trans Pattern Anal Mach Intell 29:905–910CrossRef
8.
Zurück zum Zitat Khemchandani R, Chandra S (2008) Regularized least squares support vector regression for the simultaneous learning of a function and its derivatives. Inf Sci 178:3402–3414CrossRef Khemchandani R, Chandra S (2008) Regularized least squares support vector regression for the simultaneous learning of a function and its derivatives. Inf Sci 178:3402–3414CrossRef
9.
Zurück zum Zitat Joachims T (1999) Making large-scale SVM learning practical. In: Schölkopf B, Burges C, Smola A (eds) Advances in kernel methods: support vector learning. MIT Press, Cambridge, MA Joachims T (1999) Making large-scale SVM learning practical. In: Schölkopf B, Burges C, Smola A (eds) Advances in kernel methods: support vector learning. MIT Press, Cambridge, MA
10.
Zurück zum Zitat Julier SJ, Uhlmann JK (2004) Unscented filtering and nonlinear estimation. In: Proceedings of the IEEE, pp 401–422CrossRef Julier SJ, Uhlmann JK (2004) Unscented filtering and nonlinear estimation. In: Proceedings of the IEEE, pp 401–422CrossRef
11.
Zurück zum Zitat Khemchandani R, Jayadeva Chandra S (2009) Regularized least squares fuzzy support vector regression for financial time series forecasting. Expert Syst Appl 36:132–138CrossRef Khemchandani R, Jayadeva Chandra S (2009) Regularized least squares fuzzy support vector regression for financial time series forecasting. Expert Syst Appl 36:132–138CrossRef
12.
Zurück zum Zitat Khemchandani R, Karpatne A, Chandra S (2011) Generalized eigenvalue proximal support vector regressor. Expert Syst Appl 38:13136–13142CrossRef Khemchandani R, Karpatne A, Chandra S (2011) Generalized eigenvalue proximal support vector regressor. Expert Syst Appl 38:13136–13142CrossRef
13.
Zurück zum Zitat Khemchandani R, Karpatne A, Chandra S (2013) Twin support vector regression for the simultaneous learning of a function and its derivatives. Int J Mach Learn Cybern 4:51–63CrossRef Khemchandani R, Karpatne A, Chandra S (2013) Twin support vector regression for the simultaneous learning of a function and its derivatives. Int J Mach Learn Cybern 4:51–63CrossRef
14.
Zurück zum Zitat Khemchandani R, Goyal K, Chandra S (2016) TWSVR: regression via twin support vector machine. Neural Netw 74:14–21CrossRef Khemchandani R, Goyal K, Chandra S (2016) TWSVR: regression via twin support vector machine. Neural Netw 74:14–21CrossRef
15.
Zurück zum Zitat Lagaris IE, Likas A, Fotiadis D (1998) Artificial neural networks for solving ordinary and partial differential equations. IEEE Trans Neural Netw 9:987–1000CrossRef Lagaris IE, Likas A, Fotiadis D (1998) Artificial neural networks for solving ordinary and partial differential equations. IEEE Trans Neural Netw 9:987–1000CrossRef
16.
Zurück zum Zitat Lázarao M, Santamaŕia I, Péreze-Cruz F, Artés-Rodŕiguez A (2003) SVM for the simultaneous approximation of a function and its derivative. In: Proceedings of the 2003 IEEE international workshop on neural networks for signal processing(NNSP), Toulouse, France, pp 189–198 Lázarao M, Santamaŕia I, Péreze-Cruz F, Artés-Rodŕiguez A (2003) SVM for the simultaneous approximation of a function and its derivative. In: Proceedings of the 2003 IEEE international workshop on neural networks for signal processing(NNSP), Toulouse, France, pp 189–198
17.
Zurück zum Zitat Lázarao M, Santamaŕia I, Péreze-Cruz F, Artés-Rodŕiguez A (2005) Support vector regression for the simultaneous learning of a multivariate function and its derivative. Neurocomputing 69:42–61CrossRef Lázarao M, Santamaŕia I, Péreze-Cruz F, Artés-Rodŕiguez A (2005) Support vector regression for the simultaneous learning of a multivariate function and its derivative. Neurocomputing 69:42–61CrossRef
18.
Zurück zum Zitat Liu Z, Wu Q, Zhang Y, Chen CLP (2011) Adaptive least squares support vector machines filter for hand tremor canceling in microsurgery. Int J Mach Learn Cybernet 2(1):37–47CrossRef Liu Z, Wu Q, Zhang Y, Chen CLP (2011) Adaptive least squares support vector machines filter for hand tremor canceling in microsurgery. Int J Mach Learn Cybernet 2(1):37–47CrossRef
19.
Zurück zum Zitat Managasarian OL, Wild EW (2006) Multisurface proximal support vector classification via generalized eigenvalues. IEEE Trans Pattern Anal Mach Intell 28(1):69–74CrossRef Managasarian OL, Wild EW (2006) Multisurface proximal support vector classification via generalized eigenvalues. IEEE Trans Pattern Anal Mach Intell 28(1):69–74CrossRef
20.
Zurück zum Zitat Osuna E, Freund R, Girosi F (1997) Training support vector machines: an application to face detection. In: IEEE computer society conference on computer vision and pattern recognition, pp 130–136 Osuna E, Freund R, Girosi F (1997) Training support vector machines: an application to face detection. In: IEEE computer society conference on computer vision and pattern recognition, pp 130–136
21.
Zurück zum Zitat Parlett BN (1998) The symmetric eigenvalue problem. Classics in applied mathematics, vol 20. Society for Industrial and Applied Mathematics(SIAM)(2), Philadelphia Parlett BN (1998) The symmetric eigenvalue problem. Classics in applied mathematics, vol 20. Society for Industrial and Applied Mathematics(SIAM)(2), Philadelphia
22.
Zurück zum Zitat Peng X (2010) TSVR: an efficient twin support vector machine for regression. Neural Netw 23:365–372CrossRef Peng X (2010) TSVR: an efficient twin support vector machine for regression. Neural Netw 23:365–372CrossRef
23.
Zurück zum Zitat Tikhonov AN, Arsenin VY (1977) Solution of ill posed problems. Wiley, New YorkMATH Tikhonov AN, Arsenin VY (1977) Solution of ill posed problems. Wiley, New YorkMATH
24.
Zurück zum Zitat Vapnik V.N(1998). Statistical learning theory. Wiley, New York Vapnik V.N(1998). Statistical learning theory. Wiley, New York
26.
Zurück zum Zitat Zheng S (2011) Gradient descent algorithms for quantile regression with smooth approximation. International Journal of Machine Learning and Cybernetics 2(3):191–207CrossRef Zheng S (2011) Gradient descent algorithms for quantile regression with smooth approximation. International Journal of Machine Learning and Cybernetics 2(3):191–207CrossRef
Metadaten
Titel
Generalized eigenvalue proximal support vector regressor for the simultaneous learning of a function and its derivatives
verfasst von
Reshma Khemchandani
Keshav Goyal
Suresh Chandra
Publikationsdatum
23.05.2017
Verlag
Springer Berlin Heidelberg
Erschienen in
International Journal of Machine Learning and Cybernetics / Ausgabe 12/2018
Print ISSN: 1868-8071
Elektronische ISSN: 1868-808X
DOI
https://doi.org/10.1007/s13042-017-0687-3

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