Skip to main content
Top
Published in: Engineering with Computers 2/2022

07-01-2021 | Original Article

Solving the stochastic support vector regression with probabilistic constraints by a high-performance neural network model

Authors: Amir Feizi, Alireza Nazemi, Mohammad Reza Rabiei

Published in: Engineering with Computers | Special Issue 2/2022

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This paper offers a recurrent neural network to support vector machine (SVM) learning in stochastic support vector regression with probabilistic constraints. The SVM is first converted into an equivalent quadratic programming (QP) formulation in linear and nonlinear cases. An artificial neural network for SVM learning is then proposed. The presented neural network framework guarantees obtaining the optimal solution of the SVM problem. The existence and convergence of the trajectories of the network are studied. The Lyapunov stability for the considered neural network is also shown. The efficiency of the proposed method is shown by three illustrative examples.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Abaszade M, Effati S (2018) Stochastic support vector regression with probabilistic constraints. Appl Intell 48(1):243–256MATHCrossRef Abaszade M, Effati S (2018) Stochastic support vector regression with probabilistic constraints. Appl Intell 48(1):243–256MATHCrossRef
2.
go back to reference Anguita D, Boni A (2002) Improved neural network for SVM learning. IEEE Trans Neural Netw 13(5):1243–1244CrossRef Anguita D, Boni A (2002) Improved neural network for SVM learning. IEEE Trans Neural Netw 13(5):1243–1244CrossRef
3.
go back to reference Barnett NS, Dragomir SS, Agarwal R (2002) Some inequalities for probability, expectation, and variance of random variables defined over a finite interval. Comput Math Appl 43(10–11):1319–1357MathSciNetMATHCrossRef Barnett NS, Dragomir SS, Agarwal R (2002) Some inequalities for probability, expectation, and variance of random variables defined over a finite interval. Comput Math Appl 43(10–11):1319–1357MathSciNetMATHCrossRef
5.
go back to reference Bazaraa MS, Sherali HD, Shetty CM (2013) Nonlinear programming: theory and algorithms. John Wiley & Sons Bazaraa MS, Sherali HD, Shetty CM (2013) Nonlinear programming: theory and algorithms. John Wiley & Sons
6.
go back to reference Ben-Tal A, Bhadra S, Bhattacharyya C, Nath JS (2011) Chance constrained uncertain classification via robust optimization. Math Progr 127(1):145–173MathSciNetMATHCrossRef Ben-Tal A, Bhadra S, Bhattacharyya C, Nath JS (2011) Chance constrained uncertain classification via robust optimization. Math Progr 127(1):145–173MathSciNetMATHCrossRef
7.
go back to reference Bennett KP, Mangasarian OL (1992) Robust linear programming discrimination of two linearly inseparable sets. Optim Methods Softw 1(1):23–34CrossRef Bennett KP, Mangasarian OL (1992) Robust linear programming discrimination of two linearly inseparable sets. Optim Methods Softw 1(1):23–34CrossRef
8.
go back to reference Bhattacharyya C, Shivaswamy PK, Smola AJ (2005) A second order cone programming formulation for classifying missing data. In: Advances in neural information processing systems. pp 153–160 Bhattacharyya C, Shivaswamy PK, Smola AJ (2005) A second order cone programming formulation for classifying missing data. In: Advances in neural information processing systems. pp 153–160
9.
go back to reference Boyd S, Vandenberghe L, Press CU (2004) Convex optimization. No. pt 1 in Berichte über verteilte messysteme. Cambridge University Press, Cambridge Boyd S, Vandenberghe L, Press CU (2004) Convex optimization. No. pt 1 in Berichte über verteilte messysteme. Cambridge University Press, Cambridge
10.
go back to reference Carrizosa E, Gordillo J, Plastria F (2008) Kernel support vector regression with imprecise output. Dept. MOSI, Vrije Univ. Brussel, Brussel, Belgium, Tech. Rep Carrizosa E, Gordillo J, Plastria F (2008) Kernel support vector regression with imprecise output. Dept. MOSI, Vrije Univ. Brussel, Brussel, Belgium, Tech. Rep
11.
go back to reference Chuang CC, Su SF, Jeng JT, Hsiao CC (2002) Robust support vector regression networks for function approximation with outliers. IEEE Trans Neural Netw 13(6):1322–1330CrossRef Chuang CC, Su SF, Jeng JT, Hsiao CC (2002) Robust support vector regression networks for function approximation with outliers. IEEE Trans Neural Netw 13(6):1322–1330CrossRef
13.
go back to reference Dierckx P (1995) Curve and surface fitting with splines. Oxford University Press Dierckx P (1995) Curve and surface fitting with splines. Oxford University Press
14.
go back to reference Drucker H, Burges CJC, Kaufman L, Smola AJ, Vapnik V (1997) Support vector regression machines. Advances in neural information processing systems 9. MIT Press, Cambridge, pp 155–161 Drucker H, Burges CJC, Kaufman L, Smola AJ, Vapnik V (1997) Support vector regression machines. Advances in neural information processing systems 9. MIT Press, Cambridge, pp 155–161
15.
go back to reference Farag AA, Mohamed RM (2003) Classification of multispectral data using support vector machines approach for density estimation. In: International conference on intelligent engineering system, pp 6–8. Citeseer Farag AA, Mohamed RM (2003) Classification of multispectral data using support vector machines approach for density estimation. In: International conference on intelligent engineering system, pp 6–8. Citeseer
16.
go back to reference Gao X, Liao L (2009) A new projection-based neural network for constrained variational inequalities. IEEE Trans Neural Netw 20(3):373–388CrossRef Gao X, Liao L (2009) A new projection-based neural network for constrained variational inequalities. IEEE Trans Neural Netw 20(3):373–388CrossRef
17.
go back to reference Hao PY (2010) New support vector algorithms with parametric insensitive/margin model. Neural Netw 23(1):60–73MATHCrossRef Hao PY (2010) New support vector algorithms with parametric insensitive/margin model. Neural Netw 23(1):60–73MATHCrossRef
20.
go back to reference Hopfield J, Tank D (1986) Computing with neural circuits: a model. Science 233(4764):625–633CrossRef Hopfield J, Tank D (1986) Computing with neural circuits: a model. Science 233(4764):625–633CrossRef
21.
go back to reference Hu X, Sun C, Zhang B (2010) Design of recurrent neural networks for solving constrained least absolute deviation problems. IEEE Trans Neural Netw 21(7):1073–1086CrossRef Hu X, Sun C, Zhang B (2010) Design of recurrent neural networks for solving constrained least absolute deviation problems. IEEE Trans Neural Netw 21(7):1073–1086CrossRef
22.
go back to reference Hu X, Zhang B (2009) An alternative recurrent neural network for solving variational inequalities and related optimization problems. IEEE Trans Syst Man Cybern Part B (Cybern) 39(6):1640–1645CrossRef Hu X, Zhang B (2009) An alternative recurrent neural network for solving variational inequalities and related optimization problems. IEEE Trans Syst Man Cybern Part B (Cybern) 39(6):1640–1645CrossRef
23.
go back to reference Huang GB, Zhu QY, Siew CK (2006) Extreme learning machine: theory and applications. Neurocomputing 70(1–3):489–501CrossRef Huang GB, Zhu QY, Siew CK (2006) Extreme learning machine: theory and applications. Neurocomputing 70(1–3):489–501CrossRef
24.
25.
go back to reference Lillo WE, Loh MH, Hui S, Zak SH (1993) On solving constrained optimization problems with neural networks: a penalty method approach. IEEE Trans Neural Netw 4(6):931–940CrossRef Lillo WE, Loh MH, Hui S, Zak SH (1993) On solving constrained optimization problems with neural networks: a penalty method approach. IEEE Trans Neural Netw 4(6):931–940CrossRef
26.
go back to reference Fu Lin C, de Wang S (2004) Training algorithms for fuzzy support vector machines with noisy data. Pattern Recognit Lett 25(14):1647–1656CrossRef Fu Lin C, de Wang S (2004) Training algorithms for fuzzy support vector machines with noisy data. Pattern Recognit Lett 25(14):1647–1656CrossRef
28.
go back to reference Lobo MS, Vandenberghe L, Boyd S, Lebret H (1998) Applications of second-order cone programming. Linear Algebra Appl 284(1):193–228MathSciNetMATHCrossRef Lobo MS, Vandenberghe L, Boyd S, Lebret H (1998) Applications of second-order cone programming. Linear Algebra Appl 284(1):193–228MathSciNetMATHCrossRef
30.
go back to reference Miller R, Michel A (1982) Ordinary differential equations. Academic press, New YorkMATH Miller R, Michel A (1982) Ordinary differential equations. Academic press, New YorkMATH
31.
go back to reference Nazemi A (2013) Solving general convex nonlinear optimization problems by an efficient neurodynamic model. Eng Appl Artif Intell 26(2):685–696CrossRef Nazemi A (2013) Solving general convex nonlinear optimization problems by an efficient neurodynamic model. Eng Appl Artif Intell 26(2):685–696CrossRef
32.
go back to reference Nazemi A (2014) A neural network model for solving convex quadratic programming problems with some applications. Eng Appl Artif Intell 32:54–62CrossRef Nazemi A (2014) A neural network model for solving convex quadratic programming problems with some applications. Eng Appl Artif Intell 32:54–62CrossRef
33.
go back to reference Nazemi A (2018) A capable neural network framework for solving degenerate quadratic optimization problems with an application in image fusion. Neural Process Lett 47(1):167–192CrossRef Nazemi A (2018) A capable neural network framework for solving degenerate quadratic optimization problems with an application in image fusion. Neural Process Lett 47(1):167–192CrossRef
34.
go back to reference Nazemi A, Nazemi M (2014) A gradient-based neural network method for solving strictly convex quadratic programming problems. Cognit Comput 6(3):484–495MathSciNetCrossRef Nazemi A, Nazemi M (2014) A gradient-based neural network method for solving strictly convex quadratic programming problems. Cognit Comput 6(3):484–495MathSciNetCrossRef
35.
go back to reference Peng X (2010) TSVR: an efficient twin support vector machine for regression. Neural Netw 23(3):365–372MATHCrossRef Peng X (2010) TSVR: an efficient twin support vector machine for regression. Neural Netw 23(3):365–372MATHCrossRef
36.
go back to reference Perfetti R, Ricci E (2006) Analog neural network for support vector machine learning. IEEE Trans Neural Netw 17(4):1085–1091CrossRef Perfetti R, Ricci E (2006) Analog neural network for support vector machine learning. IEEE Trans Neural Netw 17(4):1085–1091CrossRef
37.
go back to reference Sankowski D (2003) Signal processing systems. Theory and design. N. Kalouptsidis, a Wiley-interscience Publication, New York, 1997. Int J Adapt Control Signal Process 17(3):262–263CrossRef Sankowski D (2003) Signal processing systems. Theory and design. N. Kalouptsidis, a Wiley-interscience Publication, New York, 1997. Int J Adapt Control Signal Process 17(3):262–263CrossRef
38.
go back to reference Schölkopf B, Smola AJ, Williamson RC, Bartlett PL (2000) New support vector algorithms. Neural Comput 12(5):1207–1245CrossRef Schölkopf B, Smola AJ, Williamson RC, Bartlett PL (2000) New support vector algorithms. Neural Comput 12(5):1207–1245CrossRef
39.
go back to reference Shivaswamy PK, Bhattacharyya C, Smola AJ (2006) Second order cone programming approaches for handling missing and uncertain data. J Mach Learn Res 7(47):1283–1314MathSciNetMATH Shivaswamy PK, Bhattacharyya C, Smola AJ (2006) Second order cone programming approaches for handling missing and uncertain data. J Mach Learn Res 7(47):1283–1314MathSciNetMATH
41.
go back to reference Tank D, Hopfield J (1986) Simple ’neural’ optimization networks: an A/D converter, signal decision circuit, and a linear programming circuit. IEEE Trans Circuits Syst 33(5):533–541CrossRef Tank D, Hopfield J (1986) Simple ’neural’ optimization networks: an A/D converter, signal decision circuit, and a linear programming circuit. IEEE Trans Circuits Syst 33(5):533–541CrossRef
42.
go back to reference Trafalis TB, Alwazzi SA (2007) Support vector regression with noisy data: a second order cone programming approach. Int J Gen Syst 36(2):237–250MathSciNetMATHCrossRef Trafalis TB, Alwazzi SA (2007) Support vector regression with noisy data: a second order cone programming approach. Int J Gen Syst 36(2):237–250MathSciNetMATHCrossRef
43.
44.
go back to reference Vapnik V (2013) The nature of statistical learning theory. Information science and statistics. Springer, New York Vapnik V (2013) The nature of statistical learning theory. Information science and statistics. Springer, New York
45.
go back to reference Vapnik V, Golowich SE, Smola AJ (1997) Support vector method for function approximation, regression estimation and signal processing. In: Advances in neural information processing systems, pp 281–287 Vapnik V, Golowich SE, Smola AJ (1997) Support vector method for function approximation, regression estimation and signal processing. In: Advances in neural information processing systems, pp 281–287
46.
go back to reference Vapnik V, Mukherjee S (2000) Support vector method for multivariate density estimation. In: Advances in neural information processing systems, pp 659–665 Vapnik V, Mukherjee S (2000) Support vector method for multivariate density estimation. In: Advances in neural information processing systems, pp 659–665
47.
go back to reference Yang Y, Cao J (2008) A feedback neural network for solving convex constraint optimization problems. Appl Math Comput 201(1):340–350MathSciNetMATH Yang Y, Cao J (2008) A feedback neural network for solving convex constraint optimization problems. Appl Math Comput 201(1):340–350MathSciNetMATH
48.
go back to reference Yang Y, He Q, Hu X (2012) A compact neural network for training support vector machines. Neurocomputing 86:193–198CrossRef Yang Y, He Q, Hu X (2012) A compact neural network for training support vector machines. Neurocomputing 86:193–198CrossRef
49.
go back to reference Tan Y, Xia Y, Wang J (2000) Neural network realization of support vector methods for pattern classification. In: Proceedings of the IEEE-INNS-ENNS international joint conference on neural networks. IJCNN 2000. Neural computing: new challenges and perspectives for the New Millennium, vol 6, pp 411–416 Tan Y, Xia Y, Wang J (2000) Neural network realization of support vector methods for pattern classification. In: Proceedings of the IEEE-INNS-ENNS international joint conference on neural networks. IJCNN 2000. Neural computing: new challenges and perspectives for the New Millennium, vol 6, pp 411–416
50.
go back to reference Yoshikawa T (1990) Foundations of robotics: analysis and control. East European Monographs, vol 279. MIT Press, Cambridge Yoshikawa T (1990) Foundations of robotics: analysis and control. East European Monographs, vol 279. MIT Press, Cambridge
51.
go back to reference Youshen X, Jun W (2004) A one-layer recurrent neural network for support vector machine learning. IEEE Trans Syst Man Cybern Part B (Cybern) 34(2):1261–1269CrossRef Youshen X, Jun W (2004) A one-layer recurrent neural network for support vector machine learning. IEEE Trans Syst Man Cybern Part B (Cybern) 34(2):1261–1269CrossRef
52.
go back to reference Xia Y, Wang J (2005) A recurrent neural network for solving nonlinear convex programs subject to linear constraints. IEEE Trans Neural Netw 16(2):379–386CrossRef Xia Y, Wang J (2005) A recurrent neural network for solving nonlinear convex programs subject to linear constraints. IEEE Trans Neural Netw 16(2):379–386CrossRef
53.
go back to reference Zhao Y, Liu Q (2012) Generalized recurrent neural network for \(\epsilon\)-insensitive support vector regression. Math Comput Simul 86:2–9MathSciNetMATHCrossRef Zhao Y, Liu Q (2012) Generalized recurrent neural network for \(\epsilon\)-insensitive support vector regression. Math Comput Simul 86:2–9MathSciNetMATHCrossRef
54.
go back to reference Zhao YP, Zhao J, Zhao M (2013) Twin least squares support vector regression. Neurocomputing 118:225–236CrossRef Zhao YP, Zhao J, Zhao M (2013) Twin least squares support vector regression. Neurocomputing 118:225–236CrossRef
Metadata
Title
Solving the stochastic support vector regression with probabilistic constraints by a high-performance neural network model
Authors
Amir Feizi
Alireza Nazemi
Mohammad Reza Rabiei
Publication date
07-01-2021
Publisher
Springer London
Published in
Engineering with Computers / Issue Special Issue 2/2022
Print ISSN: 0177-0667
Electronic ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-020-01214-5

Other articles of this Special Issue 2/2022

Engineering with Computers 2/2022 Go to the issue