메뉴 건너뛰기




Volumn 23, Issue 11, 2012, Pages 1690-1700

Robust support vector regression for uncertain input and output data

Author keywords

Robust; second order cone programming; support vector regression; uncertain data

Indexed keywords

ELLIPSOIDAL UNCERTAINTIES; INTERIOR POINT METHODS; NONLINEAR FORMULATION; NONLINEAR REGRESSION PROBLEMS; ROBUST; SECOND-ORDER CONE PROGRAMMING; SUPPORT VECTOR REGRESSION (SVR); UNCERTAIN DATAS;

EID: 84876925191     PISSN: 2162237X     EISSN: 21622388     Source Type: Journal    
DOI: 10.1109/TNNLS.2012.2212456     Document Type: Article
Times cited : (49)

References (45)
  • 2
    • 34249753618 scopus 로고
    • Support vector networks
    • C. Cortes and V. Vapnik, "Support vector networks," Mach. Learn., vol. 20, no. 3, pp. 273-297, 1995.
    • (1995) Mach. Learn , vol.20 , Issue.3 , pp. 273-297
    • Cortes, C.1    Vapnik, V.2
  • 3
    • 0032594959 scopus 로고    scopus 로고
    • An overview of statistical learning theory
    • Sep
    • V. Vapnik, "An overview of statistical learning theory," IEEE Trans. Neural Netw., vol. 10, no. 5, pp. 988-999, Sep. 1999.
    • (1999) IEEE Trans. Neural Netw , vol.10 , Issue.5 , pp. 988-999
    • Vapnik, V.1
  • 5
    • 78149294352 scopus 로고    scopus 로고
    • Clifford support vector machines for classification, regression, and recurrence
    • Nov.
    • E. J. Bayro-Corrochano and N. Arana-Daniel, "Clifford support vector machines for classification, regression, and recurrence," IEEE Trans. Neural Netw., vol. 21, no. 11, pp. 1731-1746, Nov. 2010.
    • (2010) IEEE Trans. Neural Netw , vol.21 , Issue.11 , pp. 1731-1746
    • Bayro-Corrochano, E.J.1    Arana-Daniel, N.2
  • 6
    • 84862192949 scopus 로고    scopus 로고
    • Domain adaptation from multiple sources: A domain-dependent regularization approach
    • Mar.
    • L. Duan, D. Xu, and I. W. H. Tsang, "Domain adaptation from multiple sources: A domain-dependent regularization approach," IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 3, pp. 504-518, Mar. 2012.
    • (2012) IEEE Trans. Neural Netw. Learn. Syst , vol.23 , Issue.3 , pp. 504-518
    • Duan, L.1    Xu, D.2    Tsang, I.W.H.3
  • 7
    • 79957992972 scopus 로고    scopus 로고
    • Feature selection using probabilistic prediction of support vector regression
    • Jun.
    • J. B. Yang and C. J. Ong, "Feature selection using probabilistic prediction of support vector regression," IEEE Trans. Neural Netw., vol. 22, no. 6, pp. 954-962, Jun. 2011.
    • (2011) IEEE Trans. Neural Netw , vol.22 , Issue.6 , pp. 954-962
    • Yang, J.B.1    Ong, C.J.2
  • 8
    • 84875884987 scopus 로고    scopus 로고
    • Simple proof of convergence of the SMO algorithm for different SVM variants
    • Jul.
    • J. Lopez and J. R. Dorronsoro, "Simple proof of convergence of the SMO algorithm for different SVM variants," IEEE Trans. Neural Netw., vol. 23, no. 7, pp. 1142-1147, Jul. 2012.
    • (2012) IEEE Trans. Neural Netw , vol.23 , Issue.7 , pp. 1142-1147
    • Lopez, J.1    Dorronsoro, J.R.2
  • 9
    • 84887252594 scopus 로고    scopus 로고
    • Support vector method for function approximation, regression estimation, and signal processing
    • Cambridge, MA: MIT Press
    • V. Vapnik, S. E. Golowich, and A. Smola, "Support vector method for function approximation, regression estimation, and signal processing," in Advances in Neural Information Processing Systems 9. Cambridge, MA: MIT Press, 1996, pp. 281-287.
    • (1996) Advances in Neural Information Processing Systems 9 , pp. 281-287
    • Vapnik, V.1    Golowich, S.E.2    Smola, A.3
  • 11
    • 4043137356 scopus 로고    scopus 로고
    • A tutorial on support vector regression
    • A. J. Smola and B. Scholkopf, "A tutorial on support vector regression," Stat. Comput., vol. 14, no. 3, pp. 199-222, 2004.
    • (2004) Stat. Comput , vol.14 , Issue.3 , pp. 199-222
    • Smola, A.J.1    Scholkopf, B.2
  • 12
    • 0042591514 scopus 로고    scopus 로고
    • Support vector fuzzy regression machines
    • D. H. Hong and C. Hwang, "Support vector fuzzy regression machines," Fuzzy Sets Syst., vol. 138, no. 2, pp. 271-281, 2003.
    • (2003) Fuzzy Sets Syst , vol.138 , Issue.2 , pp. 271-281
    • Hong, D.H.1    Hwang, C.2
  • 13
    • 33744967706 scopus 로고    scopus 로고
    • Robust classification and regression using support vector machines
    • Jul
    • T. B. Trafalis and R. C. Gilbert, "Robust classification and regression using support vector machines," Eur. J. Oper. Res., vol. 173, no. 3, pp. 893-909, Jul. 2006.
    • (2006) Eur. J. Oper. Res , vol.173 , Issue.3 , pp. 893-909
    • Trafalis, T.B.1    Gilbert, R.C.2
  • 14
    • 33847156385 scopus 로고    scopus 로고
    • Support vector regression with noisy data: A second order cone programming approach
    • Apr
    • T. B. Trafalis and S. A. Alwazzi, "Support vector regression with noisy data: A second order cone programming approach," Int. J. General Syst., vol. 36, no. 2, pp. 237-250, Apr. 2007.
    • (2007) Int. J. General Syst , vol.36 , Issue.2 , pp. 237-250
    • Trafalis, T.B.1    Alwazzi, S.A.2
  • 15
    • 33745800909 scopus 로고    scopus 로고
    • Second order cone programming approaches for handling missing and uncertain data
    • Dec
    • P. K. Shivaswamy, C. Bhattacharyya, and A. J. Smola, "Second order cone programming approaches for handling missing and uncertain data," J. Mach. Learn. Res., vol. 7, pp. 1283-1314, Dec. 2006.
    • (2006) J. Mach. Learn. Res , vol.7 , pp. 1283-1314
    • Shivaswamy, P.K.1    Bhattacharyya, C.2    Smola, A.J.3
  • 17
    • 0036856978 scopus 로고    scopus 로고
    • Robust support vector regression networks for function approximation with outliers
    • Nov
    • C. Chuang, S. Su, J. Jeng, and C. Hsiao, "Robust support vector regression networks for function approximation with outliers," IEEE Trans. Neural Netw., vol. 13, no. 6, pp. 1322-1330, Nov. 2002.
    • (2002) IEEE Trans. Neural Netw , vol.13 , Issue.6 , pp. 1322-1330
    • Chuang, C.1    Su, S.2    Jeng, J.3    Hsiao, C.4
  • 18
    • 33746606930 scopus 로고    scopus 로고
    • Robust support vector regression for biophysical variable estimation from remotely sensed images
    • Jul
    • G. Camps-Valls, L. Bruzzone, J. Rojo-Álvarez, and F. Melgani, "Robust support vector regression for biophysical variable estimation from remotely sensed images," IEEE, Geosci. Remote Sensing Lett., vol. 3, no. 3, pp. 339-343, Jul. 2006.
    • (2006) IEEE Geosci. Remote Sensing Lett , vol.3 , Issue.3 , pp. 339-343
    • Camps-Valls, G.1    Bruzzone, L.2    Rojo-Álvarez, J.3    Melgani, F.4
  • 21
    • 0041589566 scopus 로고    scopus 로고
    • Support vector interval regression networks for interval regression analysis
    • J. Jeng, C. Chuang, and S. Su, "Support vector interval regression networks for interval regression analysis," Fuzzy Sets Syst., vol. 138, no. 2, pp. 283-300, 2003.
    • (2003) Fuzzy Sets Syst , vol.138 , Issue.2 , pp. 283-300
    • Jeng, J.1    Chuang, C.2    Su, S.3
  • 22
    • 33644972832 scopus 로고    scopus 로고
    • Support vector interval regression machine for crisp input and output data
    • C. Hwang, D. Hong, and K. H. Seok, "Support vector interval regression machine for crisp input and output data," Fuzzy Sets Syst., vol. 157, no. 8, pp. 1114-1125, 2006.
    • (2006) Fuzzy Sets Syst , vol.157 , Issue.8 , pp. 1114-1125
    • Hwang, C.1    Hong, D.2    Seok, K.H.3
  • 23
    • 3042773329 scopus 로고    scopus 로고
    • Extended fuzzy regression models using regularization method
    • Aug
    • D. H. Hong and C. Hwang, "Extended fuzzy regression models using regularization method," Inf. Sci., vol. 164, nos. 1-4, pp. 31-36, Aug. 2004.
    • (2004) Inf. Sci , vol.164 , Issue.1-4 , pp. 31-36
    • Hong, D.H.1    Hwang, C.2
  • 24
    • 4644290661 scopus 로고    scopus 로고
    • Training algorithms for fuzzy support vector machines with noisy data
    • Oct
    • C.-F. Lin and S.-D. Wang, "Training algorithms for fuzzy support vector machines with noisy data," Pattern Recognit. Lett., vol. 25, no. 14, pp. 1647-1656, Oct. 2004.
    • (2004) Pattern Recognit. Lett , vol.25 , Issue.14 , pp. 1647-1656
    • Lin, C.-F.1    Wang, S.-D.2
  • 25
    • 79952740423 scopus 로고    scopus 로고
    • Chance constrained uncertain classification via robust optimization
    • Mar.
    • A. Ben-Tal, S. Bhadra, C. Bhattacharyya, and J. S. Nath, "Chance constrained uncertain classification via robust optimization," Math. Program., vol. 127, no. 1, pp. 145-173, Mar. 2011.
    • (2011) Math. Program , vol.127 , Issue.1 , pp. 145-173
    • Ben-Tal, A.1    Bhadra, S.2    Bhattacharyya, C.3    Nath, J.S.4
  • 26
    • 0001070999 scopus 로고
    • Some modified matrix eigenvalue problems
    • G. Golub, "Some modified matrix eigenvalue problems," SIAM Rev., vol. 15, no. 2, pp. 318-344, 1973.
    • (1973) SIAM Rev , vol.15 , Issue.2 , pp. 318-344
    • Golub, G.1
  • 27
    • 0000333571 scopus 로고
    • An analysis of the total least squares problem
    • Dec
    • G. Golub and C. V. Loan, "An analysis of the total least squares problem," SIAM J. Numer. Anal., vol. 17, pp. 883-893, Dec. 1973.
    • (1973) SIAM J. Numer. Anal , vol.17 , pp. 883-893
    • Golub, G.1    Loan, C.V.2
  • 28
    • 0028401357 scopus 로고
    • Recurrent neural networks and robust time series prediction
    • Mar
    • J. Connor, R. Martin, and L. Atlas, "Recurrent neural networks and robust time series prediction," IEEE Trans. Neural Netw., vol. 5, no. 2, pp. 240-254, Mar. 1994.
    • (1994) IEEE Trans. Neural Netw , vol.5 , Issue.2 , pp. 240-254
    • Connor, J.1    Martin, R.2    Atlas, L.3
  • 29
    • 0028428006 scopus 로고
    • A robust backpropagation learning algorithm for function approximation
    • May
    • D. S. Chen and R. C. Jain, "A robust backpropagation learning algorithm for function approximation," IEEE Trans. Neural Netw., vol. 5, no. 3, pp. 467-479, May 1994.
    • (1994) IEEE Trans. Neural Netw , vol.5 , Issue.3 , pp. 467-479
    • Chen, D.S.1    Jain, R.C.2
  • 30
    • 84942484786 scopus 로고
    • Ridge regression: Biased estimation for nonorthogonal problems
    • E. Hoerl and R. W. Kennard, "Ridge regression: Biased estimation for nonorthogonal problems," Technometrics, vol. 12, no. 1, pp. 55-67, 1970.
    • (1970) Technometrics , vol.12 , Issue.1 , pp. 55-67
    • Hoerl, E.1    Kennard, R.W.2
  • 31
    • 0020207081 scopus 로고
    • Linear regression analysis with fuzzy model
    • Nov
    • H. Tanaka, S. Uejima, and K. Asai, "Linear regression analysis with fuzzy model," IEEE Trans. Syst. Man Cybern., vol. 12, no. 6, pp. 903-907, Nov. 1982.
    • (1982) IEEE Trans. Syst. Man Cybern , vol.12 , Issue.6 , pp. 903-907
    • Tanaka, H.1    Uejima, S.2    Asai, K.3
  • 32
    • 0000325717 scopus 로고
    • Fuzzy least squares
    • Dec
    • P. Diamond, "Fuzzy least squares," Inf. Sci., vol. 46, pp. 141-157, Dec. 1988.
    • (1988) Inf. Sci , vol.46 , pp. 141-157
    • Diamond, P.1
  • 33
    • 0042496087 scopus 로고
    • Multivariate Chebyshev inequality
    • Dec
    • A. W. Marshall and I. Olkin, "Multivariate Chebyshev inequality," Ann. Math. Stat., vol. 31, no. 4, pp. 1001-1014, Dec. 1960.
    • (1960) Ann. Math. Stat , vol.31 , Issue.4 , pp. 1001-1014
    • Marshall, A.W.1    Olkin, I.2
  • 35
    • 0000561116 scopus 로고
    • On the implementation of a primal-dual interior point method
    • S. Mehrotra, "On the implementation of a primal-dual interior point method," SIAM J. Opt., vol. 2, no. 4, pp. 575-601, 1992.
    • (1992) SIAM J. Opt , vol.2 , Issue.4 , pp. 575-601
    • Mehrotra, S.1
  • 36
    • 33845326781 scopus 로고    scopus 로고
    • Robust support vector machines for classification and computational issues
    • Feb
    • T. B. Trafalis and R. C. Gilbert, "Robust support vector machines for classification and computational issues," Optim. Methods Softw., vol. 22, no. 1, pp. 187-198, Feb. 2007.
    • (2007) Optim. Methods Softw , vol.22 , Issue.1 , pp. 187-198
    • Trafalis, T.B.1    Gilbert, R.C.2
  • 37
    • 0347243182 scopus 로고    scopus 로고
    • Nonlinear component analysis as a kernel eigenvalue problem
    • B. Schölkopf, A. Smola, and K. R. Muller, "Nonlinear component analysis as a kernel eigenvalue problem," Neural Comput., vol. 10, no. 5, pp. 1299-1319, 1998.
    • (1998) Neural Comput , vol.10 , Issue.5 , pp. 1299-1319
    • Schölkopf, B.1    Smola, A.2    Muller, K.R.3
  • 38
    • 0041940559 scopus 로고    scopus 로고
    • Applications of second-order cone programming
    • M. S. Lobo, L. Vandenberghe, S. Boyd, and H. Lebret, "Applications of second-order cone programming," Linear Algebra Its Appl., vol. 284, nos. 1-3, pp. 193-228, 1998.
    • (1998) Linear Algebra Its Appl , vol.284 , Issue.1-3 , pp. 193-228
    • Lobo, M.S.1    Vandenberghe, L.2    Boyd, S.3    Lebret, H.4
  • 40
    • 84876931673 scopus 로고    scopus 로고
    • [Online]
    • I. Polik. (2010). SeDuMi [Online]. Available: http://sedumi.ie.lehigh.edu
    • (2010) SeDuMi
    • Polik, I.1
  • 41
    • 0033296299 scopus 로고    scopus 로고
    • Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones
    • J. F. Sturm, "Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones," Optim. Methods Softw., vol. 11, nos. 1-4, pp. 625-653, 1999.
    • (1999) Optim. Methods Softw , vol.11 , Issue.1-4 , pp. 625-653
    • Sturm, J.F.1
  • 42
    • 79955702502 scopus 로고    scopus 로고
    • LIBSVM: A library for support vector machines
    • C. Chang and C. Lin, "LIBSVM: A library for support vector machines," ACM Trans. Intell. Syst. Technol., vol. 2, no. 3, pp. 1-27, 2011.
    • (2011) ACM Trans. Intell. Syst. Technol , vol.2 , Issue.3 , pp. 1-27
    • Chang, C.1    Lin, C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.