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Volumn 21, Issue 9, 2010, Pages 1381-1395

A neural network of smooth hinge functions

Author keywords

Function approximation; hinging hyperplanes (HHs); neural networks; nonlinear identification; sigmoidal functions; smooth hinging hyperplanes (SHHs)

Indexed keywords

APPROXIMATION ERRORS; DIFFERENTIABILITY PROPERTIES; FUNCTION APPROXIMATION; FUNCTIONAL APPROXIMATION; GENERAL FUNCTIONS; HINGING HYPERPLANES; NON-DIFFERENTIABILITY; NONLINEAR IDENTIFICATIONS; OPTIMAL ERROR; SIGMOIDAL ACTIVATION FUNCTIONS; SIGMOIDAL FUNCTIONS; SIMULATION EXPERIMENTS; UPPER BOUND;

EID: 77956338893     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/TNN.2010.2053383     Document Type: Article
Times cited : (11)

References (21)
  • 1
    • 0027599793 scopus 로고
    • Universal approximation bounds for superposition of a sigmoidal function
    • May
    • A. Barron, "Universal approximation bounds for superposition of a sigmoidal function," IEEE Trans. Inform. Theory, vol. 39, no. 3, pp. 930-945, May 1993.
    • (1993) IEEE Trans. Inform. Theory , vol.39 , Issue.3 , pp. 930-945
    • Barron, A.1
  • 2
    • 0027602489 scopus 로고
    • Hinging hyperplanes for regression, classification, and function approximation
    • May
    • L. Breiman, "Hinging hyperplanes for regression, classification, and function approximation," IEEE Trans. Inform. Theory, vol. 39, no. 3, pp. 999-1013, May 1993.
    • (1993) IEEE Trans. Inform. Theory , vol.39 , Issue.3 , pp. 999-1013
    • Breiman, L.1
  • 3
    • 0035201779 scopus 로고    scopus 로고
    • Error bounds for approximation with neural networks
    • Oct.
    • M. Burger and A. Neubauer, "Error bounds for approximation with neural networks," J. Approx. Theory, vol. 112, no. 2, pp. 235-250, Oct. 2001.
    • (2001) J. Approx. Theory , vol.112 , Issue.2 , pp. 235-250
    • Burger, M.1    Neubauer, A.2
  • 4
    • 0030196823 scopus 로고    scopus 로고
    • Comparison of adaptive methods for function estimation from samples
    • Jul.
    • V. Cherkassky, D. Gehring, and F. Mulier, "Comparison of adaptive methods for function estimation from samples," IEEE Trans. Neural Netw., vol. 7, no. 4, pp. 969-984, Jul. 1996.
    • (1996) IEEE Trans. Neural Netw. , vol.7 , Issue.4 , pp. 969-984
    • Cherkassky, V.1    Gehring, D.2    Mulier, F.3
  • 5
    • 0032274383 scopus 로고    scopus 로고
    • Hinging hyperplane trees for approximation and identification
    • Dec.
    • S. Ernst, "Hinging hyperplane trees for approximation and identification," in Proc. 37th IEEE Conf. Decision Control, Dec. 1998, pp. 1166- 1271.
    • (1998) Proc. 37th IEEE Conf. Decision Control , pp. 1166-1271
    • Ernst, S.1
  • 6
    • 33744937909 scopus 로고    scopus 로고
    • Evolutionary product unit based neural networks for regression
    • A. M. Estudillo, F. M. Estudillo, C. H. Mart́nez, and N. G. Pedrajas, "Evolutionary product unit based neural networks for regression," Neural Netw., vol. 19, no. 4, pp. 477-486, 2006.
    • (2006) Neural Netw. , vol.19 , Issue.4 , pp. 477-486
    • Estudillo, A.M.1    Estudillo, F.M.2    Mart́nez, C.H.3    Pedrajas, N.G.4
  • 7
    • 0742321288 scopus 로고    scopus 로고
    • Multiobjective evolutionary optimization of the size, shape, and position parameters of radial basis function networks for function approximaztion
    • Nov.
    • J. Gonźalez, I. Rojas, J. Ortega, H. Pomares, F. J. Ferńandez, and A. F. Díaz, "Multiobjective evolutionary optimization of the size, shape, and position parameters of radial basis function networks for function approximaztion," IEEE Trans. Neural Netw., vol. 14, no. 6, pp. 1478- 1495, Nov. 2003.
    • (2003) IEEE Trans. Neural Netw. , vol.14 , Issue.6 , pp. 1478-1495
    • Gonźalez, J.1    Rojas, I.2    Ortega, J.3    Pomares, H.4    Ferńandez, F.J.5    Díaz, A.F.6
  • 8
    • 0032207495 scopus 로고    scopus 로고
    • Efficient algorithms for function approximation with piecewise linear sigmoidal networks
    • Nov.
    • D. R. Hush and B. Horne, "Efficient algorithms for function approximation with piecewise linear sigmoidal networks," IEEE Trans. Neural Netw., vol. 9, no. 6, pp. 1129-1141, Nov. 1998.
    • (1998) IEEE Trans. Neural Netw. , vol.9 , Issue.6 , pp. 1129-1141
    • Hush, D.R.1    Horne, B.2
  • 10
    • 0036165028 scopus 로고    scopus 로고
    • Comparison of worst case errors in linear and neural network approximation
    • Jan.
    • V. Kurkov́a and M. Sanguineti, "Comparison of worst case errors in linear and neural network approximation," IEEE Trans. Inform. Theory, vol. 48, no. 1, pp. 264-275, Jan. 2002.
    • (2002) IEEEi Trans. Inform. Theory , vol.48 , Issue.1 , pp. 264-275
    • Kurkov́a, V.1    Sanguineti, M.2
  • 11
    • 57349097663 scopus 로고    scopus 로고
    • Geometric upper bounds on rates of variable-basis approximation
    • Dec.
    • V. Kurkov́a and M. Sanguineti, "Geometric upper bounds on rates of variable-basis approximation," IEEE Trans. Inform. Theory, vol. 54, no. 12, pp. 5681-5688, Dec. 2008.
    • (2008) IEEE Trans. Inform. Theory , vol.54 , Issue.12 , pp. 5681-5688
    • Kurkov́a, V.1    Sanguineti, M.2
  • 12
    • 0036505609 scopus 로고    scopus 로고
    • On the geometric convergence of neural approximations
    • Mar.
    • E. Lavretsky, "On the geometric convergence of neural approximations," IEEE Trans. Neural Netw., vol. 13, no. 2, pp. 273-282, Mar. 2002.
    • (2002) IEEE Trans. Neural Netw. , vol.13 , Issue.2 , pp. 273-282
    • Lavretsky, E.1
  • 13
    • 0037255446 scopus 로고    scopus 로고
    • A new EM-based training algorithm for RBF networks
    • M. Ĺazaro, I. Santamaŕia, and C. Pantaléon, "A new EM-based training algorithm for RBF networks," Neural Netw., vol. 16, no. 1, pp. 69-77, 2003.
    • (2003) Neural Netw , vol.16 , Issue.1 , pp. 69-77
    • Ĺazaro, M.1    Santamaŕia, I.2    Pantaléon, C.3
  • 14
    • 0030119952 scopus 로고    scopus 로고
    • Random approximants and neural networks
    • Y. Makovoz, "Random approximants and neural networks," J. Approx. Theory, vol. 85, no. 1, pp. 98-109, 1996.
    • (1996) J. Approx. Theory , vol.85 , Issue.1 , pp. 98-109
    • Makovoz, Y.1
  • 16
    • 0031147146 scopus 로고    scopus 로고
    • PWL nonlinear adaptive filter via RLS and LMS algorithms
    • May
    • N. Plaziac, C. T. Ledinh, and J. P. Adoul, "PWL nonlinear adaptive filter via RLS and LMS algorithms," IEEE Trans. Signal Process., vol. 45, no. 5, pp. 1364-1367, May 1997.
    • (1997) IEEE Trans. Signal Process. , vol.45 , Issue.5 , pp. 1364-1367
    • Plaziac, N.1    Ledinh, C.T.2    Adoul, J.P.3
  • 17
    • 0010242173 scopus 로고
    • Smooth hinging hyperplanes: An alternative to neural nets
    • Sep.
    • P. Pucar and M. Millnert, "Smooth hinging hyperplanes: An alternative to neural nets," in Proc. 3rd Eur. Control Conf., Sep. 1995, pp. 1173- 1178.
    • (1995) Proc. 3rd Eur. Control Conf. , pp. 1173-1178
    • Pucar, P.1    Millnert, M.2
  • 18
    • 0032069336 scopus 로고    scopus 로고
    • On the hinge-finding algorithm for hinging hyperplanes
    • May
    • P. Pucar and J. Sjöberg, "On the hinge-finding algorithm for hinging hyperplanes," IEEE Trans. Infor. Theory, vol. 44, no. 3, pp. 1310-1319, May 1998.
    • (1998) IEEE Trans. Infor. Theory , vol.44 , Issue.3 , pp. 1310-1319
    • Pucar, P.1    Sjöberg, J.2
  • 19
    • 0242440101 scopus 로고    scopus 로고
    • Identification of piecewise affine systems via mixed-integer programming
    • J. Roll, A. Bemporad, and L. Ljung, "Identification of piecewise affine systems via mixed-integer programming," Automatica, vol. 40, no. 1, pp. 37-50, 2004.
    • (2004) Automatica , vol.40 , Issue.1 , pp. 37-50
    • Roll, J.1    Bemporad, A.2    Ljung, L.3
  • 20
    • 0029483769 scopus 로고
    • Nonlinear black-box modeling in system identification: A unified overview
    • J. Sjöberg, Q. Zhang, and L. Ljung, "Nonlinear black-box modeling in system identification: A unified overview," Automatica, vol. 31, no. 12, pp. 1691-1724, 1995.
    • (1995) Automatica , vol.31 , Issue.12 , pp. 1691-1724
    • Sjöberg, J.1    Zhang, Q.2    Ljung, L.3
  • 21
    • 0033307330 scopus 로고    scopus 로고
    • Globally optimal fuzzy decision trees for classification and regression
    • Dec.
    • A. Súarez and J. F. Lutsko, "Globally optimal fuzzy decision trees for classification and regression," IEEE Trans. Pattern Anal. Mach. Intell., vol. 21, no. 12, pp. 1297-1311, Dec. 1999.
    • (1999) IEEE Trans. Pattern Anal. Mach. Intell. , vol.21 , Issue.12 , pp. 1297-1311
    • Súarez, A.1    Lutsko, J.F.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.