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Volumn 51, Issue 3, 2005, Pages 1003-1010

Nonparametric regression estimation by normalized radial basis function networks

Author keywords

Covering numbers; Empirical risk minimization; Nonparametric regression estimation; Normalized radial basis function networks.

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; EIGENVALUES AND EIGENFUNCTIONS; ERROR ANALYSIS; MATHEMATICAL MODELS; OPTIMIZATION; PROBABILITY; REGRESSION ANALYSIS; THEOREM PROVING;

EID: 15244362346     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2004.842632     Document Type: Article
Times cited : (20)

References (29)
  • 2
    • 0027599793 scopus 로고
    • "Universal approximation bounds for superpositions of a sigmoidal function"
    • May
    • A. R. Barron, "Universal approximation bounds for superpositions of a sigmoidal function," IEEE Trans. Inf. Theory, vol. 39, no. 3, pp. 930-945, May 1993.
    • (1993) IEEE Trans. Inf. Theory , vol.39 , Issue.3 , pp. 930-945
    • Barron, A.R.1
  • 3
    • 0024861871 scopus 로고
    • "Approximations by superpositions of sigmoidal functions"
    • G. Cybenko, "Approximations by superpositions of sigmoidal functions," Math. Contr., Signals, Syst., vol. 2, pp. 303-314, 1989.
    • (1989) Math. Contr., Signals, Syst. , vol.2 , pp. 303-314
    • Cybenko, G.1
  • 4
    • 0024053797 scopus 로고
    • "Automatic pattern recognition: A study of the probability of error"
    • Jul
    • L. Devroye, "Automatic pattern recognition: A study of the probability of error," IEEE Trans. Pattern Anal. Mach. Intell., vol. 10, no. 4, pp. 530-543, Jul. 1988.
    • (1988) IEEE Trans. Pattern Anal. Mach. Intell. , vol.10 , Issue.4 , pp. 530-543
    • Devroye, L.1
  • 6
    • 0000083059 scopus 로고
    • m-splines"
    • [i#m-splines," RAIRO Anal. Numér., vol. 12, no. 4, pp. 325-334, 1978.
    • (1978) RAIRO Anal. Numér. , vol.12 , Issue.4 , pp. 325-334
    • Duchon, J.1
  • 7
    • 0027632576 scopus 로고
    • "Strong universal consistency of neural network classifiers"
    • Jul
    • A. Faragó and G. Lugosi, "Strong universal consistency of neural network classifiers," IEEE Trans. Inf. heory, vol. 39, no. 4, pp. 1146-1151, Jul. 1993.
    • (1993) IEEE Trans. Inf. Theory , vol.39 , Issue.4 , pp. 1146-1151
    • Faragó, A.1    Lugosi, G.2
  • 8
    • 0003085388 scopus 로고
    • "Rates of convergence for radial basis functions and neural networks"
    • R. J. Mammone, Ed. London, U.K.: Chapman and Hall
    • F. Girosi and G. Anzellotti, "Rates of convergence for radial basis functions and neural networks," in Artificial Neural Networks for Speech and Vision, R. J. Mammone, Ed. London, U.K.: Chapman and Hall, 1993. pp. 97-113.
    • (1993) Artificial Neural Networks for Speech and Vision , pp. 97-1113
    • Girosi, F.1    Anzellotti, G.2
  • 9
    • 0001219859 scopus 로고
    • "Regularization theory and neural network architectures"
    • F. Girosi, M. Jones, and T. Poggio, "Regularization theory and neural network architectures," Neural Comput., vol. 7, pp. 219-267, 1995.
    • (1995) Neural Comput. , vol.7 , pp. 219-267
    • Girosi, F.1    Jones, M.2    Poggio, T.3
  • 12
    • 0002192516 scopus 로고
    • "Decision theoretic generalizations of the PAC model for neural net and other learning applications"
    • D. Haussler, "Decision theoretic generalizations of the PAC model for neural net and other learning applications," Inform. Comput., vol. 100, pp. 78-150, 1992.
    • (1992) Inform. Comput. , vol.100 , pp. 78-150
    • Haussler, D.1
  • 13
    • 0024880831 scopus 로고
    • "Multilayer feed-forward networks are universal approximators"
    • K. Hornik, S. Stinchcombe, and H. White, "Multilayer feed-forward networks are universal approximators," Neural Netw., vol. 2, pp. 359-366, 1989.
    • (1989) Neural Netw. , vol.2 , pp. 359-366
    • Hornik, K.1    Stinchcombe, S.2    White, H.3
  • 14
    • 0000624821 scopus 로고
    • "ε-entropy and ε-capacity of sets in function spaces"
    • A. N. Kolmogorov and V. M. Tihomirov, "ε-entropy and ε-capacity of sets in function spaces," Transl. Amer. Math. Soc., vol. 17, pp. 277-364, 1961.
    • (1961) Transl. Amer. Math. Soc. , vol.17 , pp. 277-364
    • Kolmogorov, A.N.1    Tihomirov, V.M.2
  • 15
    • 0030109050 scopus 로고    scopus 로고
    • "Nonparametric estimation and classification using radial basis function nets and empirical risk minimization"
    • Mar
    • A. Krzyzak, T. Linder, and G. Lugosi, "Nonparametric estimation and classification using radial basis function nets and empirical risk minimization," IEEE Trans. Neural Netw., vol. 7, no. 2, pp. 475-487, Mar. 1996.
    • (1996) IEEE Trans. Neural Netw. , vol.7 , Issue.2 , pp. 475-487
    • Krzyzak, A.1    Linder, T.2    Lugosi, G.3
  • 16
    • 0032022221 scopus 로고    scopus 로고
    • "Radial basis function networks and complexity regularization in function learning"
    • Mar
    • A. Krzyzak and T. Linder, "Radial basis function networks and complexity regularization in function learning," IEEE Trans. Neural Netw., vol. 9, no. 2, pp. 247-256, Mar. 1998.
    • (1998) IEEE Trans. Neural Netw. , vol.9 , Issue.2 , pp. 247-256
    • Krzyzak, A.1    Linder, T.2
  • 17
    • 0035421744 scopus 로고    scopus 로고
    • "Convergence and rates of convergence of radial basis functions networks in function learning"
    • A. Krzyzak and H. Niemann, "Convergence and rates of convergence of radial basis functions networks in function learning," Nonlin. Anal. vol. 47, pp. 281-292, 2001.
    • (2001) Nonlin. Anal. , vol.47 , pp. 281-292
    • Krzyzak, A.1    Niemann, H.2
  • 18
    • 15244360624 scopus 로고    scopus 로고
    • "Nonparametric Regression Estimation by Normalized Radial Basis Function Networks"
    • Universität Stuttgart, Mathematisches Institut A. Stuttgart, Germany, Preprint 2002-15
    • A. Krzyzak and D. Schäfer, "Nonparametric Regression Estimation by Normalized Radial Basis Function Networks," Universität Stuttgart, Mathematisches Institut A, Stuttgart, Germany, Preprint 2002-15, 2002.
    • (2002)
    • Krzyzak, A.1    Schäfer, D.2
  • 19
    • 0029307575 scopus 로고
    • "Nonparametric estimation via empirical risk minimization"
    • May
    • G. Lugosi and K. Zeger, "Nonparametric estimation via empirical risk minimization," IEEE Trans. Inf. Theory., vol. 41, no. 3, pp. 677-687, May 1995.
    • (1995) IEEE Trans. Inf. Theory. , vol.41 , Issue.3 , pp. 677-687
    • Lugosi, G.1    Zeger, K.2
  • 20
    • 0000672424 scopus 로고
    • "Fast learning in networks of locally-tuned processing units"
    • J. Moody and J. Darken, "Fast learning in networks of locally-tuned processing units," Neural Comput., vol. 1, pp. 281-294, 1989.
    • (1989) Neural Comput. , vol.1 , pp. 281-294
    • Moody, J.1    Darken, J.2
  • 21
    • 0000106040 scopus 로고
    • "Universal approximation using radial-basis-function networks"
    • J. Park and I. W. Sandberg, "Universal approximation using radial-basis-function networks," Neural Comput., vol. 3, pp. 246-257, 1991.
    • (1991) Neural Comput. , vol.3 , pp. 246-257
    • Park, J.1    Sandberg, I.W.2
  • 22
    • 0001002401 scopus 로고
    • "Approximation and radial-basis-function networks"
    • J. Park, I.W. Sandberg, "Approximation and radial-basis-function networks," Neural Comput., vol. 5, pp. 305-316, 1993.
    • (1993) Neural Comput. , vol.5 , pp. 305-316
    • Park, J.1
  • 24
    • 0030135939 scopus 로고    scopus 로고
    • "Side effects of normalizing radial basis function networks"
    • R. Shorten and R. Murray-Smith, "Side effects of normalizing radial basis function networks," Int. J. Neural Syst., vol. 7, pp. 167-179, 1996.
    • (1996) Int. J. Neural Syst. , vol.7 , pp. 167-179
    • Shorten, R.1    Murray-Smith, R.2
  • 25
    • 0025206332 scopus 로고
    • "Probabilistic neural networks"
    • D. F. Specht, "Probabilistic neural networks," Neural Netw., vol. 3, pp. 109-118, 1990.
    • (1990) Neural Netw. , vol.3 , pp. 109-118
    • Specht, D.F.1
  • 26
    • 0001024505 scopus 로고
    • "On the uniform convergence of relative frequencies of events to their probabilities"
    • V. N. Vapnik and A. Y. Chervonenkis, "On the uniform convergence of relative frequencies of events to their probabilities," Theory Probab. its Applic., vol. 16, pp. 264-280, 1971.
    • (1971) Theory Probab. Its Applic. , vol.16 , pp. 264-280
    • Vapnik, V.N.1    Chervonenkis, A.Y.2
  • 28
    • 0025635525 scopus 로고
    • "Connectionist nonparamemc regression: Multilayer feedforward networks that can learn arbitrary mappings"
    • H. White, "Connectionist nonparamemetric regression: Multilayer feedforward networks that can learn arbitrary mappings," Neural Netw., vol. 3, pp. 535-549, 1990.
    • (1990) Neural Netw. , vol.3 , pp. 535-549
    • White, H.1
  • 29
    • 0028341934 scopus 로고
    • "On radial basis function nets and kernel regression: Approximation ability, convergence rate and receptive field size"
    • L. Xu, A. Krzyzak, and A. L. Yuille, "On radial basis function nets and kernel regression: Approximation ability, convergence rate and receptive field size," Neural Netw., vol. 7, pp. 609-628, 1994.
    • (1994) Neural Netw. , vol.7 , pp. 609-628
    • Xu, L.1    Krzyzak, A.2    Yuille, A.L.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.