Approximation capability of interpolation neural networks

Neurocomputing

Volumn 74, Issue 1-3, 2010, Pages 457-460

  Cao, Feilong ^a   Lin, Shaobo ^b   Xu, Zongben ^b  

^a CHINA JILIANG UNIVERSITY   (China)

^b XI'AN JIAOTONG UNIVERSITY   (China)

Author keywords

Best approximation; Interpolation; Neural networks

Indexed keywords

APPROXIMATION CAPABILITIES; APPROXIMATION EFFECTS; BEST APPROXIMATIONS; FUNCTIONAL APPROACH; HIDDEN LAYERS; HIDDEN NEURONS; HIDDEN NODES; INPUT NEURONS; INTEGRABLE FUNCTIONS; TARGET FUNCTIONS;

INTERPOLATION;

NEURAL NETWORKS;

ARTICLE; ARTIFICIAL NEURAL NETWORK; INFORMATION PROCESSING; MACHINE LEARNING; MATHEMATICAL ANALYSIS; PRIORITY JOURNAL;

EID: 78649483125     PISSN: 09252312     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neucom.2010.08.018     Document Type: Article

References (24)

1. Cao F.L., Zhang Y.Q., He Z.R. Interpolation and rates of convergence for a class of neural networks. Appl. Math. Model 2009, 33:1441-1456.
2. Chen D.B. Degree of approximation by superpositions of a sigmoidal function. Approx. Theory Appl. 1993, 9:17-28.
3. Chen T.P., Chen H. Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical system. IEEE Trans. Neural Network 1995, 6:911-917.
4. Chui C.K., Li X. Approximation by ridge functions and neural networks with one hidden layer. J. Approx. Theory 1992, 70:131-141.
5. Cybenko G. Approximation by superpositions of sigmoidal function. Math. Control Signals Syst. 1989, 2:303-314.
6. Funahashi K.I. On the approximate realization of continuous mapping by neural networks. Neural Networks 1989, 2:183-192.
7. Lorentz G.G. Approximation of Functions 1966, Rinehart and Winston, New York.
8. Hornik K., Stinchcombe M., White H. Multilayer feedforward networks are universal approximation. Neural Networks 1989, 2:359-366.
9. G.B. Huang, H.A. Babri, General approximation theorem on feedforward networks, in: 1997 IEEE International Conference Neural Networks (ICNN97), Houston, TX, 1997.
10. Huang G.B., Babri H.A. Upper bounds on the number of hidden neurons in feedforward networks with arbitrary bounded nonlinear activation functions. IEEE Trans. Neural Network 1998, 9(1):224-229.
11. G.B. Huang, Q.Y. Zhu, C.K. Siew, Extreme learning machine: a new learning scheme of feedforward neural networks, in: Proceedings of the International Joint Conference on Neural Networks (IJCNN04), Budapest, Hungary, July 25-29, 2004.
12. Huang G.B., Zhu Q.Y., Siew C.K. Extreme learning machine: theory and applications. Neurocomputing 2006, 70:489-501.
13. Huang G.B., Chen L., Siew C.K. Universal approximation using incremental constructive feedforward networks with random hidden nodes. IEEE Trans. Neural Networks 2006, 17(4):879-892.
14. Huang G.B., Chen L. Convex incremental extreme learning machine. Neurocomputing 2007, 70:3056-3062.
15. Huang G.B., Chen L. Enhanced random search based incremental extreme learning machine. Neurocomputing 2008, 71:3460-3468.
16. Ito Y. Independence of unscaled basis functions and finite mappings by neural networks. Math. Sci. 2001, 26:117-126.
17. Ito Y., Saito K. Superposition of linearly independent functions and finite mappings by neural networks. Math. Sci. 1996, 21:27-33.
18. Leshno M., Lin V.Y., Pinks A., Schocken S. Multilayer feedforward networks with a nonpolynomial activation function can approximant any function. Neural Networks 1993, 6:861-867.
19. Llanas B., Sainz F.J. Constructive approximate interpolation by nerual networks. J. Comput. Appl. Math. 2006, 188:283-308.
20. Llanas B., Lantarón S. Hermite interpolation by neural networks. Appl. Math. Comput. 2007, 191:429-439.
21. n: error estimates for radial basis and band-limited functions. SIAM J. Math. Anal. 2004, 36:284-300.
22. Pinkus A. Approximation theory of the MLP model in neural networks. Acta Numer. 1999, 143-195.
23. Sontag E.D. Feedforward nets for interpolation and classification. J. Comput. Syst. Sci. 1992, 45:20-48.
24. T.F. Xie, F.L. Cao, The ridge function representation of polynomials and an application to neural networks, Acta Math. Sinica, English Series, in press, doi:. http://10.1007/s10114-011-9407-1.