The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
Approximation capability to functions of several variables, nonlinear functionals, and operators by radial basis function neural networks
Abstract
The purpose of this paper is to explore the representation capability of radial basis function (RBF) neural networks. The main results are: 1) the necessary and sufficient condition for a function of one variable to be qualified as an activation function in RBF network is that the function is not an even polynomial, and 2) the capability of approximation to nonlinear functionals and operators by RBF networks is revealed, using sample data either in frequency domain or in time domain, which can be used in system identification by neural networks.
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Cites
Multilayer feedforward networks are universal approximators
Hornik, K., Stinchcombe, M., & White, H. (1989) · Neural Networks · doi:10.1016/0893-6080(89)90020-8 · Cited by 21,728
Approximation by superpositions of a sigmoidal function
Cybenko, G. (1989) · Mathematics of Control, Signals, and Systems · doi:10.1007/bf02551274 · Cited by 13,883
On the approximate realization of continuous mappings by neural networks
Funahashi, K.-I. (1989) · Neural Networks · doi:10.1016/0893-6080(89)90003-8 · Cited by 4,206
Cited by
Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators
Lu, L., Jin, P., Pang, G., Zhang, Z., & Karniadakis, G. E. (2021) · Nature Machine Intelligence · doi:10.1038/s42256-021-00302-5 · Cited by 3,418
Huang, G.-B., & Babri, H. A. (1998) · IEEE Transactions on Neural Networks · doi:10.1109/72.655045 · Cited by 538
Fazzolari, M., Alcala, R., Nojima, Y., Ishibuchi, H., & Herrera, F. (2013) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2012.2201338 · Cited by 296
A study on effectiveness of extreme learning machine
Wang, Y., Cao, F., & Yuan, Y. (2011) · Neurocomputing · doi:10.1016/j.neucom.2010.11.030 · Cited by 269
Metadata
- Authors
- Chen, T., & Chen, H.
- Venue
- IEEE Transactions on Neural Networks
- Published
- 1995-07
- Volume
- 6
- Issue
- 4
- Pages
- 904-910
- ISSN
- 1045-9227 (ISSN-L)
- OpenAlex
- W2157890204
- Cited by
- 394
- References
- 3
- FWCI
- 7.18
- Type
- journal article
- Language
- en
- Open access
- closed
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- Chen, T., & Chen, H. (1995). Approximation capability to functions of several variables, nonlinear functionals, and operators by radial basis function neural networks. IEEE Transactions on Neural Networks. https://doi.org/10.1109/72.392252
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
