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Approximation capability to functions of several variables, nonlinear functionals, and operators by radial basis
IEEE Transactions on Neural Networks
|January 1, 1995
Summary
Radial basis function (RBF) networks can approximate nonlinear functions. A key finding is that activation functions in RBF networks cannot be even polynomials for effective representation.
Area of Science:
- Artificial Intelligence
- Machine Learning
- Neural Networks
Background:
- Radial basis function (RBF) networks are a class of artificial neural networks.
- Understanding the representation and approximation capabilities of RBF networks is crucial for their application in complex modeling tasks.
Purpose of the Study:
- To investigate the representation capabilities of radial basis function (RBF) neural networks.
- To determine the conditions for suitable activation functions in RBF networks.
- To reveal the approximation power of RBF networks for nonlinear functionals and operators.
Main Methods:
- Analysis of function properties for activation functions in RBF networks.
- Exploration of RBF network approximation capabilities using data from frequency and time domains.
Main Results:
- Identified the necessary and sufficient condition for activation functions in RBF networks: the function must not be an even polynomial.
- Demonstrated the capability of RBF networks to approximate nonlinear functionals and operators.
- Showcased the utility of RBF networks in system identification using domain-specific data.
Conclusions:
- The study provides a critical condition for selecting activation functions in RBF networks.
- RBF networks exhibit significant potential for approximating complex nonlinear systems.
- The findings support the application of RBF networks in system identification and other advanced modeling areas.
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