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Stochastic choice of basis functions in adaptive function approximation and the functional-link net.
1Dept. of Electr. Eng. and Appl. Phys., Case Western Reserve Univ., Cleveland, OH.
IEEE Transactions on Neural Networks
|January 1, 1995
Summary
The random vector functional-link (RVFL) net is a universal approximator for continuous functions. This adaptive network efficiently approximates functions with a convergence rate of O(C/√n), enhancing machine learning capabilities.
Area of Science:
- Machine Learning
- Computational Mathematics
- Artificial Intelligence
Background:
- Adaptive function approximation is crucial for machine learning and data analysis.
- Existing methods often face challenges in efficiency and accuracy for complex functions.
- The random vector functional-link (RVFL) net offers a novel approach to function approximation.
Purpose of the Study:
- To provide a theoretical justification for the random vector version of the functional-link (RVFL) net.
- To establish the RVFL net's capabilities as a universal approximator.
- To analyze the efficiency and convergence rate of the RVFL net in function approximation.
Main Methods:
- Formulating a limit-integral representation of the function to be approximated.
- Evaluating the integral using the Monte-Carlo method for theoretical analysis.
- Investigating neural networks with hidden nodes implemented as products of univariate functions or radial basis functions.
Main Results:
- The RVFL net is proven to be a universal approximator for continuous functions on bounded finite-dimensional sets.
- The RVFL net demonstrates efficient approximation with an error convergence rate of O(C/√n), where n is the number of basis functions.
- Similar universal approximation and efficiency results are observed for neural nets using product or radial basis function hidden nodes.
Conclusions:
- The RVFL net provides a theoretically sound and efficient method for adaptive function approximation.
- The findings support the RVFL net's potential for various machine learning applications requiring accurate function approximation.
- Further research can explore methods to enhance the accuracy of multivariate function approximations using RVFL nets.
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