### Abstract

The function approximation problem is to find the appropriate relationship between a dependent and independent variable(s). Function approximation algorithms generally require sufficient samples to approximate a function. Insufficient samples may cause any function approximation algorithm to result in unsatisfactory predictions. To solve this problem, a function approximation algorithm called Weighted Kernel Regression (WKR), which is based on Nadaraya-Watson kernel regression (NWKR), is proposed. In the proposed framework, the original NWKR algorithm is enhanced by expressing the observed samples in a square kernel matrix. The WKR is trained to estimate the weight for the testing phase. The weight is estimated iteratively and governed by the error function to find a good approximation model. Four experiments are conducted to show the capability of the WKR. The results show that the proposed WKR model is effective in cases where the target function is non-linear and the given training sample is small. The performance of the WKR is also compared with other existing function approximation algorithms, such as artificial neural networks (ANN).

Original language | English |
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Pages (from-to) | 5947-5960 |

Number of pages | 14 |

Journal | International Journal of Innovative Computing, Information and Control |

Volume | 7 |

Issue number | 10 |

Publication status | Published - 2011 Oct |

### Keywords

- Artificial neural network
- Non-linear function
- Small samples
- Weighted kernel regression

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Information Systems
- Software
- Theoretical Computer Science

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## Cite this

*International Journal of Innovative Computing, Information and Control*,

*7*(10), 5947-5960.