### 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 |
---|---|

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 |

### Fingerprint

### 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

### Cite this

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

*7*(10), 5947-5960.

**Function and surface approximation based on enhanced Kernel Regression for small sample sets.** / Shapiai, Mohd Ibrahim; Ibrahim, Zuwairie; Khalid, Marzuki; Jau, Lee Wen; Pavlovic, Vladimir; Watada, Junzo.

Research output: Contribution to journal › Article

*International Journal of Innovative Computing, Information and Control*, vol. 7, no. 10, pp. 5947-5960.

}

TY - JOUR

T1 - Function and surface approximation based on enhanced Kernel Regression for small sample sets

AU - Shapiai, Mohd Ibrahim

AU - Ibrahim, Zuwairie

AU - Khalid, Marzuki

AU - Jau, Lee Wen

AU - Pavlovic, Vladimir

AU - Watada, Junzo

PY - 2011/10

Y1 - 2011/10

N2 - 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).

AB - 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).

KW - Artificial neural network

KW - Non-linear function

KW - Small samples

KW - Weighted kernel regression

UR - http://www.scopus.com/inward/record.url?scp=80053555784&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80053555784&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:80053555784

VL - 7

SP - 5947

EP - 5960

JO - International Journal of Innovative Computing, Information and Control

JF - International Journal of Innovative Computing, Information and Control

SN - 1349-4198

IS - 10

ER -