Function and surface approximation based on enhanced kernel regression for small sample sets
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...
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ICIC International
2011
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my.utm.296842019-04-25T01:18:25Z http://eprints.utm.my/id/eprint/29684/ Function and surface approximation based on enhanced kernel regression for small sample sets Shapiai, Mohd. Ibrahim Ibrahim, Zuwairie Khalid, Marzuki Lee, Wen Jau Pavlovic, Vladimir Watada, Juilzo TK Electrical engineering. Electronics Nuclear engineering 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). ICIC International 2011-10 Article PeerReviewed Shapiai, Mohd. Ibrahim and Ibrahim, Zuwairie and Khalid, Marzuki and Lee, Wen Jau and Pavlovic, Vladimir and Watada, Juilzo (2011) Function and surface approximation based on enhanced kernel regression for small sample sets. International Journal of Innovative Computing, Information and Control, 7 (10). pp. 5947-5960. ISSN 1349-4198 http://www.ijicic.org/ijicic-10-06023.pdf |
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TK Electrical engineering. Electronics Nuclear engineering Shapiai, Mohd. Ibrahim Ibrahim, Zuwairie Khalid, Marzuki Lee, Wen Jau Pavlovic, Vladimir Watada, Juilzo Function and surface approximation based on enhanced kernel regression for small sample sets |
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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). |
| format |
Article |
| author |
Shapiai, Mohd. Ibrahim Ibrahim, Zuwairie Khalid, Marzuki Lee, Wen Jau Pavlovic, Vladimir Watada, Juilzo |
| author_facet |
Shapiai, Mohd. Ibrahim Ibrahim, Zuwairie Khalid, Marzuki Lee, Wen Jau Pavlovic, Vladimir Watada, Juilzo |
| author_sort |
Shapiai, Mohd. Ibrahim |
| title |
Function and surface approximation based on enhanced kernel regression for small sample sets |
| title_short |
Function and surface approximation based on enhanced kernel regression for small sample sets |
| title_full |
Function and surface approximation based on enhanced kernel regression for small sample sets |
| title_fullStr |
Function and surface approximation based on enhanced kernel regression for small sample sets |
| title_full_unstemmed |
Function and surface approximation based on enhanced kernel regression for small sample sets |
| title_sort |
function and surface approximation based on enhanced kernel regression for small sample sets |
| publisher |
ICIC International |
| publishDate |
2011 |
| url |
http://eprints.utm.my/id/eprint/29684/ http://www.ijicic.org/ijicic-10-06023.pdf |
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13.211869 |