Enhanced Nadaraya-Watson kernel regression: surface approximation for extremely small samples
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 approximation algorithm to result in unsati...
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my.utm.296482017-02-05T00:01:24Z http://eprints.utm.my/id/eprint/29648/ Enhanced Nadaraya-Watson kernel regression: surface approximation for extremely small samples Shapiai, Mohd. Ibrahim Ibrahim, Zuwairie Khalid, Marzuki Jau, L. W. Pavlovich, V. 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 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, is proposed. In the proposed framework, the original Nadaraya-Watson kernel regression 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 is governed by the error function to find a good approximation model. Two 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 surface 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). IEEE Explorer 2011 Book Section PeerReviewed Shapiai, Mohd. Ibrahim and Ibrahim, Zuwairie and Khalid, Marzuki and Jau, L. W. and Pavlovich, V. (2011) Enhanced Nadaraya-Watson kernel regression: surface approximation for extremely small samples. In: Proceedings - AMS 2011: Asia Modelling Symposium 2011 - 5th Asia International Conference on Mathematical Modelling and Computer Simulation. IEEE Explorer, USA, pp. 7-12. ISBN 978-076954414-4 http://dx.doi.org/10.1109/AMS.2011.13 10.1109/AMS.2011.13 |
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TK Electrical engineering. Electronics Nuclear engineering Shapiai, Mohd. Ibrahim Ibrahim, Zuwairie Khalid, Marzuki Jau, L. W. Pavlovich, V. Enhanced Nadaraya-Watson kernel regression: surface approximation for extremely small samples |
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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 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, is proposed. In the proposed framework, the original Nadaraya-Watson kernel regression 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 is governed by the error function to find a good approximation model. Two 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 surface 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). |
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Book Section |
author |
Shapiai, Mohd. Ibrahim Ibrahim, Zuwairie Khalid, Marzuki Jau, L. W. Pavlovich, V. |
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Shapiai, Mohd. Ibrahim Ibrahim, Zuwairie Khalid, Marzuki Jau, L. W. Pavlovich, V. |
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Shapiai, Mohd. Ibrahim |
title |
Enhanced Nadaraya-Watson kernel regression: surface approximation for extremely small samples |
title_short |
Enhanced Nadaraya-Watson kernel regression: surface approximation for extremely small samples |
title_full |
Enhanced Nadaraya-Watson kernel regression: surface approximation for extremely small samples |
title_fullStr |
Enhanced Nadaraya-Watson kernel regression: surface approximation for extremely small samples |
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Enhanced Nadaraya-Watson kernel regression: surface approximation for extremely small samples |
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enhanced nadaraya-watson kernel regression: surface approximation for extremely small samples |
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IEEE Explorer |
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2011 |
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http://eprints.utm.my/id/eprint/29648/ http://dx.doi.org/10.1109/AMS.2011.13 |
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