Comparison of Algorithmic and Machine Learning Approaches for the Automatic Fitting of Gaussian Peaks |
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Authors: | R E Abdel-Aal |
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Affiliation: | (1) Centre for Applied Physical Sciences, Research Institute, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia, SA |
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Abstract: | Fitting Gaussian peaks to experimental data is important in many disciplines, including nuclear spectroscopy. Nonlinear least
squares fitting methods have been in use for a long time, but these are iterative, computationally intensive, and require
user intervention. Machine learning approaches automate and speed up the fitting procedure. However, for a single pure Gaussian,
there exists a simple and automatic analytical approach based on linearisation followed by a weighted linear Least Squares
(LS) fit. This paper compares this algorithmic method with an abductive machine learning approach based on AIM
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(Abductory Induction Mechanism). Both techniques are briefly described and their performance compared for analysing simulated
and actual spectral peaks. Evaluated on 500 peaks with statistical uncertainties corresponding to a peak count of 100, average
absolute errors for the peak height, position and width are 4.9%, 2.9% and 4.2% for AIM, versus 3.3%, 0.5% and 7.7% for the
LS. AIM is better for the width, while LS is more accurate for the position. LS errors are more biased, under-estimating the
peak position and over-estimating the peak width. Tentative CPU time comparison indicates a five-fold speed advantage for
AIM, which also has a constant execution time, while LS time depends upon the peak width. |
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Keywords: | : Abductive networks Gaussian peaks Least Squares fit Machine learning Peak fitting Spectral analysis Spectroscopy |
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