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 1 (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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Abdel-Aal, R. Comparison of Algorithmic and Machine Learning Approaches for the Automatic Fitting of Gaussian Peaks. Neural Comput Applic 11, 17–29 (2002). https://doi.org/10.1007/s005210200012
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DOI: https://doi.org/10.1007/s005210200012