Comparison of Algorithmic and Machine Learning Approaches for the Automatic Fitting of Gaussian Peaks

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.