Evolutionary Gaussian Decomposition
Roman Yu. Pishchalnikov, Denis D. Chesalin, Vasiliy A. Kurkov, Andrei P. Razjivin, Sergey V. Gudkov, Alexey Semenovich Dorokhov, Andrey Yu. Izmailov · Mathematics · 2025
We present a computational approach for performing the Gaussian decomposition (GD) of experimental spectral data, called evolutionary Gaussian decomposition (EGD). The key feature of EGD is its ability to estimate the optimal number of Gaussian components required to fit a target function, which can be any experimental functional dependence. The efficiency and robustness of EGD are achieved through the use of the differential evolution (DE) algorithm, which allows us to tune the performance of the method. Based on statistics from the independent trials of DE, EGD can determine the number of Gaussians above which further improvement in fit quality does not occur. EGD works by collecting statistics on local minima in the vicinity of the estimated optimal number of Gaussians, and, if necessary, repeats this process several times during optimization until the desired results are obtained. The method was tested using both synthetic spectral-like functions and measured spectra of photosynthetic pigments. In addition to the local minima statistics, the most significant factors that affect the results of the analysis were the median and minimum values of the cost function. These values were obtained for each different number of Gaussian functions used in the evaluation process.