Evolutionary Gaussian Decomposition

Roman Y. Pishchalnikov (), Denis D. Chesalin, Vasiliy A. Kurkov, Andrei P. Razjivin, Sergey V. Gudkov, Alexey S. Dorokhov and Andrey Yu. Izmailov
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Roman Y. Pishchalnikov: Prokhorov General Physics Institute of the Russian Academy of Sciences, 119991 Moscow, Russia
Denis D. Chesalin: Faculty of Biology, Lomonosov Moscow State University, 119991 Moscow, Russia
Vasiliy A. Kurkov: Prokhorov General Physics Institute of the Russian Academy of Sciences, 119991 Moscow, Russia
Andrei P. Razjivin: Belozersky Research Institute of Physico-Chemical Biology, Moscow State University, 119992 Moscow, Russia
Sergey V. Gudkov: Prokhorov General Physics Institute of the Russian Academy of Sciences, 119991 Moscow, Russia
Alexey S. Dorokhov: Federal State Budgetary Scientific Institution “Federal Scientific Agroengineering Center VIM” (FSAC VIM), 109428 Moscow, Russia
Andrey Yu. Izmailov: Federal State Budgetary Scientific Institution “Federal Scientific Agroengineering Center VIM” (FSAC VIM), 109428 Moscow, Russia

Mathematics, 2025, vol. 13, issue 17, 1-17

Abstract: 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.

Keywords: Gaussian decomposition; differential evolution; data fitting; optimization; absorption spectrum; pigments (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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