title: ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð°ÑÐ¿ÐµÐºÑÐ¾Ð² ÑÐµÐ½Ð·Ð¾ÑÐ½ÑÑ ÑÐ°Ð·Ð»Ð¾Ð¶ÐµÐ½Ð¸Ð¹ Ð´Ð»Ñ Ð´Ð°Ð½Ð½ÑÑ ÑÐ»ÑÐ¾ÑÐ¾Ð¼ÐµÑÑÐ¸Ð¸
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Study of the mathematical aspects of tensor decomposition for fluorometry data
Creators: name: Ð¯Ð²Ð¾ÑÑÐº, Ð¢Ð°ÑÑÑÐ½Ð°
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2022
Subjects: Ð°Ð½Ð°Ð»Ð¸Ð· Ð¼Ð½Ð¾Ð³Ð¾Ð¼ÐµÑÐ½ÑÑ Ð´Ð°Ð½Ð½ÑÑ
ÑÐµÐ½Ð·Ð¾ÑÐ½ÑÐµ ÑÐ°Ð·Ð»Ð¾Ð¶ÐµÐ½Ð¸Ñ
ÑÐ»ÑÐ¾ÑÐ¾Ð¼ÐµÑÑÐ¸Ñ
ÑÐµÑÐµÐ´ÑÑÑÐ¸Ð¹ÑÑ Ð¼ÐµÑÐ¾Ð´ Ð½Ð°Ð¸Ð¼ÐµÐ½ÑÑÐ¸Ñ ÐºÐ²Ð°Ð´ÑÐ°ÑÐ¾Ð²
tensor decomposition
parafac
alternative least squares mathod
multi-way analysis
split-half analysis

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description: This work is devoted to the study of mathematical aspects of tensor expansionsÂ for fluoresense data of dissolvedÂ rganic matter in the ground ice samples. TheÂ research set the following goals:Introductory processing of the data.Â Search for the decomposition rank. Study of the application of various heuristicsfor the analysis of the obtained results. Research using synthetic data. Comparison of sets of pairs of excitation and emission spectra using differentmetrics. Analysis and search for a possible component classifier based onthe results obtained. This work was carried out with information received from the fluorimeterÂ data received from Institute for Geology and Mineral Resources of the WorldÂ Ocean (VNIIOkeangeologia). A fluorometer is a device that is used to obtainÂ fluorescence parameters: intensity, distribution of wavelengths of an emissionÂ spectrum after being excited by a certain spectrum of light. Using these obtainedÂ parameters, it is possible to find specific molecules in a sample and their concentrationÂ in each sample. A significant difficulty is the determination of the decompositionÂ rank at which an interpretable solution can be obtained - spectra and concentrations.In the course of the work, the dependences of the rank on the correlation of theÂ obtained components, the rate of convergence of the method were considered,Â and the split-half analisis the data was applied.Various metrics were studied to determine the equivalence class of the spectraof molecules.