maisМоделирование и анализ информационных системModeling and Analysis of Information Systems1818-10152313-5417Yaroslavl State University10.18255/1818-1015-2025-4-330-359mais-1979Research ArticleTheory of DataПрименение тензоров в многомерном компонентном анализе категоризованных признаковApplication of tensors in multivariate component analysis of categorized featureshttps://orcid.org/0000-0003-4242-1471БанинАлександрBaninAlexander A.aabanin1@chsu.ruЧереповецкий государственный университетРоссияCherepovets State UniversityRussian Federation202505122025324330359Copyright © Банин А.A., 20252025Банин А.Banin A.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.mais-journal.ru/jour/article/view/1979

При моделировании социальных процессов и явлений зачастую приходится обрабатывать данные, относящиеся к категоризованным признакам, выявлять причинно-следственные связи между такими данными, выделять наиболее существенные показатели. Исследование существующих подходов к анализу зависимостей между категоризованными переменными выявило ряд проблем при применении этих методов для многомерных категоризованных данных (тензоров). Поэтому в статье предлагается подход для изучения зависимостей между такими переменными с использованием многомерного компонентного анализа. Данный подход предполагает применение матриц развертки тензора, полученных для каждой его оси (категоризованного признака). Метод позволяет построить интегральные характеристики (компоненты) по элементам исходного тензора, сформировать матрицы компонентных нагрузок и рассчитать ядро тензора, имеющего меньшее число градаций категоризованных признаков (меньшее число измерений на осях тензора), чем исходный тензор. В статье предложен метод ранжирования градаций категоризованных переменных по степени совокупного влияния на них компонентных нагрузок, основанный на вычислении векторных норм. Изложенный подход к изучению зависимостей между многомерными категоризованными переменными продемонстрирован на примере трехмерного тензора с формой (4;10;10) и категоризованными признаками: группа нозологии, сфера деятельности, группа профессионально значимых качеств. Рассмотренный в статье алгоритм изучения многомерных категоризованных данных с применением многомерного компонентного анализа предполагается включить как аналитический инструмент информационно-аналитического регионального портала «ПЕРСПЕКТИВА-PRO», который может быть использован для разработки траекторий цифрового сопровождения лиц с инвалидностью и лиц с ОВЗ с учетом их личностных и вариативных характеристик.

When modeling social processes and phenomena, it is often necessary to process data related to categorized features, identify cause-and-effect relationships between such data, and determine the most significant indicators. A study of existing approaches to analyzing dependencies between categorized variables revealed several problems when applying these methods to multidimensional categorized data (tensors). Therefore, this article proposes an approach to studying dependencies between such variables using multidimensional component analysis. This approach involves applying tensor unfolding matrices obtained for each of its axes (categorized features). The method allows for the construction of integral characteristics (components) based on the elements of the original tensor, the formation of component loading matrices, and the calculation of the tensor core, which has fewer gradations of categorized features (lower number of dimensions in the tensor axes) than the original tensor. The article proposes a method for ranking the gradations of categorized variables by the degree of cumulative influence of component loadings, based on the calculation of vector norms. The described approach to studying dependencies between multidimensional categorized variables is demonstrated using a three-dimensional tensor with the shape (4;10;10) and categorized features: nosology group, field of activity, and group of professionally significant qualities. The algorithm for analyzing multidimensional categorized data using multidimensional component analysis, discussed in this article, is intended to be incorporated as an analytical tool into the regional information and analytical portal "PERSPEKTIVA-PRO." This tool can be used to develop a digital support trajectory for people with disabilities and special needs, taking into account their personal and variable characteristics.

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The authors declare that there are no conflicts of interest present.