Analysis of certain aspects of digitalization in the field of providing educational services to the population using statistical analysis and machine learning methods

Digital transformation in all areas of life has accelerated significantly since COVID-19. Significant progress in the field of professional skills in digital technologies has been observed throughout the world and in Russia, in particular, in the last five years. It is a challenge and an opportunity when issues of integration and growth coincide with each other. Digitalization in the field of public services is developing rapidly in our country. Russia needs educational systems appropriate to the digital age, as well as additional programs for the education and retraining of that part of the adult population that has long abandoned their studies. This is a two-pronged task, dealing with both basic digital skills and a modern understanding of literacy. The goal of developing digital educational services for the population is to create an accessible and effective learning system for all categories of citizens. The paper uses clustering and classification methods to group homogeneous objects based on a wide range of socio-economic and financial indicators that are important for studying the development of digitalization in the services provided to the population. The objective of the study is to identify, using objective methods of mathematical data analysis (without any use of subjective assessments), the presence or absence of a relationship between the socio-economic parameters of a region’s development in the Russian Federation and paid educational services provided to the population. The regions are clearly divided into two large, almost equal groups based on this set of indicators. A comparative analysis of hierarchical clustering and classical clustering using the K-means method is presented. Hierarchical clustering is preferred over classical clustering. Consistent results were obtained using both methods. The importance of the geographical factor and homogeneity in the economic development of regions grouped into clusters was concluded. Moscow stands out for its digitalization development compared to other regions, as evidenced by both clustering methods.

1. Safonov S.A., Zander E.V. Assessment of digital transformation of the social sphere and regional features of digitalization of social services. The Digital Economy. 2022;(4):53-62. (In Russ.). URL: https://doi.org/10.34706/DE-2022-04-07

2. Kuchumov I.V. Theoretical foundations of data clustering methods in intellectual analysis. The Digital Eonomy. 2024;(1):69-77. (In Russ.). URL: https://doi.org/10.34706/DE-2024-01-08

3. Afyan A. I., Polozova D. V., Gordeeva A. A. Digital transformation of the Russian state healthcare system: opportunities and contradictions. Digital Law. 2021;2(4):20-39. (In Russ.). URL: https://doi.org/10.38044/2686-9136-2021-2-4-20-39

4. Nyrkov A. S. The impact of digitalization on the availability and quality of social services in the Russian Federation. A Young Scientist. 2025;20(571):522-524. (In Russ.). URL: https://www.elibrary.ru/xsfosr

5. Nazarov V. L., Zherdev D. V., Buinacheva A. V. Current problems of digital transformation in secondary education. The Education and science journal. 2023;25(4):109-166. (In Russ.) URL: https://doi.org/10.17853/1994-5639-2023-4-109-166

6. Tishchenko A. S., Tokareva G. S. Digital Transformation of General Education: Analysis of Changes. RUDN Journal of Informatization in Education. 2026;23(1):105-119. (In Russ.). URL: http://doi.org/10.22363/2312-8631-2026-23-1-105-119

7. Senko O.V., Kuznetsova A.V., Voronin E. M., Kravtsova O.A., Borisova L. R., Kirilyuk I. L., et al. Methods of data mining in research on the COVID-19 epidemic. Journal of the Belarusian State University. Mathematics. Computer science. 2022;1:83-96. (In Russ.). URL: https://doi.org/10.33581/2520-6508-2022-1-83-96

8. Kuznetsova Yu.O., Borisova L. R., Kuznetsova A.V., Senko O.V. Transparent interface for forecasting in machine learning. In: Data Analytics and Management in Data-intensive Areas. Moscow: Federal Research Center “Informatics and Management” of the Russian Academy of Sciences; 2017:493-495. (In Russ.).URL: https://elibrary.ru/ougrxt

9. Kuznetsova A.V., Borisova L. R., Demina I.A. Machine learning methods for predicting the course of the disease using the example of the development of severe pneumonia. Digital Solutions and Artificial Intelligence Technologies. 2025;1(1):6-19. (In Russ.). URL: https://www.elibrary.ru/rzxxyo

10. Matviyevsky S.S., Borisova L.R. Clusterization of the countries of the Asia-Pacific region according to the values of inclusive economic growth. Bulletin of the University. 2023;1:112-121. (In Russ.). URL: https://doi.org/10.26425/1816-4277-2024-1-112-121

11. Borisova L.R. Comparative analysis of the Russian regions using machine learning methods for a set of indicators of electronic services. Digital Sociology. 2024;7(40):33-43. (In Russ.). URL: https://doi.org/10.26425/2658-347X-2024-7-4-33-43

12. Repina S.I. Quality verification of clusters using silhouette analysis. Economics and Society. 2024;9(124):958-975. (In Russ.). URL: https://doi.org/10.5281/zenodo.13918451

13. Rousseeuw P. J. Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. Journal of Computational and Applied Mathematics. 1987;20(1):53-65. (In Russ.). URL: https://doi.org/10.1016/0377-0427(87)90125-7

14. Romanello M. et al. The 2022 report of the Lancet Countdown on health and climate change: health at the mercy of fossil fuels. The Lancet 400 (suppl). 2022. URL: https://doi.org/10.1016/S0140-6736(22)01540-9

15. Kislyakov A. N., Polyakov S.V. Hierarchical clustering methods in the problem of searching for anomalous observations based on groups with broken symmetry. Management Consulting. 2020;5:116-127. (In Russ.). URL: https://doi.org/10.22394/1726-1139-2020-5-116-127