Application of clustering methods in the economic analysis of regions

Technological and digital transformation, penetrating all economies, makes demands on the social infrastructure readiness level. The purpose of the article is to evaluate regions’ education infrastructure readiness for digital transformation, to identify the differentiation of regions of the Russian Federation using machine learning methods. Clustering of the Russian Federation regions was carried out according to the degree of digital equipment of educational institutions. Clustering was carried out using self-organizing Kohonen maps and classical clustering methods, in particular the Linkage method. The results obtained showed the possibility of distributing the regions into four uneven clusters that have significant differences. It is noted that in the regions of the Russian Federation, the organizations carrying out educational activities in higher education programs have the highest computer availability, while the schools have the lowest one. These studies can be used for further analysis and decision-making that increase the efficiency of digital development of the regions of the Russian Federation, including for the search for economic solutions in the field of infrastructure development.

Keywords: digital transformation, clustering, differentiation of regions, education infrastructure, machine learning, neural networks, self-organizing Kohonen maps


  1. Ya. I. Kuzminov, I. D. Frumin, I. V. Abankina et al. How to make education an engine of social and economic development? M.: NRU HSE, 2019. (In Russ.)
  2. Poslanie prezidenta Rossiyskoy-Federacii V. V. Putina Federalnomu Sobraniyu [Message from the President of the Russian Federation V. V. Putin to the Federal Assembly], December 1, 2016. (In Russ.) news/copy/53379.
  3. K. Schwab. The fourth industrial revolution. Penguin, 2017. 192 p.
  4. Strategiya-nauchno-tehnologicheskogo-razvitiya-Rossiyskoy-Federacii [Strategy of scientific and technological development of the Russian Federation] approved by the Decree of the President of the Russian Federation № 642 of 01.12.2016. (In Russ.) cons_doc_LAW_207967
  5. E. A. Alpeeva, E. A. Merzlyakova, A. V. Sysoev. Theoretical approaches to the study of socially oriented infrastructure of the region//Ekonomika v Promyshlennosti [Industrial Economics]. 2018. Vol. 11. № 4. P. 412-417. (In Russ.)
  6. Z. F. Garipova, L. R. Khalitova. Development of social infrastructure as a priority direction for increasing the competitiveness and competitiveness of the territorial system// Finansovaya ekonomika [Financial Economics]. 2020. № 2. P. 263-267. (In Russ.)
  7. Yu. A. Kuznetsova. Social infrastructure within the framework of the concept of competitiveness of the territory//Mezhdunarodnyy zhurnal prikladnyh i fundamentalnyh issledovaniy [International Journal of Applied and Fundamental Research]. 2017. № 8-2. P. 333-337. (In Russ.)
  8. N. P. Kuzmich. Development of social infrastructure of rural areas of the region in order to improve the quality of life of the population//Ekonomika-vchera-segodnya-zavtra [Economy: yesterday, today, tomorrow]. 2019. Vol. 9. № 4А. P. 392-399. (In Russ.)
  9. A. L. Sabinina, V. V. Sokolovsky, N. A. Shulzhenko, N. A. Sycheva. On the development strategy of multifunctional complexes of social infrastructure in the «Smart City» paradigm//Finansy-i-kredit [Finance and Credit]. 2020. Vol. 26. № 7 (799). P. 1469-1495. (In Russ.)
  10. O. A. Busari. The role of economic and social infrastructure in economic development: a global view.
  11. B. Ibama, S. S. Owukio, C. Wocha. Comparative Study of Social Infrastructure Provision in Ikwerre and Etche Local Government Areas of Rivers State Using Geographic Information System//Scientific Research Journal (SCIRJ), Vol. III. Iss. V. May 2015.
  12. G. Torrisi. Public infrastructure: definition, classification and measurement issues. University Library of Munich, Germany, MPRA Paper, 2009.
  13. N. S. Ilyushenko. [Digital learning: Prospects and risks of the digital turn in education]//Trudy 2 Mezhdunarodnoy konferencii Proektirovanie buduschego. Problemy-cifrovoyrealnosti. IPM im. M. V. Keldysh [Proc. of the 2nd International Conference Designing the future. Problems of Digital Reality of Keldysh Institute of Applied Mathematics]. Moscow, 2019. P. 215-225. (In Russ.)
  14. L. Davis. Digital Learning: What to Know in 2019/Evolving Ed. January 25, 2019.
  15. G. V. Novikova. [Questions of the expediency of using virtual reality technologies in the education of schoolchildren and students]//Trudy 4 Mezhdunarodnoy konferencii Proektirovanie buduschego. Problemy-cifrovoy-realnosti. IPM im. M. V. Keldysh [Proc. of the 2nd International Conference Designing the future. Problems of Digital Reality of Keldysh Institute of Applied Mathematics]. Moscow, 2021. P. 276-286. (In Russ.)
  16. L. V. Mezentseva. Online courses are no less effective than offline formats. Proven experimentally. IG nauchno obrazovatelnyy portal NIU VSE [IQ, a research and educational portal of the NRU HSE], 2018. (In Russ.) /217043836.html.
  17. The case in the helmet. 21.05.2018. (In Russ.)
  18. Ukaz Pprezidenta Rossiyskoy Federacii ot 07.05.2018 № 204 o nacionalnyh celyah i strategicheskih zadachah razvitiya-Rossiyskoy Federacii na period do 024 goda [Decree of the President of the Russian Federation of 07.05.2018 № 204 «On national goals and strategic objectives of the development of the Russian Federation for the period up to 2024»]. (In Russ.)
  19. T. Bierhold. For a better understanding of Industry 4 — An Industry 4 maturity model. University Of Twente, Enschede The Netherlands, 2018. https://essay.utwentenl/75330/1/Bierhold_BA_BMS.pdf.
  20. A. K. Petrova, N. V. Lashmanova, A. B. Zhernakov. An approach to assessing the digital maturity of industrial enterprises based on fuzzy logic//Innovatsii [Innovation]. 2020. № 10. P. 75-82. (In Russ.)
  21. Regions of Russia. Socio-economic indicators. 2020: statisctics. M.: Rosstat, 2020. 1242 p. (In Russ.)
  22. A. A. Zatsarinny, K. K. Kolin. [Theory and practice of digital transformation of society in the framework of the priorities of scientific and technological development of Russia]//Trudy 2 Mezhdunarodnoy konferencii Proektirovanie buduschego. Problemy-cifrovoy-realnosti. IPM im. M. V. Keldysh [Proc. of the 2nd International Conference Designing the future. Problems of Digital Reality of Keldysh Institute of Applied Mathematics]. Moscow, 2019. P. 29-39. (In Russ.)
  23. N. B. Paklin, V. I. Oreshkov. Biznes analitika ot dannyh k znaniyam [Business analytics: from data to knowledge]. M.: Peter, 2013. 704 p. (In Russ.)
  24. T. Calinski, J. Harabasz. A dendrite method for cluster analysis//Communications in Statistics. Vol. 3. № 1. 1974. P. 1-27.
  25. L. Kaufman, P. J. Rousseeuw. Finding Groups in Data: An Introduction to Cluster Analysis. Hoboken, NJ: John Wiley & Sons, Inc., 1990.
  26. D. L. Davies, D. W. Bouldin. A Cluster Separation Measure//IEEE Transactions on Pattern Analysis and Machine Intelligence. 979. Vol. PAMI-1. № 2. P. 224-227.
  27. D. Arthur, S. Vassilvitskii. K-means++: The Advantages of Careful Seeding//SODA ‘07: Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms. 2007. P. 1027-1035.
  28. G. McLachlan, D. Peel. Finite Mixture Models. Hoboken, NJ: John Wiley & Sons, Inc., 2000.
  29. M. Charrad, N. Ghazzali, V. Boiteau, A. Niknafs. NbClust: An R Package for Determining the Relevant Number of Clusters in a Data Set//Journal of Statistical Software. 2014. 61 (6). P. 1-36.
  30. C. Fraley, A. E. Raftery, T. B. Murphy, L. Scrucca. Mclust Version 4 for R: Normal Mixture Modeling for Model-Based Clustering, Classification, and Density Estimation. Technical Report № 597, Department of Statistics, University of Washington. 2012.
  31. E. D. Ignatieva, O. S. Mariev. [Improving the methodology and tools for analyzing the potential for self-development of socio-economic subsystems in the region]//Vestnik UrFU seriya Ekonomika i Upravlenie [Vestnik UrFU. Economics and Management Series]. 2011. № 5. P. 105-114. (In Russ.)
  32. T. Kohonen. Self-Organizing Maps (Third Extended Edition). New York, 2001. 501 p.