Methods of Sustainable Clustering of Russian Regions by Employment

The problem of the imbalance in the labor market of the Russian Federation cannot be solved without leveling the heterogeneity of its regions by socio-economic and demographic characteristics, since the labor market is a dynamic complex system that is influenced by a variety of factors, such as the economic, demographic situation, quality of education, interests of market participants, technological progress and digitalization, psychological aspects, etc. The article discusses the application of cluster and discriminant analysis methods on socio-economic data, highlights the regional features of the labor market in Russia. Cluster analysis was carried out using traditional hierarchical and iterative methods: the “Nearest Neighbor” method, the “Far Neighbor” method, the “Ward” method and the k-means method, as well as the fanny fuzzy clustering method. The results obtained by these five methods were evaluated for consistency. The conducted discriminant analysis allowed us to obtain a stable cluster structure in terms of the number of employed people by type of economic activity, dividing the regions of Russia into four main groups characterized by positive, average, neutral and negative behavior. Thanks to the construction of profiles of the obtained clusters, poorly informative types of economic activity were identified, employment in which has little effect on the division of regions into groups. The article evaluates the errors of cluster analysis methods for the final stable clustering. The regions with high and low levels of employment are analyzed, atypical subjects of the Russian Federation are identified and their industry specialization is considered. A comparative analysis of the formed groups and atypical regions was carried out, regions that can be conditionally assigned to any cluster were identified. The final typologization of the regions of Russia by the number of employed by type of economic activity has been developed taking into account territorial, social, sectoral and climatic features.