Neural network modeling of tourism development as a factor of sustainable economic growth in Russian regions

. The features of the development of the tourism sector in the regions of the Russian Federation, which have an impact on the socio-economic development of the country, have been investigated. Analysis of the current state of the tourism sector, classified as the main types of economic activity, is relevant and important for increasing the competitiveness of the regions of the Russian Federation and ensuring the economic security of the state. The study is aimed to model and analyze tourist cluster formations in Russia. The study of tourist activity in the regions of Russia based on the indicators of the database of the Federal State Statistics Service was carried out using a new promising approach cluster analysis using the scientific and methodological apparatus of artificial neural networks. The distribution of Russian regions into five tourist clusters has been obtained as a result of clustering multidimensional data using neural networks - self-organizing Kohonen maps, which are focused on self-study, and modern information technologies. In neural network modeling, the six-dimensional space of tourism development indicators was mapped, taking into account the topology, into a two-dimensional space, which made it possible to visualize the results of grouping regions by tourist clusters. The features of the development of the tourism sector in the regions of the Russian Federation have been revealed by the totality of the considered indicators The obtained results state that there is a strong variation in the number of regions by tourist clusters and the ametric nature of the development of tourist activity in the regions of Russia. The results of the study are of practical significance for the strategic planning of the tourism sector development, which ensures the development of domestic and inbound tourism. Analysis of the functioning of the tourism sector in the regions of the Russian Federation allows concluding the necessity to take a set of measures to stimulate effective investment activity in a number of tourism clusters, harmonizing the strategies of the state and business, which will contribute to the renewal and competitiveness of this type of economic activity.


Introduction
Ensuring sustainable economic growth in each region of the Russian Federation and the country as a whole corresponds to one of the main directions in solving the key tasks of economic policy [1]. The development of the tourism sector [2,3] is a significant factor contributing to the sustainable development and competitiveness of the regional economy.
The tourism sector is associated with various industries that integrate and form the provision of the tourism industry and travel: hotel business, transport, catering, arts and crafts, utilities and other activities. This industry is significant for the sustainable development of the economy taking into account the number of organizations, entrepreneurs, and the population involved in the tourism industry, as well as the associated social and economic effect. Tourism also plays an important role in protecting the natural and cultural heritage of the territories. As one of the largest and fastest growing economic sectors in the world, tourism promotes economic growth and socio-economic development of the regions, including through the creation of jobs. Increased investment in tourism infrastructure leads to an increase in the standard of living of the population and an increase in the attractiveness of cities and rural settlements for tourists. Empirical research results show that an increase in the number of tourists by 1% leads to an increase in economic growth of 0.41% [4]. In the countries of the Organization for Economic Cooperation and Development, the tourism sector accounts for 4.4% of GDP, 6.9% of employment and 21.5% of exports of services [5].
The COVID-19 pandemic has had a significant impact on the tourism industry, with 1 billion fewer tourist trips around the world, and a loss of $ 1.3 trillion in total export revenue from international tourism, from 100 to 120 million jobs are under the threat of cutting [6] According to a report by the World Travel and Tourism Council, the total contribution of the tourism sector to world GDP is estimated at 10.4 %. The significant contribution of tourism to the GDP of the Russian Federation is shown by the data (Figure 1), which indicate a positive dynamics of the contribution of the tourism sector to the GDP of Russia. It is worth noting that tourism refers to the type of economic activity in which the maximum multiplicative effect is found to accelerate Russian economic growth. Investments in the tourism industry create added value in such economic activities as construction and production of building materials, transport, trade and services. One of the possibilities for further increasing the role of tourism in the socio-economic development of the regions of the Russian Federation can be contained in the creation of favorable conditions for the development of small and medium-sized businesses in the tourism sector. At the same time, it is relevant to study the development of the tourism sector of the economy, in order to harmonize the strategies of the state and business in the field of tourism.
In the last few years, there has been a growing interest in studying the impact of sustainable tourism development on economic growth.
The works of many scientists are devoted to the development of tourist clusters in Russia, as a rule, the authors propose to form tourist and tourist-recreational zones within one or several neighboring regions [7,8,9,10,11]. The article features a new approach to modeling tourist areas using the scientific apparatus of artificial neural networks.

Materials and methods
Tourist as well as sports activities are characterized by multidimensional data sets. The multidimensionality of the initial data determines the use of classical statistical methods of analysis, which demonstrate very high efficiency. In this article, neural networks are used for cluster analysis of multidimensional datathe most important direction of artificial intelligence, which is one of the most advanced and promising tools and provides new approaches to the study of multidimensional problems -Kohonen self-organizing maps (SOM). These neural networks are a representative of the class of unsupervised neural networks [12,13,14,15]. Kohonen SOMs are qualified as an effective tool for cluster analysis and visual representation of multidimensional statistical data [12,14]. To conduct research, there were used neural networks implemented in the Deductor -analytical software package.

Results
The study of the development of the tourism sector of the economy of the Russian regions was conducted on the basis of the statistical database of the Federal State Statistics Service for 2018.
In neural network modeling, the six-dimensional space of tourism development indicators in the regions of Russia was mapped, taking into account the topology, onto a two-dimensional self-organizing map (Fig. 2). Let's consider the descriptive statistics (Table 1), the important mission of which is to discover the distribution law of the studied indicators. Key characteristics: measures of central tendency, dispersion, and the distribution forms of the indicators, which are presented in table. 1, state the absence of symmetry in their distributions. This confirms the difference in the measures of the central tendency, which are identical for the normal distribution law, distinguished by symmetry and unimodality. Dispersion measures that characterize the spread, i.e. the "width" of the distribution, and the measures of the form of the studied indicators also confirm the asymmetric form of their distributions.  Table 1 shows that the asymmetry is positive for all indicators, therefore, the right tail will be thicker than the left one, and the top is shifted to the left. In the case when the distributions are symmetrical, the skewness is zero.
The values of the kurtosis characterize the shape of the top of the graph of the onedimensional vertical distribution. The data in Table 1   It is noteworthy that according to Table 3, the regions of the Northwestern Federal District were divided into clusters as follows: one region joined cluster A, three regionscluster D, and seven regionscluster E. Three regions joined Cluster C, six regionscluster D, and five regionscluster E from the fourteen regions of the Volga Federal District.
The results (Table 3) indicate that all the studied indicators X1 -X6 take maximum values in the regions of the tourist cluster A (Moscow and St. Petersburg), both in comparison with their values in other tourist clusters, and in comparison with the all-Russian values. All indicators of regional tourism development in the subjects of the Russian Federation included in tourist clusters B and C exceed the national average, and in the regions of the tourist cluster E, the indicators are less than the national average. The state indicators of the tourism sector in the regions included in the tourist cluster D demonstrate multidirectional development.