writing articles, citations, indices of authors and more. Thus, another task set in the paper is to study the geographical distribution, as well as economic, by using certain economic and social indicators.

The first researches and works related to the evaluation of authors citation are related to the derivation of correct index or rating formula. Data set used in the work contains such two indices: hindex, hm-index. First of all, the quality of the author citation represetation using the h-index is debatable, because many scholars and publicists argue the low efficiency and incompetence of this approach [1][2][3][4].Since this work aims to study self-citation and by comparing the h-indices of the authors with and without self-citation, the question of study correctness has been emerged. Many papers dwells upon direct citation analysis limited to a specific cluster of authors tied to publishing platforms. In the result of the analysis, data about distribution of citations by person partners as a physical being, as well as by their intellectual characteristics or areas such as education have been obtained [1,3].

The problem of self-citation research is quite popular [5][6][7][8][9]. It leads to the availability of many sources of data related to it. The study of these data is limited to cluster, regression analysis. So this paper describes experiments using neural networks to identify or refute the existence of nonlinear, complex relationships between many possible parameters of the author and his level of self-citation, to identify patterns or limited human resources in certain areas. However, when the issue of citation is extended to authors nationalities, there is a gap in the availability of intelligence analysis of the number of self-citations in parts of the world or countries, as most studies are unidirectional.

The study of relationships between different parameters, proving the presence or absence of these relationships, as well as establishing their analytical form requires certain mathematical and algorithmic apparatus, such as classical methods, correlation analysis, regression analysis, least squares method for approximation [5], backpropagation algorithm as a method of learning neural networks (including multilayer perceptrons) and Deep Learning method [10][11][12][13]. Some algorithms used in the work have a high level of complexity and do not require additional changes or descriptions [14][15][16][17][18][19][20][21], because it does not meet the objectives of this research. They are actuality for content analysis or web resources monitoring based on machine learning [22][23][24][25][26][27][28][29][30], for example, citation and self-citation analysis in scientific and technical articles for dataset formation [31][32][33][34][35][36]. Such algorithms include the Adam method -a stochastic algorithm for finding the numerical value of the FBZ gradient. However, some algorithms for generating the required type of data, their visualization or tokenization have been supplemented or changed specifically for this research. Some of them are given as an example based on algorithm supplemented algorithm for filling the correlation matrix and the corresponding heat map:

Step 1. Initiate a single matrix of the attribute's numbers order. The value that are not on the main diagonal equals to the special NaN value.

Step 2. Choose the type of triangular matrix.

Step 3. Pass cyclic the cells of matrices with incremental parameters i, j

Step 3.1. If i ≠ j belongs to the matrix Step 3.1.1. If the upper triangular matrix is chosen and i>j (in cell i, j), then assign the value of Pearson correlation coefficient [5] between the attributes of numbers i and j.

Step 3.1.2. If the lower triangular matrix is chosen and i<j (in cell), then assign the correlation coefficient value between the attributes by numbers i and j (in the cell i and j).

Step 3.2. If i = j, then skip step Step 4. Choose two color nodes.

Step 5. Interpolate the color nodes values on the interval [-1, 1], for NaN values it is necessary to return transparent color.

Step 6. Fill the matrix with the appropriate color values.

Step 7. Display the color table according to the values of the matrix cells Another example is tokenization, which is used to convert some string fields of data windows into corresponding numerical vectors. Fig. 1 shows the activity diagram describing this algorithm.

The study of selected parameters distribution is based on several datasets, including data about 160 thousand of unique authors [8], world GDP information in 2020, as well as dataset of the global distribution of corruption indices -CPI, 2019. The first dataset about authors contains 46 fields and more than 161,441 lines. Each field has an encrypted name, the description of which is given in Fig. 2. However, only some of them were actually used in the study, namely: author country, number of author articles for the period 1960 -2019, number of author citations for 2019 (including and exclusively with self-citation -Fig. 3), author h-index for 2019 (including and exclusively with self-citation -Fig. 4), as well as the top category of the author (from the categories of ScienceMetrix). For example, for general statistics within 12% of self-citation -160 thousand; with <1% -about 9700 authors; from> 12% -approximately 65400 people, and from> 30% -approximately 7500 (Fig. 6-7). The next dataset is the data on GDP of countries according to the World Bank (Fig. 8) [6]. From this dataset, two fields were used in the work -the ISO3 representation of the country name and the actual value of GDP. The third dataset (Fig. 9) is one used in the work, the information in which is obtained from Transparency Internationalthe international organization against corruption [2]. This dataset is suitable for separate study, but in this paper is used as a source of information to test the hypothesis. In order to use, convert and process data from datasets using R the best is to translate the obtained data into csv format. Since one of the investigation tasks is to study the percentage of self-citation depending on other parameters, and in the initial data they are given as a tape value, it is necessary to develop a program for converting a column of data, for example: When working with data approaches and technologies, the tidy verse group has been used. Since the important work is the visualization and representation on graphs of many parameters simultaneously, the basic principles of developing such graphs using ggplot2, ggridges and patchwork have been considered. The main type of graphs is lollipop. The developed template looks like this:

Replacement of the variable F with any available in the data frame will allow to build different graphs, for example from Fig. 10. Classic point graphs with a regression line also are used. There is an example code to create: Another important type of displaying the relationship between data is the thermal map, the algorithm of which was described in the previous section, in particular, the supplemented algorithm can be performed as follows:

Relatively new type of many samples' properties representation, their distribution or relationship are the so-called joyplot or ridgeline. In this paper it is performed using point gradient by the following code:

The results of this graph type are shown in Fig. 13. After describing features of building data graphical representation, construction of some algorithms for data processing has been demonstrated. First of all, the method of data conversion of the authors dataset has been considered. It is necessary to combine all records by country and then convert the grouped fields into new ones, for example, the number of published articles by authors of one country should be summed, the level of self-citation should be turned into the average one, and the h-index of country authors should be generalized.

After creating the new data window, it is possible to merge it with two others that have a common field -country names. For croquet combination without forming NA values, firstly, it is needed to find the intersection of three sets of existing countries in each dataset and then select only those countries that are part of the new set:

In the part of the work responsible for the study of the considered properties geo-economic distribution properties, the deviation to the exponential regression has been performed. If to use the built-in function lm and compose the formula as y ~ exp (x), then there will be a problem that the best parameters for the regression function f (x) = c + exp (x) will be selected.

However, in the general case, the exponential function has the form of a * b ^ x, which is why the formula ln (y) ~ x is chosen to perform the correct regression analysis, which is equivalent to the function ln (f (x)) = c1 + c2x, which is equal to f (x) = exp (c1) exp (c2x), where a = exp (c1), and b = exp (c2):

The last important part of the experiments descriptions is the neural networks development. The paper represents four different in architecture and set of activation functions, single and multilayer perceptrons, i.e. fully connected networks (Fig. 11).

TensorFlow was used as a library for python to build perceptrons and the model itself was built using the Functional API:

To build a dataset for learning and testing models from the initial worksheet about the authors developed code:

The general relationship between the parameters is the first step in considering the data. It was carried out with the help of class correlation analysis, by constructing thermal map of the correlation matrix (Fig. 12).

The first important aspect which should be highlighted is the second sub-diagonal presence with a correlation coefficient is closed to 1. This linear data cloud is a correlation between citation parameters (number, h-index, hm-index, etc.) with and without self-citation. The presence of such correlation means that in the general case, self-citation does not have a strong impact on the performance of authors and therefore is not used as self-plagiarism or as a source of increasing the author rating. The next important aspect is the self-citation percentage correlation to other parameters. The last column of the map from Fig. 7 is almost all painted according to zero correlation. This means that at least there is no linear relationship between self-citation and parameters presented in the dataset. Proving of the hypothesis that there is no connection between the parameters available in the data set and self-citation will be done by building neural networks and analyzing of their results.

The next stage of data review is the distribution of citation parameters and articles publication by countries. At the beginning, it is necessary to create a data window according to the algorithm described in the previous paragraph of this paper. Firstly, the statistical distributions of the fields selected from the dataset are considered, in particular, they are built as joyplot. Because the ranges and data intervals between these articles, h-index, self-citation percentage and citations are very different, all column data values have been normalized. The diagram in Fig. 13 shows a certain similarity in the distribution of these parameters, in particular, all have positive asymmetry and are higher than normal excess.

It is important to notice that the correlation coefficient between the average percentage of selfcitations from the dataset, as well as the calculated percentage grouped according to the data is 0.95 respectively and can be considered as a correct calculation of the average percentage. The next stage is to consider individual distributions of parameters relative to the country. In Fig. 14. the top 60 (unsorted values) and 23 countries are shown in terms of the total number of articles. Part of the chart with the top 23 countries shows that the top is occupied by economically developed countries or large economies, in particular, this observation suggests the existence of correlation between economic development and the number of articles. GDP was chosen as an indicator of economic development. In contrast to GDP, an indicator of corruption in the states was added to obtain information on the dependence of the level of corruption, in particular in the educational and scientific spheres, on the abuse of self-citation among authors. The next considered parameter is the total number of the country authors citation. The graph in Fig. 15 shows the top 60, top 23 and the position of Ukraine. Each lollipop has two labels, the larger one is responsible for quoting with self-citation and without the smaller one. This graph already shows the presence of high correlation between these parameters. Ukraine ranks 49th in the number of articles, which is equal to 10029, such a small number is due to the incompleteness of the dataset, because it includes only the most popular authors in the world. Again, the first place is behind the United States, second -China, third -Great Britain and so on. Ukraine ranks 65th along with Hungary and Peru. The distribution of the percentage of self-citations by countries is given below, the graphical representation of the data is shown in Fig. 15. Unfortunately, according to this parameter, Ukraine is in the top five, ranking fourth, with approximately equal self-citation of 34%. The smallest number of self-citations are in small countries in the Caribbean, such as Barbados and Santa Lucia. In particular, the lack of visual link between self-citation and the economic development of the state suggests that there is no correlation between GDP and the percentage of selfcitation. The most interesting approach to considering of selected primers for countries is developed for the h-index. Since the h-index data is on the controversial boundary between nominal and relative data types, it is incorrect to estimate the country by the average value, so it was decided to calculate the hindex of authors h-indices in a particular country. The algorithm for constructing such a parameter is described in the previous section. The first graph from Fig. 16 is sorted by the number of citations for 2019, and it can be seen that for the first 60 countries there is a correlation between these fields. Again, the United States ranks first, with an h-index of 55. Ukraine ranks 68th, with an index of 16, along with a number of other countries.

To display the global picture of the geographical distribution of these parameters, a graph is constructed Fig. 17.Deciphering graph values is quite intuitive, countries are sorted by number of articles, the number is indicated by the color of lolipop, the value of lolipop consists of two parts, most of them are responsible for the h-index of the country on the h-index of authors including self-citation, the size of the lolipop indicates the percentage of self-citation. Some interesting points can be seen from the graph: Russia is in the top 23 countries, but the percentage of self-citation of this country clearly stands out among others, and it falls out of the picture and the h-index, because it is quite low compared to neighboring countries.

After conducting graphical intelligence analysis, the values of GDP and CPI of countries were added to the data. The first step is correlation analysis. Fig. 18 shows thermal map of the correlation matrix. This map shows the presence of linear relationship between the h-indices of countries, which confirms one of the previous assumptions. The correlation matrix also confirms a fairly obvious relationship between the number of articles and citations (with and without self-citation). All correlation coefficients with self-citation are negative. In particular, the largest modulus correlation is between self-citation and the corruption rate, which allows a weak linear relationship between them, the higher the CPI (i.e. the more transparent the various spheres of government are) the lower the level of self-citation abuse is, but it is impossible to insist on the straight relationship.

Another assumption concerns the country GDP and the number of articles. The map shows that there is a linear relationship between GDP and the number of citations. However, a little deeper analysis was done to confirm the connection. Thus, scatter plots, i.e. correlation fields, were constructed between the value of GDP and the country authors citation numbers for different countries quantities, in particular for 40, 90 and all available ones. Figure 19 shows that with a smaller sample, the correlation coefficient decreases significantly and only with the inclusion of countries such as the United States, China and the United Kingdom, the coefficient increases to the value obtained from the matrix. The fourth graph from Fig. 18 deals with the study of self-citation relationships between different parameters, and is a correlation field between the value of self-citation percentage and GDP. It shows the chaos and lack of specific dependence. Additionally, a study of extraordinary results of the weak linear relationship between the h-index and GDP and CPI. Comparison of correlation fields are shown in Fig. 20. First three graphs in Fig. 19 show a regression line constructed by using the lm-function. Similar additions to the graph are made for scatter charts from Fig. 20. Before describing the results of neural networks the another observation about the distribution of self-citation has been given but this time through the prism of the field to which the author belongs (top sphere from the dataset).It is similar to the creation of data window with data about countries, performed by grouping data records by category and country. After that, three-dimensional histogram was constructed (Fig. 23), where the third dimension describes the percentage of self-citation and is determined by color. Since the global view of the histogram is not the most comfortable for visual analysis, a subset of countries for which a separate chart is built. Fig. 24 shows that the highest level of self-citation is in the field of mathematics and statistics in Mexico, however, if considering Fig. 23, it is clear that the largest number of self-citations predominates in the field of physics and information technology.

The last point of the research is the construction of neural networks to study the existence of nonlinear connections between those available in the first dataset about the world authors and their selfcitation. As it was described in the previous section, four different simple single-and multilayer perceptrons were created with different activation functions and randomization distribution of filling the initial values of weights and displacements. After tokenization of the fields denoting the country, institute and three different categories of the author, a new .csv file with a training and test sample has been created (Fig. 25).The resulting file contains 37 columns, respectively 36 properties, and 161,441 records. When forming the training and test sample, the ratio 80/20 was chosen. that no network has any level of accuracy in determining the level of the author self-citation on the available parameters, so it can be argued that these properties have no significant relationship with the level of self-citation.

The comprehensive research, which was aimed to test a number of assumptions about the relationship between the numerical characteristics of the world authors activity on the level of their selfcitation has been made. The study did not reveal any patterns, relationships between the investigated properties. Such results lead to certain assumptions about the individualization of characteristics, motives, level of intellectual and moral development of authors, as well as general trends in science, existing problems of society, etc. to the level of self-citation. Psychological analysis may show a link between self-citation abuse and its use as it is a need.

Further research requires to expand the subject area by finding other possible sources of data.

On the other hand, the other part of the study that is the geo-economic distribution of certain parameters has more positive results. The analysis has confirmed a number of hypotheses, including the connection between the economic development of the country and its ability to create scientific papers, articles with sufficient quality as there is a link between authors citation and the country GDP.

The following analysis can be carried out with in-depth division of the components of GDP, possibly with the expansion of geographical areas, which authors are grouped by.

There may be a number of other indicators that have an impact on the characteristic of the state in terms of scientific articles authors views. The paper considers the level of corruption in countries as an example of possible indices / parameters. In particular, data on the level of education, research costs and the availability of private research and art centers are suitable for analysis.

So, the analysis of the geo -economic distribution of parameters in a specific sample of countries -Ukraine, Poland, Georgia, Slovakia and Romania has been made.

The graph in Fig. 28 shows that the largest number of articles was published in Poland, with Ukraine in third place. The following graphs from Fig. 29 show that Poland ranks first in all rankings, except for self-citation, where the championship, unfortunately, belongs to Ukraine.

In the result of the research, the study on the presence, analytical view or lack of links between the geo-economic distribution of human resources that produce certain scientific papers and articles has been conducted. The paper presents and uses possible approaches to estimate the country, for example, with a double overlap of the h-index. In a comprehensive study of the parameters and generalized characteristics of the world the authors give examples of using classical and modern mathematical information apparatus to find and prove the presence of patterns in data including the use of graphical data representation and small neural networks combination.