The article examines the key principles of using applied intelligent systems in the economic analysis of Ukraine's innovation potential, which significantly improves the processes of management algorithm construction and, as a result, creates a favorable environment for innovative development. It presents an algorithm for measuring the country's innovation potential, which is based on basic methods applied for the analysis, distribution, and classification of input data space. The advantages of applying the principal component method are identified, along with a procedure for using it to determine key indicators for assessing the country's innovation potential. An approach to determining innovation potential is formed based on intelligent data processing, allowing for the analysis and visualization of large volumes of data, as well as the identification of trends, key factors, and indicators influencing innovation activity in Ukraine. The research also justifies the feasibility and proposes an approach to using modern intelligent systems for continuous monitoring and control of the level of innovation activity, as well as for identifying and forecasting risks and issues, and determining possible ways to address them.
In modern conditions of globalization and rapid technological development, the use of applied intelligent systems (AIS) is of paramount importance. They enable more accurate, faster, and more comprehensive analysis of large amounts of data. AIS facilitates the automation of economic and legal data analysis processes, providing fast access to information and conducting complex analysis, thereby enhancing effectiveness. Leveraging machine learning algorithms and big data analysis, AIS can identify trends in economic and legal processes and forecast the country’s innovation potential.
The complexity of processes determining the country’s innovation potential is driven by high dimensionality, multi-level structure of mathematical models, and the number of interrelations between input and output variables. This necessitates the application of advanced approaches
0000-0002-1354-4838 (N. Vnukova); 0000-0003-3665-0585 (N. Opeshko); 0000-0003-3398-9276 (S. Hlibko); 0000-0001-9124-9511 (D. Davydenko), 0000-0001-9642-3611 (V. Pyvovarov); 0000-0003-0390-1931 (O.Peredrii); © 2024 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). to processing analytical data to support optimal managerial decision-making. This justifies the relevance of conducting this research.
The purpose of the research is to develop an algorithm for determining the country’s innovation potential using applied intelligent systems based on identifying influencing factors and uncovering hidden relationships between variables in statistical data.
To achieve the stated goal, the following tasks were addressed: 1) formulation of the initial set of indicators of innovation potential based on analysis of literature sources;
2) proposal of an algorithm for determining the level of innovation potential, which includes a) identification of hidden relationships between variables by constructing a correlation matrix; b) selection of the most representative indicators using the principal component analysis method; c) calculation of the resulting integral indicator using the taxonomic indicator of development method.
The research papers of Ukrainian and foreign scientists are devoted to determining the innovation potential based on the use of applied intelligent systems.
In the article by Vakaliuk V. A. [
Riabovolyk T. F. [
The article by Hryhoruk P. M. And Khrushch N. A. [
Scientists Yepifanova I. Yu. and Hladkova D. O. [
As a result of the research by Semenchenko N. V. and Moroz O. S. a system of primary indicators for assessing the level of innovative development of an enterprise was formed, which allows to analyze it in terms of its components (innovative potential and innovative process). Furthermore, this system serves as the foundation for a hierarchical model aimed at analyzing the innovation development of the enterprise.
Additionally, research into the innovation potential of regions was undertaken by
Zhykhor O. B. [
In J. Gladevich’s article [
Furthermore, the issue of modeling economic processes, including indicators of innovation
potential, has been addressed by foreign scientists: Atashbar, T. [
Thus, contemporary economic trends indicate the necessity of algorithmizing economic processes for their further enhancement through the application of artificial intelligence. In the context of analyzing innovation potential in scientific works, the problem of identifying hidden relationships between indicators of innovation potential and justifying the selection of the most representative among them remains insufficiently explored, which is the aim of this research.
To compute the composite index of a country’s innovation potential, it is proposed to devise a procedural algorithm that encompasses various combinations of statistical analysis methods aimed at obtaining an overarching assessment of a substantial volume of data (Figure 1). k s a T d o h t e M t l u s e R
Source data (indicators of innovative potential
of Ukraine) Task 1: Determination of hidden relationships between variables Task 2: Elimination of multicollinearity (if available)
І Correlation analysis
Task 3: Determination of representativeness (the most significant and informative indicators)
ІІ Method of principal
components ІІІ Taxonomic analysis
(step by step) An integral indicator of the innovative
potential of the country
As illustrated in Figure 1, the following methods were employed in this study to achieve the
research objective: correlation analysis [
The construction of the pairwise correlation coefficient matrix is a common method within
the framework of applied intelligent systems. Calculating correlation coefficients allows for the
for the identification of the strength and directions of relationships between the variables under
investigation, as the key issue in building adequate mathematical models is the presence of
correlated independent variables, i.e., the absence of multicollinearity effects [
Based on the calculation of pairwise correlation coefficients for a set of indicators, a matrix is constructed (Formula 1). If the entire dataset consists of m variables (factors) X, each containing n observations, then the matrix of pairwise correlation coefficients R is calculated, which will be symmetric with respect to the main diagonal.
1 | 1 = 2 | . . . 1
1 1 2
. . . 1 2 1 2 1 . . . 2 . . . . . . 1 |
For the purpose of interpreting the calculated coefficients of pairwise correlation, the
Chedoke scale [
After eliminating the multicollinearity effect, there arises the need to determine the most representative indicators using the principal component method of factor analysis. The essence of the factor analysis method lies in identifying hidden interdependencies between indicators that characterize various aspects of the country’s innovation potential over a certain period of time and have different natures, reducing them to a smaller set and using new, most important characteristics that explain a significant portion of the variation in the values of the analyzed data. The essence of the factor analysis method consists of uncovering hidden interdependencies between indicators that characterize various aspects of the innovation potential over a certain period and have different natures, reducing them to a smaller set and using new, most important characteristics that explain a significant portion of the variation in the values of the total sample data.
The principal component method allows for the extraction of m principal components or
generalized features from m original features. The mathematical model of the principal
component method is based on the logical assumption that the values of a set of interdependent
features generate some common outcome and has the following form [
The basic factor analysis model is determined by the formula:
’ = ∑ + ∑ where ′ is centered (normalized) value of the jth feature; – the weight (or loading) of the j-th feature on the r-th common factor; – r-common factor; – the weight (or loading) of the j-th feature on the r-characteristic individual factor; – characteristic (individual) factor related only to this j-characteristic. consider characteristic factors, and the number of components equals the number of features. Consequently, after excluding components based on the smallest proportion of total variance, the remaining components will be significantly fewer than the number of features.
The final stage in determining the innovation potential of a country is the formation of an approach for its integral evaluation. There are several methods for constructing an integral indicator for analyzing complex phenomena, among which taxonomic analysis has been chosen for this study. This method allows for the systematization of multidimensional statistical information and obtaining a single comprehensive assessment. The universality of taxonomic analysis enables its use for analyzing the properties of a single unit characterized by feature values specified in the form of time series, which forms a generalized picture of changes. The sequence of steps in calculating the taxonomic indicator of innovation potential is presented in Stages of taxonomic analysis of the innovative potential of the country
Calculation procedure = || 1 where is standardized value of indicator i in time period j; is value of indicator i in time period j; ̅ is arithmetic mean value of indicator i for all periods; is standard deviation of indicators.
0 = { , if the stimulus indicator , if the indicator is a disincentive 0 is reference value of the indicator.
=1 С 0 = √∑( − 0 )2 0 = √ 1 ∑(С 0 − ̅)2, where 0 is standard deviation; ̅ is average distance between observations. where С0 is the maximum possible deviation from the standard.
С0 = ̅ + 2 0, = С 0 С0 where is dynamic indicator of development.
where is taxonomic indicator of development.
The analysis conducted using the taxonomy method (Table 1) allows us to establish the scale and directions of changes, forecast their impact on the main parameters of innovation potential, identify the most important growth factors, and make appropriate management decisions or directions for state policy based on this.
For the formation of the initial set of indicators that can be used for the analysis of the country’s
innovation potential, a number of scientific studies have been analyzed [
In the next stage of the research, selected indicators of Ukraine’s innovation potential for the years 2000-2021 were calculated based on data from the State Statistics Service of Ukraine [20] and the National Bank of Ukraine [21], as identified through analysis of literature sources (Table 2). 1 forecast data for 2000-2009; 2 forecast data for 2021.
Table 2 shows that only indicators that correlate with each other and may have a close relationship have been selected due to their heterogeneity and scale of values. Therefore, the presented indicators have been chosen for further factor analysis.
For eliminating the multicollinearity effect between the indicators, a matrix of pairwise correlation coefficients was calculated, which is presented in Figure 2.
As seen from the data presented in Figure 2, a number of indicators exhibit a strong linear relationship with each other (the correlation coefficient exceeds the value of 0.7). To address multicollinearity, further factor analysis is conducted to determine the optimal set of indicators for assessing the level of innovation potential in Ukraine, incorporating 6 indicators.
For practical implementation of the principal component analysis method using the data provided in Figure 2, the Statgraphics Centurion 19 package was utilized. This package allows for the examination of individual and cumulative variance, the proportion of total variance explained by each component, and cumulative variance characterizing the selected principal components (Figure 3).
The obtained results of the factor analysis for indicators of innovation potential are presented in Figure 3, where the necessary number of factors is determined by the magnitude of cumulative variance. A value of cumulative variance at the level of 70% is considered sufficient. This indicates that the formed factors explain 70% of the variability of the studied process, while 30% is explained by other factors. Thus, the results of the factor analysis demonstrate that it is advisable to conduct an assessment of the country’s innovation potential based on three obtained factors, which explain 84.40% of the variability of the assessment.
In the next stage of the research, an assessment of the significance of indicators based on the size of the loadings was conducted to reduce the dimensionality of the number of indicators. Factor loadings were obtained following the varimax procedure (see Appendix 1), demonstrating the correlation between indicators and factors. Using the principal component method, five most representative indicators of the country’s innovation potential were identified.
According to the previously developed algorithm, in the subsequent stage of the research, an integrated indicator of innovation potential was calculated using the taxonomy analysis method. Intermediate indicators and the resulting assessment of Ukraine’s innovation potential for the years 2010-2021 are provided in Appendix 2. It was determined that the taxonomy development index presented in Appendix 2 can range from [0;1], with the closer the value of the composite index to one, the higher the country’s innovation potential.
Based on the developed algorithm, the research identifies the dynamics of Ukraine’s innovation potential from 2000-2021, as presented in Figure 4.
0,42 0,38 0,15 0,07 0,02
0,23 0,11 0,07 0,30 0,32 0,10 0,35
An integral indicator
of the innovative potential of the country
As seen in Fig. 4, the highest values of Ukraine’s innovation potential were in 2002, 2016, and 2021, while the lowest were in 2005, 2008, and 2011. The provided statistics allow for the identification of fluctuations in the country’s innovation potential over time; however, for a qualitative interpretation of the assessment results, there is a need to develop a scale for distributing indicators at the level.
The research proposes a scale for determining the level of a country’s innovation potential based on the Fibonacci ratio [22]. According to this ratio, changes in indicator values most often occur in the range between 38.2% and 61.8%. In this case, the scale for evaluating innovation potential takes the form [0;1]. According to the approach in [23], after multiplying this difference sequentially by 0.382 and 0.618 and subtracting each of the obtained sums from the «maximum», values of intervals were obtained within which changes are most likely to occur according to the Fibonacci ratio. The obtained interval [0; 0.382) is divided into 2 smaller intervals at the levels of 38.2% and 61.8% (0.236 and 0.382).
As a result of scaling according to the Fibonacci ratio, four ranges of the level of a country’s innovation potential were obtained, which are presented in Table 3.
Based on the scale in Table 3, the levels of Ukraine’s innovation potential for the years 20102021 were determined, presented in the form of a distribution matrix in Figure 5.
Sufficient level
Critically low level
Average
Year 2000,2002,2013,2015, 2016,2018,2020,2021 2003,2004,2005,2006,
2007,2008,2011 2001,2009,2010,2012, 2014,2017,2019
0,15 0,32
The team of authors thanks the Armed Forces and Territorial Defense of Ukraine for the opportunity to participate in the conference
Thus, the researchers developed an algorithm for determining the integral indicator of the country’s innovation potential through a system of quantitative indicators by: selecting the initial set of indicators based on the synthesis of methodological approaches in the scientific literature; eliminating high functional dependency between indicators using correlation analysis; reducing the number of coefficients using multidimensional factor analysis – principal component method. The initial data for conducting correlation and multidimensional factor analysis were derived from a sample of 22 observations (data for 2000-2021). Based on the results of factor analysis, it was established that it is advisable to assess the innovation potential based on three obtained factors, which collectively account for 84.4% of the variability of the initial variables. Among the set of indicators for each factor, diagnostic features were determined using the «weight center» method, which have the most significant properties of the set of output data. Based on the taxonomic indicator of development, integral indicators of Ukraine’s innovation potential for 2010-2021 were calculated and their qualitative interpretation was provided according to the scale developed based on the Fibonacci relationship. The proposed algorithm allows for continuous monitoring and control of innovation potential, identifying and forecasting risks and potential issues, as well as determining possible ways to address them.
telecommunication,
computer and information services (X1), million dollars. USA
non-resident investors to the total volume of innovation costs (X4)
company's own funds in the total volume of innovation costs (Х5), %
The number of types of innovative products
introduced in the reporting year (Х9), units 2000 2001 2002 2003 2004 2005 2006 [20] Economic statistics / Science, technologies and innovations. URL: https://www.ukrstat.gov.ua/ [21] External sector statistics. URL: https://bank.gov.ua/ua/statistic/sector-external. [22] Guide to mastering the Fibonacci retracement URL: https://academy.binance.com/uk/articles/a-guide-to-mastering-fibonacci-retracement [23] L. I. Piddubna, Competitiveness of international tourist insurance services, Scientific Bulletin of the Odesa National Economic University. Collection of scientific works. Odesa, 2020. No. 3-4 (276-277). P.112-124.
1. Matrix of factor loadings of the obtained principal components
2.Calculation of innovative potential of Ukraine
and the reference vector (С 0)
development ( ) Taxonomic indicator of development ( ) 0,7447 -0,0840 0,0178 -0,1309 -0,9591 0,5069 -0,0170 0,3201 0,9488 0,1885