Determining the key factors of the innovation gap between EU countries

Abstract

Innovation plays a crucial role in ensuring economic growth and competitiveness of national economies, creating conditions for their sustainable development. By focusing on supporting innovation, the EU is particularly helping to accelerate the development of those member states that lag far behind the EU average. This requires the selection of the indicators reflecting the development of innovation that determine the differences between member countries to the greatest extent. Therefore, the aim of the study is to identify the key factors of the innovation gap (FIG) between EU countries based on a comparison of indicators characterizing the national innovation systems (NIS). For this purpose, 22 relative indicators were selected from the indicators included in the Global Innovation Index to form an array of empirical data. At the first stage, the EU countries were divided into four clusters using the k-means method. At the second stage, using the decision tree method, a group of indicators was identified that together distinguish the obtained clusters to the greatest extent and, accordingly, determine the differences between EU countries and can be considered as FIG, namely: “Researchers”, “GERD financed by business”, “Joint venture/strategic alliance deals”, “Software spending”, and “High-tech manufacturing”. This allows individual member states to prioritize the development of those indicators (i.e. FIG) that most determine their position in the EU and therefore improve their NIS. At the EU level, this will contribute to the complementarity of the NIS, overcome differences between member states and increase the overall level of convergence in innovation.

Full text

“Determining the key factors of the innovation gap between EU countries”
AUTH ORS
Maxim Polyakov
Igor Khanin
Gennadiy Shevchenko
Vladimir Bilozubenko
Maxim Korneyev
ARTICLE INFO
Maxim Polyakov, Igor Khanin, Gennadiy Shevchenko, Vladimir Bilozubenko and
Maxim Korneyev (2023). Determining the key factors of the innovation gap
between EU countries. Problems and Perspectives in Management, 21(3), 316-
329. doi:10.21511/ppm.21(3).2023.25
DOI http://dx.doi.org/10.21511/ppm.21(3).2023.25
RELEASED ON Tuesday, 15 August 2023
RECE IVED ON Thursday, 29 June 2023
ACCEPTED ON Friday, 04 August 2023
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This work is licensed under a Creative Commons Attribution 4.0 International
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JOURNAL "Problems and Perspectives in Management"
ISSN PRINT 1727-7051
ISSN ONLINE 1810-5467
PUBLISHER LLC “Consulting Publishing Company “Business Perspectives”
FOUNDER LLC “Consulting Publishing Company “Business Perspectives”
NUMBER OF REFERENCES
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NUMBER OF FIGURES
0
NUMBER OF TABLES
3
© The author(s) 2023. This publication is an open access article.
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Problems and Perspectives in Management, Volume 21, Issue 3, 2023
http://dx.doi.org/10.21511/ppm.21(3).2023.25
Abstract
Innovation plays a crucial role in ensuring economic growth and competitiveness of
national economies, creating conditions for their sustainable development. By focusing
on supporting innovation, the EU is particularly helping to accelerate the development
of those member states that lag far behind the EU average. is requires the selection
of the indicators reecting the development of innovation that determine the dier-
ences between member countries to the greatest extent. erefore, the aim of the study
is to identify the key factors of the innovation gap (FIG) between EU countries based
on a comparison of indicators characterizing the national innovation systems (NIS).
For this purpose, 22 relative indicators were selected from the indicators included in
the Global Innovation Index to form an array of empirical data. At the rst stage, the
EU countries were divided into four clusters using the k-means method. At the second
stage, using the decision tree method, a group of indicators was identied that together
distinguish the obtained clusters to the greatest extent and, accordingly, determine the
dierences between EU countries and can be considered as FIG, namely: “Researchers”,
“GERD nanced by business”, “Joint venture/strategic alliance deals”, “Soware spend-
ing”, and “High-tech manufacturing”. is allows individual member states to priori-
tize the development of those indicators (i.e. FIG) that most determine their position
in the EU and therefore improve their NIS. At the EU level, this will contribute to
the complementarity of the NIS, overcome dierences between member states and
increase the overall level of convergence in innovation.
Maxim Polyakov (USA), Igor Khanin (Ukraine), Gennadiy Shevchenko (Ukraine),
Vladimir Bilozubenko (Ukraine), Maxim Korneyev (Ukraine)
Determining the key
factors of the innovation
gap between EU countries
Received on: 29 of June, 2023
Accepted on: 4 of August, 2023
Published on: 15 of August, 2023
INTRODUCTION
In the modern economy, innovations are recognized as a preferred
factor for the growth and competitiveness of national economies, cre-
ating conditions for sustainable socio-economic development and
public well-being. e aggravation of economic, social, resource, and
environmental problems in recent years necessitates various trans-
formations and transition to new production and economic models,
which, along with rapid technological changes, increases the impor-
tance of innovations that will ensure overall prosperity in the future.
e EU, which is one of the world’s economic centers, focuses on building
an innovative, competitive economy capable of competing with dynam-
ically developing global players and gaining leadership. is requires the
unity of all twenty-seven member states around a common course of so-
cio-economic development, ensuring synchronized progress of member
states to improve the EU’s overall position in the global economic space.
e commitment of EU member countries to progress is closely linked to
innovations based on excellence, openness, high standards, human po-
tential development, ideas for protecting the planet, and other principles
© Maxim Polyakov, Igor Khanin,
Gennadiy Shevchenko, Vladimir
Bilozubenko, Maxim Korneyev, 2023
Maxim Polyakov, Doctor of Economics,
Associate Professor, Noosphere
Ventures Inc., Menlo Park, USA.
Igor Khanin, Doctor of Economics,
Professor, National University of Water
and Environmental Engineering,
Ukraine.
Gennadiy Shevchenko, Ph.D. in
Engineering Sciences, Associate
Professor, Association Noosphere,
Ukraine.
Vladimir Bilozubenko, Doctor of
Economics, Professor, University of
Customs and Finance, Ukraine.
Maxim Korneyev, Doctor of
Economics, Professor, University
of Customs and Finance, Ukraine.
(Corresponding author)
is is an Open Access article,
distributed under the terms of the
Creative Commons Attribution 4.0
International license, which permits
unrestricted re-use, distribution, and
reproduction in any medium, provided
the original work is properly cited.
www.businessperspectives.org
LLC “P “Business Perspectives”
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Sumy, 40022, Ukraine
BUSINESS PERSPECTIVES
JEL Classification C38, O38, O57
Keywords innovations, national innovation system, indicators,
clustering, classication analysis, factors of innovation
gap between countries, innovation policy, convergence
Conict of interest statement:
Author(s) reported no conict of interest

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of sustainable development. In this context, it is expected to ensure a high level of activity and achievements
in the eld of innovation, building ecient national innovation systems (hereinaer referred to in the sin-
gular and plural forms as NIS). To consolidate the EU member states, it is natural to reduce their dierenti-
ation in innovation, increase the level of convergence across the union, and agree on development strategies.
is is especially important for lagging member states to ensure accelerated development and increase their
contribution to the global competitiveness of the whole association.
e EU implements appropriate policies to overcome the so-called innovation gap among member
countries, which requires assessing and comparing the level of innovation development. Given the com-
plexity of modern NIS, which are described by a large set of dierent indicators, an eective solution
to this problem requires, among other things, identifying the specic factors that cause the innovation
gap. Standard statistical monitoring and existing comparative analysis and ranking approaches (e.g.,
European Innovation Scoreboard, EIS) do not allow for this to be fully realized, as they are not designed
to identify links between factors that may indicate such dierentiation. Considering the experience of
analytical research, it is advisable to use Data Mining methods, namely cluster and classication analy-
sis, which, in combination, allow identifying hidden patterns in large data sets, to determine the factors
of dierentiation between certain objects.
1. LITERATURE REVIEW
e EU unites a group of highly developed coun-
tries in the world that have powerful NIS, belong-
ing to the global leaders in the eld of innovations
(WIPO, 2022), as well as a number of countries
that act as moderate and emerging innovators.
(European Commission, 2023). Empirical studies
conrm the comprehensive socio-economic signif-
icance of innovations and their positive correla-
tion with economic growth indicators in practical-
ly all EU countries (Vetsikas et al., 2017; Maradana
et al., 2019). e mandatory focus on innovation in
the EU is proclaimed in the context of transition-
ing to sustainable development, for which the syn-
chronicity of progress among all member countries
is of utmost importance (Szopik-Depczyńska et
al., 2018; Shkarupa et al., 2020; Petrushenko et al.,
2021; Oharenko et al., 2021; Kostakis & Tsagarakis,
2022; Filatova et al., 2023).
e objectives of ensuring global competitiveness
in the EU have acquired collective signicance, spe-
cial content, and reached a supranational level, em-
phasizing increased attention to innovative activi-
ties (Ciocanel & Pavelescu, 2015; Kral & Janoskova,
2023; Kartika et al., 2023). First and foremost, this
concerns high-tech industries, where competition
and changes in global exports are directly linked
to innovative factors. Recognizing these sectors
as the main drivers of economic growth and em-
ployment, the EU actively supports the imple-
mentation of innovations to strengthen its overall
competitive positions in the global markets (Braja
& Gemzik-Salwach, 2020). e issues of competi-
tiveness, linked to adapting to systemic changes,
are closely intertwined with new trends in produc-
tion transformation, including the transition to
the “green economy” (Melnyk, 2016; Apak & Atay,
2015; Boros et al., 2023) and digitalization (Marti &
Puertas, 2023), where the innovation gap becomes
a crucial prerequisite, hindering the progress of the
entire union. At the global level, the EU competes
with powerful and rapidly developing players, par-
ticularly the USA and China. e issues of compet-
itiveness are linked to the problem of global leader-
ship and directly concern the sphere of innovations.
Comparing positions in the global markets for
high-tech goods and services reveals Europe’s rela-
tive weakness. erefore, the EU strives to increase
its economic power and level of competitiveness in
the global markets, which depends on successes in
the eld of innovations (Marčeta & Bojnec, 2020;
Melnyk, 2022).
To increase its level of competitiveness and achieve
global leadership, the EU needs synchronized
strengthening and implementation of the innova-
tive potential of individual member countries. In
this context, international comparisons allow iden-
tifying leaders and outsiders among the EU coun-
tries, determining the strengths and weaknesses of
each country, and accordingly identifying the com-
ponents of the NIS that need improvement and the

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parameters that need to be enhanced to improve
their positions. is will contribute to bridging the
gaps between countries at the level of the entire
union.
Given the history of expansion and the natural di-
versity of the EU’s economic landscape, the problem
of inequality between countries is signicant and
persistent. is is particularly evident in the eld of
innovations, which ultimately determines econom-
ic outcomes and societal well-being. Moreover, this
necessitates the identication of the FIG among
countries within the EU, i.e., the reasons for their
dierentiation and inequality, which allows us to
understand the dierences in NIS and identify
ways to bring countries closer together in terms of
qualitative and quantitative parameters of the in-
novation eld. In particular, this can be the basis
for accelerated development of those countries that
lag far behind the average level in the whole union
(Zabala-Iturriagagoitia et al., 2021). Given the spec-
icity of the innovation phenomenon and NIS, the
key problem is the evaluation of prerequisites and
the measurement of innovation activity outcomes.
is evaluation requires encompassing a broad set
of components of innovative potential and the ef-
fects of its utilization. Consequently, it necessitates
summing up a wide range of various specialized
parameters that characterize NIS based on the are-
as of its functioning (Barbero et al., 2021). Instead,
this makes it dicult to assess the level of inno-
vation development of countries in general, the ef-
fectiveness of the NIS and, even more so, relevant
comparisons between countries.
In global practice, a certain established set of indi-
cators has been formed to characterize the struc-
ture, dynamics, and eectiveness of NIS, which
are used to assess the level of innovation develop-
ment of a particular country. ese characteristics
are utilized in ocial statistics, and various con-
gurations are used to calculate composite indices.
For dierent assessment tasks and international
comparisons, multi-criteria analysis methods are
applied (Paredes-Frigolett et al., 2021; Carayannis
et al., 2018; Hamdan & Hussein, 2020; Dubyna et
al., 2023; Vávrová & Přečková, 2023), but it also
cannot provide answers to all the questions that
are necessary for the development of innovation
policy. Taking this into account, the EU has de-
veloped new approaches to statistical monitoring,
comprehensive indicators for assessing the lev-
el and eectiveness of innovation activity, which
are essential for comparing countries and making
managerial decisions (Janger et al., 2017). At the
same time, an assessment is carried out regarding
the degree of achieving specic strategic goals of
the EU related to innovations as a prerequisite for
growth, competitiveness, or certain transforma-
tions. Additionally, attention is focused on chang-
es in the level of convergence among Union coun-
tries, based on overcoming the innovation gap. For
this purpose, specialized analytical approaches
are mainly used, such as national and regional in-
novation scoreboards, comprehensive indices, and
rankings.
e NIS of dierent countries signicantly dier
from one another, which complicates the com-
parison of their potential (input indicators) and
performance (output indicators). Multi-criteria
comparison of the structure of innovation sys-
tems among EU countries, considering their het-
erogeneity, allows highlighting their unique char-
acteristics, strengths, and weaknesses, while also
raising the question of the possibility of integrat-
ing the NIS themselves (Cirillo et al., 2019). As for
the EU, it is necessary and appropriate to compare
the NIS between member states to understand the
correlation, state, and assessment of the dynamics
of development of the innovation systems of the
member states, and to determine the directions of
their eective interaction (mutual complementa-
tion). e innovation performance of the EU and
other global players can also be compared to po-
sition them competitively, set benchmarks and
build up certain parameters to overcome Europe’s
lagging behind (Jurickova et al., 2019).
To assess and compare NIS in the EU, a large sys-
tem of statistical monitoring of innovative activ-
ities has been established, and an annual EIS is
being prepared. Based on the summary of a set
of indicators, the EIS calculates the Summary
Innovation Index, which allows for the ranking of
member states, which are divided into four groups
(Innovation leaders, Strong innovators, Moderate
innovators, Emerging innovators). is is a rela-
tive comparison of the level of innovation devel-
opment of EU countries (as well as several other
European countries and global players), evaluat-
ing the performance and variability of their NIS.

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is allows individual countries to identify the
problems in the eld of innovation that are caus-
ing them to lag behind the leaders, enabling the
formulation of a more eective innovation pol-
icy (Bielińska-Dusza & Hamerska, 2021; Zabala-
Iturriagagoitia et al., 2021).
EIS has undoubtedly become a powerful approach
to statistical monitoring and a useful tool for de-
veloping innovation policy (Borrás & Laatsit,
2019). However, it provides only a supercial as-
sessment of the EU’s dierentiation in innovation,
while its underlying causes, i.e., the architecture of
leadership and lagging behind, remain unclear. At
the same time, addressing this issue is crucial for
bridging the innovation gap among EU countries,
the signicant magnitude and persistence of which
are conrmed by ocial EU statistics and other in-
ternational innovation indices. At the same time, it
is precisely the focus on bridging the innovation gap
that largely determines the content of the EU’s in-
novation policy measures, whose overall objective
is to promote convergence among member coun-
tries, supporting them while considering dierent
levels of development and individual challenges.
e solution to this task, by the way, involves ex-
panding the role of the EU and strengthening its
innovation policy (Kowalski et al., 2021), which re-
quires an appropriate analytical framework.
Intra-EU comparisons are particularly valuable for
member states that are lagging behind. A signicant
challenge for them is to approach the average level of
innovation indicators within the union, narrowing
the gap with leading and strong innovator countries.
To achieve this, outsider countries need to enhance
and accelerate the development of their NIS, align-
ing their eorts with the overall direction of the
EU (Sandu et al., 2015; Švarc & Dabić, 2021). In the
context of resource scarcity, this requires identify-
ing priority areas for improving the NIS (indicators),
which should be focused on to eectively improve
the position.
A separate area of international comparisons with-
in the EU is to identify the dierences between
candidate countries and member states, which
is particularly relevant in the eld of innovation.
Considering the economic and transformative
signicance of innovation, assessing this dier-
entiation helps narrow the gaps between candi-
date countries and the average level of indicators
among EU member states, creating conditions for
full integration. Comparing and utilizing the ex-
perience of EU countries allows candidate coun-
tries not only to develop their innovation potential
and align with the overall development course of
the EU but also to determine the optimal func-
tional positions of their R&D systems within the
entire union (Aytekin et al., 2022).
Earlier it was said about the objective need to com-
pare the EU with other global players, with respect
to which competition is vital. Such comparisons
make it possible, when dening the architecture
of global innovation leadership, to identify the
strengths and weaknesses of individual players,
determine the importance of certain factors as
triggers of progress, and highlight priority areas
for change in the current context. is helps the
EU to keep pace with the dynamic technological
and structural changes that are unfolding in the
world today and will determine the balance of
power in the economy of the future (Forge et al.,
2013; Vilaplana, 2020; Kowalski, 2020). e assess-
ment of the innovation gap between the EU, the
USA, and China is used to develop the innovation
systems of member countries, increase high-tech
exports, and facilitate technology transfer (Marxt
& Brunner, 2013).
In recent years, various international analytical
rankings have gained wide popularity, becom-
ing an integral part of monitoring and an impor-
tant basis for making management decisions. In
the eld of innovations, the most authoritative is
the Global Innovation Index (GII), which is pre-
pared by Cornell University, INSEAD, and WIPO
(Brás, 2023). e GII assesses various dimensions
of countries’ innovation systems, their innovation
competence and competitiveness. e primary
data that form the basis for the GII calculation
can be used in a certain set for other comparative
studies, expressing cause-and-eect combinations
in the eld of innovation (Yu et al., 2022; Huarng
& Yu, 2022).
us, there is a real need for the EU to identify the
main FIG of its member states, and overcoming
them will accelerate convergence, strengthen glob-
al competitiveness, and ensure overall socio-eco-
nomic progress. is is also an important task

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from the perspective of both the EU as a whole
and individual member states to improve the NIS
and increase the eectiveness of innovation policy,
especially for countries that are lagging behind.
2. AIM
Based on the comparison of indicators character-
izing the NIS, this study aims to identify the key
factors of innovation gap between EU countries.
3. METHODS
e EU, as an international organization built
on supranational integration, aims to promote
the development of science and technology. It
implements measures to support research and
innovations, improving conditions for their
dissemination in the economy and implemen-
tation. Specically, the EU develops infrastruc-
ture and funds R&D, including the Framework
Programmes for Research and Technological
Development, and creates mechanisms for inter-
national cooperation in research and innovation
at all levels (e.g., the European Research Area, the
Innovation Union). e EU focuses its policy on
supporting innovation activities at the sectoral
level, coordinating and complementing innova-
tion policies at the level of member countries. At
the supranational level in the eld of innovation,
the goal is to achieve convergence, which involves
aligning indicators of innovation activities en-
compassing all elements of R&D systems. is
concerns, rst and foremost, the improvement of
the performance of those countries that are signif-
icantly lagging behind , Moderate and Emerging
innovators according to the EIS, which is neces-
sary to improve the EU’s global position.
e innovation gap between countries is under-
stood as a generalization of their dierences in spe-
cic indicators that characterize the eld of innova-
tion and NIS. Reducing the level of dierentiation
(gap) in specic indicators leads to convergence.
e key factors of innovation gap (FIG) are those
indicators that are most related to the dierences
between all countries in a given set, i.e., they are
the main cause of inequality and determine the
level of dierentiation between countries.
e latest data characterizing the eld of innova-
tions across 132 countries worldwide are provided
by the aforementioned GII, which encompasses 81
indicators. Considering the dierent scales and dif-
culties of comparing the innovation systems of
EU countries, a group of 22 primary relative indica-
tors was selected from the general list of indicators
included in the GII to illustrate the proposed ap-
proach (the indicators calculated for the measure-
ment of the GII were not selected). ese indicators
primarily characterize the prerequisites for innova-
tion generation and only partially the eectiveness
of NIS. A comprehensive assessment of the innova-
tion performance of countries requires a somewhat
dierent range of outcome indicators, which is not
carried out in this study.
e list of indicators selected to characterize
the EU’s innovation eld is presented in Table 1.
Table 1. List of key indicators characterizing the
innovaon systems of EU countries (2022)
Source: Compiled by the authors based on WIPO (2022).
Variable Indicators
x1Expenditure on educaon, % GDP
x2Terary enrolment, % gross
x3Graduates in science and engineering, %
x4Researchers, FTE/mln pop. *
x5Gross expenditure on R&D, % GDP
x6Venture capital investors, deals/bn PPP$* GDP
x7Venture capital recipients, deals/bn PPP$* GDP
x8Knowledge-intensive employment, %
x9Firms oering formal training, %
x10 GERD* performed by business, % GDP
x11 GERD* nanced by business, %
x12 GERD* nanced by abroad, % GDP
x13 Joint venture/strategic alliance deals/bn PPP$* GDP
x14 Patent families/bn PPP$* GDP
x15 Intellectual property payments, % total trade
x16 High-tech exports, % total trade
x17 Patents by origin/bn PPP$* GDP
x18 PCT* patents by origin/bn PPP$* GDP
x19 Scienc and technical ar cles/bn PPP$* GDP
x20 Citable documents H-index
x21 Soware spending, % GDP
x22 High-tech manufacturing, %
Note: * FTE/mln pop. – full-time equivalent per million
population; bn PPP$ – billion US dollars purchasing
power parity; GERD – gross expenditure on research and
development; PCT – Patent Cooperation Treaty.
When evaluating the selected set of indicators, it is
necessary to note that they are heterogeneous, specif-
ic, and collectively allow for the coverage of various

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characteristics of the National Innovation System
(NIS) of a specic country. ere are no duplicate or
mutually exclusive indicators. Possible interrelation-
ships and mutual inuences among these indicators
are not considered in this study. Equal signicance
is attributed to the inuence of all the selected in-
dicators on the NIS. From a change perspective, all
indicators have the same direction towards maxi-
mizing, without saturation or minimum require-
ment. In general, it can be said that the obtained
set of indicators meets the conditions of consisten-
cy, comprehensiveness, and diversity in describing
the properties of the complex object – the National
Innovation System (NIS), and therefore, it can be
used for assessing the level and determining the
FIG among EU countries.
e comparison of indicators characterizing the
innovation systems of EU countries and the iden-
tication of factors causing their innovation gap
is intended to be carried out in two stages based
on addressing two basic Data Mining objectives –
clustering and classication.
e rst stage involves dividing the set of EU
countries into clusters, which means creating rela-
tively homogeneous groups.
e indicators presented in Table 1 form a feature
space for clustering. Prior to clustering the data
array, it is necessary to assess the clustering possi-
bilities, which can be done using 3D visualization,
particularly with a specialized tool available on
the scientic web portal ScienceHunter. Aer that,
it is advisable to determine the optimal number of
clusters using two tools – dendrogram and specif-
ic indices (Sum of Squared Errors Index, Davies-
Bouldin Index, Trace Index, Calinski-Harabasz
Index, Dunn Index, PBM Index). e correspond-
ing tools are also available on the mentioned web
portal.
Given the nature of the data, the widely recog-
nized k-means method (with the Euclidean dis-
tance metric) is proposed for clustering, which is
commonly used in economic research and is eec-
tive when data objects form suciently compact
clusters that are well separated from each oth-
er. e calculation methodology for the k-means
method is well-known and does not require ad-
ditional explanations in this article. e tools for
performing the relevant calculations are available
on the ScienceHunter web portal.
e second stage involves determining, based on
classication analysis, the indicators that contrib-
ute the most to the dierentiation of the obtained
clusters (classes). For classication, the data will
be mathematically processed using the logic-com-
binatorial method “decision trees” (Vasylenko &
Shevchenko, 1979) as it allows for the identication
of relatively small combinations of indicators with
maximum, if possible absolute, discriminating
power, indicating the most signicant dierences
between clusters and, accordingly, dierentiation
between countries. Considering the essence of the
classication objective, the indicators that strongly
dierentiate the clusters can be considered as the
FIG among countries.
e basis for classication is the sampling set,
formed by an array of empirical data constructed
from Table 1, with countries divided into clusters
(classes) obtained during the clustering process in
the rst stage. e assessment of the discriminative
capability (quality) of the sampling set and each of
the indicators included in it, followed by the identi-
cation of the FIG, is carried out using the relevant
tools available on the ScienceHunter web portal.
e discriminative capability of the FIG is deter-
mined using the following formula:
( )
1
1
,..., max ,
Y
i ij YY
m
Vx x km
∆
∆∈Γ

=

∑
(1)
where
k
is the number of classes (clusters),
Y
m
is
the number of objects belonging to class (cluster)
,Y
( )
12
, ,..., 0 1 ,
i i ij ij ij
tt t t k∆= ≤ ≤ −
1,...,j= Γ
means the arbitrary set of parameter values
( )
1
,..., 1 ,
i ij
xx n≤Γ≤
Y
m∆
denotes the number
of sampling sets of the
m
class, for which the rela-
tion
( )
1,...,
ij ij
x tj= = Γ
is performed,
ij
t
are the
values of parameters
ij
x
in the set of
,∆
Γ
means
variety of all sets of parameter values
1,..., .
i ij
xx
When there is a complete separation (dierence)
between classes, this evaluation takes on the max-
imum value of 1 (Vasylenko & Shevchenko, 1979).
It is essential to note that such an evaluation is
directly calculated from the sampling set. If mul-
tiple groups of indicators with suciently high
discriminative capability are identied, which can
be considered as part of the FIG, two approaches

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can be applied: First, selecting one primary group
with the maximum discriminative capability, and
second, creating a unied list of characteristics
from these groups based on repetitions.
4. RESULTS
Aer processing the empirical data represented as
a feature space based on the prepared list of indi-
cators (Table 1) and conducting the corresponding
calculations, the set of 27 EU member countries
was divided into four clusters (determined as the
optimal number of clusters). e results of clus-
tering of EU countries are presented in Table A1.
Clustering provides broad possibilities for analy-
sis. First, this is an assessment of the level of in-
novation development of each country relative to
each other and, accordingly, to each of the result-
ing clusters of countries, considering, for example,
the arithmetic mean. In terms of the geography of
innovations in the EU, the obtained clusters char-
acterize the concentration of innovation potential
in certain groups of countries (dierent regions of
Europe). Additionally, innovation centers can be
identied within these clusters (for example, lead-
ing countries), and specic indicators can explain
the distribution of particular resources or activ-
ities that require further investigation. ese ob-
tained clusters can be further compared with the
assessments of the EIS (European Commission,
2023). Each of the clusters of EU countries has its
own distinctive features, namely:
• Cluster I is formed by countries such as
Denmark, Finland, and Sweden, in other words,
it brings together some of the most successful
EU countries that demonstrate the highest level
of science, education, and the technology sec-
tor, and are leaders in transformations related
to sustainable development. is accounts for
their corresponding high positions in the eld
of innovation, localized in Northern Europe.
is is conrmed by the EIS where Sweden,
Finland, and Denmark belong to the highest
category of “innovation leaders” and occupy
the top three positions in the ranking.
• Cluster II is predominantly formed by countries
from Western Europe, namely Austria, Belgium,
France, Germany, Ireland, Luxembourg,
Netherlands, as well as Portugal and Slovenia.
ese countries have a balanced, sustainable
economy, a well-developed technological sec-
tor, and an innovative system. Many of them
are EU leaders in innovation and modern eco-
nomic development trends. According to the
EIS, Netherlands and Belgium belong to the
category of “innovation leaders”, while Austria,
Ireland, Luxembourg, Germany, and France
belong to the second level – “strong innovators”
(however, Cyprus from this group did not enter
cluster II, presumably due to relatively low in-
dicators of innovation potential). Portugal and
Slovenia are classied as “moderate innovators”
in the EIS. From a geographical perspective,
cluster II obtained in this study clearly indicates
that the “core” of the EU’s innovation economy
is concentrated in Western Europe.
• Cluster III is formed by relatively successful
countries from dierent regions of Europe,
namely, the Czech Republic, Estonia, Greece,
Hungary, Lithuania, Poland, Slovakia, and
Spain. ese countries have a reasonably de-
veloped economy, predominantly positive dy-
namics, and signicant achievements in the
eld of innovations. However, they need to al-
locate more resources to the development of
their innovation systems, focusing on the key
FIG that will be further selected. According
to the EIS, the Czech Republic, Estonia,
Lithuania, Greece, and Spain are appropriate-
ly classied as “moderate innovators,” while
Hungary, Poland, and Slovakia belong to the
lower-level group of “emerging innovators”
(these countries are increasing their innova-
tion potential, which has determined their
placement in cluster III in this study).
• Cluster IV is formed by countries with rel-
atively low indicators in the eld of inno-
vations, namely, Bulgaria, Croatia, Cyprus,
Italy, Latvia, Malta, and Romania. From a
geographical perspective, the cluster encom-
passes countries from Southern, Central, and
Eastern Europe, which have recently become
members of the EU and are lagging behind in
building a modern innovation system. ese
countries need the highest dynamics, primar-
ily in terms of the indicators that will be se-
lected as FIG, and, accordingly, the greatest

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support from the EU. According to the EIS,
Cyprus belongs to the group of “strong inno-
vators” (probably due to relatively high-per-
formance indicators, whereas this research fo-
cuses on potential indicators), while Italy and
Malta belong to the group of “moderate inno-
vators” (likely for similar reasons as Cyprus).
Bulgaria, Croatia, Latvia, and Romania are
classied into the expected groups of “emerg-
ing innovators”.
Aer dividing the EU member states into clusters
(classes) based on indicators characterizing the eld
of innovations, the second stage involved data clas-
sication processing. e quality check of the en-
tire training dataset, meaning its overall resolution
capacity, showed a maximum of 100%. erefore,
combinations of indicators should be selected,
whose resolution capacity is close to absolute. As
a result of using the corresponding computational
tools available on the ScienceHunter web portal, two
combinations of indicators with the highest resolu-
tion capacity were obtained, i.e., FIG, with a maxi-
mum of four indicators in each combination: rst
– 4, 11, 13  22 (resolution capacity – 92.89%); sec-
ond – 4, 13, 21  22 (resolution capacity – 93.21%).
Considering that three indicators are present in
both combinations, obviously being the most signif-
icant, eliminating duplication, the obtained indica-
tors were combined into a single list, namely:
• 4 “Researchers” (FTE/mn pop.) – this indicator
assesses the number of professionals (full-time
employment per million population) engaged
in research and development activities and ac-
tively involved in improving or developing con-
cepts, theories, models, technologies, instru-
ments, soware, or work methods, essentially
contributing to the creation of new knowledge.
is factor is extremely important, as it charac-
terizes the potential for R&D and, accordingly,
the ability to generate new knowledge in terms
of human resources;
• 11 “GERD nanced by business” (%) – this
indicator assesses gross R&D expenditures
funded by commercial enterprises as a per-
centage of total gross R&D expenditures, re-
ecting the relative scale of the resources and
activities involved. e signicance of this in-
dicator lies in its characterization of the level
of business involvement in the eld of inno-
vation, its overall innovative activity, and the
generation of new knowledge through R&D
for further transformation into innovations;
• 13 “Joint venture/strategic alliance deals” (bn
PPP$ GDP) – this indicator assesses the num-
ber of deals related to the creation of joint ven-
tures/strategic alliances per billion dollars of
GDP (PPP-adjusted). It characterizes the rela-
tive intensity of cooperation among companies
in terms of the scale of deals in the form of joint
ventures (where companies create a single legal
entity through a merger) and strategic alliances
(where companies work together without cre-
ating a legal entity), for example, in the devel-
opment and market promotion of innovations.
Companies combine their potentials, which in-
creases the likelihood of successful implementa-
tion of innovative projects;
• 21 “Soware spending” (% GDP) – this indi-
cator estimates total soware costs, which in-
clude the cost of purchased or leased soware
packages, such as operating systems, database
systems, programming tools, utilities, and ap-
plications as a percentage of GDP (this does
not include expenses related to in-house so-
ware development or soware development
for users under outsourcing arrangements).
is indicator is of utmost importance in
the context of the emerging digital economy,
which necessitates and opens up a signicant
new eld for implementing innovations relat-
ed to digital transformations;
• 22 “High-tech manufacturing” (%) – this in-
dicator assesses the level of development of
the modern high-tech sector by determining
the share of the total volume of high-tech and
medium-high-tech products in the total out-
put of the manufacturing industry. For this
purpose, the OECD classication “Denition
of Technology Intensity” is used based on the
International Standard Industrial Classication
and data from the United Nations Industrial
Development Organization (INDSTAT-2 and
INDSTAT-4 databases). e indicator is criti-
cally important as high-tech manufacturing is a
special source of economic growth, generating
the highest GDP multiplication. In the context

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of the Fourth Industrial Revolution, high-tech
manufacturing is characterized by active imple-
mentation of innovations, intensies science
and education, creates preconditions for the
growth of the service sector, and thus acts as a
“locomotive” for the development of innovations
in the economy.
e selected set of indicators explains the reasons
for dierentiation and innovation gap among the
EU countries, which means the barriers to achiev-
ing convergence. is contributes to a deeper un-
derstanding and enables the appropriate quantita-
tive assessment of the innovation gap, for example,
based on the calculation of minimum, average,
and maximum values (Table 2).
It is important to focus on understanding the fol-
lowing. First, due to the wide range of vectors for
the development of National Innovation Systems
(NIS) and limited resources available to coun-
tries, there is a need for targeted concentration of
resources on key areas, which are precisely deter-
mined by FIG. ese indicators can be considered
as a priority and should be increased primarily
through the appropriate concentration of resourc-
es and eorts, which will allow a particular coun-
try to improve its position in this aggregate more
eectively. Second, the identied FIG give a general
idea of the structure of “innovativeness” of individu-
al countries, show the architecture of leadership in a
given set of countries, allow identifying comparative
advantages and determining the possible specializa-
tion of certain countries, and assess the compati-
bility of their NIS at the EU level. However, in the
context of studying the innovation gap between EU
countries, the selection of a specic set of key indi-
cators is only a working hypothesis. is initial stage
should be followed by a fundamental analysis of why
these indicators have become dierentiating factors,
what is the specicity of each of them in specic
countries and in the EU as a whole, what underly-
ing patterns they reect, etc. Only then is it possible
to achieve a deep understanding of the situation for
strategic decision making.
5. DISCUSSION
e obtained research results can be used in the
management practice of improving the NIS and
for shaping innovation policy at the level of mem-
ber states and the EU as a whole, as well as serve as
a basis for various analytical and scientic studies.
e use of the proposed methodology in dynamics
makes it possible to form a mechanism for para-
metric adjustment of goals and target indicators of
innovation policy, identify breakthrough points to
eliminate the weaknesses of a particular NIS, thus
acting at the forefront of problems and within the
framework of the real external situation.
e proposed methodology is especially impor-
tant for EU countries that follow the leaders and
signicantly lag behind, as well as for EU institu-
tions seeking to ensure convergence among mem-
ber countries and achieve sustainability of overall
progress. For countries that need to improve their
positions, this methodology allows a clear under-
standing of the problems and limitations of their
innovation systems and helps them focus on en-
hancing priority parameters. As a result, it estab-
lishes a connection between innovation policy and
the current context, ensuring its adaptability to
respond to the changing situation within the EU
countries collectively. For the systematic adjust-
ment of innovation policy at the national level, it is
necessary to establish corresponding managerial
mechanisms and tools to inuence NIS based on
specic indicators. e application of the meth-
Table 2. Minimum (min), average (aver.) and maximum (max) values of the indicators idened as FIG
for the obtained clusters of EU countries
Indicator
(FIG)
Value of indicators
Cluster I Cluster II Cluster III Cluster IV
min aver. max min aver. max min ave r. max min av er. max
х47527,40 7716,67 7930,40 4769,10 5285,47 5911,70 3109,20 3704,59 4358,10 952,90 2058,34 2671,8 0
х11 54,30 58,77 62,40 50,10 5 7,89 64,50 34,00 44,41 52,9 0 24,30 43,59 58,7 0
х13 0,20 0,23 0,30 0,00 0,08 0,20 0,00 0,01 0,10 0,00 0,09 0,40
х21 0,50 0,50 0,50 0,10 0,46 0,60 0,10 0,34 0,60 0,10 0,26 0,60
х22 44,60 4 7,23 48,80 16,30 43,93 58,50 17, 0 0 39,90 61,50 15,00 28,31 43,50

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odology for selecting FIG as priority development
directions in the eld of innovation can become
a part of specialized strategic programs aimed at
overcoming the lagging position of a particular
country and implementing specic scenarios for
accelerating the development of innovation sys-
tems in dierent countries.
At the EU level, the presented methodology for
identifying the FIG can be applied not only to en-
sure the convergence of countries in the eld of in-
novation, but also to determine the advantages of
their specialization and, accordingly, the areas of
cooperation, complementarity, and integration of
the innovation systems of the member states. e
obtained results can strengthen the basis for jus-
tifying supranational support measures for indi-
vidual countries to target the improvement of NIS
indicators in a particular group of countries to
achieve appropriate collective change. In addition,
the proposed combination of cluster and classi-
cation analysis makes it possible to describe the
EU’s innovation landscape and spatial problems in
terms of innovation development, complementing
the current statistical monitoring system. In ad-
dition to recommendations on supranational sup-
port for innovation, the proposed methodology
can be used to compare the EU with other global
players, which will allow for a better understand-
ing of the directions of intensifying its innovation
development to be at the forefront of technology
and strengthen competitiveness.
e resulting clustering of EU countries and the
identied FIG are an objective but static study. e
dynamic approach involves systematic, for exam-
ple, annual (in particular, at the beginning and end
of the year) repetition of the cluster-classication
analysis, which will allow assessing relevant chang-
es and identifying trends in the countries’ innova-
tion systems. If the proposed approach is used an-
nually, the selected indicators can be considered as
triggers for tactical transformations of the NIS. e
presented methodology for nding FIG can also be
used for national regions at the scale of countries or
the EU as a whole in specic sectors of innovation
(digital, environmental, social innovation, etc.). For
EU candidate countries, this approach allows for
comparisons with EU member states and identies
the main areas for approximation to the EU’s inno-
vation performance, which can be seen as the basis
for a policy of catch-up development.
CONCLUSION
Considering that innovations are the key driver of sustainable economic growth and development and
play a crucial role in increasing competitiveness and societal well-being, the EU aims to strengthen the
innovative economy in all member states. is implies ensuring their convergence, bridging the so-
called innovation gap to achieve overall progress, which is based on the identication of key FIG.
To address this objective, a set of 22 indicators characterizing the innovation systems of EU countries
has been formed, primarily focusing on their potential for generating innovations. Additionally, an array
of empirical data was used for calculating the GII. e developed methodology involves the use of data
mining techniques and includes two stages. At the rst stage, clustering was performed (k-means method,
Euclidean distance metric), as a result of which the EU countries were divided into four clusters (class-
es), representing a relative characteristic of the level of development of their NIS. At the second stage, a
classication analysis (the decision tree method) was performed, which resulted in the identication of a
group of indicators that most strongly divide the obtained clusters and can be considered as FIG, namely,
“Researchers”, “GERD nanced by business”, “Joint venture/strategic alliance deals”, “Soware spending”,
and “High-tech manufacturing”. ese indicators determine innovation leadership in the EU as a whole
to the greatest extent and can therefore be seen as priorities for improvement. e obtained results provide
broad analytical opportunities for improving the NIS, serve as a basis for shaping the innovation policy of
member states and making tactical management decisions at the EU level. Future research in this area is
planned to identify the factors of the innovation gap between the EU and other global players, to expand
the range of analyzed indicators, especially through the parameters of innovation performance, and to
develop a methodology for long-term assessment of NIS development based on the proposed approach.

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Problems and Perspectives in Management, Volume 21, Issue 3, 2023
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AUTHOR CONTRIBUTIONS
Conceptualization: Maxim Polyakov, Igor Khanin, Gennadiy Shevchenko, Vladimir Bilozubenko,
Maxim Korneyev.
Data curation: Gennadiy Shevchenko, Vladimir Bilozubenko.
Formal analysis: Maxim Polyakov, Gennadiy Shevchenko, Vladimir Bilozubenko, Maxim Korneyev.
Investigation: Igor Khanin, Vladimir Bilozubenko, Maxim Korneyev.
Methodology: Gennadiy Shevchenko, Vladimir Bilozubenko.
Project administration: Maxim Polyakov, Igor Khanin.
Resources: Maxim Korneyev.
Soware: Gennadiy Shevchenko.
Supervision: Maxim Polyakov, Igor Khanin, Gennadiy Shevchenko, Maxim Korneyev.
Validation: Vladimir Bilozubenko, Maxim Korneyev.
Writing – original dra: Gennadiy Shevchenko, Vladimir Bilozubenko, Maxim Korneyev.
Writing – review & editing: Maxim Polyakov, Igor Khanin.
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APPENDIX A
Table A1. Clusters of EU countries by indicators characterizing their innovaon systems (2022 data)
Source: Obtained by the authors through calculations.
Clusters Countries Indicators (numbering according to Table 1)
x1x2x3x4x5x6x7x8x9x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22
I
Denmark 6,8 81,8 23 7692,2 3,0 0,3 0,1 4 8,7 40,6 1,8 59,6 0,2 0,2 4,7 0,8 5,8 10,6 4,2 65,6 51,3 0,5 48,3
Finland 6,3 93 27, 9 7527,4 2,9 0,2 0,1 47,2 50,2 2,0 54,3 0,4 0,2 6,0 1,0 4,6 12,7 6,5 55,5 42,6 0,5 44,6
Sweden 7, 6 77,3 27, 0 7930,4 3,5 0,3 0,1 56,7 61,9 2,6 62,4 0,3 0,3 6,8 2,9 7,8 10,9 7,3 5 7,7 59,5 0,5 48,8
Average for cluster I 6,9 84,0 26,0 7716,7 3,1 0,3 0,1 50,9 50,9 2,1 58,8 0,3 0,2 5,8 1,6 6,1 11,4 6,0 59,6 51,1 0,5 4 7, 2
II
Austria 5,2 86,5 30,6 5751,6 3,2 0,2 0,1 43,5 42,6 2,2 50,1 0,5 03,5 0,8 7, 3 9 3 4 0,6 44,2 0,5 45,8
Belgium 6,4 80,1 17,6 5750,1 3,5 0,2 0,1 49,6 57, 8 2,5 64,3 0,5 0,1 2,5 0,8 8,3 5,5 2,1 42,2 53,8 0,6 44,2
France 5,4 68,4 25,9 4926,2 2,4 0,2 0,1 47, 4 6 7,9 1,6 56,7 0,2 0,1 3,0 1,5 11,2 7,7 2,2 25,5 78,6 0,5 52,1
Germany 5,0 73,5 35,8 5393,1 3,1 0,2 0,1 45,7 68,4 2,1 64,5 0,2 0,1 5,2 1,0 11,7 15 3,6 2 7,7 8 7,4 0,5 56,8
Ireland 3,4 75,2 26,4 4769,1 1,2 0,2 0,1 47,3 59, 8 0,9 62,8 0,2 0,1 2,1 20,2 9,0 2,2 1,5 20,5 34,9 0,6 58,5
Luxembourg 3,6 18,4 19,2 4920,3 1,1 1,4 0,1 63,6 6 6,1 0,6 51,3 00,2 4,3 4,0 0,5 7, 1 4,2 20,7 11,6 0,2 16,3
Portugal 4,7 67, 9 27, 8 5214,8 1,6 0,1 042,7 29,0 0,9 52,2 0,1 00,6 0,9 3,9 2,7 0,7 53,4 33,1 0,6 30,5
Slovenia 4,9 7 7,9 28,6 4932,3 2,1 0 0 4 7,5 44,0 1,6 61,5 0,3 01,1 0,6 6,5 4,4 1,1 59,7 18,8 0,1 41,4
Netherlands 5,4 87,1 18,8 5911,7 2,3 0,3 0,1 52,4 5 4,1 1,5 5 7,6 0,2 0,1 4,4 7,9 13,0 8,5 3,8 44,2 69,8 0,5 49,8
Average for cluster II 4,9 70,6 25,6 5285,5 2,3 0,3 0,1 48,9 54,4 1,5 5 7,9 0,2 0,1 3,0 4,2 7, 9 6,9 2,5 37,2 48,0 0,5 43,9
III
Czech
Republic 4,3 65,6 25,9 412 7,9 2,0 0,1 040,6 43,6 1,2 35,6 0,6 00,5 0,8 23,8 2,0 0,6 37, 6 30,4 0,3 6 0,1
Estonia 5,3 74, 2 27,5 3846,1 1,8 0,7 0,4 48,2 40,7 1,0 49,1 0,2 0,1 0,6 0,3 2,9 1,6 1,0 46,9 1 7,9 0,2 30,6
Greece 3,6 148,5 27, 3 4010,4 1,5 0,1 031,7 21,6 0,7 40,2 0,2 00,4 0,4 3,1 1,7 0,3 42,8 33,8 0,6 18,1
Hungary 4,6 52,4 15,5 4358,1 1,6 0 0 38,9 29,3 1,2 52,9 0,2 00,4 1,1 14,9 1,7 0,3 26,6 29,6 0,3 59,8
Lithuania 3,9 72,0 26,0 3728,5 1,2 0,2 0,1 45,3 27,5 0,6 34 0,3 00,3 0,2 6,8 1,3 0,4 29,4 13,0 0,1 1 7,0
Poland 4,6 69,2 19,4 3292,2 1,4 0 0 41,4 21,7 0,9 5 0,7 0,1 00,3 1,2 6,4 3,5 0,3 28,0 36,8 0,3 34,1
Slovakia 4,0 46,4 22,2 316 4,3 0,9 0 0 3 7,6 43,3 0,5 43,7 0,1 00,1 0,7 8,8 1,5 0,2 26,9 17, 0 0,3 61,5
Spain 4,2 92,9 20,8 3109,2 1,4 0,1 035,5 55,2 0,8 49,1 0,1 00,6 1,4 4,4 1,8 0,8 38,8 61,7 0,6 38,0
Average for cluster III 4,3 7 7,7 23,1 3704,6 1,5 0,2 0,1 39,9 35,4 0,9 44,4 0,2 0,0 0,4 0,8 8,9 1,9 0,5 34,6 30,0 0,3 39,9
IV
Bulgaria 4,1 73,4 19,5 2402, 3 0,9 0 0 33,4 20,0 0,6 3 7,6 0,3 00,2 0,6 5,6 1,8 0,2 16,5 15,4 0,2 23,6
Croaa 3,9 67,7 28,5 2220,0 1,2 0 0 36,4 26,2 0,6 3 7,6 0,3 00,1 1,1 4,2 1,2 0,3 40,5 17,3 0,1 24,5
Cyprus 5,7 88,5 13,1 1706,1 0,8 1,3 0,1 38,0 39,7 0,4 36,4 0,2 0,2 0,9 1,3 0,9 1,9 1,4 58,2 12,3 0,2 15,9
Italy 4,3 66,1 2 2,7 2671,8 1,5 0 0 35,8 12,6 0,9 55,9 0,1 01,7 0,8 6,8 6,0 1,3 33,9 68 ,7 0,6 39,5
Latvia 4,2 94,9 19,3 2158,8 0,7 0,1 0,1 44,5 52,9 0,2 24,3 0,2 00,3 0,2 9,2 2,0 0,6 21,6 9,2 0,1 15,0
Malta 4,7 64,9 1 7,2 2296,5 0,7 0,6 0,1 46,2 49,9 0,4 58,7 00,4 1,6 6,1 4,3 3,1 1,9 24,8 6,9 0,3 36,2
Romania 3,3 51,4 2 9,1 952,9 0,5 0 0 27,2 20,5 0,3 54,6 0,1 00,1 0,9 7, 1 1,5 015,3 18,9 0,3 43,5
Average for cluster IV 4,3 72,4 21,3 2058,3 0,9 0,3 0,0 37,4 31,7 0,5 43,6 0,2 0,1 0,7 1,6 5,4 2,5 0,8 30,1 21,2 0,2 28,3