=Paper=
{{Paper
|id=Vol-3179/Paper_11.pdf
|storemode=property
|title=Application of Cluster Analysis for Condition Assessment Banks in Ukraine
|pdfUrl=https://ceur-ws.org/Vol-3179/Paper_11.pdf
|volume=Vol-3179
|authors=Hrygorii Hnatiienko,Volodymyr Domrachev,Volodymyr Saiko,Tatyana Semenenko,Violeta Tretynyk
|dblpUrl=https://dblp.org/rec/conf/iti2/HnatiienkoDSST21
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==Application of Cluster Analysis for Condition Assessment Banks in Ukraine==
https://ceur-ws.org/Vol-3179/Paper_11.pdf
Application of Cluster Analysis for Condition Assessment of
Banks in Ukraine
Hrygorii Hnatiienkoa, Volodymyr Domracheva, Tetiana Semenenkob, Volodymyr Saikoa and
Violeta Tretynykc
a
Kiev National University named by Taras Shevchenko, Volodymyrska St, 60, Kiev, 01033, Ukraine
b
Sumy State University, Ryms'koho-Korsakova St, 2, Sumy, 40000, Ukraine
c
Igor Sikorsky Kyiv Polytechnic Institute, Peremohy Ave, 37, Kiev, 03056, Ukraine
Abstract
The International Monetary Fund estimates that the coronavirus pandemic could cause a
deeper global recession than the economic downturn triggered by the 2008-2009 financial
crisis. Uncertainty about the duration of the pandemic and unpredictability of the scale of its
consequences provokes the search for ways not only to counter the threats of economic
downturn, but also ways to economic growth and promote innovation in the difficult times of
the pandemic. With this in mind, this article will analyze the application of cluster analysis to
assess the state of banks. The problem of bank clustering is classified as ill-structured. Expert
technologies and tools of artificial intelligence should be used to solve it. At the preliminary
stage of the research, expert technologies are used, on the basis of which a subset of banking
performance indicators is determined, which are essential for the decision on clustering. In
addition, the characteristics of the banks that most influence the cluster analysis are
selected.The authors propose to use an analysis based on the construction of clusters from the
main indicators that characterize the activities of banks instead of analyzing the risks of
banks, based on the calculation of economic standards. Prospects for improving methods of
regulating the activities of banks in Ukraine are considered.
Keywords1
banking operations, cluster analysis, risk, liquidity, capital adequacy, economic standard,
expert technologies, ill-structured problem
1. Introduction
The current state of Ukraine's economy is characterized by growing economic risks. For the
second year in a row, the world is in a state of quarantine, which is replaced from time to time by
stricter restrictive measures - national or local lockdowns, or, conversely, short-term mitigation when
schools, kindergartens, restaurants, cinemas, etc. open. Banks, as a result of non-repayment of loans
provided by firms for the purchase of goods, significantly reduced profits, reduced return on assets
and capital. The liquidity of the banking sector decreased. In order to maintain the liquidity of banks,
the National Bank began to fill the economy with money supply, which, in turn, provoked rising
inflation. Creating a developed and perfect model of state regulation of the national banking system
occupies a prominent place in the set of tasks for effective management of the banking sector and the
economy as a whole. The search for new tools aimed at improving the efficiency of the banking
system is becoming especially relevant today. Recently, there has been an adaptation of the banking
system to the economic situation through the use of regulatory mechanisms, which are due to the
limitation of risks due to economic standards. The most modern mathematical methods are used to
analyze banking risks. Information is the 21st Century gold, and financial institutions are aware of
Information Technology and Implementation (IT&I-2021), December 01–03, 2021, Kyiv, Ukraine
EMAIL: g.gna5@ukr.net (Hrygorii Hnatiienko); mipt@ukr.net (Volodymyr Domrachev); t.semenenko@uabs.sumdu.edu.ua (Tetiana
Semenenko); vgsaiko@gmail.com (Volodymyr Saiko); viola.tret@gmail.com (Violeta Tretynyk)
ORCID: 0000-0002-0465-5018 (Hrygorii Hnatiienko); ORCID: 0000-0002-0624-460X (Vladimir Domrachev); ORCID: 0000-0002-1308-
224X (Tatyana Semenenko); ORCID: 0000-0002-3059-6787 (Vladimir Saiko); ORCID: 0000-0002-3538-8207 (Violeta Tretynyk)
©️ 2022 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
112
this. Armed with machine learning and artificial intelligence technologies, they have the opportunity
to analyze data that originates beyond the bank office. Financial companies collect and store more and
more user data in order to revise their strategies, improve user experience, prevent fraud, and mitigate
risks [1-4]. In this article, we will talk about how Artificial Intelligence and Machine Learning are
used as well as the benefits and risks of these solutions [5-8].
The purpose of the paper is to analyze the possibility of using cluster analysis to assess the state of
banks. In addition, the possibilities of using expert decision-making technologies [9-11] to increase
the efficiency of the mathematical apparatus of data clustering [12-14], which is planned to be used to
determine the similarity of banking institutions [15, 16].
2. Research results
All manifestations of financial instability can be classified into three types: banking crises;
currency crises; crises in financial markets [5]. By instability we mean the ability of the financial
system to influence the amplitude of the economic cycle. There are a number of reasons for this, not
the least of which are credit issues. As in the theory of macroeconomic analysis, and in practice, there
is a simple trend of active growth of loans during periods of economic recovery and a sharp decline
during periods of decline. Scientists identify a number of reasons that cause banking crises. These are
market risks, liquidity shocks, asset quality, and so on.
Active state intervention remains a bottleneck for the Ukrainian banking system. There are two
forms of state regulation: direct - the direct influence of the state on aggregate supply and demand
through the creation of the public sector and redistribution of income; indirect - indirect influence of
the state through the functioning of credit, financial and tax systems. One way or another, the
government is responsible for all the processes taking place in the country. In terms of the studied
problem, we note that the regulation of the financial stability of the banking system involves the use
of a special set of tools at the stage of responding to negative trends in the functioning of the banking
system. This is especially important in times of financial instability in the world economy. Almost all
banking operations are risky. There are both general and specific reasons for this.
Analysis of current risks of commercial banks in Ukraine shows that their condition is affected by
the general economic crisis, unstable political situation in the country, incomplete formation of the
banking system, as well as the absence or imperfection of some basic legislation and even the
discrepancy between the legal framework and the real situation. Among the most significant external
factors are changes in bank interest rates, inflation, changes in lending conditions, changes in tax rates
and customs duties, changes in labor laws and more.
The ability to adequately respond to risk leads the bank to make a profit in the future and,
conversely, the desire to make a profit puts the bank in a condition of acceptance of a risk. If one risky
operation is successful, the profit from it can be so significant that it covers the losses from other
small risky operations for a long time. The Basel III standard (2010) offers an international system for
assessing liquidity risks, standards and monitoring and strengthens banks' capital requirements in
order to prevent an international credit crisis.
2.1. Systematic assessment of banking risks
According to the Guidelines for Banking Inspection "Risk Assessment System" [17], banking risks
are defined as the probability that events, expected or unexpected, may have a negative impact on the
capital and / or income of the bank. These risks arise from the specifics of banking activities carried
out in market conditions, and mean the probability of receiving income less than expected, a decrease
in the value of assets. Increased banking risks lead to significant financial losses and, as a
consequence, to the bankruptcy of banks. From the bank's point of view, risk is the potential for loss
of income or a reduction in the market value of a bank's capital due to the adverse effects of external
or internal factors. Such losses may be direct (loss of income or capital) or indirect (restrictions on the
bank's ability to achieve its business goals). In order to conduct banking supervision, the National
Bank of Ukraine has identified nine categories of risk, namely: credit risk, liquidity risk, interest rate
risk, market risk, currency risk, operational and technological risk, reputation risk, legal risk and
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strategic risk. These types of risks are not mutually exclusive. Any banking product or service can
expose a bank to several risks.
According to the Instruction on the procedure for regulating the activities of banks in Ukraine [18],
the bank's liquidity is the bank's ability to ensure timely fulfillment of its monetary obligations, which
is determined by the balance between maturity and amount of placed assets and terms and amounts of
bank obligations. also terms and amounts of other sources and directions of use of means (granting of
loans, other expenses).
The Committee on Supervision and Regulation of Banking, Supervision (Oversight) of Payment
Systems has defined new criteria for certain groups of banks for 2016. This is stated in the decision of
the Committee of December 31, 2015 № 657. According to the document, the following groups are
provided: banks with a state share (in which the state owns a share of more than 75%); banks of
foreign banking groups (banks, owners of controlling stakes in which are foreign banking
institutions); group I (banks, the share of assets of which is more than 0.5% of the assets of the
banking system); group II (banks whose share of assets is less than 0.5% of the assets of the banking
system).
One of the main indicators of the state of the bank is capital adequacy. This indicator reflects the
possibility of covering the share capital of the credit institution's risky assets. The amount of capital
determines the volume of active operations of the bank, the size of the deposit base, the ability to
borrow funds in financial markets, maximum loans, the size of the open currency position and a
number of other important indicators that significantly affect the bank [19].
Under Basel II, capital, which has been identified by supervisors as a source of contingency losses,
consists of three levels of capital. Tier 1 capital, so-called fixed capital, includes share capital and
retained earnings, and tier two capital includes additional capital. Banking institutions can also attract
short-term subordinated borrowings, ie third-tier capital, which they can use to meet the requirements
of bank capital adequacy.
The National Bank of Ukraine issued a Resolution “On Approval of the Regulations on the
Organization of the Risk Management System in Banks of Ukraine and Banking Groups”, in which it
recommended banks to introduce internal bank documents on risk management, implement measures
to implement requirements and develop appropriate software. The main risks of banks are the risk of
insufficient capital to cover possible losses and liquidity risk, which is associated with the inability of
the bank to meet its obligations to customers.
During the COVID-19 pandemic in Ukraine, the liquidity of the banking sector decreased. In order
to maintain the liquidity of banks, the National Bank began to fill the economy with money supply,
which, in turn, provoked rising inflation. The prices of monopoly producers reacted especially
actively. The question now is whether and how the Ukrainian economy will be able to keep up with
moderate inflation. How will the price of the national currency react, because our consumer sector is
too sensitive to inflation spikes. Which goods of Ukrainian exports will become a "lifeline" for the
trade balance of Ukraine. Prices in Ukraine during the pandemic are actively growing in almost all
categories of goods: only in the first quarter of 2021 inflation exceeded 4 percent, and in March this
year compared to March 2020, consumer prices rose to 8.5 percent, accelerating from 7.5 percent in
February. This is especially true of food products, whose prices, along with soft drinks, have risen by
more than 10 percent. It is also noticeable that fares in scheduled transport have risen by almost 8
percent.
For the second year in a row, the world is in a state of quarantine, which is replaced from time to
time by stricter restrictive measures - national or local lockdowns, or, conversely, some mitigation
when schools, kindergartens, restaurants, cinemas, etc. open. Businesses are closing, investment costs
are falling, people who have lost their jobs are losing skills and motivation for many months. In the
first wave of the pandemic responded, the so-called contact industries (industry of culture, leisure,
tourism, hotel, restaurant business, trade), the closure of restaurants and bars could affect farms.
Warehouses and shops are full of unsold products, which lose their meaning with the change of
seasons. As we can see, a short period was enough for the wave of economic downturn to overwhelm
such system-forming industries as agriculture, light industry, energy, and further - mechanical
engineering. Compared to past world crises, the economic downturn has been sudden and profound.
The GDP indicator is increasingly demonstrating its inability to be an adequate measure of economic
114
development indicators; new aspects arise in questions about the nature and role of money in the
functioning of a market economy. Banks, as a result of non-repayment of loans provided by firms for
the purchase of goods, significantly reduced profits, reduced return on assets and capital.
2.2. Credit risk prevention
The NBU has set the economic standard H2 in order to prevent excessive transfer of credit risk by
the bank and the risk of non-return of bank assets to creditors and depositors of the bank. The
regulatory capital adequacy ratio is defined as the ratio of regulatory capital to total assets and certain
off-balance sheet instruments, reduced by the amount of created relevant reserves for active
operations and the amount of loan collateral (investments in debt securities) by unconditional liability
or cash collateral. and weighted by the degree of credit risk. To calculate the regulatory capital
adequacy of a bank, its assets are divided into five groups according to the degree of risk and summed
up taking into account the relevant weighting ratios.
The normative value of the H2 coefficient for existing banks must be at least 10%. For banks that
start operating, this standard should be: during the first 12 months of operation from the date of
obtaining a license - not less than 15%; during the next 12 months - not less than 12%; in the future -
not less than 10% [18]. In 2017, the National Bank of Ukraine switched to the classification of banks
not by the size of assets, but on the basis of cluster analysis, in which all banks are divided into
separate groups - clusters. One cluster includes banks with similar business models, risk profiles,
nature of operations, etc. Banks of different sizes, but with joint owners, will also be merged. For each
such cluster, specific monitoring modes will be defined and appropriate monitoring groups will be
selected.
The largest banks (groups 1 and 2) are divided into three clusters: state-owned banks, large private
banks and banks that are part of international banking groups. Clusters of small banks (groups 3 and
4) are not reported and the affiliation of a bank to the cluster will be considered a banking secret.
Note that in 2015 the NBU used the division of banks into groups according to the size of assets.
The first group of the largest banks included PrivatBank, Oschadbank, Ukreximbank,
Prominvestbank, Raiffeisen Bank Aval, Ukrsotsbank, Alfa-Bank, VTB Bank, Finance and Credit,
Ukrsibbank, FUIB, UkrPasbank. The second group of large banks included Credit Agricole,
Pivdenny, ING Bank, Citibank, Khreschatyk, Fidobank, Megabank, Kredobank, Credit Dnipro,
PlatinumBank, Ukrinbank, Universal Bank and Diamantbank. Then it was decided to move to the
classification by owner.
Cluster analysis is, by excellence, an unsupervised learning technique, that identifies the complex
relationships between variables, without imposing any restriction [20. 21]. Cluster analysis focuses on
the examination of the interdependencies between variables [22, 23], its finality consisting in
gathering similar entities into more homogenous groups, named clusters [24-27].
Clustering analysis is currently one of the most popular and advanced mathematical grouping
methods both in finance and other existing sciences [28-34]. The purpose of cluster analysis is to
determine the units similar to each other in terms of their characteristics studied, and to define their
clustering structures. The banking sector is the most important partner of organizations and countries
against developing world economy and fluctuations in global competitive environment. Specifically,
cluster analysis, a classification technique, is run on the sample of Ukrainian commercial banks to test
the ability of cluster analysis to recognize vulnerable banks before they break down, as well as find
out which characteristics they have in common.
It should be noted that the assessment of financial stability, as well as the efficiency of banks is
carried out, traditionally, with the help of analytical tools, the main disadvantage of which is inability
to take into account internal dependencies that can be hidden in analytical data. In contrast, we
propose to use the tools of artificial intelligence and machine learning, which feature it is the search
for such dependencies [6].
The goal of the present study is to identify resembling credit institutions, which can be included
into homogenous groups, according to a series of prudential and profitability indicators. Our study
aims to provide an alternative to the peer group techniques, implemented by supervisory authorities in
the process of off-site surveillance. According to this technique, credit institutions are, firstly, grouped
115
by size or volume of activity, and then, for each group, are made comparative analyses between the
current values of financial indicators and the previous ones. The disadvantage stems from the fact that
this method cannot signal the impairment in the financial condition of the whole group, but only the
distress of a particular credit institution in that group.
2.3. Application of expert technologies for preparation of cluster analysis of
banks
For effective and adequate application of cluster analysis in the banking sector, it is appropriate
and even necessary to use expert technology [35, 36] in the previous stages of the study. Expert
technologies are characterized by a wide range of areas and are used, as a rule, in situations where the
use of other methods is ineffective or even impractical [37, 38].
In order to systematically assess banking risks and successfully prevent credit risks, attention
should be paid to at least the following aspects of the application of expert technologies in the
banking sector:
Selection of banking experts and formation of an expert group;
Determining the coefficients of competence of experts in the selected field;
Selection of performance indicators of banks that significantly affect the adequacy of the
division of many banks into clusters;
Selection of characteristics from the whole set of characteristics used, which will be used to
evaluate banks for their further clustering;
Choice of clustering method for adequate division of banks into groups according to selected
criteria.
Expert technology is a tool to support decision-making in poorly structured subject areas where it
is not possible to obtain reliable numerical information.
In [39, 40] the classification of decision-making methods according to the content of expert
information, the type of information obtained in conditions of uncertainty and risk is given. In [41], a
classification of decision-making problems according to the degree of their complexity is proposed.
All problems are divided into three classes:
well-structured or quantified problems in which significant dependencies can be expressed by
numerical estimates;
ill-structured or mixed problems, which are characterized primarily by qualitative (verbal), as
well as quantitative relationships between elements;
unstructured or qualitatively expressed problems that contain only a description of the most
important resources, features and characteristics, the quantitative relationships between which are
unknown.
2.3.1. Problem statement and its formalization
Note that the performance of banks can be measured on different scales. This fact should be taken
into account when using expert technology. In particular, the performance of banks can be set in:
nominal scales;
dichotomous form;
discrete form on scales with several gradations;
in the form of fixed weights, which are real numbers;
in the form of intervals of real numbers;
in the form of functions of belonging to a fuzzy set;
in the form of various combinations of the given ways of representation.
Thus, the problem of bank clustering can be classified as poorly structured. To solve it we will use
mathematical modeling, expert technologies and tools of artificial intelligence.
Suppose a set A, consisting of n objects (in our case - banks), which must be compared with
each other:
116
ai A, i I 1,..., n. (1)
Objects (banks) (1) are described by a set of m parameters (indicators), are points of parametric
space m :
i i i
a a1,..., am , a A, i I , A m ,
i
(2)
where a i , i I , j 1,..., m J , the value of the j th indicator of the i th bank.
j
On the basis of a survey of k experts there is a narrowing of the parametric space of the species
(2):
m ' m , m ' m . (3)
That is, among the whole set of parameters (1) are selected only those that are important for further
clustering of a given set of banks
a j A, i I , j J ' J , A m ' .
i
(4)
The next step in the application of expert technology is the selection of characteristics by which
objects of the species are evaluated (4). In our case, these are banks of the whole set of Ukrainian
banks that should be clustered, or banks of a certain subset.
The characteristics of banks are well developed and sound. We will mark them through
f a extr, i 1,..., s,
i
(5)
where s the number of characteristics that, in principle, can evaluate the activities of banks.
After the application of expert technologies, the set of characteristics of banks of type (5)
decreases, s ' s. Thus, the set of characteristics that are essential for solving the problem of
clustering of banks will look like:
f a extr, i 1,..., s '.
i
(6)
2.3.2. Determination of coefficients of competence of experts
Today, the weights of competence of experts, defined in various scales of measurement, are widely
used. The most common are the following ways of representing the values of weights:
arbitrary real or natural numbers i , i I ;
real numbers subject to unilateral or bilateral restrictions:
i 0, i I ; 5 i 5, i I ; 0 i 1, i I ;
real or natural numbers, taking into account the condition of centering:
0, , i I ;
iI
i i
real numbers taking into account the condition of normalization:
i 1, i 0, i I ;
iI
idealized weights:
max i 1, i 0, i I .
i I
interval form of weights:
i Н , iВ , 0 iH iB , i I .
i
weights in the form of a function of belonging to a fuzzy set.
The problem of determining the importance of banks, the importance of performance indicators of
banks and the competence of experts in most cases are similar and differ only in interpretation.
Therefore, the definition of weights in general should be considered, bearing in mind that this
problem can be interpreted in any of these aspects.
117
2.3.3. Selection of characteristics by which banks will be evaluated for their
further clustering
Characteristics that are calculated to formally determine the financial condition of banks are used
in a variety of practical situations. To solve a specific problem, in particular, the clustering of banks,
an additional expert survey should be organized. Based on the use of expert technologies, the analysis
of bank valuation tools is carried out. As a result of the application of this toolkit, from the set of all
possible characteristics of banks (5), only those (6) are selected that are essential for the decision to
combine subsets of banks into clusters.
The methods of conducting the relevant examination and the methods of aggregating expert
information depend on many factors. These procedures require further research and will be described
in future research.
2.3.4. Choice of clustering method for adequate division of banks into groups
To date, a wide range of clustering methods has been developed. These methods are characterized
by different approaches, have different conditions of application and can lead to clustering results that
do not coincide with each other. Therefore, for the situation of application of cluster analysis on many
banks, it is necessary to conduct a preliminary study of the suitability of the use of effective clustering
methods among the full range of such methods. The admissibility of the application of specific
methods of cluster analysis to the study of many banks is determined by the use of expert technology.
In the future, relevant research will be carried out and procedures will be described, which
substantiate the feasibility of using certain approaches.
Research on the feasibility of using different methods of clustering in the banking sector requires a
lot of effort and is not the subject of description in this paper.
2.4. Application of cluster analysis to many banks
The cluster approach (analysis) is a component of classification methods and consists in splitting a
given sample of objects (situations) into subsets - clusters so that each cluster consisted of similar
objects, and objects of different clusters differed significantly. The application of cluster analysis
involves the following steps:
o sampling for clustering, in our case these are indicators of banks' activity;
o determination of the characteristics by which the objects in the sample will be evaluated. (We
choose the indicators of return on assets and capital, as well as the indicator of capital adequacy);
o selection of the method of calculating the values of the degree of similarity between objects -
application of the method of cluster analysis of k-means (ordering a set of objects into relatively
homogeneous groups).
The goal is to divide n observations into k clusters so that each observation belongs to the cluster
with the closest average value. The principle of the algorithm is to find the centers of such clusters.
Clustering can be considered as a task of constructing the optimal division of objects into groups.
Each object is identified by a vector of characteristics. X = (x1 ..., xd). The optimality can be defined
as the requirement to minimize the root mean square partition error:
e2(X,L) = ∑j=1∑i=1 ||x(j)i − cj ||2,
where c j is the "center of mass" of the cluster j.
"Center of mass" of the cluster is a point in the space of characteristic vectors with the average for
this cluster values of characteristics.
2.5. Algorithm for clustering banks based on financial indicators
Let us describe the k-Mean algorithm [22]. This algorithm consists of the following steps:
1. Randomly select k points that are the initial "centers of mass" of clusters (any k of n objects,
or random points in general).
2. Assign each object to the cluster with the nearest "center of mass".
118
3. List the "centers of mass" of clusters according to the current membership.
4. If the algorithm stop criterion is not satisfied, return to step 2.
As a criterion for stopping usually choose one of two:
1. No transition of objects from cluster to cluster in step 2.
2. Minimum change of the root mean square error.
The algorithm is sensitive to the initial selection of "centers of mass".
Let us analyze some indicators of Ukrainian banks for the first half of 2021 (according to the
NBU) using cluster analysis (Tables 1, 2 and 3). Our goal is to cluster banks using their financial data.
The data can be obtained from reports (or site) of the National bank of Ukraine.
Table 1
The result of the analysis of the capital adequacy ratio
Claster
№
1 2 3 4 5 6 7 8
Centers 297 414 21 653 158 105 61 459
Number of banks 2 1 49 1 2 4 11 1
An important part of cluster analysis is to identify outliers, objects that do not naturally fall into
any larger cluster.
It is important to identify the number of banks with a low value of H2. To do this, we further
divide the banks from cluster №3 into subclusters (Table 2).
Table 2
The result of the analysis of the capital adequacy ratio
Separately Cluster №3 from Table 1
№
1 2 3 4 5 6 7 8
Centers 29 18.9 11.7 14 23 33 38 41
Number of banks 6 10 3 14 11 1 3 1
Table 3
The result of the analysis of the bank liquidity ratio
Claster
№
1 2 3 4 5 6 7 8 9 10
Centers 185 239 69 84 101 145 523 600 118 216
Number of banks 1 1 16 19 17 4 1 2 7 3
The analysis allows us to effectively identify problem banks in the early stages.
The division of banks into groups based on cluster analysis not by type of ownership or size of
capital, but by clustering according to economic standards is more appropriate to determine the risks
of banking. Economic standards are indicators of the risk of the bank.
Problematic should be those banks that for two or more indicators of economic standards fell into
the clusters responsible for riskier activities. This approach defines a new method of regulating banks
based on the division of banks into clusters according to the values of economic standards. Based on
the above analysis, it can be concluded that in the near future, at least two or three Ukrainian banks
will leave the market.
3. Results and Interpretations
A very large number of bank failures in last years triggered a financial crisis. Although
unprecedented intervention of central banks and governments helped economies to recover, the global
financial systems remains at risk. As we have previously mentioned, cluster analysis, as part of
maching learning, is an exploratory technique which organizes large amounts of observed data into a
reduced-size meaningful structure. In order to discover the hidden information in our set of financial
indicators, we have applied the clustering technique for each of the economy normatives.
119
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