=Paper=
{{Paper
|id=Vol-2105/10000019
|storemode=property
|title=Estimation of the Production Potential of Ukraine’s Regions Using
Kohonen Neural Network
|pdfUrl=https://ceur-ws.org/Vol-2105/10000019.pdf
|volume=Vol-2105
|authors=Olena Liashenko,Tetyana Kravets,Tetiana Verhai
|dblpUrl=https://dblp.org/rec/conf/icteri/LiashenkoKV18
}}
==Estimation of the Production Potential of Ukraine’s Regions Using
Kohonen Neural Network==
https://ceur-ws.org/Vol-2105/10000019.pdf
Estimation of the Production Potential of Ukraine's
Regions using Kohonen Neural Network
Olena Liashenko1, Tetyana Kravets1, Tetiana Verhai1
1 Taras Shevchenko National University of Kyiv
lyashenko@univ.kiev.ua, tankravets@univ.kiev.ua,
tanyavergai@gmail.com
Abstract. The problem of estimating the level of production potential for
different time periods is investigated. It is proposed to apply an integrated
approach to the analysis of the regional indicators complex that characterize the
level of production potential. At the first stage, the normalization of indicators
is carried out taking into account their economic content. The next stage is the
calculation of integral indicators in three different approaches. At the last stage,
the clustering of the regions by the level of production potential is carried out
using Kohonen neural network. Application the Kohonen map with the database
clustering simultaneously allows to project multidimensional data into two-
dimensional space and analyze the resulting cluster system. The choice of the
clusters number is based on the cluster indicator calculation, in contrast to the
traditional statistical approach, based on the Störges formula using. It allows to
improve the clustering results by selecting the optimal number of partition
groups. The convenient form of visualization of the clustering results enables to
localize the features and make appropriate adjustments to the rating list, based
on expert judgements.
Keywords: production potential, Kohonen neural network, level of region
development, integral estimation, competitiveness of regions.
1 Introduction
The current development of Ukraine is characterized by interregional socio-economy
disparity, an increased level of disproportion in the development of individual regions
and the emergence of differences in the sectoral structure of economic systems of
different regions. The difference in the economic development of the country as a
whole leads to the domination of some regional systems over others. Therefore, an
important stage in the analysis of the development of the country as a whole, is the
assessment of each of the regions.
This topic is relevant and open to new research because it is difficult to identify a
single set of indicators that characterize the state of regional development fully. There
is a problem of calculating the integral indicator the estimation and ranking of regions
by level of development.
The purpose of the paper is application of integrated approach to assessing the
level of development of regions of Ukraine in terms of production potential based on
the construction of integral indicators and clustering by methods of neural networks.
2 Analysis of Recent Research
The problem of disproportionate regional development is one of the most important
and actual that must be solved not in Ukraine only but also in the whole world. For
effective public administration it is necessary to assess the level of development of
regions, to identify regions with different levels of development. Therefore, a large
number of scientific papers are devoted to this sphere. A lot of scientific works are
devoted to the development and research of the problem of assessing the level of
development of regions, their competitiveness. The theoretical basis for estimation the
development of regions is considered in [1-5]. Different approaches and methods of
diagnostics of regional development are presented in works [6-18]. Depending on the
goals and objectives of the study, both statistical indicators and expert assessments are
used, methods of integrated indicators construction are used [7, 10, 14], and develop
scenario models for the development of regions [16].
Thus, (Pike, Rodriguez-Pose, Tomaney) [1] consider purposes, principles and
values of regional development, and integrated approaches to local and regional
development throughout the world. The approach provides a theoretically informed,
critical analysis of contemporary local and regional development in an international
and multi-disciplinary context, grounded in concrete empirical analysis.
Rivza, Azena, Sunina [2] study the impact of regional development on the
development of enterprise environment. In order to implement the aim the authors
investigated theories of regional development and studied the indicators of
environment development in two cities in Latvia.
Ciobanu [3] considers regional development that is currently being discussed at
national or European level, the effects of reorganization, the greatest achievement
concerning economic and social cohesion, mitigating intra- and inter regional
differences.
Korent, Vukovic, Brcic [8] apply correlation and dynamic panel data analysis on
the set of data from Croatian counties with levels and relative changes of the selected
regional growth indicators.
Meyer, De Johng, Meyer [11] construct a composite regional development index
that successfully measures all the dimensions of development in a quantitative
manner. The index was designed to be able to assess regions on a national, regional
and local level. The hypothesised index consisted of four dimensions (demographic,
social, labour and economic) that were constructed using 17 indicators.
Di Pietro et al. [12] study the influence of regional institutional environment,
measured as regional development, on capital structure of small and medium-sized
enterprises (SMEs).
Bachtler and Begg [13] highlights innovation, human capital and effective
institutions as three crucial dimensions of future regional policy.
Li and Xu [15] use multi-index comprehensive measurement to calculate the
composite index of the level of economic development of each evaluation unit for
counties in Taiwan.
Kohonen neural networks are used for solving research problems in different fields
of knowledge [19-36]. Lototskiy [19] considered the method of images fractal
compression. The algorithm of clustering by means of artificial Kohonen neural
networks was constructed.
Bacao, Lobo, Painho [20] review different initialization procedures, and propose
Kohonen's Self-Organizing Maps as the most convenient method, given the proper
training parameters.
Mingoti and Lima [21] present a comparison among some nonhierarchical and
hierarchical clustering algorithms including SOM (Self-Organization Map) neural
network and Fuzzy c-means methods.
Fayos and Fayos [22] consider time series of Circulation Weather Type, including
daily averaged wind direction and vorticity, that are self-classified by similarity using
Kohonen Neural Networks.
Dekker [23] presents a self-organizing Kohonen neural network for quantizing
colour graphics images. The network is compared with existing algorithmic methods
for colour quantization. It is shown experimentally that, by adjusting a quality factor,
the network can produce images of much greater quality with longer running times, or
slightly better quality with shorter running times than the existing methods
Nizam [24] presents a new cluster bus technique using Kohonen neural network for
the purpose of forming bus clusters in power systems from the voltage stability
viewpoint. This cluster formation will simplify voltage control in power system.
Singh et al. [25] propose and analyze Kohonen neural network tracking control of
nonlinear system. Proposed adaptive Kohonen neural network are used to recognize
class of nonlinear discrete-time systems.
3 Research Methods
The economic situation of any country is largely determined by the level of
development of industry and agriculture. So, one of the most important groups of
indicators of socio-economic development of the regions is exactly the production
potential.
Production potential is the maximum possible volume of output that the economy
is able to produce with the full involvement of all available resources in the process of
social production [6]. The assessment of the production potential of the region is
based on the analysis of its components: industrial, agricultural and investment
potential. In turn, the characteristic of the industrial potential of the region is based on
the research of the following indicators: the volume of industrial products sold
(works, services), the share of the region; volume of sold industrial products (works,
services) and volume of sold industrial products (works, services) per person.
Regarding agricultural potential, its analysis is carried out on such indicators as gross
crop production and gross livestock production. The investment potential in this
research is characterized by an indicator of capital investment.
The construction of the integral index for assessing the production potential of the
regions is carried out according to the following three approaches.
The first methodology is an integrated assessment of the competitiveness of
regions, proposed in [7]. It has a hierarchical structure, which consists of three types
of indices:
1) general integral index of the benefits of the region;
2) group integral indices of various aspects of the region's life;
3) partial integral indices characterizing the advantages of the region.
The proposed technology for calculating the regional benefits index implies the
formation of databases, that is, the formation of a matrix of output data (X),
determination of indicators of stimulant and distimulant, as well as their
normalization.
Indicators-stimulant are calculated by the formula:
X ij
k . (1)
X ij max
Indicators-distimulant:
X ij min
k , (2)
X ij
where X ij max - the maximum value of the indicator j in the region i ; - the minimum
value of indicator j in the region i .
Calculation of the consolidated integral index of investment advantages of the
region is carried out on the basis of the formula of the average geometric group
integral indexes, which characterize its main aspects:
K w r K part .1 K part .2 ... K part .r , (3)
where K part n k1 k2 ... kn , n is the number of indicators included in a certain group
indicator.
The second technique [14] also uses a hierarchical analysis scheme. At the stage of
calculation of the group indicator from the obtained normalized indicators it is
suggested to use the formula:
K part n 1 kn 1. (4)
Next, the radial diagram of regional competitiveness is being constructed
according to the group indicators. The total area of the sectors of the chart will
determine the integral index of the region's competitiveness and will be calculated
according to the following formula:
1 360
Ii
2
sin K partir K partir1 ,
r r 1
(5)
where I i - the integral index of the region i ; r - the number of groups of indicators
or the number of calculated integral indicators for each of the groups of indicators.
The third method [37] for the valuation of indicators offers the following formulas:
for indicator-stimulants:
X ij X min
kij , (6)
X max X min
for indicators-distimulants:
X max X ij
kij , (7)
X max X min
where X ij - the value of the indicator in the region i ; X max - the maximum value of
the indicator j for all regions; X min - the minimum value of indicator j for all
regions.
Then the value of the factor weight is calculated. This procedure consists of three
consecutive steps: calculation of the product of the factor load f k and the share of
the total dispersion d k that it explains; calculation of the sum of the received products
of all factors and calculation of each factor contribution to the specified amount, that
is, the actual weight of the factor in the general model:
qk
Wk . (8)
qk
k 1
The next stage is the calculation of aggregate indicators I jl , characterizing certain
aspects of economic development and the calculation of the integral index of
economic development by the following formulas:
n
I jl kijWi , (9)
i 1
r
I ej I jlWl , (10)
l 1
where kij is the normalized indicator i of the economic development block l in the
region j ; Wi is the weight of indicator i in the aggregate indicator of the block l ;
n is the number of indicators for economic development estimation; Wl is the
weight of the block l in the integral index of economic development.
In [7, 10, 14] for clusterization of regions by integral indicators, it is proposed to
determine the number of groups by the Störges formula:
N 1 3,322lg m, (11)
where m is the number of regions under consideration.
At the same time grouping is calculated by the formula:
I max I min
h , (12)
N
where I max is the maximum of integral indicators; I min is the minimum of integral
indicators.
A powerful alternative clustering method is the use of Kohonen's neural networks
(Kohonen self-organizing maps – SOM) [20-36]. It is the most well-known
unsupervised neural network approach to clustering [26]. Its advantage over
traditional clustering technique is improved visualization capabilities. SOMs find a
mapping from high dimensional input space into the feature space of reduced
dimension and make possible visualization in reduced dimensionality.
On the initial stage of SOM learning algorithm we should set the weights to small
random values, the initial neighborhood size Nm (0) and the values of parameter
function (t ) and 2 (t ) (between 0 and 1). The steps of algorithms are as follows
[26].
STEP 1: Randomly select an input pattern x to present to the SOM through the
input layer.
STEP 2: Calculate the similarity (distance) between this input and the weights of
each neuron j :
x w .
n
2
d j x wj i ji (13)
i 1
STEP 3: Select the neuron with minimum distance as the winner m
STEP 4: Update the weights connecting the input layer to the winning neuron and
its neighboring neurons according to the learning rule:
w ji (t 1) w ji (t ) c xi w ji (t ) , (14)
where c (t ) exp ri rm / 2 (t ) for all neuron j in Nm (t )
STEP 5: Continue from STEP1 for epochs; the decreased neighborhood size,
(t ) and 2 (t ) : Repeat until weights have stabilized.
The Ward clustering in general is hierarchical agglomerative clustering algorithm
[27, 28]. On the initial stage of clustering each node is defined as a cluster itself. At
each next stage two clusters with minimum distance between them are combined in
one new cluster. This distance is called Ward distance and defined as follows:
nr ns
drs xr xs ,
2
(15)
nr ns
where r and s denote two specific clusters, nr and ns are the number of data points
in the two clusters, and xr and xs denote the centers of gravity of the clusters; . is
the Euclidean norm. Starting from the full distance matrix (lower triangle matrix as
the distance measure is commutative), at every step a row and a column is stripped
(and a different row and column is updated) until the matrix is completely cleared and
only one cluster remains. The mean and cardinality of the new cluster built as product
of the combining step is as follows:
nr xr ns xs
xr( new) , (16)
nr ns
nr( new) nr ns . (17)
The SOM-Ward clustering approach is a two-level clustering approach which
combines the standard Ward’s algorithm to determine the SOM and clustering results.
Ward clustering algorithm as agglomerative hierarchical algorithm have the following
steps [29]:
1. Initialize: assign each vector to its own cluster.
2. Compute distances between all clusters.
3. Merge the two clusters that are the closest to each other.
4. Return to step (2) until there is only one cluster left.
As a specialty, the distance matrix is initialized in a manner that takes into account
the number of data records matching to the nodes of the map. Nodes with many
matching data records are weighted stronger than nodes with fewer matching records.
As distance measure we have to use a modified Ward distance
0 if nr ns 0,
d rs nr ns (18)
n n xr xs
2
otherwise.
r s
While determining the distance, both the Ward distance and the topological
properties of SOM are taken into account. In other words, the distance between two
nonassociated clusters is considered as infinite and only the associated clusters are
combined. Low SOM-Ward distance value represents a more natural clustering for
the map, and high value represents an artificial clustering for the map. By this means,
users can select the optimal cluster number in a flexible manner [30].
For the SOM-Ward clustering the distance is redefined as
d if clustersrand sareadjacentintheSOM ,
drs rs (19)
otherwise.
The modified SOM-Ward clustering algorithm combines a method of displaying
data using self-organizing maps with a classical hierarchical Ward clustering
algorithm [31, 32]. This method offers its own clustered indicator, which defines the
reasonable number of clusters into which the input sample is broken [33].
4 Research results
The statistical data of 24 regions (excluding Kyiv) for the period 2010-2016 [37] is
used for estimation of the productive potential of the regions. Results of ranking of
regions by integral indicator of production potential are presented in Table 1. The
calculations were carried out according to three methods mentioned above. Method 1
is described by formulas (1) – (3), method 2 – formulas (1), (2), (4), (5) and method 3
– formulas (8) – (10). For the convenience of the user, the methods were implemented
in the EXCEL environment. The clustering algorithm and the variance analysis are
implemented in EXCEL and SOMine. The ratings that adduced for comparison are
based on the results of the regions in 2010, 2013 and 2016.
Table 1. Places of regions of Ukraine in the ranking on the level of production potential
Regions The first method The second method The third method
2010 2013 2016 2010 2013 2016 2010 2013 2016
Vinnytsia 11 9 7 10 8 8 12 11 9
Volyn 21 20 18 22 19 18 21 20 18
Dnipropetrovsk 1 1 1 1 2 1 2 2 1
Donetsk 2 2 5 2 1 6 1 1 2
Zhytomyr 17 17 15 18 18 17 18 17 15
Zakarpattia 23 23 23 23 23 23 22 23 23
Zaporizhia 5 7 6 4 10 7 3 4 4
Ivano-
13 14 16 13 14 15 13 14 14
Frankivsk
Kiev 3 3 2 3 3 2 6 5 5
Kirovohrad 19 16 14 15 15 13 19 16 16
Luhansk 7 6 22 9 6 22 4 6 21
Lviv 9 8 8 8 9 5 9 8 7
Mykolaiv 12 12 11 12 12 11 11 12 10
Odessa 8 10 10 7 7 9 8 10 11
Poltava 4 4 4 5 4 4 5 3 3
Rivne 18 19 20 21 21 21 17 19 17
Sumy 15 15 13 16 16 14 14 13 13
Ternopil 22 22 21 20 20 20 23 22 22
Kharkiv 6 5 3 6 5 3 7 7 6
Kherson 20 21 19 19 22 19 20 21 20
Khmelnytskyi 14 13 12 14 13 12 15 15 12
Cherkasy 10 11 9 11 11 10 10 9 8
Chernivtsi 24 24 24 24 24 24 24 24 24
Chernihiv 16 18 17 17 17 16 16 18 19
From Table 1 it follows that the use of different techniques gives close results for
leaders and outsiders ranking. Donetsk and Dnipropetrovsk regions occupied the first
and second places in the level of production potential in 2010 and 2013, and
Dnipropetrovsk region is also the leader in 2016. As for the Donetsk region, it
dropped to 5-6 places by the results of the use of the first and second methodology.
Donetsk region remained in second place for the third method. But according to all
approaches, the value of productive potential level of this region has significantly
decreased compared with 2013 and 2010. This is not surprising given the situation in
the east of the country. The worst indicators for all years showed the Chernivtsi
region (24th place) and the Zakarpattia region (23). Over the researched period, the
following regions improved their results: Vinnytsia, Kiev, Lviv, Poltava, Mykolaiv,
Kharkiv, Cherkasy. As well as minor but positive changes have taken place in the
Volyn, Zhytomyr, Kirovohrad, Sumy and Khmelnytskyi regions.
There were 5 clusters allocated for 24 regions using the Störges formula. In Table
2 shows the clustering of regions of Ukraine by the level of production potential in
2016 for each of the three methods.
It should be noted that for regions with average values of integral indicators,
calculated according to different approaches, there are significant differences in the
distribution of regions by clusters and their mutual ordering. The Kohonen neural
network was used to verify the results and identify stable homogeneous groups of
regions.
Table 2. Clusterization of the regions of Ukraine by the level of production potential in 2016
Level of
The first method The second method The third method
competitive
Dnipropetrovsk Dnipropetrovsk
MAXIMUM Dnipropetrovsk (1)
(1) (1)
HIGH Kiev (2) Kiev (2) -
Donetsk (2)
Kharkiv (3) Poltava (3)
MODERATE Poltava (4) - Zaporizhia (4)
Donetsk (5) Kiev (5)
Kharkiv (6)
Zaporizhia (6)
Vinnytsia (7)
Lviv (8) Lviv (7)
Kharkiv (3)
Cherkasy (9) Cherkasy (8)
MEDIUM Poltava (4)
Odessa (10) Vinnytsia (9)
Lviv (5)
Mykolaiv (11) Mykolaiv (10)
Khmelnytskyi
(12)
Donetsk (6)
Zaporizhia (7)
Vinnytsia (8) Odessa (11)
Odessa (9) Khmelnytskyi
Sumy (13)
Cherkasy (10) (12)
Kirovohrad (14)
Mykolaiv (11) Sumy (13)
Zhytomyr (15)
Khmelnytskyi (12) Ivano-Frankivsk
Ivano-Frankivsk
Kirovohrad (13) (14)
(16)
Sumy (14) Zhytomyr (15)
Chernihiv (17)
Ivano-Frankivsk Kirovohrad (16)
LOW Volyn (18)
(15) Rivne (17)
Kherson (19)
Chernihiv (16) Volyn (18)
Rivne (20)
Zhytomyr (17) Chernihiv (19)
Ternopil (21)
Volyn (18) Kherson (20)
Luhansk (22)
Kherson (19) Luhansk (21)
Zakarpattia (23)
Ternopil (20) Ternopil (22)
Chernivtsi (24)
Rivne (21) Zakarpattia (23)
Luhansk (22) Chernivtsi (24)
Zakarpattia (23)
Chernivtsi (24)
Calculations were made according to the statistics of 2016. The same indicators as
in previous methods were considered. The SOM-Ward method performed clustering
of input data and calculated the clustered indicator [34] for each of the possible
cluster numbers (see Fig. 1).
Fig. 1. Cluster indicator diagram
The horizontal axis of the diagram indicates the number of clusters, the vertical
axis shows the indicator value for each cluster system. The diagram can be interpreted
as follows: if the indicator value is high for a particular cluster system, then clustering
can be considered as "natural" for the constructed map. Accordingly, when the
indicator value is low for some cluster system, clustering is "artificial." Consequently,
the peaks of the clustered indicator graph represent true clustering.
According to calculations, the largest indicator corresponds to 18 clusters, the next
maximum is 8 clusters. But, given that the number of investigated objects is 24, it is
expedient to group the regions into the 8 clusters. Fig. 2 shows the division of regions
into 8 groups by the level of production potential in 2016. In brackets, under the name
of the region, the average place in the ranking is indicated by the results of previous
calculations. Note that the regions-leaders tend to the left side of the map, and
outsiders tend to the right side of the map. The division of regions into five groups
(Fig. 3), which was proposed earlier, is considered in parallel, in order to compare the
results. It should be noted that the indicator for such a number of clusters was very
low, clustering in five groups is artificial and not entirely correct.
The adequacy of the constructed clusterization models was verified using a
dispersion analysis. For each investigated indicator, the intergroup and intragroup
components of the variance were calculated and the hypothesis of their significant
difference was checked. The results of the calculations confirmed the quality of
clustering at the level of significance of 5% (Table 3).
Table 3. Results of the dispersion analysis
Dispersion
Intergroup
Indicator inside the F p
variance
cluster
Gross crop production 1,65 0,21 66,44 0,00009
Gross livestock production 0,74 0,04 151,75 0,00001
Volume of sold industrial
0,53 0,04 107,08 0,00003
products (works, services)
Volume of sold industrial
products (works, services), 0,50 0,04 101,75 0,00003
share of the region
Volume of sold industrial
products (works, services) 0,15 0,18 7,29 0,01728
per person
Capital investments 0,16 0,22 6,11 0,02551
C4
C8 C6
C1
C7 C3
C5 C2
Fig. 2. Distribution of regions into 8 groups by level of productive potential (year 2016).
C5
C1
C3
C4
C2
Fig. 3. Distribution of regions into 5 groups by level of productive potential (year 2016).
Fig. 4 presents a profile of contributions of indicators in the formation of 8 clusters
(the contributions of indicators are arranged from the bottom up according to their
ordering in the performed calculations out and marked with different colors).
The Dnipropetrovsk region is in the first place with the highest value of the integral
indicator and is isolated in the C8 cluster. All cluster metrics are at levels above the
average significantly. The next cluster (C7) consists of the Kiev region, which has
somewhat lower levels of indicators.
Vinnytsia (8) and Cherkasy (9) are in the same cluster (C5), which is characterized
by a very high level of gross livestock production and gross crop production. One can
note that on Fig. 3 Kiev, Vinnytsia and Cherkasy regions form one of the 5 clusters.
However, Kiev region is significantly different from the other two regions by the
level of capital investment, therefore, its allocation to a separate cluster is justified.
Poltava (3) and Kharkiv (4) regions from the C3 cluster have the values of
indicators that are higher significantly than the average level. Also, the following
cluster C4 consists of two regions: Zaporizhia (6) and Donetsk (5) regions. In Fig. 3
all four regions form one cluster. However, the C4 cluster, unlike C3, includes regions
whose agricultural production indicators are lower significantly than the average
level. Odessa (10), Mykolaiv (11), Sumy (12), Kirovohrad (15), Chernihiv (17) and
Kherson (20) form the C2 cluster (Fig. 2) and the C3 cluster (Fig. 3). All indicators of
these regions are lower than the average level, except of gross crop production
indicator.
The C1 cluster includes Lviv (7), Ivano-Frankivsk (14), Khmelnytskyi (13),
Zhytomyr (16), Volyn (18), Rivne (19), Ternopil (21) regions. All indicators of this
group of regions are at a level that is significantly lower than the average. The C6
cluster is characterized by the largest deviation in the negative side of all studied
indicators and includes the following areas: Luhansk (22), Zakarpattia (23),
Chernivtsi (24). Note that in Fig. 3 clusters C1 and C6 have been united into one
cluster. Separating the last three regions into a separate group is logical and
reasonable.
Fig. 4. Profile of contributions to the formation of 8 clusters.
At the next step Kohonen maps are built without taking into account the six regions
that have ranked as the leaders. That is done in order to improve the results of
conducted clustering and the allocation of stable homogeneous groups. This approach
allows to reveal structural features of the aggregate of regions with average values of
integral indicators.
Fig. 5. Distribution of regions into 11 groups by level of productive potential (year 2016)
In Fig. 5 the distribution of regions into 11 clusters is presented and new groups are
allocated. The proximity of following regions is detected: Sumy and Khmelnytskyi;
Zhytomyr, Rivne, Ivano-Frankivsk, Volyn; Kirovohrad, Chernihiv, Kherson. It should
take into account the location of the region on the map, compared with its neighbors,
proximity to the leaders or outsiders of the rating.
During clustering using the Kohonen network, it was discovered that distribution
into five clusters does not allow to make qualitative grouping and ranking of regions.
Note that the rating estimation of the region did not always coincide with the location
of the region itself on the map in terms of ratings of the closest neighbors by cluster.
Therefore, there are grounds for improvement and modification of the proposed
algorithms for determining the competitiveness of regions, taking into account the
possibility of the Kohonen neural networks.
Also, it should be noted that the city of Kiev was not included in the list of studied
regions. If we take into account the indicators of the city of Kiev, this will greatly
complicate the processes of ranking and clustering, because most regions have low
rates compared to the city of Kiev. Therefore it is expedient to compare the indicators
of the city of Kiev with the indicators of areas with the highest level of production
potential.
5 Conclusion
By means of various methodological approaches, the level of Ukraine’s regions
production potential was assessed by taking into account the industrial, agricultural
and investment potential of the regions in different time moments. Further clustering
of the studied regions was accomplished with the Kohonen neural maps. Using
Kohonen maps with simultaneous database clustering made it possible to design
multidimensional data in two-dimensional space, visually analyze the obtained cluster
system and improve the results of clustering by choosing the optimal number of
distribution groups. The number of clusters calculated according to the statistical
approach was artificial. The construction of the Kohonen map allowed to improve the
situation and select a reasonable number of clusters.
Note that the rating estimation of the region did not always coincide with the
location of the region itself on the map in terms of ratings of the closest neighbors by
cluster. This is due to the fact that the whole database and the nonlinear model of
clustering were used in constructing the map and conducting clustering, in contrast to
the methods for calculating total integral indicators and even grouping. A convenient
form of visualization of the results of clustering allows to localize the features and
make appropriate adjustments to the rating lists based on expert considerations.
During the research period, the growth of all indicators in most areas was
observed, and therefore the value of the integral index of production potential
improved year after year. But this tendency is not typical for all regions of Ukraine.
The presence of significant regional differences in development requires the
introduction of an effective arrangement for implementing the regional policy of
Ukraine.
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