=Paper=
{{Paper
|id=Vol-2422/paper16
|storemode=property
|title=Analysis of Regional Development Disparities in Ukraine Using Fuzzy Clustering
|pdfUrl=https://ceur-ws.org/Vol-2422/paper16.pdf
|volume=Vol-2422
|authors=Kateryna Gorbatiuk,Olha Mantalyuk,Oksana Proskurovych,Oleksandr Valkov
|dblpUrl=https://dblp.org/rec/conf/m3e2/GorbatiukMPV19
}}
==Analysis of Regional Development Disparities in Ukraine Using Fuzzy Clustering==
https://ceur-ws.org/Vol-2422/paper16.pdf
194
Analysis of Regional Development Disparities in Ukraine
Using Fuzzy Clustering
Kateryna Gorbatiuk[0000-0003-1477-4085], Olha Mantalyuk[0000-0002-0162-4312],
Oksana Proskurovych and Oleksandr Valkov
Khmelnytskyi National University, 11, Instytutska Str., Khmelnytskyi, 29000, Ukraine
kt_datsyuk@ukr.net, olyasiko1@gmail.com,
pov1508@gmail.com, pulolalala@ukr.net
Abstract. Disparities in the development of regions in any country affect the
entire national economy. Detecting the disparities can help formulate the proper
economic policies for each region by taking action against the factors that slow
down the economic growth. This study was conducted with the aim of applying
clustering methods to analyse regional disparities based on the economic
development indicators of the regions of Ukraine. There were considered fuzzy
clustering methods, which generalize partition clustering methods by allowing
objects to be partially classified into more than one cluster. Fuzzy clustering
technique was applied using R packages to the data sets with the statistic
indicators concerned to the economic activities in all administrative regions of
Ukraine in 2017. Sets of development indicators for different sectors of economic
activity, such as industry, agriculture, construction and services, were reviewed
and analysed. The study showed that the regional cluster classification results
strongly depend on the input development indicators and the clustering technique
used for this purpose. Consideration of different partitions into fuzzy clusters
opens up new opportunities in developing recommendations on how to
differentiate economic policies in order to achieve maximum growth for the
regions and the entire country.
Keywords: regional development disparities, clustering methods, hierarchical
cluster technique, fuzzy clustering technique, fuzzy clusters, fuzzy c-means
algorithm.
1 Introduction
Economic policies that take into account differences in regional development should
be coordinated using scientific approaches to achieve maximum results in each region
and for the whole country. This article is dedicated to the problem of clustering
Ukrainian regions in different groups accordingly to their economic development
levels. The usefulness of such division is obvious. Really, having at disposal the
partitioning into different clusters based on economic indicators, a decision maker can
elaborate economic policy measures, which are specific for every cluster and similar
for all the regions inside the same cluster. So, the number of policy options substantially
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reduce in comparison with the case, when the decision is made on each particular
region.
Clustering also provides an opportunity to identify groups of regions that are most
attractive as objects of domestic and foreign investment. Undoubtedly, the use of
cluster analysis for improving regional policy will increase the efficiency of the
economic system as a whole, which is especially important for today's Ukraine and is
a necessary condition for its economic growth.
Nowadays, a good deal of research representing manifold of cluster analysis
approaches and tools has been conducted and reflected at the relevant literary sources.
Nevertheless, search for the most acceptable clustering methods still retains its
relevance. The reason is that every method has its own advantages and disadvantages.
Fuzzy clustering methods permit the gradual assessment of the membership of data
elements in a cluster which is described by a membership function valued in the real
unit interval [0; 1]. So, in fuzzy clustering it is assumed that the boundaries between
groups are not well defined, like in the case of most natural systems. Therefore, fuzzy
clustering approaches make it possible to more adequately describe and solve the real
problem, such as estimating regional development disparities.
This article presents a study on application of hard cluster analysis methods and
clustering methods based on fuzzy sets theory. A new approach to evaluating regional
disparities in Ukraine using a fuzzy clustering technique is given. There were used
statistical data on indicators of economic activities in different regions of Ukraine in
2017. The considered methods are especially useful for the case of qualitative economic
indicators.
This article consists of six sections. The first one substantiates the background of the
conducted research. In the second section, review of the scientific literature on research
topic is presented. The third part reveals the theoretical basis of the proposed clustering
techniques. The course of the study and its main results are presented in the fourth and
fifth parts of this paper. The final part contains conclusions based on the research results
and discussing areas for the further studies in the field of exploring fuzzy clustering
methods and adapting them to regional clustering tasks.
2 Literature Review
Regional disparities are closely connected to unequal economic development of the
regions in different sectors. So, economic disparities are associated with differences in
regional qualitative and quantitative economic indicators. Economic disparities are
generally assessed using such indicator as gross national product (GNP), combined with
the analysis of tax revenues, the growth of industry and agriculture, demographic trend,
infrastructure and services [1].
Studies on estimating and classifying of regional development disparities have been
performed by many researchers [1-9] all over the world. The most common approaches,
which are used for this purpose, are econometric modeling [4, 8, 9], Klassen typology
theory [1-3] and different clustering techniques [1, 2, 6]. At the same time, among
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clustering methods, k-means clustering and hierarchical clustering are most widely
used.
The Klassen typology and the developed fuzzy-Klassen model are discussed in the
paper [3] along with giving the recommendations on their use in modeling regional
development disparities.
The use of clustering techniques in the tasks of classification of regions by the level
of economic indicators is represented in articles [1, 2, 6]. Also, there were proposed to
join the traditional clustering approaches with fuzzy methods, based on fuzzy sets
theory of L. Zadeh [10], and a lot of researches were done to apply them in practice.
The theoretical basics on clustering methods, fuzzy clustering algorithms and their
program software implementations are considered in numerous works [11-30]. In this
study, we used the fuzzy clustering approaches to identify disparities in the
development of Ukrainian regions, which allow us to explore and utilize the advantages
of this technique.
3 Research Methodology
Clustering is one of the important data mining techniques that enable the discovery of
hidden relationships from data [15]. The goal of the clustering is to divide the set of
data items into several number of groups c, called clusters. The result of any cluster
algorithm is the mapping of data items to a specific group.
In general, clustering techniques are divided into two types, Hierarchical and
Partitioned clustering [22]. Partition clustering algorithms divide the data sets into
clusters assigning dissimilar data objects to different clusters.
Hierarchical cluster techniques are generally classified into two types, which are
agglomerative and divisive clustering [22]. These cluster methods form a dendrogram,
which represents nested grouping pattern and similarity level in classification process.
At certain group level, dendrogram will break into another group level, thus producing
a different data group. In hierarchical clustering, objects that belong to a child cluster
also belong to the parent cluster [13].
Hierarchical cluster methods classify data by similarity of distance between two data
points. The classical methods for distance measures are Euclidean and Manhattan
distances, which are defined as follow [19]:
n
2
d euc x, y x y ,
i i (1)
i 1
n
d man x, y xi yi , (2)
i 1
where x and y – two vectors of length n; deuc(x, y) – Euclidean distance; dman(x, y) –
Manhattan distance.
Also, there are many other methods to calculate the distance information, but the
right choice of distance measures, which depends on the type of the data and the
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researcher questions, is very important, as it has a strong influence on the clustering
results [19].
The conventional (hard or hard) clustering methods restrict that each point of the
data set belongs to exactly one cluster [14]. Fuzzy set theory proposed by Zadeh [10]
in 1965 gave an idea to describe the uncertainty of belonging to particular class by a
membership function. Applications of fuzzy set theory in cluster analysis were early
proposed in the work of Bellman, Kalaba, Zadeh [23] and Ruspini [17].
Basic fuzzy clustering techniques include: fuzzy clustering based on fuzzy relation,
fuzzy clustering based on objective functions, and the fuzzy generalized K-nearest
neighbour rule – one of the powerful nonparametric classifiers [14].
For all fuzzy clustering algorithms, it is necessary to pre- assume the number c of
clusters because, in general, the number c should be unknown [14]. The quality of the
classification of data into partitions depends on the value of the parameter c that is
provided to the algorithm [15].
Fuzzy clustering is a soft clustering technique for classifying data into groups. In
fuzzy clustering each data point belongs to all the clusters with varying memberships
and these membership values range between zero and one [15].
Most of the clustering algorithms follow a similar structure [11]: (1) select initial
cluster centers, (2) calculate the distances between all points and all cluster centers, (3)
update the partition matrix until some termination threshold is met. In particular, the
classification of fuzzy algorithms is represented in [11].
The most well-known fuzzy clustering algorithms are: fuzzy c-means, fuzzy k-
means, (ISODATA), Gustafson Kessel (GK) algorithm [13] etc.
The fuzzy c-means (FCM) algorithm involves the processes in which there is
calculation of cluster centers and assignment of points to these centers using a formula
of Euclidian distance [13]. The fuzzy c-means algorithm is one of the most widely used
fuzzy clustering algorithms. It is a soft clustering algorithm which was firstly studied
by Dunn (1973) [28] and generalized by Bezdek (1974; 1981) [29, 30]. The centroid of
a cluster is calculated as the mean of all points, weighted by their degree of belonging
to the cluster [19]. The above process is kept on repeating itself until the stabilization
of cluster centers.
This algorithm assigns a membership value to the data items for the clusters within
a range of 0 to 1. Thus, the concepts of fuzzy sets of partial membership are
incorporated and forms overlapping clusters for supporting it [13]. Consequently, the
data objects closer to the centers of clusters have higher degrees of membership than
objects scattered in the borders of clusters [20].
We can apply clustering algorithms using the R software. The following R packages
are used for calculations in our research: 1) cluster, ppclust and fclust for computing
fuzzy clustering and 2) factoextra for visualizing clusters [27].
The function hclust() (cluster R package) performs a hard hierarchical cluster
analysis using a set of dissimilarities for the n objects being clustered. Initially, each
object is assigned to its own cluster and then the algorithm proceeds iteratively, at each
stage joining the two most similar clusters, continuing until there is just a single cluster.
At each stage distances between clusters are recomputed according to the particular
clustering method being used [26].
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The function fanny() (cluster R package) can be used to compute fuzzy clustering
[26]. It stands for fuzzy analysis clustering and returns an object including the following
components: the fuzzy membership matrix containing the degree to which each
observation belongs to a given cluster; Dunn’s partition coefficient (a low value
indicates a very fuzzy clustering, whereas a value close to 1 indicates a near-hard
clustering); the clustering vector containing the nearest hard grouping of observations
etc. [19].
The function fcm() (pplcust R package), which applies the fuzzy c-means algorithm
also can be used to compute fuzzy clustering. It returns an object including the
following components: the fuzzy membership matrix; Initial and final cluster
prototypes matrices; the Dunn’s Fuzziness Coefficients; the within cluster sum of
squares by cluster etc. [19].
4 Case study: Grouping Regions Using Different Clustering
Techniques
4.1 Data Set Description
The data for our study was taken from the State Statistics Service of Ukraine [31]. We
used the statistic information about the economic activities in 2017 taken by all regions.
There we selected some basic indicators of economic activities and we divided them
into two groups by their meaning. So, the first group included the indicators of the
extraction of aquatic bioresources and the agriculture activities, and the second group
included the indicators of the retail trade, services and the industrial activities. All of
them were explored and their corresponding values were used in clustering analysis of
the regional development. The list of those indicators and their summary statistics are
presented in the Tables 1, 2.
Table 1. First group of indicators with their statistics.
Indicator Mean MedianSt. Dev.Range
Extraction of aquatic bioresources by fishery water bodies 3793.6 1207.5 5648.1 25163
Value of agricultural products sold by agricultural enterprises 14404.614571.7 8143.1 31251
The cost of sold agricultural products from plant growing 11826.213293.4 6483.3 20141
The cost of sold agricultural products from animal husbandry 2578.5 2079.9 2672.2 12694
Dynamics of sown areas of agricultural crops, all categories 1158.9 1194.3 520.4 1757.2
Dynamics of sown areas of agricultural crops, agricultural 811.5 916.1 416.8 1311.5
enterprises
Dynamics of sown areas of agricultural crops, agricultural 347.6 307.0 139.3 494.5
households
In the Table 3, the column “Id” contains the inner identification number of the region
which is used for convenience for all following computing results and outputs.
We considered the values of these indicators, gathered in 2017, for all 24
administrative regions in Ukraine (Table 3).
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Table 2. Second group of indicators with their statistics.
Indicator Mean MedianSt. Dev. Range
Regional structure of turnover of retail trade 27429.919576.8 18943.0 66619.1
Completed construction works 3344.9 1932.9 3114.4 10659.9
Volume of industrial products sold 82165.943406.2 95282.4 407469.9
Regional structure of retail trade turnover of retail enterprises18757.812174.2 15042.1 52768.5
Used fuel, (103) 4075.6 1961.8 5092.7 18645.3
Volume of services sold by enterprises in the service sector, 3994.8 2108.6 4053.2 14932.1
(103)
Table 3. Administrative regions of Ukraine.
Id Region Id Region
1 Vinnytsya 13 Mykolayiv
2 Volyn 14 Odesa
3 Dnipropetrovsk 15 Poltava
4 Donetsk 16 Rivne
5 Zhytomyr 17 Sumy
6 Zakarpattya 18 Ternopil
7 Zaporizhya 19 Kharkiv
8 Ivano-Frankivsk 20 Kherson
9 Kyiv 21 Khmelnytskiy
10 Kirovohrad 22 Cherkasy
11 Luhansk 23 Chernivtsi
12 Lviv 24 Chernihiv
So, there were built two data sets accordingly to each set of indicators. We denoted
them as the First data set and the Second Data set. Then, we used both data sets for
clustering the regions, based on different groups of indicators, and compared the results.
4.2 Clustering Results
Before starting the fuzzy clustering analysis, we can apply the hierarchical clustering
method, using a linkage method “single”, to both data sets. The results of clustering are
illustrated by the cluster dendrograms (Fig. 1, 2), where we can see the data points
hierarchically arranged into larger groups dependently on the distances between them.
Fig. 1. Results of hierarchical clustering for the First data set.
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Fig. 2. Results of hierarchical clustering for the Second data set.
4.2.1 Three Clusters.
For the number of clusters equal to three (c = 3) we conducted the hierarchical
clustering by hclust() function [26], using a linkage method “complete”, and obtain the
hard clusters for two data sets (Fig. 3-4, Table. 4).
Fig. 3. Three clusters for the First data set.
Fig. 4. Three clusters for the Second data set.
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Table 4. Hierarchical clustering results for c = 3.
Regions
Clusters
First data set Second data set
1 1, 3, 9, 10, 13, 14, 15, 17, 19, 3, 4
21, 22, 24
2 7 14
3 2, 4, 5, 6, 8, 11, 12, 16, 18, 20, 1, 2, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19,
23 20, 21, 22, 23, 24
The fuzzy clustering methods, applied to both data sets, allowed us to obtain the
fuzzy clusters which are characterized by membership coefficients indicated the
strength of belonging to the particular cluster for all regions.
We illustrated the fuzzy clusters by several charts (Fig. 5-6) and the table with the
values of the membership coefficients obtained by the fcm() function [19] (Table 5).
Table 5. Membership coefficients for three clusters.
Region Cluster 1 Cluster 2 Cluster 3
1 0.0069988 0.9614778 0.0315234
2 0.9883655 0.0037207 0.0079138
3 0.0566142 0.3906423 0.5527436
4 0.4711571 0.0926725 0.4361704
5 0.8075004 0.0546427 0.1378569
6 0.8708132 0.0448172 0.0843696
7 0.2282767 0.2399224 0.5318009
8 0.9796605 0.0066517 0.0136878
9 0.0922669 0.6869528 0.2207803
10 0.1287994 0.1990442 0.6721564
11 0.961364 0.0117415 0.0268945
12 0.9448046 0.0166844 0.038511
13 0.0256044 0.0501941 0.9242015
14 0.0454997 0.1413717 0.8131286
15 0.0240021 0.9032314 0.0727665
16 0.9895505 0.003367 0.0070825
17 0.0661397 0.4907331 0.4431272
18 0.5549239 0.1266133 0.3184627
19 0.0109116 0.9509052 0.0381831
20 0.1418759 0.0755601 0.782564
21 0.1426764 0.3478379 0.5094857
22 0.0523409 0.5193732 0.4282859
23 0.9098461 0.0304336 0.0597202
24 0.0167552 0.9196494 0.0635953
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The values of membership coefficients vary from 0 to 1 and indicate with different
conditional formatting pattern the strength of belonging to the particular cluster for all
regions.
The next plot (Fig. 5) shows the overlapping clusters on the set of all data points. It
is the scatterplot of the first two principal components which were derived from the
data. It also says that, in our case, 85.3% (62.8%+22.5%) of the information about the
multivariate data is captured by this plot.
Fig. 5. Plot of three fuzzy clusters for the First data set.
On the following plot (Fig. 5, 6), the data points with the highest values of the
membership coefficients are combined into three different clusters to determine which
data points more likely are in each cluster.
Fig. 6. Plot of three combined clusters for the First data set.
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The similar information is shown on the scatterplot (Fig. 7), which says that 85.33 %
of the information about the multivariate data is explained by two principal
components.
Fig. 7. Plot of the fuzzy clusters for the First data set.
Another fuzzy clustering method fanny() [26] gave us a slightly different result (Fig. 8).
Fig. 8. Plot of three combined clusters by fanny() function for the First data set.
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To estimate the goodness of the clustering results, we can plot the silhouette coefficients
which quantify the quality of clustering achieved. The silhouette plot (Fig. 9) displays
a measure of how close each point in one cluster is to points in the neighbouring clusters
and allows to determine the optimal number of clusters visually.
Fig. 9. Plot of the silhouette coefficients for the First data set.
The plot of silhouette coefficients, built by the last clustering results, shows the average
level of the silhouette width 0.38. It is not sufficient result and we can see that some
data points are not enough close to points in the neighbouring clusters. Especially, the
points in the third cluster are very close to the decision boundary between two
neighbouring clusters or even might have been assigned to the wrong cluster.
A similar analysis was performed for the Second data set (Fig. 10-11).
Fig. 10. Plot of the fuzzy clusters for the Second data set.
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Fig. 11. Plot of the silhouette coefficients for the Second data set.
The scatterplot of two principal components (Fig. 10), which were derived from the
data, shows the overlapping clusters on the set of all data points, and also, we can see
that around 96.3% (77.8%+18.5%) of the information about the multivariate data is
explained by these components.
Then, the data points with the highest values of the membership coefficients
combined into three different clusters are presented in the Table 6 and show which of
them more likely are in each cluster.
The plot of silhouette coefficients (Fig. 11), built by the clustering results of fanny()
method applied to the Second data set, shows the average level of the silhouette width
0.56. It is rather sufficient result and we can see that most of data points are assigned
to the right cluster. But some of them are still on the wrong place.
The summarized results of fuzzy clustering by fcm() function applied to both data
sets are presented in the Table 6.
Table 6. Fuzzy clustering results for c = 3.
Regions
Clusters
First data set Second data set
2, 4, 5, 6, 8, 11, 12, 16, 18,
1 7, 9, 12, 14, 19
23
1, 2, 5, 6, 8, 10, 11, 13, 15, 16, 17, 18, 20, 21, 22, 23,
2 3, 7, 10, 13, 14, 20, 21
24
3 1, 9, 15, 17, 19, 22, 24 4, 3
As we can see, there were obtained the three fuzzy clusters for each set of economic
indicators, and the different partitions of Ukrainian regions show the regional
development disparities, which could be analysed and used in decision making process
concerned to the economic strategies.
206
Looking at the fuzziness of these partitions, we can admit that the regions with the
average values of membership coefficients are on the boundary of the neighbour
clusters, and the strategies for them must be the mixture of the corresponding strategies
of the neighbour clusters.
4.2.2 Four Clusters.
The similar clustering analysis (Fig. 12) were conducted for the case of four clusters
(c = 4). The results obtained by hierarchical clustering (hclust(), “complete”) are in the
Table 7.
Fig. 12. Four clusters for the First data set.
Table 7. Hierarchical clustering results for c = 4.
Regions
Clusters
First data set Second data set
1 3, 10, 13, 14, 17, 21, 22 3
2 1, 9, 15, 19, 24 4
3 7 14
4 2, 4, 5, 6, 8, 11, 12, 16, 18, 1, 2, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20,
20, 23 21, 22, 23, 24
The fuzzy clusters also are presented by different values of membership
coefficients (we do not place them here because of the size). But these fuzzy clusters
are quite completely described by the overlapping shapes at Fig. 13 and we can say that
the plot of two principal components capture around 85.3% of the information about
the multivariate data.
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Fig. 13. Plot of the fuzzy clusters for the First data set.
The fuzzy clusters based on the Second data set we represented by the plot, where the
data points with the highest values of the membership coefficients are combined into
four different clusters (Fig. 14). Here we have the only two big groups of data points
and two data points are stand alone in different clusters. So, the further analysis with
larger number of clusters is not rational.
Fig. 14. Plot of the fuzzy clusters for the Second data set.
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The summarized results of fuzzy clustering by fcm() function applied to both data sets
are presented in the Table 8.
Table 8. Fuzzy clustering results for c = 4.
Regions
Clusters
First data set Second data set
1 1, 9, 15, 19, 24 1, 2, 5, 6, 8, 10, 11, 13, 15, 16, 17, 18, 20, 21, 22, 23, 24
2 7, 13, 14, 20 3
3 3, 10, 17, 18, 21, 22 7, 9, 12, 14, 19
4 2, 4, 5, 6, 8, 11, 12, 16, 23 4
So, there were obtained the four fuzzy clusters for each set of economic indicators.
These different classifications of Ukrainian regions show the disparities in regional
development, which can be analysed and used in the decision-making process
concerning economic strategies. Including into the analysis the fuzzy nature of obtained
partitions, we will gain the new quality of forming of the economic strategies for
different regions.
5 Results and Discussion
The results of fuzzy clustering obtained in this study allows to consider in more detail
the similarities in the economic development levels of the Ukrainian regions, which are
assigned to the same clusters, and reveal the dissimilarities between the regions
assigned to the different clusters. The membership coefficients give us the information
how far are the development levels within clusters and between clusters.
This alternative approach can help determine the regional development disparities
according to certain indicators. As we showed in this research, the results of partitioning
strongly depend on the indicators selected for the analysis, and any clustering technique
should be used only along with the substantial analysis of the subject of interest. Before
conducting fuzzy clustering, in order to ensure proper economic interpretation of
clustering results, a profound analysis of the nature of all economic indicators and
relationships between them should be used.
In general, fuzzy clustering results could not be significantly different from hard
clustering results. It is quite reasonable, and we could see this in practice. Although the
concepts of hard and fuzzy clustering are rather different, they have common features,
and the clusters obtained by different methods predominantly overlap.
The main findings in this research were the conclusions about the regional
disparities in the levels of different kinds of economic activities in Ukraine in 2017.
Thus, after the analysis of most agricultural indicators, we mark that among Ukrainian
regions, Zaporizhya is the region, which level is significantly different from others. But
the analysis of most industrial indicators allows to sign that Dnipropetrovsk and
Donetsk regions, as well, are the regions, which levels significantly differ from others.
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6 Conclusion
Regional disparities in economic development level had been analysed in this study by
different clustering techniques. We obtained the classifications based on two groups of
economic indicators observed in 2017 for all Ukrainian regions. Now, we can conclude
that the regional inequalities across Ukrainian regions can be reduced by the right
economic policies if the information about the actual magnitude of differences between
the regions will be available before the decision-making process. The fuzzy clustering
methods give us the instrument for the estimating these degrees of differences based on
the analysis of regional economic activities in target sectors.
We showed, that implementation of fuzzy clustering methods in analysis of
regional disparities have many advantages, but it needs to be accompanied with the
cluster validity process and substantial analysis of the economic indicators, which we
take as the base of the clustering investigation. In further researches, we need to take
into consideration the necessity of aggregating the different fuzzy clustering results for
developing recommendations on how to differentiate economic policies in order to
achieve maximum growth for the regions and the entire country.
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