Cluster analysis of the efficiency of the recreational forest use of the region by separate components of the recreational forest use potential is provided in the article. The main stages of the cluster analysis of the recreational forest use level based on the predetermined components were determined. Among the agglomerative methods of cluster analysis, intended for grouping and combining the objects of study, it is common to distinguish the three most common types: the hierarchical method or the method of tree clustering; the K-means Clustering Method and the two-step aggregation method. For the correct selection of clusters, a comparative analysis of several methods was performed: arithmetic mean ranks, hierarchical methods followed by dendrogram construction, Kmeans method, which refers to reference methods, in which the number of groups is specified by the user. The cluster analysis of forestries by twenty analytical grounds was not proved by analysis of variance, so the re-clustering of certain objects was carried out according to the nine most significant analytical features. As a result, the forestry was clustered into four clusters. The conducted cluster analysis with the use of different methods allows us to state that their combination helps to select reasonable groupings, clearly illustrate the clustering procedure and rank the obtained forestry clusters.
The intensive development of recreation in the world creates motivation to use significant reserves of recreational resources. To expand the use of forest recreational resources, it is necessary to use for this purpose not only nature reserves, but also to involve more and more forests of state forestry farms in this use. The reserves of recreational forest use on the territory of Ukraine are significant. Therefore, there is a need to assess their development on the basis of the classification of forestry areas on many analytical grounds. Taking into account the fact that such classification is a rather ___________________ Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). time-consuming task, it is proposed to carry out forests clustering with the help of software.
The use of cluster analysis methods is dictated primarily by the fact that they help to build scientifically based classifications, identify internal links between the observed population units. In addition, cluster analysis methods can be used to compress information, which is an important factor in the conditions of constant increase and complication of statistical data flows. That is why this type of statistical analysis is of great importance when analyzing the development of recreational facilities. It should be noted that recently cluster analysis has received considerable attention from domestic and foreign experts in various scientific fields. One of the reasons is that modern science is increasingly relying on classification for its development. Moreover, this process deepens as knowledge specialization grows, which in its turn is based largely on objective classification. Another reason is related to the accompanying deepening of specialized knowledge, the increase in the number of variables, taken into account in the analysis of certain objects.
Clustering of the studied forests will allow the effective management of recreational areas, taking into account the reserves for improving the development of areas for selected components and also to develop at the state level the Strategy of recreational forest use development in Ukraine for the maintenance of the National recreational product competitive in the domestic and world markets. Taking into consideration the fact that each region of Ukraine is characterized by its natural and climatic conditions, ethnic traditions and historical and cultural recreational features, there is a problem of qualitative analysis and assessment of the level of recreational facilities development. 2
and Kathryn J. H. Williams [
[
Markus A. Meyer, Joachim Rathmann and Christoph Schulz proved in [10] that visitors cluster along major paths or regions in urban and rural forest, recreation of the local population is highly driven by relaxation, forest structures and demographic factors play a minor role for forest benefits, forest benefits do not strongly vary within the area of the forests, forest management should focus on avoiding nuisances to support forest benefits. They found a weak connection between recreational behavior and demand for specific forest characteristics. For local recreation, we recommend to provide a basic level of highly rated FB and to avoid nuisances rather than designing forests for a desired appearance.
Tina Gerstenberg, Christoph F. Baumeister, Ulrich Schraml and Tobias Plieninger
in [
The purpose of Kee-Cheo Lee and Kee-Rae Kang [
Hyun-Kyu Shin and Hong-Chul Shin in [12] segmented recreational forest’s visitors for marketing based on purpose of visit. Using the factor analysis, cluster analysis, cross tab, and t-test to find out different behavioral intention in each cluster, the result elicited some implications. First, 2 clusters were founded and has difference in behavioral intentions. Cluster 1 (married, 200~300 hundred won income) has higher satisfaction, revisit intention, recommendation intention. The result shows that market researcher in recreational forest should approach different marketing strategy and has various facilities, active program. This research needs to survey broad region to generalized result [12].
Thus, having considered the scientific works of both foreign and domestic
researchers of the recreational forest management problems and without diminishing
their scientific value to improve development of recreational forest management, it is
possible to consider and necessarily classify the recreational region for a component
that is its own manufacturer [
As it is known, for complex evaluation of every economic process or its components,
the methods of integrated indicators calculation are conventionally applied using
different economic and mathematical methods and approaches. The complex
evaluation is required to define the potential of recreational forest management,
considering the development of all its components. Therefore, in [
management potential determined the efficiency of recreational forest use of regional
territories by individual components of recreational forest management potential using
indicators specified in table 1. A taxonomic method based on determination of
taxonomic indicators of each component [
typical forestry of the Western region of Ukraine was selected, including 8 forestries.
infrastructure of forestries, it was not possible to calculate a required system of indicators, shown in table 1. However, the taxonomic indicators were calculated based on the actual statistical base on the resource and social components of each forestry.
Therefore, based on obtained calculations we can conclude that recreational forest
management in Ukraine is low, confirmed by the level of recreational forest
management potential (table 2). Of 8 analysed forests only in Forestry 1 the potential
level is average, in two forestries the integrated indicator of recreational forest
management potential level has been set at a level below average, and the remaining 5
forests have a low level of recreational forest management. Graphically obtained results
are shown in figure 1 [
Indicator Substantiation
ritories, km2 use
places, quantity territory intended for recreational forest management
vegetation It describes the level of recreation applicability
rast) of recreational ter- It is determined as a contrast ratio degree of the resting ritory place relative to a recreant's permanent residence
creational forest mana- It shows attractiveness of recreational forest gement management
costs for growing 1 ha They reflect the effect, achieved by improving the forest of recreational forest as a means of labor in recreation sphere
employees number of staff involved in recreational activities
health, recreational complexes) is a simultaneous
ha of forest the day, during weekends, weekdays
cationers on the recrea- It shows an average length of stay of visitors on the tional territory, h recreational territory of forest area
ting activities of recrea- It characterizes the development level of marketing activities tional territories Component Indicator Substantiation ment compo- Efficiency of innovation nent implementation of re- It characterizes the innovation level and efficiency of creational forest mana- recreational innovation use gement
Proportion of foreign in- It shows amount of recreational activity financing at the nvaelstamcteinvtistieisnfirneacnrceiantigo- expense of foreign financial sources
Thus, according to the results of economic and mathematical modelling of the integrated indicator of recreational forest management potential level, it can be concluded that the recreational forest management potential in Ukraine is low (figure 1), so measures should be taken to improve recreational activity results and develop this industry. As the calculations indicate, first of all, it is urgent to develop economic and innovation investment components of the recreational forest management potential in Ukraine.
recreational forest use level in the studied forests, we consider it necessary to conduct a fuzzy cluster analysis of forestry based on the analysis of forest use potential individual indicators for the studied objects. The main stages of cluster analysis of the recreational forest use level by predetermined components are shown in the figure 2.
observations xij. In this case, the original set consists of m elements described by n parameters, and each of its lines can be interpreted as a point or vector placed in idimensional space with coordinates equal to the value of n features for a particular forestry. Thus, in the observation matrix xij is the value of feature i for j forestry; j – a number of classification objects (forestry); i – a number of features of the objects.
where: w is the number of study periods, n is the number of indicators of each recreational forest management potential, xik – indicator value k of each specific component for a year (k = 1 n, і = 1w).
As indicators of recreational forest use management level assessment are reflected in various measures, they need to be standardized. One of the most common means of (1) statistical generalization for inhomogeneous populations is the standardization of indicators by the ratio of deviation (xi) to the unit of standardization. In our case, σi is chosen as the standardization unit. These features should be normalized using the following formula: (2) (3) (4) when
= = ∑
1 1 w 2 2 sk w i1 (xik xk ) where: zij – standardized value of indicator j for the i-th study period; xij – standardized value of indicator j for the i-th study period; xj – arithmetic mean of kj indicator; σj – standard deviation of k indicator; w – a number of periods.
to each other than objects from different clusters. Such a classification with the help of software and computer system STATISTICA, can be performed simultaneously on a fairly large number of analytical features. In our case, clusters will be called geographically concentrated and interconnected by the level of recreational potential of forestry.
grouping and combining objects of study, it is common to distinguish three most common types: hierarchical method (I) or the method of tree clustering; K-means
I. Hierarchical clustering is used in the formation of clusters by determining the distances between objects and allows you to graphically visualize the results of the study in the form of a dendrogram. These distances can be determined in one-dimensional or multidimensional space. However, an important step in conducting a cluster analysis is to select the correct method for calculating the distances between the studied objects. The main ways to determine distances are: Euclidean distance, square of Euclidean distances, distance of city squares (Manhattan), Chebyshev distance, power distance.
methods of cluster analysis. Unlike hierarchical methods, which did not require prior assumptions about the number of clusters, to be able to use this method it is necessary to have a hypothesis about the most probable number of clusters. K-means Clustering Method builds k clusters located at as large distances from each other as possible. Note that the K-means Clustering Method assumes that the number of clusters includes observations with the closest average value. The method is based on minimizing the sum of the distances squares between each observation and the center of its cluster, i.e. the function. In this case, the choice of the number of clusters is based on the research hypothesis. If it is not present, it is recommended to create 2 clusters, further 3, 4, 5, comparing the received results. The input will be Xu = {x1u, x2u,…, xmu} – a set of unmarked data; Xkl = {x1l, x2l,…, xpl} is a set of marked data in the class k, Xl=Kk=1Xkl. At the output, we want to obtain separated K sets {Ck} Kk = 1 of Xu, which minimizes the objective function in k-means. Set parameters: = ∑ ∈ (6) 1. t = 0.
= ∑ ∈
For unlabeled data: for xiu xu provide to Ckt+1 a cluster obtained from k = arg mink||xiu – μkt||2.
(5) (7) (8) t←t+1.
Another component of the algorithm is based on the discrepancy KL, which is a measure of the mismatch between the two probability distributions. Taking into account the K-dimensional probability vector of assignment of clusters p and q corresponding to points respectively xp and xq, the discrepancy KL between p and q is given by the formula: ( ‖ ) = ∑ log , where K is the number of clusters. In this approach, we use a symmetric variant of the discrepancy KL, because we are dealing only with the optimization of the loss function for p and q simultaneously: , = ( ‖ ) + ( ‖ )
analysis, especially if the number of clusters is unknown from the beginning. For this purpose, the model of the neural network-based cluster data analysis system was described on the basis of k-means and KL discrepancy methods.
features into homogeneous in the appropriate sense groups or clusters. This means that the task of classifying data and identifying the appropriate structure in it is solved.
simple grouping, and which all comes down to creating groups by the number of similarities.
The need for an objective division of different economic objects into groups exists constantly, because this classification allows you to find methods for effective management of these objects. Methods of cluster analysis allow to solve the following tasks: classification of objects taking into account the features that reflect the essence, nature of objects; verification of the assumptions about the presence of some structure in the studied set of objects, i.e. search for the existing structure; building new classifications for phenomena that have been little studied when it is necessary to establish the existence of relationships within the population and try to introduce a structure into it.
composition and number of clusters depends on the selected breakdown criteria. When reducing the original data set to a more compact form, certain distortions may occur, and individual features of individual objects may be lost by replacing their characteristics with generalized values of cluster parameters.
requirements: 1) within groups, objects must be closely related; 2) objects of different groups must be far from each other; 3) other things being equal, the distribution of objects by groups must be uniform. The key point in cluster analysis is the choice of metrics (or measures of proximity of objects), which crucially depends on the final version of the objects division into groups with a given algorithm of division.
objects G into m (m is an integer) of clusters (subsets) G1, G2,…, Gm, so that each object Gj belongs to one and only one subset of the breakdown and that objects belonging to the same cluster are similar, while objects belonging to different clusters are heterogeneous. The solution to the problem of cluster analysis is the breakdowns that satisfy some criterion of optimality. This criterion may be some functionality that expresses the levels of different breakdowns desirability and groups, called the objective function. For further research, it was possible to use the methods of theories of complex systems and equipment made by tools used to examine the necessary systems of complexity, which were used in conventional [4; 3; 14; 13].
Component
study (Forestris) form “natural clusters”. To do this, use the method of hierarchical classification, in which we select the following characteristics: Amalgamation (joining) rule: Complete Linkage, Single Linkage and Ward’s method; Distance metric is:
Tree Diagram f or 15 Cases
Single Linkage Euclidean distances 6,0 5,5 5,0 e c n a t s iD4,5 e g a k n iL 4,0 3,5 3,0
C_12
C_10 C_15
C_14
C_8
C_6 C_7
C_5
C_13
C_11 C_4
C_3
C_2
C_1 C_9
( , ) = ∑ ( − ) (9)
conclusions that the investigated forestries form 5 natural clusters. Let’s test the above hypothesis by dividing the original data of K-means clustering into 5 clusters and check the significance of the difference between the obtained groups.
iterative method of cluster analysis, in particular the K-means clustering algorithm with division into three clusters. After the procedures performed by using the previously mentioned computer program, the results of clustering were obtained, which are shown in figure 6.
Tree Diagram f or 15 Cases
Ward`s method Euclidean distances
C_8
C_6 C_7
C_5
C_12
C_14 C_15
C_4 C_13
C_10
C_11
C_2 C_3
C_9
C_1 Cluster 1 Cluster 2 Cluster 3 Cluster 4 Cluster 5 4 3 2 1 0 -1 -2 -3 -4
Plot of Means for Each Cluster Var3
Var5
Var7
Var9
Var11 Var13 Var15 Var17 Var19
Variables
which (table 5) indicate the relative quality of the clustering procedure: intergroup values of variances (Between SS) do not significantly exceed intragroup values (Within
significant features of the previously performed analysis of variance. To implement clustering, we use the method of hierarchical classification, in which we select the following characteristics: Amalgamation (joining) rule: Complete Linkage, Single
standardized). The obtained clustering results are shown in the figures 7-9.
that the studied forests form 4 natural clusters. Let’s test the above hypothesis by dividing the original data of K-means clustering into 4 clusters and check the significance of the difference between the obtained groups.
The best results in terms of meaningful interpretation were obtained by using an iterative method of cluster analysis, in particular the K-means clustering algorithm with division into four clusters. After the procedures performed by using the previously mentioned computer program, the results of clustering are obtained, which are shown in figure 10.
3,4 3,2 3,0 2,8 e c n tsa2,6 i D ge2,4 a k n i L2,2 2,0 1,8 1,6
Variable Var2 Var3 Var4 Var5 Var6 Var7 Var8 Var9 Var10 Var11 Var12 Var13 Var14 Var15 Var16 Var17 Var18 Var19 Var20 Euclidean distances C_12
C_10 C_11
C_6
C_15
C_13 C_14
C_4 C_5
C_8
C_7
C_2 C_3
C_9
C_1 Fig. 7. Tree diagram for 15 forestries (Single Linkage).
Tree Diagram f or 15 Cases
Complete Linkage
C_4 C_5
C_14 C_15
C_13
C_8
C_7
C_10
C_12 C_3
C_2 C_11
C_9
C_1 2,5 2,0 1,5 1,0 0,5 0,0 -0,5 -1,0 -1,5 -2,0
Plot of Means for Each Cluster Var2
Var3
Var5
Var7
Var9 Var13 Var16 Var19 Var20 Variables Cluster 1 Cluster 2 Cluster 3 Cluster 4
Fig. 10. Average level of normed values of indicators for the selected clusters.
Cluster Number No. 1 No. 2 No. 3 No. 4
Euclidean Distances between Clusters (Апробація) Distances below diagonal Squared distances above diagonal
No. 1 No. 2 No. 3 No. 4 0,000000 2,445802 1,394819 1,277132 1,563906 0,000000 1,068632 1,250228 1,181025 1,033747 0,000000 1,106422 1,130103 1,118136 1,051866 0,000000
of which (table 7) indicate the high quality of the clustering procedure: intergroup values of variances (Between SS) significantly exceed intragroup values (Within SS), and the level of p-significance is much better than the normative (0.05).
Also, the contribution to the division of objects into groups is characterized by the values of Fisher’s criterion (F-criterion) and its significance level (p): the higher the values of the first and the smaller the values of the second, the better the clustering. For all parameters, without exception, the significance level approaches 0, which indicates the high statistical significance of the F-criterion. Depending on the levels of these indicators, forestry was grouped into four clusters (table 8).
performed: the arithmetic mean, hierarchical methods followed by dendrogram construction, K-means Clustering Method, which refers to reference methods in which the number of groups is specified by the user. The cluster analysis using different methods allows us to state that their combination helps to select reasonable groupings, visually illustrate the clustering procedure and rank the obtained clusters.
Thus, the results of the cluster analysis on 9 analytical grounds confirmed the hypothesis of separation of 4 clusters from 15 forestries. The first cluster is formed by five forestries 1, 2, 9, 11, 12, which are characterized by an average area of recreational territories, biggest number of recreational sites and recreational capacity, lowest quality factor of forest vegetation, proportion of total forestry costs on maintenance of recreational sites, wear coefficient of recreational fixed assets, cost amount on marketing activities of recreational territories, proportion of foreign investments in recreational activities financing, quantity of grants (programs) won to finance recreational activities. The second cluster is formed by three forestries 4, 5, 6. This cluster is characterized by the highest level of recreational territories, quality factor of forest vegetation, cost amount on marketing activities of recreational territories, proportion of foreign investments in recreational activities financing, an average level of recreational capacity and number of recreational sites, lowest level of proportion of total forestry costs on maintenance of recreational sites, wear coefficient of recreational fixed assets, quantity of grants (programs) won to finance recreational activities. The third cluster includes four forestries 3, 7, 8, 10, which have the following characteristics: the highest level of wear coefficient of recreational fixed assets, recreational capacity and quantity of grants (programs) won to finance recreational activities, average area of recreational territories, number of recreational sites and recreational capacity, quality factor of forest vegetation, cost amount on marketing activities of recreational territories and quantity of grants (programs) won to finance recreational activities, lowest proportion of total forestry costs on maintenance of recreational sites. The fourth cluster includes 3 forestries 13, 14, 15 and is characterized by the highest level of the proportion of total forestry costs on maintenance of recreational sites and wear coefficient of recreational fixed assets, lowest number of recreational sites and recreational capacity, quality factor of forest vegetation, recreational capacity, cost amount on marketing activities of recreational territories and quantity of grants (programs) won to finance recreational activities and quantity of grants (programs) won to finance recreational activities, the lowest of recreational sites.
was performed: arithmetic mean, hierarchical methods followed by dendrogram construction, K-means method, which refers to the reference methods in which the number of groups is specified by the user. The cluster analysis, using different methods, allows us to state that their combination allows to select reasoned groupings, visually illustrate the clustering procedure and rank the obtained clusters.