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Eduvest � Journal of Universal Studies Volume 3
Number 2, Februari 2023 p- ISSN
2775-3735- e-ISSN 2775-3727 |
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APPLICATION OF
BLOCK-BASED K-MEDOIDS AND WARD'S METHOD TO CLASSIFY PROVINCES IN INDONESIA
BASED ON ENVIRONMENTAL QUALITY INDEX |
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Kariyam1,2,
Abdurakhman2, Adhitya Ronnie Effendie2 1Department of Statistics,
Faculty of Mathematics and Natural Sciences, Universitas Islam Indonesia,
Indonesia 2Department of Mathematics,
Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada,
Indonesia Email: [email protected],
[email protected], [email protected] |
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ABSTRACT |
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Environmental quality is an
essential aspect of the world's sustainability. This paper presents a
combination of several methods to obtain a profile of provinces in Indonesia
according to the environmental quality indices. We apply the block-based
k-medoids algorithm, Ward's method, and the Hartigan index to determine the
number of clusters. Based on Hartigan index suggested classifying 34
provinces in Indonesia into four groups. A comparison of the mean vector of
four groups using multivariate analysis of variance concluded that three
areas have the best environment quality index and eight regions require
serious attention to improve their environmental quality methods. |
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KEYWORDS |
block-based
k-medoids, Ward, environmental, clustering |
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This
work is licensed under a Creative Commons Attribution-ShareAlike
4.0 International |
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INTRODUCTION
The Environmental
Performance Index (EPI) is a numerical and quantitative-based method for
measuring the environmental performance of a country's policies. The 2022 EPI
use forty performance indicators and ranks 180 countries on their national
efforts to protect environmental health, enhance ecosystem vitality, and
mitigate climate change. These indicators measure how closely governments meet
internationally established sustainability targets for specific environmental
issues (Wolf et al., 2022). Based on the 2022 EPI ranking, Indonesia
is 164th out of 180 countries. Meanwhile, Indonesia ranks 22 out of 25
countries in the Asia Pacific region. This rating is certainly not encouraging. Indonesia's ecosystem
vitality indicator strongly correlates with the EPI score.
Environmental quality management is crucial for the sustainable
development and preservation of natural resources in a region, such as a province
in Indonesia. Effective management of the environment ensures clean air and
water, wildlife and habitat protection, and pollution and waste reduction.
Additionally, it supports public health, economic growth, and tourism and helps
mitigate the effects of climate change. By implementing sound environmental
practices, a province in Indonesia can secure a better future for its citizens
and the planet. The government is responsible for implementing policies and
regulations that protect the environment and ensure its preservation for future
generations. Effective environmental quality management is essential for
Indonesia's livable and thriving province.
The Ministry of
Environment and Forestry in Indonesia uses the Environmental Quality Index
(EQI) as an indicator of environmental management performance. Three aspects
used to measure EQI are Air Quality Index (AQI), Water Quality Index (WQI), and
Land Cover Quality Index (LCQI)
(Zhang, 2018; Inhaber, 1976; Wear et al., 1998; Berlemann, 2013; and Zhang, 2015). EQI is
used as information material to support policy-making processes related to
environmental protection and management.
Through EQI, we can find out how far the condition and status of the
environmental quality of a region are in terms of water quality, air quality
and land cover quality. Indonesia is an archipelagic country consisting of 34
provinces. The Ministry of Environment and Forestry
in Indonesia conducted a separate analysis of these three indicators (MEF RI, 2019). The
grouping of the province based on the environmental
quality index can be carried out simultaneously to facilitate the monitoring of environmental quality.
Clustering provinces in Indonesia based on EQI can bring several
benefits, such as the government can better monitor and manage the different
regions, ensuring the implementation of appropriate policies and programs for
each group. Based on the EQI, authorities can prioritize and allocate resources
to areas that require the most attention, leading to effective and efficient
use of resources. The environmental quality index provides a transparent and
objective measure of environmental performance, which can hold governments
accountable for their actions and decisions. The EQI also provide a
comprehensive picture of the state of the environment, which can inform
decision-making and policy development at the local, regional, and national
levels.
A block-based
k-medoids (Block-KM) algorithm is one of the
center-based clustering methods (Kariyam et al., 2022). As distance variance block KM (Var-KM) (Kariyam et al., 2022), a Block-KM is a variant of flexible
k-medoids (FKM) (Kariyam et al., 2022), which consist of two phases. The first stage of Block-KM is similar to
FKM. This process guarantees no empty cluster and some identical objects in the
same group. While the second phase of Block-KM is similar to
Var-KM. The
second stage of Block-KM uses initialization as a basis to update final medoids
only once from the initial groups, so this method is more efficient than FKM. In comparison, Ward's method is one of the popular
methods in hierarchical clustering. Ward's
method minimizes the total variance in the distance between newly formed
clusters. It works by iteratively combining the two closest clusters into a
larger cluster and updating the distances between all other clusters to reflect
this change.
This study aims to classify provinces in Indonesia according to the
environmental quality index simultaneously. We use Block-KM and Ward's method to cluster it. Then we
identify groups of regions with the best environmental quality index and
regional classes that require serious handling to improve environmental
quality. To achieve these objectives, we combined a clustering
method and multivariate analysis of variance. By comparing and benchmarking against other group provinces, regions
with lower environmental quality scores can be motivated to improve their
performance and adopt best practices.
RESEARCH METHOD
Materials
�������� In this study, we use secondary data on the 2019
EQI from the Center for Data and Information published by the Ministry of
Environment and Forestry of the Republic of Indonesia
(MEF RI, 2019). The Environmental Quality Index is a
generalization of the EQI of all districts/cities and provinces in Indonesia. The EQI
consists of three indicators: the water, air, and land cover quality indices.
The weights of the three indicators of EQI are determined
by:
where WQI is
the water quality index, AQI is the air quality index, and LCQI is the land
cover quality index.
�������� Water quality indicators are calculated based on seven parameters, namely Total Suspended Solid (TSS), Dissolved Oxygen (DO), Biochemical Oxygen Demand (BOD), Chemical Oxygen Demand (COD), Total Fosfat, Fecal Coli, and Total Coliform (MEF RI, 2019; Inhaber, 1976; Berlemann, 2013). The water quality index (WQI) calculation uses the pollutant index method with the concept that the higher the pollutant index value, the worse the water quality. This method can determine the status of the WQI monitored against water quality standards with one data series, so it only requires a little cost and time. The quality standard used in the analysis of the pollutant index is the classification of class II water quality standards based on Government Regulation 82 of 2001 (IGR RI, 2001). Furthermore, the WQI value of each province was calculated from the WQI average of all samples in that province.
�������� Air quality index (AQI) has two parameters, namely Sulfur Dioxide (SO2) and Nitrogen Dioxide (NO2) (MEF RI, 2019; Zang et al., 2018). The AQI value is calculated based on ambient air quality measurements in the district/city. The sampling locations represent industrial, residential transportation, and office areas using the manual passive sampler method. Meanwhile, the land cover quality index is measured based on the land cover area. The LCQI was calculated by comparing the forest and administrative area (DIC, 2019; Wear et al., 1998; Zhang et al., 2015). Based on the Law of the Republic of Indonesia number 41 of 1999, each province has a minimum forest area of about thirty per cent of the total area (IGRL RI, 1999). The LCQI calculation assumes that regions with a forest area of thirty per cent of their administrative area are assigned a value of 50. At the same time, those with the highest LCQI value (100) are areas that have an area of 84.3 per cent of their administrative scope. The overall data in this study consists of 34 objects (provinces), each of which observes three environmental quality indicators.
Methods
In this study, we compare
the block-based k-medoids algorithm (Block-KM) and Ward's method. We use
Hartigan index to obtain the optimal number of clusters. Then we describe
profile of each group based on the Multivariate Analysis of Variance (MANOVA).
A Block-based K-Medoids Partitioning Methods
Kariyam et al. 2022 have proposed a block-based
k-medoids (Block-KM) algorithm to partition a dataset. The outline of the
combined two stages in the Block-KM algorithm is as follows,
(i)
For each object,
���������� where
���������� where
(ii)
Arrange object
(iii)
For each cluster, update the current
medoid based on the object that minimizes the average distance. Suppose,
where
(iv)
Assigning each object to the nearest
medoid and calculating the sum of the total distance within a cluster,
where
(v)
Repeat steps (iii) and (iv) until a
pre-determined number of iterations is met.
Ward's Hierarchical Clustering Method
Ward's
hierarchical clustering method considers
minimizing the 'loss' of information from joining two groups. This method applies to any data,
especially to small data. Ward's method
is usually implemented with loss of information taken as
an increase in an error sum of square criterion,
where
Hartigan's Index
Hartigan, 1975 proposed an index to determine the number of clusters (also known as the Hartigan index). This
index is calculated based on the trace of
homogeneity within groups,
The number of clusters is
the smallest
of
where:
p��� =�
the number of variables
Multivariate Analysis of Variance
Multivariate
analysis of variance (MANOVA) is a statistical
technique used to analyze the relationship between two or more dependent
variables and one or more independent variables (Johnson & Wichern, 2009). It is an extension of the Analysis of Variance
(ANOVA). MANOVA tests the hypothesis that the means of two or more dependent
variables are equal across levels of tne or more
independent variables.
In this paper, we use MANOVA to compare several mean vectors arranged
according to some (more than two) groups. It provides a way to evaluate the overall effect of the independent
variable on all the groups simultaneously rather than evaluating the effect on
each dependent variable individually.
RESULT AND DISCUSSION
The data used
to group provinces in Indonesia are a quality index of water, air, and land
cover. The data standardized to a hundred, where this number indicates the
maximum value of the environmental quality index. The clustering methods are
the Ward and block-based k-medoids partitioning methods. Implementing the
Hartigan Index to these data concludes that the number of groups is four. This
amount is based on the smallest group resulting in a Hartigan Index below ten,
as shown in Figure 3.
Figure 3 The plot of the
Hartigan Index on Several Group Sizes
The
dendrogram plot in Figure 4 was carried out simultaneously using three
environmental quality indicators and the Ward method. The first group consists
of seven provinces, the second group eight provinces, the third group ten
provinces, and nine provinces in the fourth group, as shown in Figure 4.
Figure 4 The Plot of Dendrogram
with Ward method
The profile
of each group is executed based on three indicators of the environment quality
index, as shown in Fig. 5. The group with the best environmental
quality consists of nine provinces marked in dark green. This group includes
the provinces of Aceh, Jambi, East Nusa Tenggara, Central Kalimantan, East
Kalimantan, Central Sulawesi, Gorontalo, West Sulawesi, and Maluku. Provinces
with the worst environmental quality are in the first group, characterized by
the lightest colour. This group's members are dominated by Java provinces,
namely East Java, Central Java, West Java, Yogyakarta Special Region (SR), Special
Capital Region (SRC) of Jakarta, Banten, and one province on the island of
Sumatera, North Sumatera. Eight provinces with better environmental quality
than those on the Java Islands, including Riau, Riau Islands, South Sulawesi,
Lampung, Bangka Belitung, and Bali. Meanwhile, ten provinces, namely West
Sumatera, West Kalimantan, Southeast Sulawesi, West Nusa Tenggara, Bengkulu,
North Sulawesi, North Kalimantan, North Maluku, West Papua, and Papua, are the
provinces with the best second environmental quality.
Figure 5 The profile of
provinces in Indonesia based on the Environment Quality Index with Ward's
method
Figure 6 The profile of
provinces in Indonesia based on the Environment Quality Index with Block-KM
The application of Block-KM for finding four groups of provinces in Indonesia based on the environmental quality index is as in Figure 6. The Block-KM method classifies the provinces of Aceh, East Kalimantan, North Kalimantan, Central Sulawesi, North Maluku, West Papua, and Papua in the same group (fourth group) with the best environmental quality. The seven provinces (first group) with the worst environmental quality according to the Block-KM method were the same as the results of the Ward method and added one region, namely Lampung. According to the Block-KM process, the ten provinces (third group) with the best second environmental quality are the Jambi, East Nusa Tenggara, South Sumatera, Central Kalimantan, South Kalimantan, South Sulawesi, Gorontalo, Maluku, West Nusa Tenggara, and West Sumatera. The other nine provinces fall into cluster two. There are 16 out of 34 or 47.1% of regions in the same quality order resulting from Ward's method and Block-KM algorithm.
To see the profile of each group by multiple comparison tests between groups produced by Ward's method, as shown in Table 1.�
Table 1 The Multiple Comparison Test on the clustering result of Ward's Method
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Indicators |
Conclusion |
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1. Air Quality Index 2. Water Quality Index 3. Land Cover Quality Index |
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Using the 95% confidence level, the average air quality index of the seven provinces in the first group is statistically lower than the other groups. The average index is the same in the other three groups. The average water quality index for the first group is statistically the same as the average for group three and is more diminutive than for groups two and four. Meanwhile, the average land cover quality index of the first group was statistically the same as the second group and smaller than groups three and four.
The multiple comparison tests between groups produced by the Block-KM method are as in Table 2.
Table 2 The Multiple Comparison Test on the clustering result of
the Block-KM Method
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Indicators |
Conclusion |
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1. Air Quality Index 2. Water Quality Index 3. Land Cover Quality Index |
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In descending order, statistically, the average air
quality index in groups four, two and three have the same mean. The water
quality index for group three has a higher average than the other groups. For
the land cover quality index, group four has a higher mean than the other
groups. The average for all indicators in group one is significantly lower than
in other groups. These clustering results using the Block-KM method concluded
that the eight provinces in the first group must seriously develop strategies
to improve environmental quality.
CONCLUSION
In this paper, we have discussed the application of a
block-based k-medoids algorithm and the Ward method to group provinces in
Indonesia based on data from the water quality index, air quality index, and
land cover quality index. Both ways produce four groups. Application MANOVA to
compare the vector mean of the four groups concluded that the three areas with
the best environmental quality index are Aceh, East Kalimantan, and Central
Sulawesi provinces. The region that needs serious attention to improve the
quality of their environment is Nort Sumatera, Lampung, Special Capital Region
Jakarta, Banten, West Java, Special Region Yogyakarta, Central Java, and East
Java.
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