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Sinkron : Jurnal dan Penelitian Teknik Informatika
Volume 7, Number 3, July 2022
DOI : https://doi.org/ 10.33395/sinkron.v7i3.11598
e-ISSN : 2541-2019
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*Corresponding author
This is an Creative Commons License This work is licensed under a Creative
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2089
OPTIMIZATION MODEL IN CLUSTERING
THE HAZARD ZONE AFTER AN
EARTHQUAKE DISASTER
Monica Natalia br Bangun1, Open Darnius2, Sutarman 3
University North Sumatera, Medan, Indonesia
1) monicanatab@gmail.com, 2) opendarnius@gmail.com, 3) sutarman@usu.ac.id
Abstract. There are a large number of approaches to clustering problems,
including optimization-based methods involving mathematical
programming models to develop efficient and meaningful clustering
schemes. Clustering is one of the data labeling techniques. K-means
clustering is a partition clustering algorithm that starts by selecting k
representative points as the initial centroid. Each point is then assigned to
the nearest centroid based on the selected specific proximity measure. This
writing is focused on the grouping of post-earthquake hazard zones based
on grouping with regard to certain characteristics which aim to describe the
process of partitioning the N-dimensional population into K-sets based on
the sample. This research consists of three steps, namely standardization,
data clustering using K-means and data interpolation using the K-means
clustering algorithm and zoning of 7 variables, namely magnitude, depth,
victim died, the victim didn’t die, public facilities were heavily damage,
public facilities were slightly damage, and affected areas.
Keywords: Earthquake, Hazard, K-means clustering
INTRODUCTION
Indonesia is located at the confluence of active tectonic plates, active mountain paths, and tropical
climates, making some of its areas vulnerable to natural disasters. The most frequent natural disasters are
earthquakes. This is because it occurs at shallow depths and has a large enough magnitude and is located
near settlements and population activities. With the study of the hazard of ground shaking, there is a basis
for making regional spatial planning policies based on earthquake hazard mitigation. The first step that
can be taken is to determine the hazard zone area to facilitate the evacuation of people affected by the
earthquake. Utilization of earthquakes can be done by grouping the data according to the information in
the data, so that the hazard zones after the earthquake can be known.
According to (Senduk et al., 2019), grouping is an unsupervised learning, where a group of data is
directly grouped based on the level of similarity without supervision. Each group, called a cluster,
consists of objects that are grouped based on the principle of maximizing intraclass similarity and
minimizing interclass similarity. That is, object clusters are formed so that objects in the cluster have a
high similarity compared to each other, but are somewhat different from objects in other clusters (Sun et
al., 2012).
Clustering algorithm has been applied to a variety of problems, including exploratory data analysis,
data mining, image segmentation and mathematical programming. K-means is one of the general methods
for partitioning which is quite efficient in terms of variance in groups. K-means clustering groups data
groups into a predetermined number of clusters, based on the Euclidean distance as a measure of
Sinkron : Jurnal dan Penelitian Teknik Informatika
Volume 7, Number 3, July 2022
DOI : https://doi.org/ 10.33395/sinkron.v7i3.11598
e-ISSN : 2541-2019
p-ISSN : 2541-044X
*Corresponding author
This is an Creative Commons License This work is licensed under a Creative
Commons Attribution-NonCommercial 4.0 International License.
2090
similarity. The purpose of the K-Means method is to minimize data variation in the same cluster while in
different clusters the variation in data will be maximized (Witten et al., 2011). K-means clustering is the
most widely used partition clustering algorithm, and one of the simplest and most efficient clustering
algorithms proposed in the data clustering literature. The K-means procedure is easy to program and
computationally economical, making it feasible to process very large samples on a digital computer. The
concept of K-means represents a generalization of the average of ordinary samples and is naturally geared
towards studying the asymptotic behavior in question, the object of which is to establish some kind of law
of large numbers for K-means.
Decision-making problems are often formulated as optimization problems. Mathematical optimization
will model various problem cases and find the right and fast way or method to solve it. Mathematical
optimization is aimed at methods to obtain a solution that maximizes an objective function and minimizes
risk. Based on the evidence above, this study will cluster all earthquake events that occurred in Indonesia
for 5 years to see the patterns that occur, making it easier to classify the hazard zone areas after the
earthquake.
LITERATURE REVIEW
Data Clustering
Data grouping is one of the data labeling techniques (Aggarwal & Reddy, 2014). In data grouping,
given unlabeled data and must put similar samples in one pile, called clusters, and different samples must
be in different clusters. Clustering is useful in several machine learning and data mining tasks including
image segmentation, information retrieval, pattern recognition, pattern classification, network analysis,
and so on. This can be seen as an exploratory task or a preprocessing step. If the goal is to explore and
reveal hidden patterns in the data, clustering becomes an exploratory task in its own right. However, if the
resulting cluster will be used to facilitate other data mining or machine learning tasks
Clustering Methods
The clustering methods (Gulia, 2016) can be classified into the following categories:
Partitioning Method
Suppose given object database 'n' and partition method construct partition 'k' data. Each
partition will represent a cluster and k n. This means it will classify the data into k groups,
which satisfies the requirement that each group contains at least one object and each object
must belong to exactly one group. For a specified number of partitions (e.g., k), the partition
method creates the initial partition. Then use iterative relocation techniques to increase the
partition by moving objects from one group to another.
Hierarchical Method
This method creates a hierarchical decomposition of a given set of data objects. There are two
approaches here. First, the Agglomerative (bottom up) approach starts with each object
forming a separate group. It keeps merging objects or groups that are close to each other. It
continues to do so until all groups are merged into one or until the termination condition
applies. Second, the Divisional (top-down) approach starts with all objects in the same cluster.
In continuous iteration, a cluster is split into smaller clusters. It goes down until every object
in a cluster or termination condition applies. This method is rigid, that is, once a merge or split
is performed, it can never be undone.
Clustering Techniques
The different approaches to data clustering can be explained by the taxonometric representation of the
clustering methodology (Jain et al., 1999). There is a difference between hierarchical and partitional
Sinkron : Jurnal dan Penelitian Teknik Informatika
Volume 7, Number 3, July 2022
DOI : https://doi.org/ 10.33395/sinkron.v7i3.11598
e-ISSN : 2541-2019
p-ISSN : 2541-044X
*Corresponding author
This is an Creative Commons License This work is licensed under a Creative
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2091
approaches (the hierarchical method returns a series of nested partitions, whereas the partitioning method
returns only one) (Madhulatha, 2012).
The partitioning method has advantages in applications involving data sets. Partitioning techniques
typically generate clusters by optimizing a criterion function defined either locally (on a subset of
patterns) or globally (defined across all patterns). The combinatorial search of the set of possible labels
for the optimum value of a criterion is obviously very difficult computationally. Therefore, in practice, the
algorithm is usually executed several times with different initial states, and the best configuration
obtained from all processes is used as the output cluster.
The most intuitive and frequently used criterion function in partition clustering techniques is the
Squared Error Algorithms, which tends to work well with isolated and compact clusters. The squared
error for grouping L of patterns of H (containing k clusters) is
Where is the pattern to belonging to the cluster and is the center of the cluster
K-means is the simplest and most commonly used algorithm using the squared error criterion
(MacQueen, 1967). It starts with a random initial partition and continues to reassign patterns to clusters
based on the similarity between the pattern and the cluster center until the convergence criteria are met
(e.g., there is no reassignment of any patterns from one cluster to another, or the squared error stops
significantly reducing after several iteration). The K-means algorithm is popular because it is easy to
implement, and the time complexity is O(n), where n is the number of patterns. The main problem with
this algorithm is that it is sensitive to the initial partition selection and may converge to the local
minimum of the criterion function value if the initial partition is not selected correctly (Ahmed et al.,
2020).
K-MEANS
K-means clustering is the most widely used partition clustering algorithm. It starts by selecting k
representative points as the initial centroid. Each point is then assigned to the nearest centroid based on
the selected specific proximity measure (Nagari & Inayati, 2020). The first iteration initializes three
random points as centroids. In the next iteration the centroid changes position until it converges. Various
measures of proximity can be used in the K-means algorithm when calculating the nearest centroid. The
choice can significantly affect the centroid assignment and the quality of the final solution. Various types
of measures that can be used here are Manhattan distance (L1 norm), Euclidean distance (L2 norm). The
objective function used by K-means is called Sum of Squared Errors (SSE) or Residual Sum of Squares
(RSS). Given a dataset D= {x1, x2, …, xN} consist of N points, denoted using K-means clustering by C=
Sinkron : Jurnal dan Penelitian Teknik Informatika
Volume 7, Number 3, July 2022
DOI : https://doi.org/ 10.33395/sinkron.v7i3.11598
e-ISSN : 2541-2019
p-ISSN : 2541-044X
*Corresponding author
This is an Creative Commons License This work is licensed under a Creative
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2092
{C1, C2, …, Ck …, CK}. The goal is to find the grouping that minimizes the SSE score. Iterative
assignment and update steps of the K-means algorithm aim to minimize the SSE score for a given set of
centroids.
The steps in the K-means clustering algorithm are:
1) Determine the number of clusters
2) Determine the centroid value
In determining the value of the centroid for the beginning of the iteration, the initial value of the
centroid is done randomly. Meanwhile, if determining the value of the centroid which is the stage
of the iteration, the following formula is used:
,
where:
is the centroid/average of the i-th cluster for the j-th variable
is the amount of data that is a member of the i-th cluster
is the index of the cluster
is the index of the variable
is the value of the k-th data in the cluster for the j-th variable
3) Calculates the distance between the centroid point and the point of each object. To calculate the
distance can use the Euclidean Distance, namely
,
where:
is Euclidean Distance
is the number of objects,
are the coordinates of the object and
are the coordinates of the centroid.
4) Object grouping
To determine cluster members is to take into account the minimum distance of the object. The
value obtained in the data membership in the distance matrix is 0 or 1, where the value is 1 for
data allocated to clusters and 0 for data allocated to other clusters.
5) Return to stage 2, repeat until the resulting centroid value remains and the cluster members do not
move to another cluster.
RESULT AND DISCUSSION
In this study, data were obtained from the BMKG in 2014-2018 with a total of 57 data used as shown in
table 1. Table1. Earthquake Data
No.
Obs
Region
Date
Time
(WIB)
X1
X2
X3
X4
X5
X6
X7
X8
1
Kebumen, Central Java
25-Jan-14
05:14:20
6.5
48
0
0
3
177
4
14
2
South OKU, South Sumatra
31-Mar-14
04:13:42
5.4
10
0
0
1
8
1
1
3
Ambon, Maluku
02-May-14
08:43:34
5.7
10
0
3
0
67
1
3
4
Tanah Datar, West Sumatra
10-Sep-14
17:46:19
5.0
10
0
2
0
238
2
4
Sinkron : Jurnal dan Penelitian Teknik Informatika
Volume 7, Number 3, July 2022
DOI : https://doi.org/ 10.33395/sinkron.v7i3.11598
e-ISSN : 2541-2019
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2093
5
Ternate, North Maluku
15-Nov-14
02:31:44
7.3
10
0
0
0
0
1
1
…
…
…
…
…
…
…
…
…
….
…
…
…
…
…
…
…
…
…
…
…
…
…
…
55
Lombok, NTB
6-Dec-18
08:02:46
5.4
11
0
0
0
3
1
12
56
Wajo
16-Dec-18
22:06:46
4.4
2
0
0
0
2
1
1
57
Manokwari, West Papua
28-Dec-18
10:03:33
6.1
26
0
0
0
1
1
3
Where :
X1 : Magnitude (SR)
X2 : Depth (Km)
X3 : Victim Dies
X4 : Victim Not Died
X5 : Public Facilities Heavy Damage
X6 : Minor Damage Public Facilities
X7 : Affected Area
X8 : Less Affected Area Clustering Simulation
The results and discussion of the hazard zone grouping are described starting with data collection, data
standardization, correlation test, principal component analysis is carried out if the data used are
correlated, then continued with cluster analysis (clusters) and then completed with K-means cluster
analysis using the Minitab application.
Before performing the K-means cluster analysis, a new column is added, named Initial. Initial column
taken from the Earthquake Depth Scale in the catalog of destructive earthquakes is used as a benchmark
in the formation of clusters so that in this grouping it is divided into 3 clusters.
Cluster 1 : Shallow Earthquake (depth < 60km) causes damage big
Cluster 2 : Medium Earthquake (60km <depth> 300km) minor damage
Cluster 3 : Shallow Earthquakes ( depth > 300km ) are not dangerous
For cluster 1 is given the number 1, cluster 2 is given the number 2, cluster 3 is given the number 3
Next, the K-Means Cluster Analysis was carried out with the initial partition column and the results
were named Experiment 1 (Exp 1) as follows:
TABLE 1. FINAL PARTITION EXP 1
Number of
observations
Within cluster
sum of squares
Average distance from
centroid
Maximum distance from
centroid
Cluster1
46
333,647
1,812
11.177
Cluster2
11
52,319
2,069
3,146
As a comparison material for selecting the right cluster, the K-Means Cluster Analysis was carried out
again without an initial partition column, and the results were named Experiment 2 (Exp 2) as follows:
TABLE 1. FINAL PARTITION EXP 1
Number of
observations
Within cluster sum
of squares
Average distance from
centroid
Maximum distance from
centroid
Cluster1
6
174.950
5,105
8,221
Cluster2
30
26,174
0.838
2.108
Sinkron : Jurnal dan Penelitian Teknik Informatika
Volume 7, Number 3, July 2022
DOI : https://doi.org/ 10.33395/sinkron.v7i3.11598
e-ISSN : 2541-2019
p-ISSN : 2541-044X
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Cluster3
21
71,841
1,748
2,681
Based on the results of the sum of cluster 1, cluster 2, and cluster 3 in the column within cluster sum
squares, a total of 386,966 for Exp 1 and 272,965 for Exp 2.
So that the cluster used uses the final partition in experiment 2. There are 6 areas in cluster 1 with a
large level of damage (danger), 30 areas are in cluster 2 with light damage (less dangerous) and 21 areas
are in cluster 3 which is an area not harmful.
Principal Component Analysis (PCA) was pioneered by Karl Pearson in 1901 for nonstochastic variables,
PCA is a technique for forming new variables which are linear combinations of the original variables.
According to (Jain et al., 1999) PCA is a technique used to simplify data by transforming the data linearly
to form a new coordinate system with maximum variance. PCA concentrates on explaining the structure
of variance and covariance through a linear combination of the original variables, with the main objective
of reducing data and making interpretations. I start with the data on the p variable of the number of n data.
As shown in the table, the linear combination of the variables, the main components are obtained,
namely:
Based on the results of the centroid cluster (attachment 10), then a clustering model is made using the
main components obtained:
For Cluster 1:
For Cluster 2:
For Cluster 3:
The first cluster is dominated by the following variables:
The second cluster is dominated by the following variables:
The third cluster is dominated by the following variables:
CONCLUSION
Based on the research that has been done using the K-Means algorithm, it can be concluded that the
results of Cluster 1 are 6 areas with major damage (danger), Cluster 2 is 30 areas with light damage (less
dangerous) and Cluster 3 is 21 areas which are harmless area. Testing data on Minitab using the K-Means
algorithm can display the same 3 (three) classes with manual calculations. So that the K-Means algorithm
can be used for clustering the hazard zone after an earthquake.
Sinkron : Jurnal dan Penelitian Teknik Informatika
Volume 7, Number 3, July 2022
DOI : https://doi.org/ 10.33395/sinkron.v7i3.11598
e-ISSN : 2541-2019
p-ISSN : 2541-044X
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ACKNOWLEDGMENTS
Would like to acknowledge Mr. Open Darnius and Mr. Sutarman who became my supervisor as well
as assisting in the completion of master’s studies at the mat5hematics department of University North
Sumatera.
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