K-means Nonhierarchical Cluster and Dbscan Outlier Detection In the
Grouping of Stock Issuers
ATIEK IRIANY, HENIDA RATNA AYU PUTRI, HARRY MARINGAN TUA
Statistics, Faculty of Mathematics and Natural Sciences, Brawijaya University, Malang, INDONESIA
Abstract: Group analysis aims to group objects based on similar characteristics so that they are in one group
homogeneous and between groups heterogeneous. Study this aim group issuer share in Indonesia based on
volatility, liquidity, and market capital. This study uses the non-hierarchical K-Means Clustering method, because
the number of samples is big and the number of groups are known. The K-Means Clustering grouping method
produces as many as 6 groups with different characteristics. 2. Group 1 consists of stock issuers with quite high
volatility and liquidity. The characteristic of group 2 is that it consists of stock issuers with the lowest volatility.
Big Capital is the nickname for group 3 because it has market capital or the asset value is very large among all
groups and the volatility is very small, and liquid. In Group 4, stock issuers have the highest volatility and the
lowest liquidity. Results of profile interpretation in group 5, issuer’s stocks have the highest liquidity and market
capital is quite low. Share issuers in group 6 have the volatility highest. Group 3 is recommended as an option
for investing. Because, having market capital or large asset values, liquid, and volatility is low enough to
minimize risk. The originality of this research is that there is no combination of methods between grouping in
fields with k-means clustering and detection of sales with DBSCAN, especially in the field of issuer share in
Indonesia.
Key-words: Clustering, Stock Issuers, K-Means, Liquidity, Volatility
Received: September 18, 2022. Revised: May 21, 2023. Accepted: June 15, 2023. Published: July 20, 2023.
1. Introduction
Group analysis is a method used to classify data
by trying to separate component data into several
groups. Group analysis is a multivariate grouping
technique used for grouping objects into groups based
on their characteristics [1]. Homogeneity within the
group was high while between groups was
heterogeneous.
Stocks are the best choice used by the younger
generation and investors to invest because they are
attractive and can be obtained with small capital. In
addition, stocks also tend to be liquid and not time-
bound, such as long-term deposits, so stocks are
considered one of the most popular investment
instruments in the world. Shares are areas or accounts
that are valued for various financial instruments
related to the ownership of a company. Companies that
are listed on the Indonesia Stock Exchange or have
submitted an initial public offering (IPO) can sell their
shares to the public. As many as 680 issuers of shares
were listed on the Indonesia Stock Exchange in March
2020, and it continues to increase from time to time.
All listed shares have different characteristics, both in
terms of company origin and share price movements in
the (technical) market. Based on IDX's annual report,
it was found that the Indonesia Stock Exchange
experienced unexpected things in the last few years. In
2020, the JCI was very low due to a decrease in sales
volume that occurred during the Covid-19 pandemic.
Currently, Indonesia is still being affected by the
Covid-19 pandemic, and this has resulted in the stock
market experiencing volatility high enough. This study
uses the non-hierarchical K-Means Clustering method,
because the sample size is large and the number of
groups is known. Syakur, et al. [2] reported that the
use of the elbow method in K-Means Clustering helps
determine the number of groups based on the decrease
in the number of squared largest deviations. Research
by Patel, et al. [3] explains that data standardization
and elimination of outliers produce an average
minimum squared deviation and increase clustering
efficiency. The Elbow method and DBSCAN can be
an option for overcoming the weaknesses of K-Means
Clustering so that the group profile interpretation
results are better. Based on this description, grouping
needs to be done to see how the character of each group
of stock issuers is formed.
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Atiek Iriany, Henida Ratna Ayu Putri, Harry Maringan Tua
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The variables in this study are volatility, liquidity,
and market capital. This study aims to classify stock
issuers in Indonesia using K-Means Clustering with
two auxiliary methods to improve the quality of
grouping results, namely the elbow method and
Density-based spatial clustering of applications with
noise (DBSCAN). The use of these two methods in
combination has never been done before, especially
when applied to grouping stock issuers. It is hoped that
this research can be used as a consideration for
investors in allocating funds to certain stock issuers
that have good ratings or are by the profile. The
limitation in this study is when determining the
optimal number of groups using only the elbow
method and in determining the maximum distance
between two objects in one group that is allowed to use
the K-distance graph. The originality of this research
is that there is no combination of methods between
grouping in fields with k-means clustering and
detection of sales with DBSCAN, especially in the
field of issuer share in Indonesia. The originality of the
research can be further explained in the following
table. The following table will explain some of the
previous studies by comparing the pluses, minuses,
along with the shortcomings of the methods that can
be completed in this study.
Table 1. Plus Minus Interesting Facts This Research
Title
Plus
Minus
Interestin
g
Integration
K-Means
Clustering
Method and
Elbow
Method For
Identificatio
n of The
Best
Customer
Profile
Cluster
(Syakur et
al., 2017)
Indonesia
n SMEs
still do
not have
customer
mapping.
This
research
helps
map
customer
s using
the K-
Means
method
This study
has not
implement
ed outlier
detection.
It is
important
to carry out
outlier
detection
before
clustering
because it
can affect
the results
of
clustering.
This
study has
not
performe
d outlier
detection
.
Optimizatio
n of Data
Grouping in
the K-Means
Method with
Outlier
Analysis
Research
has done
outlier
detection
before
cluster
analysis.
Outlier
detection
does not
use the
DBSCAN
method.
DBSCAN
This
study has
not
performe
d outlier
detection
using the
(Ariawan,
2019)
has
advantages
that are
adjusted to
the
distance.
DBSCA
N
method.
Impact of
Outlier
Removal
and
Normalizati
on Approach
in Modified
K-Means
Clustering
Algorithm
(Mehta dan
Patel, 2011)
This
study
uses a
different
outlier
method,
namely
using R-
estimator
s.
The R-
estimator
method
utilizes the
rank value,
and does
not pay
attention to
the
distance
from each
object
Research
has not
done
outlier
detection
using the
DBSCA
N
method.
2. Literature Review
2.1. K-Means Clustering
K-Means clustering is a distance based non-
hierarchical grouping method that seeks to partition
data into two or more groups. Objects that have the
same characteristics will be grouped into one group
and if they are different they will be grouped into
another group. The purpose of this grouping is to
minimize the variance within a group and maximize
the variance between groups. Before the grouping
process, determine the number of groups. Each object
will be calculated as the the distance to each group
center, the smallest distance is used to determine the
group. The K-Means procedure is:
1. Specifies as the number of clusters you want to
form
2. Allocate objects into clusters randomly
3. Determine the cluster center ( centroid ) from the
existing data in each cluster with equation (2.1).
Remarks :
: th cluster centers on th variable (
)
n : a lot of data in the cluster to-
4. Determine the distance between each object and
each centroid by calculating the distance between
each object and each centroid using the distance
measure square Euclidean distance with equation
(2.2).
Remarks :
(2.1)
(2.2)
(2.1)
(2.2)
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: Square Euclidean Distance cluster ke- for
variable to-
: cluster index
: the index of the variable
: the value of the th object in the cluster that
for the variable
: cluster centroids ke- for variable to-
5. Calculating the objective function with the formula
(2.3).
Description :
n : amount of data
c : the number of clusters
: membership data object to-th and cluster-
th
: square Euclidean distance space
between object ke- to the cluster centroid to-
6. Allocating each data to the nearest centroid
/average which is formulated in equation (2.4).
7. Repeat steps 3-6 until there is no movement of the
object or no change in the objective function.
2.2.Euclidean distance
The Euclidean distance is the most commonly
used measure of similarity distance. Euclidean distance
between objects and the center of the group which
is in the variable dimension, then it is defined in
equation (2.5).
(2.5)
Information:
= distance of the object to the center of
the group
= the value of the object to the variable
to-
= center of group to - on variable to -
= 1,2,...,
= 1,2,...,
= 1,2,...,
= the number of groups
= many objects
= number of variables
These distances can be formed into an ordered
matrix into matrix with the order .
D =
According to Dillon & Goldstein [4], before
calculating the Euclidean distance, the original data
should be standardized first if it has different unit sizes,
which can lead to high standard deviation values,
which can result in invalid group analysis calculations.
Standardize data in the form of a z-score, with the
formula shown in equation (2.6) below.
(2.6)
Information:
= the standard value-
= data value to-
= average
= standard deviation
2.3.Elbow Method
Moment determines the number of groups,
methods Elbows own method with count score the sum
of the squared deviations in each group. At a certain
point, there will be a graph of the largest decrease with
a curve called the elbow criterion, then it becomes the
number the best group [5]. The equation for the sum of
squared deviations could be shown in the following
equation (2.7).
(2.7)
Description :
= 1,2,...,
= the number of groups
= value of the th object
= center of the group -
(2.3)
(2.4)
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2.4.DBSCAN
The Density-based Spatial Clustering of
Application with Noise (DBSCAN) method is a
density-based clustering method from the position of
the observed data with the principle of grouping
objects that are relatively close together. In this
method, two inputs (input values) are required before
clustering. The first input is the epsilon value which is
the maximum distance between two objects in one
allowed cluster, and the second input is the minimum
number of objects to form a cluster (minPts).
According to Sander¸ et al. [6], if the data has more
than two variables, the minPts is twice the number of
variables. The epsilon value can be chosen using a k-
distance graph where k equals minPts. The optimal
epsilon value is obtained at the point of maximum
curvature. The distance method used in the DBSCAN
method is the Euclidean distance. A pair of objects is
said to be neighboring if the distance between the two
objects is less than the epsilon value.
In addition, there are two conditions for object
adjacency, namely directly density-reachable and
density-reachable. Object " x " is said to be directly
density-reachable (directly connected) with object " p
" if object " x " is adjacent to object " p " and the
number of neighbors of object " p " is more than equal
to minPts. An object is said to be density-reachable if
there is another object “ x ” that connects object “ p ”
with observations “ q ”, but object “ x ” must be
directly density-reachable [7]. An illustration of the
condition of neighboring objects can be seen in Figure
1.
Figure 1. Illustration of directly density-reachable
and density-reachable observations.
DBSCAN clustering results can be divided into
three types, namely core points, border points, and
noise points. Core points are objects that are in a
cluster. Border points are objects that are between two
clusters. Noise points are objects that are neither core
points nor border points and are outside the cluster [8].
In practice, in this study the DBSCAN method was
used to identify objects detected as noise.
2.5.Volatility
Volatility is measurement statistics for fluctuation
prices during a period certain [9]. Size the show
decrease and increase prices in a short period and no
measure level price, however level variations from one
period to period next. High volatility reflects
characteristics that supply and demand are not normal.
Market volatility occurs consequence entry of
information new to in the market or stock exchange.
As a result, market participants do evaluation return to
their assets trade. In an efficient market, the level price
will do the adjustment with fast so that formed price
reflect information new the [10]. Based on some of
these explanations, it can be concluded that stock price
volatility is an important variable where this variable
measures the distance between stock price fluctuations,
if it is too high, it is certain that the stock price will rise
or fall very quickly. Stock price volatility is calculated
using the standard deviation of the percentage change
in price.
2.6.Liquidity
Liquidity is the price and how easily an asset is
converted into cash by selling it [11]. From the
perspective of market participants, a market is a liquid
when the market has a high volume, which can be
traded instantly with minimal price impact. Harris [12]
defines liquidity as the ability to carry out commercial
transactions in large quantities, which can be done
quickly and at low cost if desired. Liquidity is an
important characteristic of the market as a function of
providing information about the possibility of trading
at a certain size, at a certain price and at a certain time,
in which market functions the market is running well
(well-functioning market). This characteristic provides
an opportunity for traders to consider factors other than
size, price, and timing that affect the probability of a
trade. The greater the volume of a stock traded every
day, the more liquid the stock will be. The median of
stock volume is used as an indicator of the liquidity of
a stock. The choice of the median as an indicator is due
to its robustness against outliers (unlike the mean) so
that the results obtained are not biased.
2.7.Market Capital
Market capitalization is necessary to calculate
because is one of the usual criteria, investors use to
decide is will buy a share something a company, as
well as reflect the total value of the company or the
price aggregate share of something a company.
Becomes investors target disbursing investment funds.
Market value, also known as market price, is price of
stock on the current market this. If the stock market or
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Atiek Iriany, Henida Ratna Ayu Putri, Harry Maringan Tua
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the exchange is closed, the market price is price
closing. If the market price is multiplied by the total
issued shares or circulate, then obtained market value
or market capitalization [13]. Market capitalization is
the size of outstanding shares to the public, counted
from the total outstanding shares multiplied by the
price share end [14]. Then, the market capitalization is
score total company public that has record shares on
the stock exchange [15]. Next market capitalization is
the market value of shares issued (shares outstanding)
by stock issuer [16]. Based on the opinions that have
been stated above, can taken conclusion that market
capitalization is the score magnitude share circulated
that has been listed on the stock exchange. Market
capital got through multiplication between total shares
with price share. The more big the Italian market cap
so the more difficult for price share played by a handful
of people.
3. Methodology
3.1.Data Source
Data obtained from stock market transactions
through the yahoo finance website from 2017 to 2021.
A total of 471 issuers shared used in the study of this.
There are 11 variables used in the study is Liquidity,
Volatility and Market Capital (Rp). Because there is
different unit variables so need to conduct
standardization.
3.2.Method Analysis
Stages analysis performed for complete problem
in this study.
1. Do preprocessing data and statistics descriptive
with present data in shape table with count
minimum, average, maximum, and IQR values in
the data.
2. Look if there are different units for the variables
used. If there is a difference unit, then conducted
based on data standardization the following
equation (3.1).
(3.1)
Information:
= the standard value of each data i of the each
variable p
= the data value i of the each variable p
= the average of the each variables p
= standard deviation of each variable p
3. Do DBSCAN for detect issuer share outlier with
inputs minPts = 22, and epsilon which will
searching for use k-distance graph. If there is
outlier so issuer share eliminated. The DBSCAN
procedure is presented in Figure 3.1. following.
Figure 2. DBSCAN procedure
4. Do the elbows method to get the optimal number
of groups, by calculating the sum of the squared
deviations every many groups using the following
equation (3.2).
(3.2)
Description :
k = 1,2,… ,K
K = many groups
= value object i
= center group k
5. Do method K-Means Clustering with the number
of groups obtained from the previous stage. K-
Means Clustering produce served on the
following diagrams.
Figure 3. K-Means Clustering Procedure
6. Get profile group which formed and interpreted
the result.
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Atiek Iriany, Henida Ratna Ayu Putri, Harry Maringan Tua
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Number of Groups (k)
Sum of Squared Deviations
4. Results and Discussion
4.1. Results Analysis Descriptive
The results of the descriptive analysis obtained,
namely, most of the issuer's stock volatility is 4%.
Issuer share ATIC or PT. Anabatic Technologies Tbk,
and MASA, that is PT. Multistrada Arah Sarana Tbk
has volatility highest as big 286% as well as 131%
because of change in price. Part big issuer shares have
liquidity big 0.067% with a maximum of 2.68% owned
by ERAA or PT. Erajaya self-sufficiency Tbk. On
variable market capital, Most of the stock issuers have
asset values as big IDR 11.8 trillion, with the lowest as
big IDR 22.1 billion owned by PT. Century Textiles
Industry Tbk and the highest Rp. 501.8 trillion is
owned by PT. Bank People Indonesia (Persero) Tbk.
Figure 4. Volatility per year (Maximum)
4.2. Results Application DBSCAN
Method DBSCAN with python software produces
output in the form of labels group of each issuer of
stock, with -1 as category noise or outlier and other
numbers as a particular group category. Stock issuers
who get the label 1 are stock issuers categorized noise
or outliers. Based on the results DBSCAN as many 24
issuer shares detected as an outlier. Issuer share which
was detected as outlier on method DBSCAN served in
Table 1. Table 1. Outlier Share Issuer
4.3. Results Application Elbows method
Results from the total square deviation of every
many groups were visualized to determine the number
of groups (k) that have scored optimal. Results
visualization served in Figure 6.
Figure 6. Results of the Elbow method
The information obtained from Figure 6 is k with
the score which optimal is at one moment many groups
= 6, which is the point with a decrease in high JKD
values, and slope perfect. So in the application elbows
method, it can be concluded that the optimal value for
applying multiple groups is 6.
4.4. Results Application K-Means
Clustering
Analysis results group on issuer share in
Indonesia, use method non-hierarchical K- Means
Clustering with many groups (k) = 6, the results
obtained are the number of stock issuers in every group
as presented in Figure 7.
Figure 7. The results of grouping with the K- Means
Clustering
Based on Figure 2, obtained the conclusion is that
many issuer share every group enough diverse. The
order of grouping from smallest to largest is group 6 as
much 1 issuer share, group 3 as much 27 issuer share,
group 5 as many as 35 stock issuers, group 1 as many
as 68 issuers of shares, group 4 as many 130 issuer
share, and group 2 as much 186 stock issuers. The
details issuers formed in 6 groups the shown in Table
3.
Issuer share which detected as an outlier
ACST, AKRA, ANTM, ASII, ATIC, BBCA,
BBNI, BBRI, BMRI, BOGA, BULL, BYAN, CPIN,
ELSA, ERAA, HMSP, ICBP, MAPI, MASA, MDKA,
SMA, TLKM, TPIA, UNVR
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Table 3. Details Member Issuers in the 6 Groups
Formed
Group 1
ACES, AGII, AISA, ALDO, APLN, ASRI, ASSA,
BABP, READ, FATHER, BBYB, BEST, BFIN, BHIT,
BIMA, BJBR, BKSL, BNBA, BRMS, BSDE, BWPT,
CINT, CTRA, DGIK, DKFT, DSFI, DYAN, EMTK,
ESSA, FREN, GJTL, GPRA, IKAI, IMAS, INDX, ISSP,
ITMG, JPFA, KAEF, KBLI, KRAS, LPKR, MAIN,
MBSS, MCOR, MPMX, MPPA, PANR, PBRX, PNBS,
POLY, PTRO, PWON, RAJA, RALS, RBMS, SDMU,
SMDR, SMRA, SOCI, SRTG, TKIM, TMAS, TRIS,
WINS, WSBP,
WTON, ZBRA
Group 2
AALI, ABDA, ABMM, ADES, ADMF, ADMG,
AKKU, ALTO, AMAG, AMFG, ANJT, APIC, ARGO,
ARNA, ARTI, ASDM, ASGR, ASMI, ASRM, AUTO,
BALI, BATA, BAYU, BBMD, BBRM, BCAP, BCIC,
BDMN, BEKS, BIPI, BIPP, BIRD, BISI, BJTM, BLTA,
BNGA, BNII, BOLT, BPFI, BPII, BRNA, BSIM, BSSR,
BTEK, BTPN, BUDI, BUKK, CASS, CEKA, CENT,
CFIN, CITA, CLPI, CMNP, CNKO, CPRO, CSAP,
CTBN, CTTH, DEFI, DEWA, DILD, DLTA, DMAS,
DSNG, DUTI, DVLA, ECII, EKAD, EMDE, EPMT,
FAST, GAMA, GDYR, ECHO, GMTD, GZCO, HADE,
HEROES, HEXA, HOTL, IATA, IGAR, IKBI, IMPC,
INAI, INCI, INDS, INPC, INTA, IPOL, JECC, JGLE,
JIHD, JKON, JRPT, JSPT, JTPE, KDSI, KIAS, KIJA,
KINO, KKGI, KOPI, KPIG, LINK, LMPI, LPCK, LPGI,
LPPS, LTLS, MAGP, MAYA, MBAP, MDLN, MDRN,
MERK, META, MFIN, MICE, MIDI, MIRA, MITI,
MKNT, MLBI, MMLP, MRAT, MSKY, MTFN,
MTLA, MYOH, NIRO, NISP, NOBU, NRCA, PANS,
PJAA, PNBN, PNIN, PNLF, POWR, PPRO, PRAS,
PRDA, PSAB, PSKT, PTSP, RANC, RICY, BREAD,
RUIS, SCCO, SGRO, SHID, SHIP, SIDO, SILO, SIMP,
SIPD, SKLT, SMAR, SMCB, SMSM, SPMA, SRSN,
STAR, STTP, SULI, SUPR, TAXI, TBLA, TCID,
TGKA, TIRT, TOBA, TOTL, TOTO, TRST, TSPC,
TURI, ULTJ, UNIC, UNSP, VIVA, VOKS, WOMF
Group 3
ADRO, AGRO, AMRT, BNLI, BRPT, CASA,
DNET, DSSA, EXCL, GEMS, GGRM, HRUM, INCO,
INDF, INKP, INTP, ISAT, JSMR, KLBF, MEGA,
MIKA,
MYOR, PTBA, SMGR, TBIG, TOWR, UNTR
Group 4
AGRS, AHAPS, AIMS, AKPI, ACTION, ALKA,
ALMI, AMIN, APEX, APII, APLI, ARII, ARTA, ASBI,
ASJT, STEEL, BBHI, BBLD, BIKA, BINA, BKDP,
BKSW, BLTZ, BMAS, BMSR, BNBR, BRAM, BTON,
BVIC, CANI, CNTX, DART, DAYA, DNAR, DPNS,
ERTX, ESTI, fish, FMII, FORU, FPNI, GDST, GLOB,
GOLD, GSMF, GWSA, HDFA, HITS, IBFN, IBST,
ICON, IDPR, IMJS, INAF, INCF, INDR, INPP, INRU,
INTD, ITMA, JAVA, KARW, KBLM, KBLV, KICI,
KOBX, COINS, KONI, LION, LMAS, LMSH, LPIN,
LPLI, LRNA, MBTO, MDIA, MFMI, MLPT, MREI,
MTSM, MYTX, NELY, NIKL, OASA, OKAS, OMRE,
PADI, PALM, PBSA, PDES, PEGE, PGLI, PICO,
PNSE, PSDN, PTIS, PTSN, PUDP, PYFA, RDTX
Rally, RIGS, WHEEL, SAFE, SDPC, SDRA,
SKBM, SMBR, HR, SMMT, SONA, SQMI, SRAJ,
SSTM, TALF, TBMS, TFCO, TIFA, TIRA, TMPO,
TPMA, TRIM, KEEP GOING, VICO, VINS, VRNAs,
WAPO, WICO,
YPAS, YULE
Group 5
ABBA, ADHI, ARTO, BBKP, BBTN, BCIP,
BGTG, BMTR, EARTH, DOID, ENRG, INDY, KREN,
LEAD, LPPF, LSIP, LET, MEDC, MLIA, MLPL,
MNCN,
MTDL, PGAS, PKPK, PTPP, SAME, SCMA,
SSIA, SSMS, TARA, TINS, WEHA, WIIM, WIKA,
WSKT
Group 6
ELTY
Result of analysis group consider similarity
volatility, liquidity, as well market capital on each
issuer stock.
4.5. Interpretation Profile Group
After getting results grouped and has know the
issuer share member in every group, next is to interpret
the characteristics of each group by comparing Q1,
median, Q3, and IQR using data origin.
Group 4 with the member as much 130 issuer
share have volatility Very spread among all groups. A
total of 65 issuer shares in group 4 have volatility from
4% to 5.5%. Gap highest median volatility by 20%.
Because ELTY did a stock split or split the shares into
more shares many with a score nominal more low per
sheet. Group 5 with 35 members of issuer shares has
liquidity which is highly dispersed among all groups.
A total of 18 issuer shares in group 5 have liquidity
from 0.2% to 0.35%. Group 5 has the highest liquidity
median among all groups. Issuer share on group 5
tends easy traded. Group 3 with the member of as much
27 issuer share which served on Attachment 8. have
market capital Very spread in Among all group. As
much 14 issuer shares in group 3 has a market capital
between IDR 35.8 trillion to IDR 57.9 trillion. This
matter evidenced by stock issuers in group 3 is
companies big with score asset tall, that is Warehouse
Salt (GGRM), Semen Indonesia (SMGR), Jasamarga
(JSMR), and united Tractors (UNTR).
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5. Conclusion
Based on the results and discussion obtained
conclusion is as follows.
1. Application K-Means Clustering with distance
euclidean on stock issuer data in Indonesia
obtained results that many member group 1 as
much 68 issuer shares, group 2 as much 186
issuer shares, group 3 as much 27 issuer shares,
group 4 as much 130 issuer shares, group 5 as
much 35 issuer shares, and group 6 as many as
1 shares issuer.
2. Group 1 members issuer shares with volatility
and liquidity enough tall. Characteristic from
group 2, that is members stock issuers with
volatility Lowest. big Capital is a nickname for
group 3, because have market capital or score
asset very big in Among all groups as well as
volatility very small, and liquid. In Group 4,
stock issuers have volatility high and the lowest
liquidity. Interpretation results from profile on
group 5, issuer shares have liquidity highest and
market capital enough low. Issuer shares in
group 6 has the volatility highest.
Acknowledgement
Thank you to all parties for their support and input
in the preparation of this research. All the support and
input given is very useful for the perfection of this
research. This research did not receive any specific
grant from funding agencies in the public, commercial,
or not-for-profit sectors. The authors report there are
no competing interests to declare.
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The authors equally contributed in the present
research, at all stages from the formulation of the
problem to the final findings and solution.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
Thank you to all parties for their support and input
in the preparation of this research. All the support and
input given is very useful for the perfection of this
research. This research did not receive any specific
grant from funding agencies in the public, commercial,
or not-for-profit sectors. The authors report there are
no competing interests to declare.
Conflict of Interest
The authors have no conflicts of interest to declare
that are relevant to the content of this article.
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(Attribution 4.0 International, CC BY 4.0)
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PROOF
DOI: 10.37394/232020.2023.3.4
Atiek Iriany, Henida Ratna Ayu Putri, Harry Maringan Tua
E-ISSN: 2732-9941
28
Volume 3, 2023
