JOIV : Int. J. Inform. Visualization, 5(4) - December 2021 415-421

INTERNATIONAL JOURNAL
ON INFORMATICS VISUALIZATION

INTERNATIONAL
JOURNAL ON
INFORMATICS
VISUALIZATION

journal homepage : www.joiv.org/index.php/joiv

Feature-reduction Fuzzy c-means Clustering for Basketball Players
Positioning
Yessica Nataliani a,*
a

Department of Information System, Satya Wacana Christian University, Diponegoro 52-60, Salatiga, 50711, Indonesia
Corresponding author: *yessica.nataliani@uksw.edu

Abstract— One of the best-known clustering methods is the fuzzy c-means clustering algorithm, besides k-means and hierarchical
clustering. Since FCM treats all data features as equally important, it may obtain a poor clustering result. To solve the problem, feature
selection with feature weighting is needed. Besides feature selection by assigning feature weights, there is also feature selection by
assigning feature weights and eliminating the unrelated feature(s). THE Feature-reduction FCM (FRFCM) clustering algorithm can
improve the FCM clustering result by weighting the features and discarding the unrelated feature(s) during the clustering process.
Basketball is one of the famous sports, both international and national. There are five players in basketball, each with a different
position. A player can generally be in guard, forward, or center position. Those three general positions need different characteristics of
players’ physical conditions. In this paper, FRFCM is used to select the related physical feature(s) for basketball players, consisting of
height, weight, age, and body mass index. to determine the basketball players’ position. The result shows that FRFCM can be applied
to determine the basketball players’ position, where the most related physical feature is the player’s height. FRFCM gets one incorrect
player’s position, so the error rate is 0.0435. As a comparison, FCM gets five incorrect player’s positions, with an error rate of 0.2174.
This method can help the coach decide the basketball new player’s position.
Keywords— Feature-reduction; clustering; fuzzy c-means; basketball; position.
Manuscript received 24 Aug. 2021; revised 22 Sep. 2021; accepted 26 Nov. 2021. Date of publication 31 Dec. 2021.
International Journal on Informatics Visualization is licensed under a Creative Commons Attribution-Share Alike 4.0 International License.

Furthermore, currently, high-dimensional data is widely
used for data analysis. Of course, high-dimensional data
needs more computation time. Therefore, the use of feature
selection is very important [6]. Feature weight can be used to
support feature selection, where each feature has its weight
[7], [8]. Feature-weighted has been used for clustering
algorithms, for example, sparse k-means, entropy-weighted kmeans, feature-weighted k-means, feature-weighted FCM,
weighted FCM with feature-weight learning, etc. [9]. Some
literature applied feature selection and featured weight in
clustering to discard unrelated features. There are featurereduction FCM [9], feature-reduction k-means for multi-view
data [10], feature-reduction scheme for possibilistic c-means
[11], and dimensionality-reduction using PCA and k-means
[12]. Basketball is one of the famous sports, both international
and national. The National Basketball Association (NBA) is
a well-known international basketball event. In Indonesia, one
big event is named the Indonesian Basketball League (IBL).
12 teams are competing in IBL. One of them is Satya Wacana
Saints [13]. This team consists of 23 students of Satya
Wacana Christian University in Salatiga.

I. INTRODUCTION
In pattern recognition, cluster analysis is unsupervised
learning. Clustering is a method to find groups, such that the
similar characteristics data will be in the same cluster, and
data with different characteristics will be in the other clusters.
Many areas use cluster analysis, such as business, image
processing, education, etc. k-Means is the most popular
clustering method, where each data point belongs to exactly
one cluster. k-Means is extended to be fuzzy c-means (FCM),
where each data point can be included into several clusters,
depending on the cluster membership values [1], [2].
A dataset is defined by a number of points and dimensions
(attributes, features). In general, the clustering process treats
all features to be equally important. However, some features
may be unrelated and affect the clustering performance. It is
important to find the related features to obtain a better
clustering result [3]. Feature selection can solve the problem
by removing unrelated and redundant data to reduce the
computation time, and the clustering performance can be
improved [4], [5].
415

cluster center, with ∑
= 1, ∀", is the " #$ point, is
the % #$ cluster center, and 1 < ( < ∞ is the fuzzy exponent.
The Euclidean distance,
,
= ‖ − ‖, is the
#$
#$
distance between the " point and the % cluster center. Since

In basketball, there are five players, where each player can
be on the shooting guard, point guard, small forward, power
forward, or center position. Each position needs different
players’ physical conditions, e.g., height, weight, age, and
body mass index (BMI). Some experts said that
anthropometric or body measurements could determine the
athlete's career, especially in basketball [14], [15]. Physical
condition is important for coaches to choose a new player,
besides his/her talent. Players’ physical conditions affect the
players’ position in basketball. Unsuitable positions allow
players not to play optimally [16], [17]. The players’ physical
condition can generally determine the position. If the player
is tall and big, he can be in the center or power forward
position. If the player is small and agile, he can be on the
guard position [18].
In general, the players’ positions can be divided into three
positions, i.e., guard, forward, and center. Players in the guard
position are more often outside the paint area. The team puts
the smallest and most agile players for this position. Guards
have less physical contact with opposing players than the
forward and center positions. Guards usually are the brain of
attack on a team. This position consists of two kinds, point
guard and shooting guard. The second position is forward. A
player in this position is a player whose job is to see an open
position near the paint area, to break through the opponent's
defense, or in other words, to drive inside. A forward is
usually tall and strong because his main job is to defend and
rebound. Players in this position must have a medium level of
shooting accuracy. This position consists of two types, small
forward and power forward. The last position is center.
Players in this position are often called the big man, who is in
charge of guarding their paint area and attacking the
opponent's paint area. The center position is more likely to
physically collide with opposing players in scoring or
blocking the opponent's center position. This position is held
by the tallest and biggest player [19].
Clustering can be used to find a suitable position for each
player. Players with similar physical conditions will be
grouped into the same position, and players with different
physical conditions will be in different positions. In this
paper, the grouping of the positions of Satya Wacana Saint
basketball team based on their physical conditions with FCM
will be discussed. The physical conditions used here are
referred to as height, weight, age, and BMI. Furthermore, the
feature-reduction method with FCM will be used to find the
most important features that can determine the player’s
position, so it can help the coach decide whether a new
basketball player is more suitable in what position.
There are some variants of feature-weighted clustering.
Some of them are modifying the k-means and FCM clustering
objective function into a new objective function by adding
feature weight. Before some feature-weighted clustering is
presented, FCM clustering will be described first.

,

= , ∑-

- −

-

, where

is the number of

attributes (features or dimension), then Eq. (1) can be written
as in Eq (2).
∑ ∑, =∑
(2)
-−
-

The updating formula for the membership value and the
cluster center are shown in Eqs. (3) and (4),
=

:8<;:8

6

.∑178 /01 2341 5 9

:8<;:8

∑>=78.∑6 /01 23=1 5 9
178
- =

;
∑@
078 ?04 /01
;
∑@
078 ?04

(3)
(4)

where " = 1, … , ; % = 1, … , ; A = 1, … , .
The FCM clustering algorithm can be described as follows,
Input: points , number of clusters , and threshold B > 0.
D
1) Initialize random cluster centers,
, % = 1, … , .
2) Let the iteration rate, E = 1.
F
3) Compute the membership values,
using Eq. (3).
F
4) Update the cluster centers,
using Eq. (4).
F
F2
G < B, then STOP, else go back to step
5) If G
−
c and E = E + 1.
Output: cluster points I , % = 1, … , [1].
The stopping condition used in this algorithm is when there is
no significant difference between the cluster center in the next
iteration.
B. Feature-weighted Clustering
Some extensions from k-means for feature-weighted
clustering are presented. Weighted k-means added the feature
weights during clustering iteration processes. The objective
L
∑ ∑function is
, ,J = ∑
K-−
- ,
#$
where K- is the feature weight of the A feature and M is a
constant. Entropy weighted k-means is also an extension of kmeans by adding a weight entropy term. The objective is to
minimize the within-cluster distance and maximize the
negative weight entropy. Its objective function is
, ,J =
∑ ∑ ∑K - -− - +
γ ∑ ∑- OK - log K - S, where K - is the feature weight of
the A #$ feature in the % #$ cluster and T are a constant [9].
Sparse k-means is also used to select features by assigning
feature weights in the interval [0,1] at first and then updating
the feature's weight (s) with small weights into 0. Whether a
feature weight is small or not is determined based on a
threshold [20].
Besides k-means, FCM is also extended into some methods
for feature-weighted clustering. Weighted FCM added
feature-weight learning to improve the FCM performance,
where
the
objective
function
is
, ,J =
∑
∑ ∑K- - − - [9]. The other method is
simultaneous clustering and attributes discrimination
(SCAD1). In SCAD1, each cluster has a different feature
weight. SCAD1’s objective function is
, ,J =

A. FCM Clustering
Let =
,…,
be a dataset on ℝ with
is the
number of data and is the number of dimensions. The FCM
objective function is defined in Eq. (1).
∑
, =∑
,
(1)
where is the cluster number, is the number of points,
=
[0,1] is the membership value of the " #$ points and the % #$
416

∑
∑ ∑∑- U K - ,
K - - − - +∑
where U is a constant which indicates the importance of
feature weights in each cluster [21]. All these methods
consider feature-weighted clustering, so selecting the related
feature(s) needs to be done manually.
Another modification from FCM objective function is for
feature-reduction. The feature-reduction idea is to eliminate
the unrelated feature(s) automatically. Some methods have
been proposed by modifying the FCM clustering objective
function. For example, feature-reduction for FCM clustering
algorithm, where the objective function is
, ,J =
∑
∑ ∑U- K- O - − - S + ∑- OK- log U- K- S
[9]. Another method is feature-reduction fuzzy co-clustering
algorithm (FRFCoC). The objective function is
, ,J =
∑ ∑ ∑V - U- K- O - − - S +
α1 ∑- OK- log U- K- S + α2 ∑%=1 ∑"=1O "% log "% S +
α3 ∑%=1 ∑A=1OV%A log V%A S, where V - is the feature
membership for the % #$ cluster center and the A #$ feature, α ,
α , αZ are constants. Its objective function consists of four
terms, one term is a modification from the FCM objective
function and three terms are the entropy terms of feature
weight, fuzzy membership, and feature membership [22].

, ,J = ∑

∑-

∑

∑-

U- KOK- log U- K- S

-−

-

+

(5)

where is the number of features, - is the cluster center of
the % #$ cluster and the A #$ feature, K- = [0,1] is the feature
weight of the A #$ feature, with ∑- K- = 1. Here, a constant
U- is used to handle the dispersion and variation of each
feature. The formula of U- is shown in Eq. (6),
\]^_ /

U- = − [ `^a / [

∑@
078 /0

(6)

-

∑@
078 /0 2

hi

/ 5

where mean
=
and var
=
, ∀A.
2
The updating formula for the membership, the cluster
center, and the feature weight are computed as in Eqs. (7), (8),
and (9), respectively,
=

:8<;:8

6

.∑178 j1 k1 /01 2341 5 9

∑>=78.∑6

K- =

(7)

;
∑@
078 ?04 /01

(8)

5
>
@
;
8
o:> ∑478 ∑078 p04 l1.q01 :r419 s
]mn
l1
@

(9)

- =

C. Basketball Players’ Position Analysis
Some analysis about basketball players’ position has been
presented in the literature. Pion et al. [23] found that artificial
neural networks can provide a specific position characteristic
in basketball. They mentioned that multivariate variance
analysis could not predict the specific players’ position
accurately. Zhang et al. [24] used clustering to see the
performance of NBA players according to their
anthropometric features and their playing performance.
Erga and Nataliani have researched feature selection with
FCM for basketball players’ positioning. They combined four
physical conditions, i.e., height, weight, age, and BMI, one by
one to get the best clustering result, which was measured by
the accuracy rate. Height and BMI are the best combinations
to determine the player’s position [19].

:8<;:8

j k / 23=1 5 9
178 1 1 01
;
∑@
078 ?04

5
>
@
;
8
o:> ∑478 ∑078 p04 l1.q01:r41 9 s
]mn
l1
@

∑6
t78

The FRFCM clustering algorithm is described as follows,
Input: points , number of clusters , and threshold B > 0.
D
1) Initialize random cluster centers,
, % = 1, … , and
D
define the initialization of feature weight, J- =
[1⁄ ] × , A = 1, … , .
2) Let the iteration rate, E = 1.
3) Compute U- using Eq. (6)
F
4) Compute the membership values,
using Eq. (7).
F
5) Update the cluster centers,
using Eq. (8).
F
6) Update the feature weights, J- using Eq. (9).
7) Discard the feature(s) if the feature weight is less than
1⁄w .

8) Adjust J-

II. MATERIALS AND METHOD

∑-

Some datasets may contain unimportant features that affect
the clustering results. These unimportant features should be
discarded to make a better clustering result. Yang and
Nataliani [9] proposed a method of feature-reduction for FCM
clustering algorithm, abbreviated with FRFCM. In the
FRFCM clustering, the features are weighted with feature
weights. Feature(s) with small feature weights must be
discarded during the clustering process. In this way, FRFCM
clustering method improves FCM clustering. FRFCM
automatically computes different feature weights of each
feature by modifying the objective function of FCM in Eq. (2)
and
adding
a
feature-weighted
entropy
term,
∑- OK- log U- K- S. This algorithm can eliminate the
unrelated features with small feature weights, such that a
better clustering result can be obtained and computation time
can be decreased.
The objective function of FRFCM clustering is defined in
Eq. (5).

F

K- = 1.

using K-x =

k1
6 @yz

∑t78

kt

, in order to keep

F
F2
G{ < B, then STOP, else go back
9) If {GJ- G − GJ-

hk
hk
to step 3) with =
and E = E + 1. Since
is
F
F
obtained, then points,
and the cluster center,
need to be updated.
Output: cluster points and feature weight [9].
The stopping condition used in this algorithm is when there is
no significant difference between the feature weight of the
current iteration and the next iteration. According to the
algorithm, the flowchart of FRFCM algorithm is shown in
Fig. 1.
This paper applies FRFCM to find the important and
related feature(s) on basketball players' positioning. There are
four features used to determine the position of a player, i.e.,
height, weight, age, and BMI.

417

TABLE I
BASKETBALL PLAYERS’ DATA
Player’s Name

Height

Weight

Age

BMI

Anjas Rusadi Putra
Antoni Erga
Ardian Ariadi
Aldi Falentino
Alexander Franklyn
Bryan Adha Elang
David Liberty Nuban
Elyakim Tampa'i
Febrianus Gregory
Fransiscus Bryan
Henry Cornelis Lakay
Raymond Putra Fajar
Randy Ady Prasetya
Mas Kahono Alif
Rian Sanjaya
Janson Kurniawan
M. Yassir Alkatiri
Martin
Steven Ray
Jody Sebastian
Peter Surjantoro
Fauji
Ridho Pamungkas

190
179
180
171
184
196
190
175
181
183
196
195
202
192
178
178
184
179
178
204
171
186
189

75
76
83
70
82
98
80
75
76
80
96
130
77
79
73
69
74
76
75
110
72
85
85

23
20
26
20
20
22
22
23
21
20
22
21
23
19
22
21
19
21
21
21
19
22
24

20
23
26
24
25
37
22
25
23
24
25
34
19
21
23
22
22
23
24
26
24
25
25

Actual
Position
Forward
Guard
Guard
Guard
Guard
Center
Forward
Guard
Guard
Guard
Center
Center
Center
Forward
Guard
Guard
Forward
Guard
Guard
Center
Guard
Forward
Forward

Fig. 2 Basketball players’ data

All computations in this paper use the fuzzy exponent of
( = 2. The error rate (ER) is used to measure the clustering
performance. The formula of ER is ER = 1 − ∑
I ,
where I is the number of incorrect points in cluster %.
The smaller the ER indicates, the better the clustering
performance.
In the FCM clustering process, the first step is to determine
the clusters, where = 3, consisting of guard, forward, and
center positions. After the cluster centers are initialized, then
the membership is computed. The calculation of the cluster
center and membership value are updated continuously until
the stop condition is reached. Table II shows the final
membership values of FCM clustering result. From Table II,
for example, the first player, Anjas Rusadi Putra, according to
FCM clustering result, he is more suitable on Cluster 2, with
the membership value of 0.7130, than on Cluster 1 (with the
membership value of 0.2635), and even more, does not

Fig. 1 Flowchart of FRFCM clustering algorithm

III. RESULTS AND DISCUSSION
The data was collected from all 23 players of the Satya
Wacana Saints Salatiga basketball team in 2021. There are
two kinds of data collected, data of the physical conditions
and data of the position of each player. Physical condition
data consists of four features, features of height, weight, age,
and BMI. Physical condition data is used to cluster players'
positions using FCM, consisting of three positions, namely
guard, forward, and center, while player position data
compares the clustering results with actual conditions. Table
I shows each player's physical condition and actual position,
and Fig. 2 shows the matrix of scatter plots by a group for the
basketball players’ position according to their physical
conditions.
418

suitable on the Cluster 3 (with the membership value of
0.0234). For the final cluster center of FCM clustering result,
as shown in Table III, three cluster centers consist of four
features.

According to Table II, each data cluster can be determined
by choosing the highest value of membership value. The
clustering results of FCM are shown in Table IV, where 11
players are in the guard position, nine players are in the
forward position, and three players are in the center position.
Table IV shows that there are five players with incorrect
positions (see the bold font), i.e., Alexander Franklyn,
Fransiscus Bryan, Henry Cornelis Lakay, Randy Ady
Prasetya, and M. Yassir Alkatiri. Therefore, the ER of the
FCM clustering result is 0.2174.
Next, FRFCM is applied for this basketball player’s
position to see what feature(s) are related to determining the
player’s basketball position. Since the data has four features,
then for the initialization, the feature weight is defined by
D
J- = [0.25 0.25 0.25 0.25]. For the computation of
FCM, the same initialization of cluster centers with FCM,
D
, is used. After U- ,
, and
are computed, then the

TABLE II
MEMBERSHIP VALUES OF FCM CLUSTERING RESULT

Player’s name
Anjas Rusadi Putra
Antoni Erga
Ardian Ariadi
Aldi Falentino
Alexander Franklyn
Bryan Adha Elang
David Liberty Nuban
Elyakim Tampa'i
Febrianus Gregory
Fransiscus Bryan
Henry Cornelis Lakay
Raymond Putra Fajar
Randy Ady Prasetya
Mas Kahono Alif
Rian Sanjaya
Janson Kurniawan
M. Yassir Alkatiri
Martin
Steven Ray
Jody Sebastian
Peter Surjantoro
Fauji
Ridho Pamungkas

Cluster 1
0.2635
0.9673
0.4992
0.8587
0.2754
0.1612
0.0290
0.9387
0.8965
0.4623
0.1611
0.0601
0.2238
0.1061
0.9835
0.8962
0.6974
0.9733
0.9963
0.0333
0.8693
0.1220
0.0653

Cluster 2
0.7130
0.0304
0.4632
0.1207
0.7050
0.3517
0.9672
0.0548
0.0980
0.5204
0.5278
0.0854
0.6915
0.8773
0.0151
0.0932
0.2877
0.0249
0.0034
0.0646
0.1120
0.8583
0.9195

Cluster 3
0.0234
0.0023
0.0377
0.0206
0.0196
0.4871
0.0037
0.0065
0.0056
0.0173
0.3111
0.8545
0.0847
0.0166
0.0014
0.0106
0.0149
0.0018
0.0003
0.9022
0.0187
0.0197
0.0152

feature weight, J- , is updated. The result for the first
iteration shows that the features weight of weight, age, and
BMI are close to 0, while the feature weight of height is close
to 1. The threshold for discarding features is defined by
1⁄w = 1⁄w 23 4 = 0.1043. Therefore, the weight,
age, and BMI features are discarded from the clustering
process. The next step is adjusting J- , where K-x =
k1
6 @yz
∑t78
kt

Height
177.9485
189.6042
199.0460

Weight
74.4266
81.9087
115.3002

Age
20.9808
21.8875
21.1878

BMI
23.4568
23.2556
30.3886

TABLE IV
FCM CLUSTERING RESULT

Player’s name
Anjas Rusadi Putra
Antoni Erga
Ardian Ariadi
Aldi Falentino
Alexander Franklyn
Bryan Adha Elang
David Liberty Nuban
Elyakim Tampa'i
Febrianus Gregory
Fransiscus Bryan
Henry Cornelis Lakay
Raymond Putra Fajar
Randy Ady Prasetya
Mas Kahono Alif
Rian Sanjaya
Janson Kurniawan
M. Yassir Alkatiri
Martin
Steven Ray
Jody Sebastian
Peter Surjantoro
Fauji
Ridho Pamungkas

Clustering results
Cluster Position
2
Forward
1
Guard
1
Guard
1
Guard
2
Forward
3
Center
2
Forward
1
Guard
1
Guard
2
Forward
2
Forward
3
Center
2
Forward
2
Forward
1
Guard
1
Guard
1
Guard
1
Guard
1
Guard
3
Center
1
Guard
2
Forward
2
Forward

= [1.00]. The new J- is

used for the next iteration, along with the new cluster center
and the new number of features. This process is repeated until
the stop condition is reached. Table V shows the feature
weights for each feature in each iteration. Tables VI and VII
show the final membership values and the final cluster center
of FRFCM clustering results, respectively. The final cluster
center consists of just one feature, i.e., height, where the guard
players (Cluster 1) have an average height of 177.8513, the
forward players (Cluster 2) have an average height of
188.0854, and the center players (Cluster 3) have an average
height of 197.9934.

TABLE III
CLUSTER CENTER OF FCM CLUSTERING RESULT

Cluster
Cluster 1
Cluster 2
Cluster 3

, such that the new J-

Real position
Forward
Guard
Guard
Guard
Guard
Center
Forward
Guard
Guard
Guard
Center
Center
Center
Forward
Guard
Guard
Forward
Guard
Guard
Center
Guard
Forward
Forward

TABLE V
FEATURE WEIGHTS IN EACH I TERATION

Iteration
Initialization

Height
0.25

Iteration 1

1

Iteration 2

1.00

Weight
0.25
2.1265e27
-

Age
0.25
1.6183e44
-

BMI
0.25
2.9226e43
-

According to Table VI, the cluster of each data can be
determined by choosing the highest value of membership
value from Table VII. The clustering results of FRFCM is
shown in Table VIII, where 14 players are on the guard
position, five players are on the forward position, and four
players are on the center position. As can be seen in Table
VIII, there is just one player with incorrect position (see the
bold font), i.e., M. Yassir Alkatiri. He tends to be tall but
FRFCM put him on the guard position, so he will be more
suitable to play on the forward position, because he has a tall
and big body to break into the opponent's ring. Therefore, the
ER of the FRFCM clustering result is 0.0435.

419

TABLE VI
MEMBERSHIP VALUES OF FRFCM CLUSTERING RESULT

Player’s name
Anjas Rusadi Putra
Antoni Erga
Ardian Ariadi
Aldi Falentino
Alexander Franklyn
Bryan Adha Elang
David Liberty Nuban
Elyakim Tampa'i
Febrianus Gregory
Fransiscus Bryan
Henry Cornelis Lakay
Raymond Putra Fajar
Randy Ady Prasetya
Mas Kahono Alif
Rian Sanjaya
Janson Kurniawan
M. Yassir Alkatiri
Martin
Steven Ray
Jody Sebastian
Peter Surjantoro
Fauji
Ridho Pamungkas

Cluster 1
0.0245
0.9985
0.9692
0.7782
0.3577
0.0068
0.0245
0.9047
0.8891
0.5583
0.0068
0.0196
0.0332
0.0528
0.9943
0.9943
0.3577
0.9985
0.9943
0.0541
0.7782
0.0772
0.0066

Cluster 2
0.9191
0.0012
0.0253
0.1561
0.5864
0.0329
0.9191
0.0709
0.0933
0.3919
0.0329
0.1114
0.0941
0.6323
0.0045
0.0045
0.5864
0.0012
0.0045
0.138
0.1561
0.8913
0.9835

combinations consist of one feature only, two features, three
features, and all four features. The advantage of FRFCM is
that the algorithm can automatically find the related feature(s)
during the clustering process by updating the feature weight
and discarding the unrelated feature(s).

Cluster 3
0.0565
0.0003
0.0055
0.0657
0.0559
0.9604
0.0565
0.0243
0.0176
0.0498
0.9604
0.869
0.8727
0.3149
0.0012
0.0012
0.0559
0.0003
0.0012
0.808
0.0657
0.0315
0.0099

IV. CONCLUSION
The FRFCM clustering algorithm can group the basketball
players’ positions. FRFCM is done by weighting each feature
with feature weight and discards the feature(s) with a small
feature weight. The weighting and discarding processes are
included in the clustering process simultaneously. There are
four features of the players’ physical condition, i.e., height,
weight, age, and BMI. FRFCM finds the height feature as the
most related physical condition to determine the players’
position, especially for Satya Wacana Saints team. By
comparing the clustering result with the actual position,
FRFCM obtains only one incorrect position, such that the ER
is 0.0435. Different from the previous research conducted by
Erga and Nataliani [19], where height and BMI are the most
important features, they found the related feature(s) by
combining the related feature(s) one by one. This method can
help the coach to decide the basketball player’s position. For
future works, FRFCM can be implemented on highdimensional data related to more complex players’ features.
The features used are not limited to the physical conditions,
but other measurements, for example, jumping ability,
shooting score, rebound skill, can also be used to determine
the player’s position.

TABLE VII
CLUSTER CENTER OF FRFCM CLUSTERING RESULT

Cluster
Cluster 1
Cluster 2
Cluster 3

Height
177.8513
188.0854
197.9934
TABLE VIII
FRFCM CLUSTERING RESULTS

Player’s name
Anjas Rusadi Putra
Antoni Erga
Ardian Ariadi
Aldi Falentino
Alexander Franklyn
Bryan Adha Elang
David Liberty Nuban
Elyakim Tampa'i
Febrianus Gregory
Fransiscus Bryan
Henry Cornelis Lakay
Raymond Putra Fajar
Randy Ady Prasetya
Mas Kahono Alif
Rian Sanjaya
Janson Kurniawan
M. Yassir Alkatiri
Martin
Steven Ray
Jody Sebastian
Peter Surjantoro
Fauji
Ridho Pamungkas

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Real position

2
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Guard
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Guard
Center
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Guard
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Center
Center
Center
Forward
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Guard
Forward
Guard
Guard
Center
Guard
Forward
Forward

Forward
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Guard
Guard
Guard
Center
Forward
Guard
Guard
Guard
Center
Center
Center
Forward
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Guard
Guard
Guard
Guard
Center
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Forward
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