Title


Science and Technology Indonesia
e-ISSN:2580-4391 p-ISSN:2580-4405
Vol. 5, No. 3, July 2020

Research Paper

Improved the Cans Waste Classification Rate of Naïve Bayes using Fuzzy
Approach
Yulia Resti1*, Firmansyah Burlian2, Irsyadi Yani2 Des Alwine Zayanti1 Indah Meiliana Sari1

1Jurusan Matematika, Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Sriwijaya, Sumatera Selatan, Indonesia
2Jurusan Teknik Mesin, Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Sriwijaya, Sumatera Selatan, Indonesia
*Corresponding author: yulia_resti@mipa.unsri.ac.id

Abstract
Cans is one type of inorganic waste that can take up to hundreds of years to be decomposed on the ground so that recycling is
the right solution for managing cans waste. In the recycling industry, can classification systems are needed for the sorting
system automation. This paper discusses the cans classification system based on the digital images using the Naive Bayes
method, where the input variables are the pixel values of red, green, and blue (RGB) color, and the image of the can is captured
by placing it on a conveyor belt which runs at a certain speed. The average accuracy rate of the k-fold cross-validation which
is less satisfactory from the classification system obtained using the original Naive Bayes model is corrected using the fuzzy
approach. This approach succeeded in improving the average accuracy of the can classification system which was originally
from 50.26 % to 85.19 % or an increase of 34.93 %, where the standard deviation decreased from 14.01 % to only 6.29 %. A decrease
in the standard deviation of 7.72 % also indicates that this model is be�er than the ONB model.

Keywords
classification system, fuzzy, improved Naïve Bayes

Received: 2 June 2020, Accepted: 19 July 2020

https://doi.org/10.26554/sti.2020.5.3.75-78

1. INTRODUCTION

Recently, the Naïve Bayes method is widely used to classify ob-
jects based on the digital images (Hsu et al. (2017); Mansour
(2018); Park (2016)). The advantage of the Naïve Bayes classi�-
cation method is that it has a simple algorithm and works well
when the data has a higher dimensional space (Sequera et al.
(2017); Kavila et al. (2016)). However, when the input variable
is a continuous variable, the Gaussian distribution assumption
used sometimes does not provide a satisfactory accuracy rate.

The can classi�cation system can also be built based on digital
images, where the input variables are the pixel values of the color
of the can digital image. Resti et al. (2017);Resti et al. (2019a);
Resti et al. (2019b) used the red, green, and blue (RGB) color
models, while Resti et al. (2020) used the cyan, magenta, yellow,
and black (CMYK) color models to represent the pixel values of
the color of the can digital image, however the accuracy rate
obtained is not satisfactory (Resti et al. (2017); Resti et al. (2019a)
obtains an accuracy rate of less than 80%, whereas Resti et al.
(2019b); Resti et al. (2020) obtains an accuracy rate of less than
50%). There is no speci�c de�nition of a minimum accuracy
rate of a classi�cation system, but obtaining a better accuracy
rate makes the system built more accurate, e�cient and useful.

Generally the researches claim the minimum accuracy rate of
a classi�cation system for a satisfactory level at 85 % (Arono�
(1985); Foody (2008); Liu and An (2020)). Based on this fact, it is
very important to develop and modify the classi�cation system
of cans waste from previous studies so that the classi�cation
system has a higher accuracy rate and at least achieves more
than 85% accuracy.

One way to overcome this problem is to use a fuzzy approach
(Rastogi et al. (2019); Soares and Moraes (2018); Aziz et al. (2016);
Ferreira et al. (2015); Moraes (2015)). This paper discusses the
classi�cation of cans using a fuzzy approach to the Naïve Bayes
model to obtain better classi�cation results than the original
Naïve Bayes. The validation technique used is k-fold cross vali-
dation, while the process of splitting up data and classi�cation
is done with the help of R software 4.01.

2. EXPERIMENTAL SECTION

2.1. Data

The data used in this study are data of pixel values of red (X1 ),
green (X2 ), and blue (X3 ) of 250 cans which are distributed into
three types of cans; 29.6 % cans of type 1, 33.2 % cans of type 2,
and 37.2 % cans of type 3. The pixels are obtained by capturing

https://doi.org/10.26554/sti.2020.5.3.75-78


Author et. al. Science and Technology Indonesia, 5 (2020) 75-78

cans placed on conveyor belts at a speed of 0.181 m/sec where
the webcam was set at an angle of 900. The statistics summary
of the pixel values of each colour are presented in Table 1.

Table 1. Statistics Summary of Input Variables

Statistics
Input variable

X1 X2 X3
Minimum 129.2 134.7 123.8
1st Quartile 139.1 140.7 139.1

Median 141.7 143.2 142.1
Mean 142.9 143.4 142.4

3rd Quartile 145.8 146.2 145.1
Maximum 179.9 161.4 181.2

2.2. Methods

This study uses k-folds cross validation technique by splitting
data into k=10 fold to obtain the best classi�cation model (Sharma
et al., 2017). This data splitting process is carried out with the
help of software R 4.0.1. The initial step after having 10 fold
data is to randomly select one fold data as test data from the 10
folds data where 9 folds data that are not selected as test data are
used as training data. Second, determine the prior probabilities,
likelihood function parameters of each input variable, and the
posterior probabilities of each type of can in each training data
for obtained a classi�cation model using original naïve Bayes
(ONB) as in equation (1). Let X1,X2,X3 be the input variables of
pixel values of red, green, and blue successively, Kj be the j-th
cans type, j = 1, 2, 3. Probability ofKj, given X1,X2,X3 according
to the Bayes theorem is expressed as (Ferreira et al., 2015).

P(Kj|X1,X2,X3) =
P(X1,X2,X3|KjP(Kj)

P(X1,X2,X3)
= P(Kj)P(X1,X2,X3

3
∏
d=1

P(Xd |Kj)

(1)

Third, classify each can of observations in the test data using
the ONB model obtained in step 2 and create a confusion matrix
as Table 2 to obtain an accurate level of classi�cation as in equa-
tion (2), where Tjj be the percentage of cans coming from the
j-th cans type predicted exactly to the j-th cans type, whereas
Fjl is the percentage of the number of cans coming from the j-th
cans type predicted to the l-th cans type.

Table 2. Confusion matrix

Cans Type Cans Type Predicted (l-th)
Actual (j-th) 1st 2nd 3rd

1st T11 F12 F13
2nd F21 T22 F23
3rd F31 F32 T33

Accuracyrate = T11 + T22 + T33 (2)

The next step is to use a fuzzy approach such as on each input
variable of each type of can in each training data to determine
the fuzzy probability as in equations (3) to obtain a classi�cation
model using this approach to the naïve Bayes (ONB) model.

P(X) = ∫ 'T (x)f (x)dx (3)

Where for each d = 1, 2, 3, f (x)4 be the probability density
function of Gaussian distribution, 'T (x) be the membership
functions of fuzzy set in this research are denoted in eq. (4) –
(6). Let a be the element of the domain that has the greatest
membership value and b be the element of the domain that has
the smallest membership value, the membership functions for
dark color is

'T (x) =
⎧⎪⎪
⎨⎪⎪⎩

1 ; x ≤ a
b−x
b−a ; a ≤ |x| ≤ b
0 ; x ≤ b

(4)

Let � be the element of the domain which is the smallest value
and also has the smallest membership value, b be the element
of domain which is the median of data and has the greatest
membership value, and c be the element of domain which is
the greatest value but has the smallest membership value, the
membership functions for moderate color is

'T (x) =
⎧⎪⎪
⎨⎪⎪⎩

0 ; x ≤ a,ataux ≥ c
x−a
b−a ; a ≤ x ≤ bc−x
c−b ; b ≤ x ≤ c

(5)

Let � be the element of domain that has the smallest member-
ship value and b be the element of domain that has the greatest
membership value, the membership functions for light color is

'T (x) =
⎧⎪⎪
⎨⎪⎪⎩

0 ; x ≤ a
x−a
b−a ; a ≤ x ≤ b
1 ; x ≥ b

(6)

Next is to classify each can of observations on the test data
using the model obtained in previous step and make a confu-
sion matrix to obtain the classi�cation accuracy rate, and �nally
analyze the classi�cation results.

3. RESULTS AND DISCUSSION

3.1. The Original Model of Naïve Bayes

In the ONB model, the parameters of the input variables that are
assumed to be Gaussian distributions are estimated with maxi-
mum likelihood estimation. The estimated parameter results for
the 10tℎ fold are presented in Table 3. The parameters for other
folds are obtained in the same way.

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Author et. al. Science and Technology Indonesia, 5 (2020) 75-78

Table 3. Parameter Gaussian Distributions for the 10tℎ Fold

Can Input variable
type � � � � � �
1st 153.84 8.9 151.28 6.11 142.4 9.34
2nd 145.93 4.81 148.81 4.12 147.76 2.39
3rd 146.69 5.52 147.76 4.76 145.18 4.38

In this study, the 6tℎ fold data was chosen as the test data so
that the other 9 fold data as training data. Implementation of the
10tℎ fold data as training data and the 6tℎ fold data as test data
to equation (1) gives the classi�cation results as presented in
Table 4 with a classi�cation accuracy rate of 75.00%. Only cans
from the 2nd type have all been classi�ed correctly. The highest
percentage of misclassi�cation occurs in cans from the 3rd type
are classi�ed as cans of the 2nd type, which is 16.67%.

Table 4. Classi�cation Result of ONB Model for the 10tℎ Fold

Original Naïve % number of cans from type
Bayes Model 1st 2nd 3rd

% number of 1st 20.83 0 0
cans classi�ed 2nd 0 33.33 16.67
into can type 3rd 8.33 0 20.83

Accuracy rate 75.00 %

The classi�cation results of the 6tℎ fold as test data using 8
other data folds as training data for the ONB model are obtained
in the same way. The classi�cation accuracy rate of the ONB
model using the k-fold cross validation technique given in Table
5 shows that the ONB model has an average accuracy rate of
50.26 % with a standard deviation of 14.01%. The accuracy of
this model ONB can be improved signi�cantly using the fuzzy
approach as presented in section 3.2.

Table 5. Accuracy Rate of ONB Model

Training Testing Accuracy Rate
Fold Fold of ONB

1 51.85%
2 55.56%
3 29.63%
4 32.00%
5 6 50.00%
7 62.50%
8 50.00%
9 45.83%
10 75.00%

average 50.26%
Standard deviation 14.01%

3.2. Improved Model of Naive Bayes using Fuzzy Ap-
proach
The fuzzy membership function of each input variable is obtained
using equation (4) - (6) where the parameters are points with
the same distance in the interval [min, max] of pixel values. In
the 10tℎ fold data, the fuzzy membership function of variable
X1 which has a pixel value in the interval [137.59, 167.49] is
expressed by,

'D(x1) =
⎧⎪⎪
⎨⎪⎪⎩

1 ; x1 ≤ 137.59
147.56−x1

9.97 ; 137.59 ≤ x1 ≤ 147.56
0 ; x1 ≤ 162.50

(7)

'M(x1) =
⎧⎪⎪
⎨⎪⎪⎩

0 ; x1 ≤ 142.57,ataux1 ≥ 162.50
x−142.57

9.97 ; 142.57 ≤ x1 ≤ 152.54162.50−x1
9.97 ; 152.54 ≤ x1 ≤ 162.50

(8)

'L(x1) =
⎧⎪⎪
⎨⎪⎪⎩

0 ; x1 ≤ 157.52
x1−157.52

9.97 ; 157.52 ≤ x1 ≤ 167.49
1 ; x1 ≥ 167.49

(9)

The fuzzy membership function and the parameters for other
variables and fold data are obtained in the same way.

The classi�cation results of the 6tℎ fold as test data and the
10tℎfold data as training data using Fuzzy approach (IONBF)
are presented in Table 6 with an accuracy rate of 83.33 %. The
percentage of misclassi�cation in each type at 4.17 % where cans
from the 1st and 2nd types are classi�ed as cans of the 3rd type
and cans from the 2nd as type. There is not one type of can
which all of its members are classi�ed correctly as a whole.

Table 6. Classi�cation Result of IONBF Model for the 10th Fold

IONBF Model % number of cans from type
1st 2nd 3rd

% number of 1st 25 0 0
cans classi�ed 2nd 0 29.17 4.17
into can type 3rd 4.17 4.17 29.17

Accuracy rate 83.33%

The classi�cation results of the 6tℎ fold as test data using
IONBF model where 8 other fold data as training are obtained
in the same way. Accuracy Rate of IONBF model using k-fold
cross validation technique given in Table 7 noted that the IONBF
model has an average accuracy rate of 85.19 % with a standard
deviation of 6.29 %. All accuracy rate of testing data for all
training data in the IONBF model is higher than the ONB model,
as well as the average accuracy overall. The improvement of the
average accuracy rate from ONB model to IONBF of this model
is 34.93%. This fact shows that the fuzzy approach on the ONB
model can improve the classi�cation accuracy rate.

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Author et. al. Science and Technology Indonesia, 5 (2020) 75-78

Table 7. Accuracy Rate of IONBF Model

Training Testing Accuracy Rate
Fold Fold of ONB

1 83.33%
2 79.17%
3 79.17%
4 79.17%
5 6 95.83%
7 83.33%
8 91.67%
9 91.67%
10 83.33%

average 85.19%
Standard deviation 6.29%

4. CONCLUSIONS

In this study, the accuracy of the model was obtained as the
average level of accuracy of one test data that was randomly
selected using a model of 9 data fold as training data. The average
accuracy of the IONBF model using cross validation technique is
85.19% with a standard deviation of 6.29 %. This accuracy level
is higher than the average accuracy of the ONB model which is
only 50.26 % with a standard deviation of 14.01 %. The accuracy
of the ONB model can be improved by the fuzzy approach. A
decrease in the standard deviation of 7.72 % also indicates that
this model is better than the ONB model.

5. ACKNOWLEDGEMENT

This research was supported by DIPA, University of Sriwijaya,
No. SP DIPA-042.01.2.400953/2019, for the Competitive Research,
No. 0015 /UN9/SK.LP2M.PT/2019.

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© 2020 The Authors. Page 78 of 78


	INTRODUCTION
	EXPERIMENTAL SECTION
	RESULTS AND DISCUSSION
	CONCLUSIONS
	ACKNOWLEDGEMENT