Leukemia Image Segmentation Using a Hybrid Histogram-Based Soft Covering Rough K-Means Clustering Algorithm

Abstract

Segmenting an image of a nucleus is one of the most essential tasks in a leukemia diagnostic system. Accurate and rapid segmentation methods help the physicians identify the diseases and provide better treatment at the appropriate time. Recently, hybrid clustering algorithms have started being widely used for image segmentation in medical image processing. In this article, a novel hybrid histogram-based soft covering rough k-means clustering (HSCRKM) algorithm for leukemia nucleus image segmentation is discussed. This algorithm combines the strengths of a soft covering rough set and rough k-means clustering. The histogram method was utilized to identify the number of clusters to avoid random initialization. Different types of features such as gray level co-occurrence matrix (GLCM), color, and shape-based features were extracted from the segmented image of the nucleus. Machine learning prediction algorithms were applied to classify the cancerous and non-cancerous cells. The proposed strategy is compared with an existing clustering algorithm, and the efficiency is evaluated based on the prediction metrics. The experimental results show that the HSCRKM method efficiently segments the nucleus, and it is also inferred that logistic regression and neural network perform better than other prediction algorithms.

Full text

electronics
Article
Leukemia Image Segmentation Using a Hybrid
Histogram-Based Soft Covering Rough K-Means
Clustering Algorithm
Hannah Inbarani H. 1, Ahmad Taher Azar 2, 3, * and Jothi G 4
1
Department of Computer Science, Periyar University, Tamil Nadu, Salem 636 011, India; hhinba@gmail.com
2Robotics and Internet-of-Things Lab (RIOTU), Prince Sultan University, Riyadh 11586, Saudi Arabia
3Faculty of Computers and Artificial Intelligence, Benha University, Benha 13511, Egypt
4Department of Computer Science and Engineering, Sona College of Technology (Autonomous),
Salem 636005, India; jothiys@gmail.com
*Correspondence: aazar@psu.edu.sa or ahmad.azar@fci.bu.edu.eg
Received: 1 December 2019; Accepted: 1 January 2020; Published: 19 January 2020


Abstract:
Segmenting an image of a nucleus is one of the most essential tasks in a leukemia diagnostic
system. Accurate and rapid segmentation methods help the physicians identify the diseases and
provide better treatment at the appropriate time. Recently, hybrid clustering algorithms have started
being widely used for image segmentation in medical image processing. In this article, a novel hybrid
histogram-based soft covering rough k-means clustering (HSCRKM) algorithm for leukemia nucleus
image segmentation is discussed. This algorithm combines the strengths of a soft covering rough set
and rough k-means clustering. The histogram method was utilized to identify the number of clusters
to avoid random initialization. Different types of features such as gray level co-occurrence matrix
(GLCM), color, and shape-based features were extracted from the segmented image of the nucleus.
Machine learning prediction algorithms were applied to classify the cancerous and non-cancerous
cells. The proposed strategy is compared with an existing clustering algorithm, and the efficiency is
evaluated based on the prediction metrics. The experimental results show that the HSCRKM method
efficiently segments the nucleus, and it is also inferred that logistic regression and neural network
perform better than other prediction algorithms.
Keywords:
leukemia nucleus image; segmentation; soft covering rough set; clustering; machine
learning algorithm; soft computing
1. Introduction
Due to the growth of advanced medical imaging modalities, it is very difficult to analyze the
medical images manually. For this reason, an advanced and efficient computer-aided system is needed
to diagnose the diseases. This will help the hematologist to begin the treatment at the right time and
increase the patient’s survival rate. Leukemia is a cancer of blood-forming tissues that affects the bone
marrow. Leukemia is caused by the proliferation of abnormal white blood cells in the body. Leukemia
is mostly affected by people living in developed countries and children aged 14 or under. As per
the National Cancer Institute (NCI) statistics, in the United States, it is expected that there will be
62,130 persons as new cases for cancer treatment and 245,000 cases that are fatal or very serious [
1
]. In
India, leukemia stands at ninth position among diseases (tumors) among children [
2
,
3
]. Leukemia is
identified into two broad categories such as acute and chronic. Acute forms of leukemia occur when
the number of immature blood cells increases, and it is the most common type of leukemia in children.
Segmenting an image of a nucleus is one of the major challenging tasks in leukemia diagnosis. Recently,
Electronics 2020,9, 188; doi:10.3390/electronics9010188 www.mdpi.com/journal/electronics

Electronics 2020,9, 188 2 of 22
soft computing plays an important role in many research areas such as medical image processing,
pattern recognition, big data analytics, Internet of Things (IoT) analysis, bioinformatics, and so on.
The rough set theory [
4
] was proposed by Pawlak in 1982. This concept is an extension of set theory
for the study of intelligent systems characterized by insufficient and incomplete information. This
classical rough set theory is based on equivalence relations, but it can also be extended to covering based
rough sets [
5
–
7
]. In 1999, Molodtsov [
8
] proposed the concept of a soft set, which can be seen as a new
mathematical approach to vagueness. The absence of any restrictions on the approximate description in
soft set theory makes this theory very versatile and easily applicable in practice. Maji et al. [
9
] improved
Molodtsov’s idea by introducing several operations in soft set theory. In [
10
], the researcher investigated
a soft covering-based rough set as a new kind of soft rough set. This method is a combination of a
covering soft set and rough set. In [
11
], a covering-based rough k-means clustering approach is applied
to segment the leukemia nucleus. The advantage of covering-based subsets is that they generate upper
and lower approximations by using the covering feature, which brings about more roughness. Since
different clusters give rise to different results, determination of the number of clusters is a difficult
task in clustering-based segmentation. To overcome this limitation, the hybrid histogram-based soft
covering rough k-means clustering algorithm (HSCRKM) is introduced to segment the image of the
leukemia nucleus. In this algorithm, the peak values of the histogram of an image are identified
and the number of clusters is initialized. This will avoid the random initialization of a number of
clusters. Here, soft covering approximation space is also included. The term ‘covering soft set’ is more
accurate than ‘soft rough set.’ It also combines the strengths of covering soft set theory and the rough
k-means clustering algorithm to effectively segment the image of the nucleus. Soft covering rough
approximation is utilized to find the lower and upper approximation values. The performance of the
HSCRKM algorithm is evaluated using existing algorithms such as k-means clustering, fuzzy c-means
clustering, and particle swarm optimization (PSO)-based clustering. Different types of features such
as GLCM-0, GLCM-45, GLCM-90, GLCM-135, and shape color-based features are extracted from the
segmented leukemia nucleus image. Nowadays, a lot of machine learning algorithms are applied to
predict the degree of sickness. The state-of-art machine learning prediction algorithms such as neural
networks (NN) [
12
], logistic regression (LR) [
13
], support vector machine (SVM) [
14
], naive Bayes
(NB) [
15
], k-nearest neighborhood (KNN) [
13
], decision tree (DT) [
13
], and random forest (RF) [
16
] are
applied to classify the cancerous and non-cancerous leukemia cells. The empirical results show that
logistic regression and neural network efficiently predict the blast and non-blast cells when compared
with other prediction algorithms.
The main objective of this research work is to develop a diagnostic approach for the identification
of acute lymphoblastic leukemia blast cells using image processing and computational intelligence
techniques. In experimental analysis, relevant image processing and computational intelligence
techniques are applied in order to select the most suitable approach for the delineation of acute
lymphoblastic leukemia cells. The following objectives have been formulated in order to predict
leukemia: to apply computational intelligence-based algorithms for the segmentation of acute
lymphoblastic leukemia blast cells in images and to apply machine learning algorithms to evaluate the
performance of the proposed method.
The contribution of this study is summarized as follows. To find the number of clusters using
the peak value of a histogram image and compute the lower and upper approximation values based
on the soft covering approximation space, three clustering methods—k-means, FCM, and PSO-based
clustering—are preferred for segmentation comparison. Through these methods, different kinds of
features are extracted, and the efficiency of the proposed algorithm is assessed using machine learning
prediction algorithms. The HSCRKM achieves the successful results i.e., above 80% when compared
with the existing clustering algorithms. Therefore, it can be concluded that the HSCRKM clustering
algorithm works effectively with the other clustering algorithms.
In the clustering algorithm, defining the number of clusters is a very difficult task. To overcome
this limitation, the proposed algorithm identifies the peak values of the histogram of an image and

Electronics 2020,9, 188 3 of 22
initializes the number of clusters. This is one of the advantages of our proposed method, which avoids
the random initialization of a number of clusters. The next advantage of the HSCRKM algorithm is
that it combines the strengths of covering soft set theory and the rough k-means clustering algorithm
to effectively segment the image of the nucleus. Based on a literature review, the term ‘covering soft
set’ is more accurate than ‘soft rough set’, since it gives a better result than the soft rough set for several
applications. In covering rough sets, the lower and upper approximation values are computed based
on the soft covering approximation space.
Morphologically, a lymphoblast consists of a massive nucleus of irregular shape and size. In blood
sample images, it is difficult to identify the cytoplasm, because it appears rarely and even if it does, it
looks intensely colored. The nucleus and cytoplasm of lymphoblast cells reflect the morphological and
functional changes. Feature extraction plays a main role in the assessment of leukemia in blood samples.
After segmenting the nucleus using the proposed HSCRKM algorithm, salient features are extracted.
It reduces the amount of data space and the working time of an image. In this research, different
kinds of features are extracted such as gray level co-occurrence matrix (GLCM), color, and shape-based
features. These were measured from every channel of the segmented nucleus image. The efficiency of
the proposed algorithm is assessed using machine learning prediction algorithms. The performance of
the segmentation algorithms was analyzed in the light of different machine learning (ML) prediction
methods. With respect to HSCRKM clustering algorithms, most of the ML methods (except naive
Bayes) achieved greater than 80% prediction accuracy compared with the existing clustering algorithms,
viz., k-means clustering, fuzzy c-means clustering, and rough k-means clustering. It is inferred that the
proposed clustering algorithms are more effective in segmenting the nucleus image. Due to the effective
segmentation process, the extracted features have increased the prediction accuracy. To evaluate the
experimental results, we have empirically set the best accuracy to be greater than 80%. The outline of
the proposed system is shown in Figure 1.
Electronics 2020, 9, x FOR PEER REVIEW 3 of 24
In the clustering algorithm, defining the number of clusters is a very difficult task. To overcome
this limitation, the proposed algorithm identifies the peak values of the histogram of an image and
initializes the number of clusters. This is one of the advantages of our proposed method, which
avoids the random initialization of a number of clusters. The next advantage of the HSCRKM
algorithm is that it combines the strengths of covering soft set theory and the rough k-means
clustering algorithm to effectively segment the image of the nucleus. Based on a literature review,
the term ‘covering soft set’ is more accurate than ‘soft rough set’, since it gives a better result than the
soft rough set for several applications. In covering rough sets, the lower and upper approximation
values are computed based on the soft covering approximation space.
Morphologically, a lymphoblast consists of a massive nucleus of irregular shape and size. In
blood sample images, it is difficult to identify the cytoplasm, because it appears rarely and even if it
does, it looks intensely colored. The nucleus and cytoplasm of lymphoblast cells reflect the
morphological and functional changes. Feature extraction plays a main role in the assessment of
leukemia in blood samples. After segmenting the nucleus using the proposed HSCRKM algorithm,
salient features are extracted. It reduces the amount of data space and the working time of an image.
In this research, different kinds of features are extracted such as gray level co-occurrence matrix
(GLCM), color, and shape-based features. These were measured from every channel of the
segmented nucleus image. The efficiency of the proposed algorithm is assessed using machine
learning prediction algorithms. The performance of the segmentation algorithms was analyzed in
the light of different machine learning (ML) prediction methods. With respect to HSCRKM
clustering algorithms, most of the ML methods (except naive Bayes) achieved greater than 80%
prediction accuracy compared with the existing clustering algorithms, viz., k-means clustering,
fuzzy c-means clustering, and rough k-means clustering. It is inferred that the proposed clustering
algorithms are more effective in segmenting the nucleus image. Due to the effective segmentation
process, the extracted features have increased the prediction accuracy. To evaluate the experimental
results, we have empirically set the best accuracy to be greater than 80%. The outline of the proposed
system is shown in Figure 1.
Figure 1. Outline of the proposed image segmentation process.
LR | NB | SVM | KNN | NN | RF
K-Means | FCM | PSO | HSCRKM
Input Image Preprocessing
Nucleus Segmentation
Classification
Texture | Shape | Colour
Feature Extraction
Figure 1. Outline of the proposed image segmentation process.

Electronics 2020,9, 188 4 of 22
The rest of the research report is organized as follows. Section 2reviews the related literature on
clustering-based segmentation algorithms. Section 3describes the methods of the proposed algorithm
and its results. The empirical results are discussed in Section 4. Section 5states the conclusion and
indicates the future direction of this research.
2. Related Literature
In recent years, a lot of clustering algorithms have been developed for segmenting medical images.
Petal [
17
] applied k-means clustering for segmentation and the Zack algorithm for clustered
white blood cells (WBCs). The features—namely, the mean, standard deviation, area, elongation,
perimeter, color etc.—are extracted, and support vector machine (SVM) was used to classify the
cells. The proposed algorithm effectively segmented the WBCs, which produced 93.57% accuracy.
For this experiment, 27 images from the Acute Lymphoblastic Leukemia Image Database (ALL-IDB)
were utilized.
Two bare-bones particle swarm optimization (BBPSO) algorithms with and without subswarms
were introduced by Srisukkham et al. in 2017 [
18
] to diagnosis the leukemia cells. A stimulating
discriminant measure (SDM)-based clustering algorithm that combined with the genetic algorithm
(GA) was employed to segment the nucleus, cytoplasm, and background regions. The relevant features
were extracted; then, various feature selection methods such as particle swarm optimization (PSO),
cuckoo search (CS), and dragonfly algorithm (DA) were applied to select the optimal features and
reduce the dimensions. An average geometric mean was computed with different sizes of training and
test samples to evaluate the performance of the proposed methods. The BBPSO and binary BBPSO
algorithms produced 91% to 96% of the geometric mean value.
Su [
19
] developed two stages of segmentation process using k-means clustering and HMRF
(hidden Markov random field), which are used to group the six different types of AML cells from
the bone marrow images. The segmentation algorithm achieved an accuracy of 96% to 98% (average)
when compared with other existing segmentation methods.
In [
20
], k-means and fuzzy c-means clustering algorithms were applied to segment the brain tumor
images. Various feature reduction algorithms, namely probabilistic principal component analysis
(PPCA), expectation maximization-based principal component analysis (EM-PCA), the generalized
Hebbian algorithm (GHA), and adaptive principal component extraction (APEX) were employed to
reduce the dimensions of the feature set. The produced coefficient of variance (CV) values for k-means
and Fuzzy C-mean (FCM) are 0.4582 and 0.1224, respectively.
In [
21
], potential field segmentation was employed to segment the MRI brain tumor images.
This method achieved the standard deviation of 0.283, the average value of 0.517, and the median
values of 0.644. From the experimental results, it was observed that ensemble methods generated
better segmentations.
Küçükkülahlı [
22
] and Namburu [
23
] identified the number of cluster values in the clustering
algorithm using the peak value of the histogram of an image. In [
22
], the automatic segmentation
method using the histogram-based k-means clustering algorithm was developed. In [
23
], the soft
fuzzy rough c-means clustering algorithm (SFRCM) was used to segment the MRI brain tumor images.
The proposed SRFCM algorithm achieved a better Jaccard coefficient value of 0.97 for without noise
and 0.79 for with 9% Gaussian noise when compared with the existing clustering algorithms namely,
k-means, rough k-means (RKM), rough fuzzy c-means (RFCM), and generalized rough c-means
(GFCM).
Ali [
24
] introduced a new clustering algorithm based on neutrosophic orthogonal matrices
(CANOM) to segment the dental X-ray images. The experimental results show that the CANOM
simplified silhouette width criterion (SSWC) index is 0.941 and the FCM is 0.02. CANOM is also better
than Otsu and eSFCM with the values being 0.657 and 0.647, respectively. The value of CANOM is 47
times larger than that of FCM and 1.43 times larger than those of Otsu and eSFCM.

Electronics 2020,9, 188 5 of 22
In [
25
], the unsupervised fuzzy c-means (FCM) clustering technique was employed for prostate
cancer MRI images. The derived average dice similarity, Jaccard index, sensitivity, specificity, mean
absolute difference, and Hausdorffdistance is 88.68, 81.26, 90.71, 88.09, 88.09, 3.5, and 4.1 respectively.
In [
26
], the proposed multi-Otsu thresholding-based segmentation method can successfully
segmented the CT image stacks. In addition, it sows the distribution characteristics of different
components in three dimensions.
In [
27
], the enhanced adaptive fuzzy k-means (AFKM) algorithm was used to detect the three
regions such as white matter (WM), gray matter (GM), and cerebrospinal fluid spaces (CSF) in the
brain images. AFKM performed better than FCM, which produced a minimum mean square error
(MSE) value of 2.2441.
In [
28
], the clustering method intuitionistic fuzzy c-means (IFCM) was applied for medical image
segmentation. It is observed from the experimental results that the proposed method outperformed
other algorithms that achieved the average quantitative index 0.95. The chronic wound region was
detected using fuzzy spectral clustering in [
29
]. The proposed method produced 91.5% segmentation
accuracy, an 86.7% Dice index, a Jaccard score of 79.0%, 87.3% sensitivity, and 95.7% specificity.
In [
30
], the convolutional neural networks (CNN) approach is applied to identify the subtypes
of leukemia. It is observed from the experimental results that the CNN model achieves 88.25% and
81.74% accuracy for leukemia and healthy cells, respectively. From the literature review, it is inferred
that the clustering-based algorithms were applied to segment the tumor region. A brief review of the
literature on various clustering methods in image segmentation and their performances appears in
Table 1.

Electronics 2020,9, 188 6 of 22
Table 1. Overview of the literature on clustering algorithms.
Author Used Methods Objective Type of Diseases
Imaging
Modalities/Dataset
Used
No. of IMAGES Performance Metrics
and Accuracy %
Patel et al., 2015 [17]
K-mean clustering Zack
algorithm, Support vector
machines (SVM)
The K-means clustering algorithm
was used to detect the white blood
cells and the Zack algorithm was
applied to categorize the cells.
Leukemia Microscopic image
(ALL-IDB) 27 Classification
accuracy 93.57%
Srisukkham et al.,
2017 [18]
Spatial Data Mining
(SDM)-based clustering,
Genetic Algorithm (GA),
particle swarm
optimization (PSO), Bare
Bones PSO (BBPSO)
This optimization method was
utilized to diagnose leukemia.
Acute lymphoblastic
leukemia (ALL)
Microscopic image
(ALL-IDB) 180
Geometric mean 91 to
96%
Su et al., 2017 [19]K-means, Hidden
Markov random field
This algorithm segmented the
nucleus from the background,
extracted the features, and then
classified the blast cells.
Acute myeloid
leukemia
Microscopic image
(AML Patient) 61
Segmentation
accuracy 96 to 98%
(average)
Kaya et al., 2017 [20] K-means, fuzzy c-means
Comparative analysis of various
types of PCA algorithms on MRIs for
two cluster methods.
Brain tumor MRI (Hospital) -
Average
reconstruction error
rates, Euclidean
distance error rate,
CV of K-Means =
0.4582 FCM =0.1224
Cabria et al., 2017 [
21
]
Potential field clustering
The algorithm is based on an
analogy with the concept of potential
field in physics and views the
intensity of a pixel in an MRI as a
“mass” that creates a potential field.
Brain tumor MRI (BRATS) 30
SD =0.283, Average =
0.517, Median =0.644.
Küçükkülahlı et al.,
2016 [22]
Histogram-based
k-means clustering
This method to find the optimum
cluster number based on the
histogram of an image.
MATLAB media Image Dataset 10-15 Derived metrics
Ali et al., 2017 [23]
Fuzzy clustering based
on neutrosophic
orthogonal matrix
This algorithm transforms image
data into a neutrosophic set and
computes the inner products of the
cutting matrix of input. Then, pixels
are segmented using the orthogonal
principle to form clusters.
Dental X-Ray (Hospital) 22 DB index Silhouette
index =0.941

Electronics 2020,9, 188 7 of 22
Table 1. Cont.
Author Used Methods Objective Type of Diseases
Imaging
Modalities/Dataset
Used
No. of IMAGES Performance Metrics
and Accuracy %
Rundo et al., 2018 [
24
]
Fuzzy c-means (FCM)
This approach automatically
segments the prostate and image
computes the gland volume.
Prostate cancer MRI (Hospital) 7 (Patients)
Dice Similarity =
88.68, Jaccard index =
81.26, Sensitivity =
90.71, Specificity =
88.09, Mean Absolute
Difference =3.5,
Hausdorffdistance =
4.1
Zhang et al., 2017 [
25
]
Multi-Otsu thresholding
algorithm
This segmentation method can
successfully segment CT image
stacks. In addition, it sows the
distribution characteristics of
different components in three
dimensions.
Backscattered
electron images X-ray CT (Hospital) 1571 (Slice) Derived metrics
Namburu et al., 2017
[26]
classical k-means (KM),
rough k-means (RKM),
rough fuzzy c-means
(RFCM), and generalized
rough c-means (GFCM).
In this method, soft fuzzy rough
approximations are applied to obtain
the rough regions of an image and
compute the similarity of the clusters
using soft set similarity coefficient.
Brain tumor MRI (BRATS) 20 Jaccard’s coefficient =
0.97 Accuracy
Ganesh et al., 2017
[27]
Enhanced adaptive fuzzy
k-means algorithm
This approach is used to classify the
three important regions in brain:
namely, white matter, gray matter,
and cerebrospinal fluid spaces.
Brain tumor MRI (Brain Image) 3 MSE 2.2441
Kaur 2017 [28]
Intuitionistic fuzzy
sets-based credibilistic
fuzzy c-means clustering
In this method, the hesitation factor
and fuzzy entropy were utilized to
improve the noise sensitivity of
fuzzy c-means.
Brain tumor MRI (brainweb) 3 Quantitative
index 0.95
Dhane et al., 2017 [
29
]
Fuzzy spectral clustering
gray-based fuzzy
similarity measure
This approach is adopted to compute
the ulcer boundary demarcation and
estimation.
Chronic wound Digital Camera 70
Sensitivity =87.3%
Specificity =95.7%
Accuracy =91.5%
Dice index =86.7%
Jaccard score =79.0%
Ahmed et al.,
2019 [30]
Convolutional neural
network (CNN)
This approach is identify the
subtypes of leukemia. Leukemia
Microscopic image
(ALL-IDB) ASH
Image Bank
903
Accuracy =88.25%
(Leukemia) Accuracy
=81.74%
(Healthy cell)

Electronics 2020,9, 188 8 of 22
3. Methods
3.1. Basics of Soft Covering Based Rough Set
This section describes the basic properties of soft covering-based rough approximation [11].
Definition 1.
Let
CG=(F,A)
be a covering soft set over
U
if
F(a),∅
,
∀a∈A
. The pair
S=(U,CG)
is
known as soft covering approximation space. For a set
X⊆U
, the soft covering lower and upper approximations
are, respectively, defined as
S∗(X)=∪a∈AF(a):F(a)⊆X(1)
S∗(X)=∪MdS(x):x∈X. (2)
In addition,
Spos (X)=S∗(X)(3)
Sneg (X)=U−S∗(X)(4)
Sbon (X)=S∗(X)−S∗(X)(5)
are called the soft covering positive, negative, and boundary regions of X, respectively [11].
Definition 2.
Let
S=(U,CG)
be a soft covering approximation space. If
S∗(X)=S∗(X)
, then subset
X⊆U
is called soft covering. X is said to be a soft covering based rough set if S∗(X),S∗(X).
The soft covering based rough set can be applied to image segmentation with the following
considerations.
•
The set of pixels in the input image is denoted as
U U =X={xi/xi
is the value of the ith pixel
in the image}.
•
Let
CG=(F,A)
be the covering soft set to be constructed containing the pixels belonging
to clusters.
•The set of parameter Ais considered as the number of clusters ClG{i=1, 2, 3, . . . ,k}to which
the pixels fit.
•
For example, let a set of pixels in an image be denoted as
U={x1,x2,x3,x4,}
and the parameter
set
A
be denoted as number of clusters {
ClG1
,
ClG2
,
ClG3
} to which the pixels belong. The distance
between each pixel and the centroids are calculated. Based on the minimum distance, the pixels
are grouped to the clusters. Assume that the input pixels are grouped in one cluster or more than
one clusters as follows.
F(ClG1)={x2,x3,x4}
F(ClG2)={x1,x4,}
F(ClG3)={x1,x3}
Let (F,A) be represented as (F,A)={F(
ClG
)
|ClG∈
A}. The soft covering based rough set
representation of the above example is given by
(F,A)=








ClG1={x2,x3,x4}
ClG2={x1,x4,}
ClG3={x1,x3}









.
A tabular presentation of soft sets appears in Table 2. If
xi∈F(ClGi)
, then the value is one; else, it
is zero.

Electronics 2020,9, 188 9 of 22
Table 2. Soft covering-based rough set representation of an image.
UClG1ClG2ClG3
x10 1 1
x21 0 0
x31 0 1
x41 1 0
3.2. The Proposed Histogram-Based Soft Covering Rough K-Means Clustering
The proposed histogram-based soft covering rough k-means clustering is summarized in Algorithm
1. The combination of the covering soft set and rough set gives rise to a new kind of soft rough sets.
Based on the covering soft sets, soft covering rough approximation was proposed by Yüksel et al.
in 2014 [
11
,
31
], which is more accurate than the soft rough set. Here, we establish a rough k-means
clustering using soft covering-based rough approximation to segment the image of the leukemia
nucleus. Let
S∗(X)
,
S∗(X)
be denoted as soft covering lower and upper approximation, and for
S∗(X)∈S∗(X)i.e.
, in soft covering-based rough k-means clustering, the lower approximation is a subset
of the upper approximation. The pixel data
Xn=(x1,x2,. . . . . . .xn)
of the lower approximation surely
belong to the cluster; in this way, they can not have a place with some other cluster. The pixel data
Xn=(x1,x2,. . . . . . .xn)
in an upper approximation may belong to the cluster. Since their participation
is dubious, they should be an individual set from an upper approximation of at least another cluster.
The distance between the pixel data Xnand the mean smkis defined as [32]
d(Xn,smk)=kXn−smkk. (6)
The cluster center smki.e., the mean, is computed using the following equation:
smk=













wlow P
Xn∈S∗
Xn


S∗k


+wupp P
Xn∈S∗
Xn



S∗
k



f or S∗,φ
P
Xn∈S∗
Xn



S∗
k



otherwise,(7)
where


S∗k


indicates the numbers of pixels in the lower approximation of the cluster
k
and



S∗
k



is the
number of pixels in the upper approximation of the cluster
k
. The weight parameters
wlow
and
wupp
stress the significance of the lower and upper approximation of the cluster.
Explanation: In this algorithm, identify the peak value of a histogram image and use it to
define the number of clusters
k
. Initially, assign each pixel
Xn=(x1,x2,. . . . . . .xn)
to exactly one
lower approximation. Here, soft covering-based rough approximation is applied instead of rough
approximation. Determine the new means
smk
using Equation (7). Assign each pixel data to its
closest mean using Equation (6). Compute the distance between each pixel
Xn
with centroid
smk
i.e.,
d(Xn,smk)
. For each pixel, compute the relative distance (RD). If it is greater than the threshold,
then the pixel is put into the upper approximation of the cluster
k
; otherwise, put it into the lower
approximation of the cluster
h
. This algorithm is continued until all the data objects close to the cluster
remain unchanged. Finally, the clustered image is labeled by the cluster index, and the segmented
image of the nucleus is extracted.

Electronics 2020,9, 188 10 of 22
Algorithm 1:Based Soft Covering Rough K −Means Clustering Algorithm
Input :Img (Xn),k,wlow ,wupp,δ
Output :Segmented Nucleus Image Segneu
Initialization :
Xn=(x1,x2,. . . . . . .xn)// n=no.o f pixels in an image
K=hist(Img(Xn))No.o f Clusters found using the peak value o f a histogram image
wlow =Lower Approximation Weight
wupp =Upper Approximation Weight
δ=Threshold Value
Randomly assign each pixel into exactly one lower approximation.
Procedure :
Step1:Randomly assign each pixel0s data to the so f t covering approximations
Step2:Compute cluster centers smkusing Equation (7)
Step3:Assign the pixels to the approximations.
The pixel data Xndetermine its closest mean smh.
sdmin
n,h=d(Xn,smh)=min
k=1,2,...Kd(Xn,smk)
Assign Xnto the upper approximation o f the cluster h :Xn∈S∗
h.
Step4:The relative distance is de fined as
RD =d(Xn,smk)−d(Xn,smh)
ST ={t:RD ≤δ∪h,k}.
I f ST ,φthen XnS∗
t∀t∈T.
Else,XnS∗h.
Step5:Check the convergence o f the algorithm;i f not,make it conver ge,and then continue
with Step 1.
Step6:Lable the image by cluster index and extract the leukemia nucleus (Segneu ).
3.3. Performance Assessment for Segmentation Algorithms
After preprocessing, a novel HSCRKM algorithm is applied for leukemia nucleus image
segmentation. The peak values of histogram are identified, and these values will automatically
be assigned the number of clusters (K). In each iteration, the k value will change. The range of weight
of the lower and boundary region in rough k-means algorithms is (0.0
<=wlow
,
wbon <=
1.0
)
.
The relative threshold in the HSCRKM algorithm is defined as
δ
<= 1.0. The parameters’ values
are assigned as
wlow =
0.7,
wbon =
0.3,
and δ=
0.5. These values give possible stable results
in rough k-means [
30
]. Figure 2illustrates the segmentation results produced by the proposed
HSCRKM algorithm.
Electronics 2020, 9, x FOR PEER REVIEW 10 of 24
𝑆𝒕𝒆𝒑𝟑:
𝐴
𝑠𝑠𝑖𝑔𝑛 𝑡ℎ𝑒 𝑝𝑖𝑥𝑒𝑙𝑠 𝑡𝑜 𝑡ℎ𝑒 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑖𝑜𝑛𝑠.
𝑇ℎ𝑒 𝑝𝑖𝑥𝑒𝑙 𝑑𝑎𝑡𝑎 𝑋 𝑑𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑒 𝑖𝑡𝑠 𝑐𝑙𝑜𝑠𝑒𝑠𝑡 𝑚𝑒𝑎𝑛 𝑠𝑚.
𝑠𝑑,
=𝑑(𝑋,𝑠𝑚)= 𝑑(𝑋,𝑠𝑚)
,,…

𝐴𝑠𝑠𝑖𝑔𝑛 𝑋 𝑡𝑜 𝑡ℎ𝑒 𝑢𝑝𝑝𝑒𝑟 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑙𝑢𝑠𝑡𝑒𝑟 ℎ: 𝑋∈ 𝑆∗.
𝑺𝒕𝒆𝒑𝟒: 𝑇ℎ𝑒 𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑖𝑠 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑎𝑠
𝑅𝐷 = 𝑑(𝑋,𝑠𝑚)−𝑑(𝑋,𝑠𝑚)
𝑆𝑇={𝑡:𝑅𝐷𝛿 ⋀ ℎ≠𝑘}.
𝐼𝑓 𝑆𝑇≠𝜙 𝑡ℎ𝑒𝑛 𝑋𝜖𝑆∗ ∀𝑡∈𝑇.
𝐸𝑙𝑠𝑒,𝑋𝜖𝑆∗.
𝑺𝒕𝒆𝒑𝟓: 𝐶ℎ𝑒𝑐𝑘 𝑡ℎ𝑒 𝑐𝑜𝑛𝑣𝑒𝑟𝑔𝑒𝑛𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑙𝑔𝑜𝑟𝑖𝑡ℎ𝑚; 𝑖𝑓 𝑛𝑜𝑡,𝑚𝑎𝑘𝑒 𝑖𝑡 𝑐𝑜𝑛𝑣𝑒𝑟𝑔𝑒, 𝑎𝑛𝑑 𝑡ℎ𝑒𝑛 𝑐𝑜𝑛𝑡𝑖𝑛𝑢
𝑒
𝑤𝑖𝑡ℎ 𝑆𝑡𝑒𝑝 1.
𝑺𝒕𝒆𝒑𝟔: 𝐿𝑎𝑏𝑙𝑒 𝑡ℎ𝑒 𝑖𝑚𝑎𝑔𝑒 𝑏𝑦 𝑐𝑙𝑢𝑠𝑡𝑒𝑟 𝑖𝑛𝑑𝑒𝑥 𝑎𝑛𝑑 𝑒𝑥𝑡𝑟𝑎𝑐𝑡 𝑡ℎ𝑒 𝑙𝑒𝑢𝑘𝑒𝑚𝑖𝑎 𝑛𝑢𝑐𝑙𝑒𝑢𝑠 (𝑆𝑒𝑔).
Explanation: In this algorithm, identify the peak value of a histogram image and use it to define
the number of clusters 𝑘. Initially, assign each pixel 𝑋=(𝑥,𝑥,…….𝑥) to exactly one lower
approximation. Here, soft covering-based rough approximation is applied instead of rough
approximation. Determine the new means 𝑠𝑚 using Equation (7). Assign each pixel data to its
closest mean using Equation (6). Compute the distance between each pixel 𝑋 with centroid
𝑠𝑚 i.e., 𝑑(𝑋,𝑠𝑚). For each pixel, compute the relative distance (RD). If it is greater than the
threshold, then the pixel is put into the upper approximation of the cluster 𝑘; otherwise, put it into
the lower approximation of the cluster ℎ. This algorithm is continued until all the data objects close
to the cluster remain unchanged. Finally, the clustered image is labeled by the cluster index, and the
segmented image of the nucleus is extracted.
3.3. Performance Assessment for Segmentation Algorithms
After preprocessing, a novel HSCRKM algorithm is applied for leukemia nucleus image
segmentation. The peak values of histogram are identified, and these values will automatically be
assigned the number of clusters (K). In each iteration, the k value will change. The range of weight of
the lower and boundary region in rough k-means algorithms is (0.0 = 𝑤, 𝑤 = 1.0). The
relative threshold in the HSCRKM algorithm is defined as δ <= 1.0. The parameters’ values are
assigned as 𝑤 =0.7, 𝑤=0.3,and 𝛿=0.5. These values give possible stable results in rough
k-means [30]. Figure 2 illustrates the segmentation results produced by the proposed HSCRKM
algorithm.
Original image Image historgam Segmented image Nucelus extraction
K=2
Figure 2. Cont.

Electronics 2020,9, 188 11 of 22
Electronics 2020, 9, x FOR PEER REVIEW 11 of 24
Figure 2. Segmentation results produced by the proposed histogram-based soft covering rough
k-means clustering (HSCRKM) algorithm.
In Figure 2, the first column displays the original image, the second column shows the
histogram of an image that helps find the number of clusters (K), the third column displays the
clustered image, and the last column displays the extracted nucleus. It is observed that if the k value
is at its minimum, we get a better segmentation result. This helps reduce the processing time. The
parameters utilized in the clustering algorithms are presented in Figure 3.
Figure 3. Parameters utilized in clustering algorithms.
•K=3, Max Iteration = 500 K-Means Clustering
•K=3, υ=0.000001, m=2 FCM Clustering
•K=3
PSO-based Clustering •𝐾 =𝑃𝑒𝑎𝑘 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝐻𝑖𝑠𝑡𝑜𝑔𝑟𝑎𝑚 𝑖𝑚𝑎𝑔𝑒,
• 𝑤=0.7, 𝑤= 0.3, 𝑎𝑛𝑑 𝛿 =0.5
HSCRKM Clustering
K=3
K=4
K=3
K=4
Figure 2.
Segmentation results produced by the proposed histogram-based soft covering rough k-means
clustering (HSCRKM) algorithm.
In Figure 2, the first column displays the original image, the second column shows the histogram
of an image that helps find the number of clusters (K), the third column displays the clustered image,
and the last column displays the extracted nucleus. It is observed that if the k value is at its minimum,
we get a better segmentation result. This helps reduce the processing time. The parameters utilized in
the clustering algorithms are presented in Figure 3.
Electronics 2020, 9, x FOR PEER REVIEW 11 of 24
Figure 2. Segmentation results produced by the proposed histogram-based soft covering rough
k-means clustering (HSCRKM) algorithm.
In Figure 2, the first column displays the original image, the second column shows the
histogram of an image that helps find the number of clusters (K), the third column displays the
clustered image, and the last column displays the extracted nucleus. It is observed that if the k value
is at its minimum, we get a better segmentation result. This helps reduce the processing time. The
parameters utilized in the clustering algorithms are presented in Figure 3.
Figure 3. Parameters utilized in clustering algorithms.
•K=3, Max Iteration = 500 K-Means Clustering
•K=3, υ=0.000001, m=2 FCM Clustering
•K=3
PSO-based Clustering •𝐾=𝑃𝑒𝑎𝑘 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝐻𝑖𝑠𝑡𝑜𝑔𝑟𝑎𝑚 𝑖𝑚𝑎𝑔𝑒,
• 𝑤=0.7, 𝑤= 0.3, 𝑎𝑛𝑑 𝛿 =0.5
HSCRKM Clustering
K=3
K=4
K=3
K=4
Figure 3. Parameters utilized in clustering algorithms.
Figure 4shows the sample output of leukemia image segmentation using existing clustering
algorithms such as k-means clustering, FCM clustering, and PSO-based clustering algorithms. Here,
the number of clusters k is assigned as three using the elbow method.

Electronics 2020,9, 188 12 of 22
Electronics 2020, 9, x FOR PEER REVIEW 12 of 24
Figure 4 shows the sample output of leukemia image segmentation using existing clustering
algorithms such as k-means clustering, FCM clustering, and PSO-based clustering algorithms. Here,
the number of clusters k is assigned as three using the elbow method.
Original image K-means FCM PSO
Figure 4. Segmentation results by k-means, FCM, and particle swarm optimization (PSO)
algorithms.
4. Results and Discussion
4.1. Dataset
The Acute Lymphoblastic Leukemia Image Database (ALL-IDB) datasets were used for this
experiment. These data were downloaded from the website www.dti.unimi.it/fscotti/all/ [33–36].
There were 368 images—175 benign and 193 malignant—taken for this experimental analysis.
Digital microscopes are not suitable, since they are usually designed to work in the RGB color space.
In the preprocessing step, all the RGB input images are converted into a LAB color space.
4.2. Feature Extraction
The segmented image data were too large, and it was very difficult to process them. Feature
extraction is a technique to extract the relevant informative data of a segmented image. This will
Figure 4.
Segmentation results by k-means, FCM, and particle swarm optimization (PSO) algorithms.
4. Results and Discussion
4.1. Dataset
The Acute Lymphoblastic Leukemia Image Database (ALL-IDB) datasets were used for this
experiment. These data were downloaded from the website www.dti.unimi.it/fscotti/all/[
33
–
36
].
There were 368 images—175 benign and 193 malignant—taken for this experimental analysis. Digital
microscopes are not suitable, since they are usually designed to work in the RGB color space. In the
preprocessing step, all the RGB input images are converted into a LAB color space.
4.2. Feature Extraction
The segmented image data were too large, and it was very difficult to process them. Feature
extraction is a technique to extract the relevant informative data of a segmented image. This will reduce
the processing speed, time, and dimensionality of an image. In this research, 21 shape and color-based
features—namely, the area, perimeter, roundness, elongation, form_factor, length_to_diameter_ratio,
compactness, discrete_fourier_transform, mean_of_harra_coefficient, h_coefficient, v_coefficient,
variance_of_harra_coefficient, h_coefficient, v_coefficient, mean_colour_intensity for red,
green, and blue, hue, saturation, value component, and class attribute—were extracted [
37
].
Twenty-three texture-based features—namely, angular_second_moment, entropy, dissimilarity,

Electronics 2020,9, 188 13 of 22
contrast, inverse_difference, correlation, homogeneity, autocorrelation, cluster_shade,
cluster_prominence, maximum_probability, sum_of_squares, sum_average, sum_variance,
sum_entropy, difference_variance, difference_entropy, information_measures_correlation1,
information_measures_correlation2, maximal_correlation_ coefficient, inverse_difference_normalized,
inverse_difference_moment_normalized, and class attribute were extracted. These features are derived
from the gray level co-occurrence matrix (GLCM) in directions 0
◦
, 45
◦
, 90
◦
, and 135
◦
[
38
,
39
]. From the
literature review, we found that these features are widely used for leukemia image analysis.
4.3. Performance Assessments of Segmentation Algorithms
The empirical results are interpreted in two ways. First, we analyze the efficiency of various
clustering-based segmentation algorithms through state-of-the-art machine learning algorithms.
Secondly, we compare the machine learning methods using some evaluation measures such as receiver
operating characteristic (ROC) curve analysis and kappa statistics. The extracted feature set was fed
into the machine learning (ML) prediction algorithms to classify the segments indicating the tumor
and non-tumor leukemia in the image. In this experiment, there were seven ML algorithms—namely,
logistic regression (LR), naive Bayes (NB), support vector machine (SVM), k-nearest neighborhood
(KNN), neural network (NN), random forest (RF), and decision tree (DT)—were used to evaluate the
performance of the clustering algorithms.
The performance of the machine learning prediction algorithm was analyzed using various
evaluation metrics such as accuracy (A), precision (P), recall (R), F1 measure, area under the ROC
Curve (AUC), mean absolute error (MAE), and coefficient of determination (R
2
) [
40
,
41
]. It is noted that
the prediction value of R2lies between 0 and 1 for no-fit and perfect fit, respectively.
The classification results of k-means clustering, FCM clustering, PSO-based clustering, and the
proposed HSCRKM clustering algorithms are presented in Tables 3–6, respectively. The performance
of the segmentation algorithms was analyzed through different machine learning prediction methods.
The experimental results show that the proposed method HSCRKM clustering algorithm performs
better than the existing algorithms. On a closer look at the overall performance of the proposed
method, it is believed that logistic regression and neural network perform well when compared to
other prediction algorithms and also produce the highest classification accuracy i.e., 93%. It is also
observed that the naive Bayes method produces the lowest classification accuracy rate i.e., 58%.
Table 3presents the performance analysis of k-means clustering. The LR, NN, and RF algorithms
produce the highest classification accuracy of 79%. The NB algorithm gives the minimum accuracy of
65%. KNN and DT produce 72% accuracy and SVM produces 74% accuracy. The overall performance
of k-means clustering was 69%, which is computed by the average accuracy of all the datasets with all
the ML algorithms.
Table 5presents the performance analysis of FCM clustering. The LR, DT, and RF algorithms
achieve the maximum accuracy value of 88%. Obviously, it gives the lowest mean absolute error
(MAE) value. Similar to k-means clustering, the NB algorithm gives the lowest accuracy value of 81%
when compared to other algorithms. The SVM and NN give the accuracy of 83% and 84%, respectively.
The overall accuracy of FCM clustering is 77%.

Electronics 2020,9, 188 14 of 22
Table 3.
Performance analysis of k-means clustering. A: accuracy, AUC: area under the receiver
operating characteristic curve, DT: decision tree, KNN: k-nearest neighborhood, LR: logistic regression,
MAE: mean absolute error, NB: naive Bayes, NN: neural network, P: precision, R: recall, RF:
random forest.
ML Algorithms Dataset P R F1 AUC MAE R2A
LR
GLCM-0 81.00 77.00 78.00 0.821 0.134 0.195 76.74
GLCM045
79.00 79.00 78.00 0.660 0.087 0.076 79.07
GLCM-90
60.00 66.00 68.00 0.706 0.112 0.097 65.17
GLCM-135
70.00 66.00 67.00 0.805 0.128 0.159 67.44
SC 76.00 74.00 75.00 0.805 0.115 0.152 74.42
NB
GLCM-0 61.00 60.00 61.00 0.738 0.082 0.193 60.47
GLCM045
62.00 61.00 58.00 0.880 0.093 0.068 60.60
GLCM-90
54.00 51.00 50.00 0.799 0.128 0.162 51.16
GLCM-135
60.00 56.00 57.00 0.710 0.088 0.132 55.81
SC 68.00 65.00 65.00 0.618 0.110 0.047 65.11
SVM
GLCM-0 77.00 74.00 71.00 0.805 0.073 0.106 74.41
GLCM045
80.00 72.00 72.00 0.871 0.113 0.323 72.09
GLCM-90
82.00 70.00 73.00 0.792 0.032 0.143 69.77
GLCM-135
65.00 65.00 65.00 0.750 0.130 0.372 65.11
SC 73.00 70.00 67.00 0.692 0.113 0.090 69.78
KNN
GLCM-0 71.00 72.00 72.00 0.928 0.119 0.083 72.09
GLCM045
71.00 67.00 39.00 0.819 0.062 0.169 67.44
GLCM-90
69.00 67.00 67.00 0.817 0.138 0.162 67.44
GLCM-135
63.00 63.00 63.00 0.787 0.135 0.162 62.79
SC 67.00 67.00 67.00 0.839 0.112 0.135 67.44
NN
GLCM-0 79.00 79.00 76.00 0.821 0.077 0.274 79.06
GLCM045
77.00 77.00 77.00 0.806 0.139 0.348 76.74
GLCM-90
66.00 67.00 69.00 0.859 0.094 0.079 66.66
GLCM-135
72.00 70.00 71.00 0.817 0.105 0.052 69.69
SC 65.00 65.00 64.00 0.853 0.116 0.090 65.11
RF
GLCM-0 74.00 72.00 72.00 0.777 0.158 0.288 72.09
GLCM045
70.00 70.00 69.00 0.761 0.127 0.275 69.77
GLCM-90
69.00 65.00 65.00 0.798 0.106 0.182 65.11
GLCM-135
79.00 79.00 79.00 0.805 0.126 0.186 79.06
SC 67.00 67.00 67.00 0.472 0.131 0.342 67.42
DT
GLCM-0 66.00 70.00 66.00 0.865 0.073 0.192 69.76
GLCM045
80.00 79.00 76.00 0.549 0.093 0.101 79.06
GLCM-90
71.00 70.00 67.00 0.664 0.118 0.250 69.79
GLCM-135
72.00 72.00 71.00 0.852 0.118 0.250 72.09
SC 72.00 70.00 71.00 0.817 0.105 0.052 69.69
Average Overall Accuracy 69%
Table 4. Performance analysis of FCM clustering.
ML Algorithms Dataset P R F1 AUC MAE Rˆ2 A
LR
GLCM-0 79.00 79.00 76.00 0.802 0.089 0.098 79.06
GLCM045
89.00 88.00 89.00 0.950 0.080 0.401 88.37
GLCM-90
71.00 72.00 71.00 0.816 0.105 0.185 72.09
GLCM-135
88.00 86.00 82.00 0.792 0.058 0.156 86.04
SC 81.00 77.00 78.00 0.821 0.134 0.195 76.74
NB
GLCM-0 75.00 60.00 62.00 0.767 0.076 0.135 60.64
GLCM045
60.00 60.00 60.00 0.716 0.113 0.143 60.45
GLCM-90
63.00 63.00 63.00 0.787 0.135 0.162 62.79
GLCM-135
67.00 67.00 67.00 0.926 0.112 0.135 67.44
SC 84.00 81.00 81.00 0.825 0.145 0.132 81.39

Electronics 2020,9, 188 15 of 22
Table 4. Cont.
ML Algorithms Dataset P R F1 AUC MAE Rˆ2 A
SVM
GLCM-0 77.00 74.00 71.00 0.805 0.073 0.106 74.41
GLCM045
73.00 72.00 72.00 0.655 0.195 0.269 72.09
GLCM-90
75.00 74.00 73.00 0.822 0.176 0.265 74.41
GLCM-135
72.00 72.00 72.00 0.766 0.128 0.161 72.09
SC 83.00 84.00 83.00 0.849 0.053 0.167 83.72
KNN
GLCM-0 79.00 79.00 79.00 0.821 0.077 0.274 79.06
GLCM045
76.00 74.00 74.00 0.812 0.151 0.048 74.41
GLCM-90
83.00 83.00 84.00 0.893 0.122 0.368 83.72
GLCM-135
85.00 84.00 85.00 0.866 0.098 0.312 85.31
SC 79.00 80.00 79.00 0.910 0.079 0.171 79.07
NN
GLCM-0 84.00 84.00 84.00 0.745 0.125 0.349 83.72
GLCM045
87.00 85.00 82.00 0.773 0.148 0.238 84.84
GLCM-90
76.00 74.00 75.00 0.805 0.115 0.152 74.42
GLCM-135
79.00 79.00 79.00 0.805 0.126 0.186 79.07
SC 80.00 77.00 77.00 0.771 0.101 0.156 77.18
RF
GLCM-0 77.00 77.00 75.00 0.785 0.080 0.186 76.74
GLCM045
81.00 86.00 71.00 0.852 0.158 0.437 68.76
GLCM-90
80.00 77.00 77.00 0.839 0.155 0.248 76.74
GLCM-135
88.00 88.00 88.00 0.899 0.073 0.114 88.37
SC 86.00 79.00 78.00 0.795 0.086 0.090 79.06
DT
GLCM-0 84.00 83.00 83.00 0.929 0.159 0.265 82.75
GLCM045
88.00 88.00 88.00 0.953 0.050 0.138 88.37
GLCM-90
81.00 81.00 81.00 0.793 0.115 0.049 81.39
GLCM-135
87.00 86.00 86.00 0.938 0.064 0.053 86.04
SC 85.00 81.00 76.00 0.813 0.131 0.095 81.39
Average Overall Accuracy 77%
Table 5shows the efficiency of the algorithm for PSO-based clustering. In this table, it is noted
that the NN method attains 90% accuracy. The LR, SVM, KNN, and RF methods give above 80% of the
classification accuracy. The NB algorithm again provides the minimum accuracy of 67%. The overall
classification accuracy of PSO-based clustering is 78%.
Table 5. Performance analysis of PSO-based clustering.
ML Algorithms Dataset P R F1 AUC MAE R2A
LR
GLCM-0 86.00 81.00 82.00 0.717 0.141 0.279 81.39
GLCM045
88.00 86.00 85.00 0.741 0.150 0.060 86.04
GLCM-90
84.00 79.00 76.00 0.739 0.143 0.095 79.06
GLCM-135
90.00 86.00 86.00 0.963 0.065 0.093 86.04
SC 86.00 81.00 82.00 0.793 0.092 0.334 81.39
NB
GLCM-0 69.00 67.00 68.00 0.833 0.082 0.098 67.44
GLCM045
60.00 64.00 66.00 0.713 0.118 0.129 63.63
GLCM-90
56.00 61.00 58.00 0.880 0.093 0.068 60.61
GLCM-135
64.00 64.00 65.00 0.764 0.012 0.165 63.63
SC 61.00 62.00 62.00 0.876 0.118 0.148 62.69
SVM
GLCM-0 84.00 79.00 76.00 0.739 0.143 0.095 79.07
GLCM045
79.00 79.00 78.00 0.827 0.085 0.142 79.06
GLCM-90
71.00 72.00 71.00 0.816 0.105 0.185 72.09
GLCM-135
76.00 77.00 72.00 0.807 0.086 0.192 76.74
SC 81.00 81.00 79.00 0.801 0.120 0.167 81.39

Electronics 2020,9, 188 16 of 22
Table 5. Cont.
ML Algorithms Dataset P R F1 AUC MAE R2A
KNN
GLCM-0 82.00 79.00 80.00 0.811 0.123 0.017 79.06
GLCM045
71.00 73.00 71.00 0.864 0.082 0.108 72.72
GLCM-90
70.00 67.00 68.00 0.816 0.141 0.526 67.44
GLCM-135
75.00 74.00 73.00 0.822 0.176 0.265 74.41
SC 82.00 81.00 81.00 0.788 0.118 0.147 80.66
NN
GLCM-0 62.00 76.00 68.00 0.726 0.075 0.448 75.44
GLCM045
61.00 73.00 66.00 0.848 0.123 0.261 72.12
GLCM-90
88.00 84.00 83.00 0.849 0.053 0.167 83.72
GLCM-135
91.00 91.00 91.00 0.929 0.062 0.210 90.67
SC 86.00 86.00 86.00 0.950 0.070 0.070 86.12
RF
GLCM-0 84.00 81.00 81.00 0.825 0.145 0.135 81.39
GLCM045
74.00 79.00 74.00 0.885 0.114 0.264 78.77
GLCM-90
79.00 70.00 79.00 0.747 0.139 0.102 79.65
GLCM-135
78.00 78.00 77.00 0.917 0.082 0.538 77.47
SC 81.00 81.00 81.00 0.841 0.097 0.056 81.39
DT
GLCM-0 87.00 84.00 80.00 0.717 0.115 0.207 83.72
GLCM045
89.00 88.00 89.00 0.929 0.081 0.229 88.37
GLCM-90
87.00 85.00 82.00 0.662 0.086 0.125 84.84
GLCM-135
82.00 82.00 82.00 0.950 0.102 0.214 81.82
SC 90.00 88.00 88.00 0.926 0.103 0.221 88.37
Average Overall Accuracy 78%
The performance analysis of the HSCRKM algorithm is shown in Table 6. The LR, NN, and DT
algorithms achieve 93% classification accuracy. NB, KNN, and RF give accuracy values of 84%,
85%, and 86%, respectively. It is also interesting to note that the SVM gives the minimum accuracy,
i.e., 84%. The overall accuracy of the HSCRKM algorithm is 82%. The proposed method leads the
accuracy of 13% for k-means clustering, 5% for FCM, and 4% for PSO-based clustering. It means that
the accurate segmentation produces the best performance. The experimental results show that the
HSCRKM algorithm accurately segments the nucleus. From the literature review report, the various
authors produce above 90% accuracy. However, they are using a very small number of images for the
experiments. In this research, around 350 images are used to evaluate the performance of the proposed
HSCRKM algorithm.
Table 6. Performance analysis of the HSCRKM algorithm.
ML Algorithms Dataset P R F1 AUC MAE R2A
LR
GLCM-0 84.00 84.00 85.00 0.848 0.017 0.214 84.72
GLCM045
93.00 93.00 93.00 0.944 0.072 0.584 93.02
GLCM-90
87.00 86.00 86.00 0.825 0.032 0.219 87.65
GLCM-135
89.00 88.00 88.00 0.899 0.112 0.427 88.37
SC 86.00 85.00 85.00 0.965 0.047 0.138 85.65
NB
GLCM-0 70.00 70.00 70.00 0.848 0.190 0.133 69.76
GLCM045
67.00 65.00 65.00 0.782 0.128 0.171 65.11
GLCM-90
67.00 65.00 65.00 0.782 0.128 0.171 65.11
GLCM-135
61.00 58.00 56.00 0.750 0.152 0.131 58.13
SC 84.00 84.00 85.00 0.848 0.017 0.214 84.72
SVM
GLCM-0 84.00 81.00 81.00 0.760 0.140 0.206 81.39
GLCM045
84.00 81.00 81.00 0.760 0.140 0.206 81.36
GLCM-90
79.00 79.00 79.00 0.768 0.321 0.341 79.06
GLCM-135
80.00 74.00 73.00 0.780 0.132 0.122 74.41
SC 86.00 84.00 84.00 0.967 0.089 0.312 83.92

Electronics 2020,9, 188 17 of 22
Table 6. Cont.
ML Algorithms Dataset P R F1 AUC MAE R2A
KNN
GLCM-0 86.00 84.00 84.00 0.967 0.072 0.309 83.92
GLCM045
82.00 81.00 81.00 0.952 0.097 0.291 81.39
GLCM-90
75.00 72.00 71.00 0.727 0.127 0.102 72.09
GLCM-135
77.00 77.00 76.00 0.911 0.101 0.151 76.74
SC 86.00 85.00 85.00 0965 0.047 0.138 85.65
NN
GLCM-0 86.00 86.00 86.00 0.982 0.070 0.135 86.04
GLCM045
91.00 91.00 90.00 0.950 0.054 0.274 90.69
GLCM-90
84.00 84.00 85.00 0.848 0.017 0.138 84.72
GLCM-135
93.00 93.00 93.00 0.939 0.074 0.526 93.02
SC 86.00 87.00 86.00 0.965 0.047 0.138 85.65
RF
GLCM-0 82.00 81.00 81.00 0.860 0.174 0.331 81.39
GLCM045
86.00 85.00 85.00 0.965 0.047 0.138 85.65
GLCM-90
82.00 81.00 81.00 0.890 0.441 0.321 81.39
GLCM-135
84.00 84.00 85.00 0.848 0.017 0.214 84.72
SC 86.00 87.00 86.00 0.913 0.144 0.225 86.05
DT
GLCM-0 84.00 84.00 85.00 0.848 0.017 0.214 84.72
GLCM045
93.00 93.00 93.00 0.944 0.072 0.584 93.02
GLCM-90
86.00 84.00 84.00 0.967 0.072 0.309 83.72
GLCM-135
89.00 88.00 88.00 0.899 0.112 0.427 88.72
SC 91.00 91.00 90.00 0.930 0.072 0.297 90.69
Average Overall Accuracy 82%
Figure 5shows the overall prediction accuracy for various machine learning algorithms. With
respect to k-means clustering, all the machine learning algorithms produce the lowest prediction
accuracy i.e., below 80%. It is noted that with respect to PSO and FCM, some of the ML methods
(i.e., logistic regression, random forest, and decision tree) attain above 80% prediction accuracy. With
respect to the HSCRKM clustering algorithm, most of the ML methods (except naive Bayes) achieve
above 80% prediction accuracy. It can also be inferred that the proposed HSCRKM clustering algorithm
efficiently segment the nucleus, and the extracted features (based on the segments) probably increase
the prediction accuracy. To interpret the experimental results, we are manually preserving the best
accuracy range as above 80%.
Electronics 2020, 9, x FOR PEER REVIEW 18 of 24
Figure 5. Overall prediction accuracy.
4.4. Performance Assessments of Machine Learning Algorithms
4.4.1. Kappa Statistics
Figure 6 shows a comparison of the performances for various prediction algorithms and the
proposed HSCRKM algorithm in terms of Cohen’s kappa value [42], which is a statistical measure
used to evaluate the inter-rater reliability of the classifier. The reliability rate lies on a 0 to 1 scale,
where “1” means perfect agreement and less than “1” means less than perfect agreement. With
respect to the shape and color-based feature dataset, the proposed algorithm produces a substantial
agreement range [43] (i.e., 0.61 to 0.80) amidst all the existing prediction algorithms taken up for
study. Compared with other machine learning algorithms, neural networks have the capability to
learn and model nonlinear and complex relationships. It also has the ability to perceive all possible
interactions between predictor variables and the availability of multiple training algorithms. From
the figure, it is noted that the neural network algorithm produces the highest kappa value (i.e., 0.67
to 0.85), which means perfect agreement for prediction. It also produces the highest classification
accuracy when compared with other machine learning algorithms.
0
10
20
30
40
50
60
70
80
90
100
GLCM-0 GLCM045 GLCM-90 GLCM-135 SC
K-Means
LR NB SVM KNN NN RF DT
0
20
40
60
80
100
GLCM-0 GLCM045 GLCM-90 GLCM-135 SC
FCM
LR NB SVM KNN NN RF DT
0
20
40
60
80
100
GLCM-0 GLCM045 GL CM-90 GLCM-135 SC
PSO
LR NB SVM KNN NN RF DT
0
20
40
60
80
100
GLCM-0 GLCM045 GLCM-90 GLCM-135 SC
HSCRKM
LR NB SVM KNN NN RF DT
Figure 5. Overall prediction accuracy.

Electronics 2020,9, 188 18 of 22
4.4. Performance Assessments of Machine Learning Algorithms
4.4.1. Kappa Statistics
Figure 6shows a comparison of the performances for various prediction algorithms and the
proposed HSCRKM algorithm in terms of Cohen’s kappa value [
42
], which is a statistical measure used
to evaluate the inter-rater reliability of the classifier. The reliability rate lies on a 0 to 1 scale, where
“1” means perfect agreement and less than “1” means less than perfect agreement. With respect to
the shape and color-based feature dataset, the proposed algorithm produces a substantial agreement
range [
43
] (i.e., 0.61 to 0.80) amidst all the existing prediction algorithms taken up for study. Compared
with other machine learning algorithms, neural networks have the capability to learn and model
nonlinear and complex relationships. It also has the ability to perceive all possible interactions between
predictor variables and the availability of multiple training algorithms. From the figure, it is noted that
the neural network algorithm produces the highest kappa value (i.e., 0.67 to 0.85), which means perfect
agreement for prediction. It also produces the highest classification accuracy when compared with
other machine learning algorithms.
Electronics 2020, 9, x FOR PEER REVIEW 19 of 24
Figure 6. Kappa value for HSCRKM clustering.
4.4.2. ROC Curve Analysis
Receiver operating characteristic (ROC) curve analysis is a widely used validation method to
evaluate the diagnostic ability of the various prediction algorithms [44]. It can be generated by
plotting the cumulative distribution function of the true positive rate versus the false positive rate. If
the ROC curve of the prediction algorithm appears in the top left corner, then the algorithm
accurately predicts disease. If it is closer to the diagonal line, then the performance of the prediction
algorithm is less accurate. Figure 7 depicts the ROC curve analysis for the proposed algorithm
HSCRKM. The ROC curve is generated for all the extracted datasets, namely GLCM_0, GLCM_45,
GLCM_90, GLCM_135, and Shape_Colour. From Figure 6, we inferred that the shape and
color-based feature datasets produce the highest accuracy values when compared to another dataset.
It is noted that decision tree, random forest, and SVM attain similar prediction accuracy. So, the
curves appear in the same orientation. It is also noted that the neural network (NN) and logistic
regression (LR) algorithms performed better than the other machine learning algorithms. Those
algorithms curve lines almost appeared in the top left corner of the graph. The naive Bayes
algorithm curve line is executed near the diagonal line. So, this method probably attains minimum
accuracy compared to the other ML algorithms.
LR NB SVM KNN NN RF DT
GLCM-0 0.6738 0.3836 0.6211 0.6814 0.7139 0.6117 0.6738
GLCM-45 0.8525 0.3011 0.6211 0.6211 0.8058 0.8525 0.8525
GLCM-902 0.7492 0.3011 0.5452 0.4798 0.6738 0.6117 0.6472
GLCM-135 0.77 0.2053 0.4785 0.393 0.8525 0.6738 0.77
SC 0.7655 0.6738 0.6814 0.7655 0.7655 0.799 0.8058
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Kappa Value
Cohen's Kappa value
Figure 6. Kappa value for HSCRKM clustering.
4.4.2. ROC Curve Analysis
Receiver operating characteristic (ROC) curve analysis is a widely used validation method to
evaluate the diagnostic ability of the various prediction algorithms [
44
]. It can be generated by plotting
the cumulative distribution function of the true positive rate versus the false positive rate. If the ROC
curve of the prediction algorithm appears in the top left corner, then the algorithm accurately predicts
disease. If it is closer to the diagonal line, then the performance of the prediction algorithm is less
accurate. Figure 7depicts the ROC curve analysis for the proposed algorithm HSCRKM. The ROC
curve is generated for all the extracted datasets, namely GLCM_0, GLCM_45, GLCM_90, GLCM_135,
and Shape_Colour. From Figure 6, we inferred that the shape and color-based feature datasets produce
the highest accuracy values when compared to another dataset. It is noted that decision tree, random
forest, and SVM attain similar prediction accuracy. So, the curves appear in the same orientation. It is
also noted that the neural network (NN) and logistic regression (LR) algorithms performed better than
the other machine learning algorithms. Those algorithms curve lines almost appeared in the top left

Electronics 2020,9, 188 19 of 22
corner of the graph. The naive Bayes algorithm curve line is executed near the diagonal line. So, this
method probably attains minimum accuracy compared to the other ML algorithms.
Electronics 2020, 9, x FOR PEER REVIEW 20 of 24
(a) GLCM_0
(b) GLCM_45
(c) GLCM_90
Figure 7. Cont.

Electronics 2020,9, 188 20 of 22
Electronics 2020, 9, x FOR PEER REVIEW 21 of 24
(d) GLCM_135
(e) Shape
Figure 7. ROC curve analysis for HSCRKM clustering.
5. Conclusions and Future Work
Clustering is an unsupervised classification method that is widely employed for image
segmentation. Throughout the present research, a hybrid histogram-based soft covering rough
k-means clustering algorithm is proposed to segment the image of the leukemia nucleus. In this
method, the histogram is used to initialize the number of clusters. The main advantage of this
method is that it applies the soft covering rough approximation instead of rough approximation. It is
a new kind of soft rough set that efficiently deals with uncertainties. The results are interpreted in
the following two ways. (1) The efficiency of the proposed technique is compared with the popular
and frequently used clustering algorithms such as k-means clustering, FCM, and PSO-based
clustering. (2) The state-of-the-art prediction techniques in machine learning (ML) were compared
using evolution metrics.
Figure 7. ROC curve analysis for HSCRKM clustering.
5. Conclusions and Future Work
Clustering is an unsupervised classification method that is widely employed for image
segmentation. Throughout the present research, a hybrid histogram-based soft covering rough
k-means clustering algorithm is proposed to segment the image of the leukemia nucleus. In this
method, the histogram is used to initialize the number of clusters. The main advantage of this method
is that it applies the soft covering rough approximation instead of rough approximation. It is a new kind
of soft rough set that efficiently deals with uncertainties. The results are interpreted in the following
two ways. (1) The efficiency of the proposed technique is compared with the popular and frequently
used clustering algorithms such as k-means clustering, FCM, and PSO-based clustering. (2) The
state-of-the-art prediction techniques in machine learning (ML) were compared using evolution metrics.
From the experimental results, it is inferred that the HSCRKM clustering algorithm and all of
the ML methods (except for naive Bayes) achieve above 80% prediction accuracy. It is also noted that
logistic regression and neural network provide on average above 90% accuracy, which performs better
than other prediction methods. The limitation of this method is that when we go for multiple color
images such as satellite images, agricultural images, photographs etc., the number of peak values in
the histogram is increased, and consequently the processing time is also increased. This method is
more suitable for the segmentation of medical images and the extraction of specific portions with high

Electronics 2020,9, 188 21 of 22
clarity (for deep study). In the future, bio-inspired algorithms could be used to optimize the number
of clusters.
Author Contributions:
Conceptualization, J.G., A.T.A., and H.I.H.; methodology, J.G., A.T.A.; software, J.G.;
validation, J.G., A.T.A., and H.I.H.; formal analysis, A.T.A. and H.I.H.; investigation, H.I.H.; resources, H.I.H.; data
curation, J.G.; writing—original draft preparation, J.G., A.T.A., and H.I.H.; writing—review and editing, A.T.A.
and H.I.H.; visualization, J.G.; funding acquisition, A.T.A. All authors have read and agreed to the published
version of the manuscript.
Funding: This research is funded by Prince Sultan University, Riyadh, Saudi Arabia.
Acknowledgments:
The authors would like to thank Prince Sultan University, Riyadh, Saudi Arabia for supporting
and funding this work. Special acknowledgment to Robotics and Internet-of-Things Lab (RIOTU) at Prince Sultan
University, Riyadh, SA. In addition, the authors wish to acknowledge the editor and anonymous reviewers for
their insightful comments, which have improved the quality of this publication.
Conflicts of Interest: The authors declare no conflict of interest.
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