Breast cancer detection and classification using metaheuristic optimized ensemble extreme learning machine

Abstract

Breast cancer deaths are increasing rapidly due to the abnormal growth of breast cells in the women's milk duct. Manual cancer diagnosis from mammogram images is also difficult for radiologists and medical practitioners. This paper proposes a novel metaheuristic algorithm-based machine learning model and Fuzzy C Means-based segmentation technique for the classification and detection of breast cancer from mammogram images. At first instance, the fuzzy factor improved fast and robust fuzzy c means (FFI-FRFCM) segmentation is proposed for the segmentation by modifying the member partition matrix of the FRFCM technique. Secondly, a hybrid improved water cycle algorithm-Accelerated particle swarm optimization (IWCA-APSO) optimization, is proposed for weight optimization of the ensemble extreme learning machine (EELM) model. Three benchmark functions are taken for optimization to demonstrate the proposed hybrid IWCA-APSO algorithm's uniqueness. With the INbreast dataset, the IWCA-APSO-based EELM classification shown the sensitivity, specificity, accuracy, and computational time as 99.67%, 99.71%, 99.36%, and 23.8751 s respectively. The proposed IWCA-APSO-based EELM model performs better than the traditional models at classifying breast cancer.

Full text

Vol.:(0123456789)
1 3
Int. j. inf. tecnol.
https://doi.org/10.1007/s41870-023-01533-y
ORIGINAL RESEARCH
Breast cancer detection andclassification using metaheuristic
optimized ensemble extreme learning machine
RajKumarPattnaik1· MohammadSiddique1· SatyasisMishra2 ·
DemissieJ.Gelmecha2· RamSewakSingh2· SunitaSatapathy3
Received: 5 May 2023 / Accepted: 14 September 2023
© The Author(s), under exclusive licence to Bharati Vidyapeeth’s Institute of Computer Applications and Management 2023
Abstract Breast cancer deaths are increasing rapidly due
to the abnormal growth of breast cells in the women’s milk
duct. Manual cancer diagnosis from mammogram images
is also difficult for radiologists and medical practitioners.
This paper proposes a novel metaheuristic algorithm-based
machine learning model and Fuzzy C Means-based segmen-
tation technique for the classification and detection of breast
cancer from mammogram images. At first instance, the fuzzy
factor improved fast and robust fuzzy c means (FFI-FRFCM)
segmentation is proposed for the segmentation by modify-
ing the member partition matrix of the FRFCM technique.
Secondly, a hybrid improved water cycle algorithm-Accel-
erated particle swarm optimization (IWCA-APSO) optimi-
zation, is proposed for weight optimization of the ensemble
extreme learning machine (EELM) model. Three bench-
mark functions are taken for optimization to demonstrate
the proposed hybrid IWCA-APSO algorithm’s uniqueness.
With the INbreast dataset, the IWCA-APSO-based EELM
classification shown the sensitivity, specificity, accuracy,
and computational time as 99.67%, 99.71%, 99.36%, and
23.8751s respectively. The proposed IWCA-APSO-based
EELM model performs better than the traditional models at
classifying breast cancer.
Keywords Extreme learning machine· Breast cancer·
Fuzzy C means· Water cycle algorithm· Wavelet
transform· Accelerated particle swarm optimization
1 Introduction
Breast cancer is a severe illness that affects women’s breast
cells. According to the global health challenge 2020, 2.26
million cases were predicted to occur globally in 2020. In
2020, underdeveloped countries saw more breast cancer-
related fatalities [1]. Due to the lack of innovative detection
tools, underdeveloped and developing nations have higher
breast cancer-related mortality rates [2]. Breast cancer is
the most frequent disease in the world and the leading cause
of cancer-related death. Breast cancer is the most prevalent
disease in the world, and its share is nearly 12.2% of all
afresh identified cases in 2020, according to the World Can-
cer Research Fund International (WCRFI) [3]. For instance,
a study on the epidemiology of breast cancer at Hawassa
University Comprehensive Specialized Hospital (HUCSH)
found that African women, particularly those in Ethiopia, are
impacted by breast cancer at a young age due to the absence
of treatment at an early stage [4]. Segmentation is essential
for detection and aids in measuring the volume of tissue in
the breast for scheduling diagnoses. To enhance the noise
capabilities, the researchers proposed FCM-based image
segmentation methods. Hybrid Markov Penalized FCM pro-
posed by Priya etal. [5], fuzzy c means and k-means pro-
posed by Kamil etal. [6], and Intuitionist Possibilistic Fuzzy
C-Mean proposed by Chowdhary etal. [7] for breast cancer
detection. There are not enough literature for the segmenta-
tion of breast cancer based on FCM-based algorithms. The
FCM-based algorithms were developed in border sense and
applied to brain tumor. Some of the FCM-based techniques
* Satyasis Mishra
satyasismishra@gmail.com
1 Department ofMathematics, Centurion University
ofTechnology andManagement, Bhubaneswar, Odisha,
India
2 Department ofECE, Adama Science andTechnology
University, Adama, Ethiopia
3 Department ofZoology, Centurion University ofTechnology
andManagement, Bhubaneswar, Odisha, India

Int. j. inf. tecnol.
1 3
are presented as follows: Szilagyi etal. [8] developed an
improved FCM algorithm (EnFCM) for brain images.
EnFCM’s parameter (configurable) enhances segmenta-
tion outcomes but cannot remove noise altogether. The Fast
generalized FCM algorithm (FGFCM) was proposed by Cai
etal. [9] to reduce noise, but FGFCM requires additional
components to segment the images. The fuzzy local infor-
mation c-means clustering algorithm (FLICM), developed
by Krinidis etal. [10], which replaces the parameter with a
fuzzy factor in FGFCM to delimit the noise. The FLICM
speeds up segmentation, but can only reduce Gaussian noise
by 30% or less. FCM with local information and kernel met-
ric (KWFLICM), proposed by Gong etal. [11] to enhance
the segmentation capability of FLICM and increases its
robustness. Fast and Robust FCM (FRFCM) was suggested
by Tai etal. [12] for the segmentation of brain tumors to
reduce rician noise. All of the aforementioned segmenta-
tion methods were applied to strengthen the segmentation
and noise reduction capability. Motivated by the FCM-based
segmentation techniques for breast cancer detection, we have
developed a fuzzy factor improved fast and Robust FCM
(FFI-FRFCM) segmentation by updating the fuzzy factor in
the objective function. According to the literature review,
some basic segmentation techniques have been used with
breast cancer web data. However, none of the algorithms
succeed in removing the necessary image noise and detect-
ing cancer.
Controlling observation depends on the classification.
Researchers have suggested various classification strategies
based on the unpredictable nature of cancer and classifica-
tion challenges. A support vector machine (SVM) classi-
fier was proposed by Gorgel etal. [13] to categorize the
segmented masses as cancerous or non-cancerous breast
tumors. For mass classification, Lima etal. [14] suggested
a new SVM-based feature selection method along with
selected geometry and texture features. Juneja etal.[15]
proposed selective feature based improved decision tree
Algorithm for classification and Chi square test to recog-
nize the features with Wisconsin Breast Cancer Database
and achieved 99% accuracy. Pramod etal. [16] proposed
a hybrid approach based on differential evaluation evolu-
tionary algorithm and cuckoo search for identification of
ROI from the mammogram images and achieved 97.51% of
accuracy with DDSM dataset. Sharma etal. [17] proposed
feature selection approaches such as Correlation- based
selection, Information Gain based selection and Sequential
feature selection and Max Voting Classifier and achieved
99.41% classification accuracy with Wisconsin Breast Can-
cer (WDBC) datasets. Kate etal. [18] proposed gravitation
search algorithm for kapur’s entropy as a fitness function
and VGG16 and InceptionV3 model for classification with
Digital Database for Screening Mammography DDSM data-
set and achieved an accuracy of 97.98% for InceptionV3
based model and 91.92% for VGG16. A novel residual deep
convolutional neural network (DCNN) with stochastic gradi-
ent descent (SGD) and AdaGrad based optimizers was pro-
posed by Mishra etal. [19] with breast ultrasound (BUS)
images and achieved AUC 0.9906, accuracy 96.21%, and
F1-scores of, 0.9725, respectively. Kumari etal. [20] pro-
posed hybrid classifier which integrates eXtreme Gradient
Boost (XGBoost) with Random Forest (XGBoost-RF) for
classification of mammograms with Mammographic Image
Analysis Society (MIAS) and DDSM dataset and K-Fold
cross validation and achieved an accuracy for MIAS and
DDSM datasets are 98.6% and 94.3% respectively. Machine
learning algorithms were able to recognize the wide size
variations among the masses [21], but they were unable to
offer a suitable scale for the variety of masses. Some of the
metaheuristic algorithms such as the water cycle algorithm
(WCA) [22], sine cosine algorithm (SCA) [23], Teaching
and Learning based optimization (TLBO) [23], artificial bee
colony (ABC) [24], particle swarm optimization [25], APSO
algorithm [25], harmony search (HS) algorithm [26], etc.,
were proposed for optimization of weights of the machine
learning models, to improve the performance of the clas-
sification. In this research, we have proposed a parametric
improvement to the WCA algorithm and hybridized with
APSO algorithm to improve the classification of the EELM
model. The hybrid IWCA-APSO weight-optimized EELM
model is proposed for classification in order to classify can-
cerous and non-cancerous diseases from the mammogram
images.
The contributions are as follows:
• We have developed a fuzzy factor improved fast and
robust FCM (FFI-FRFCM) method by upgrading the
fuzzy factor in fuzzy partition matrix. In order to achieve
results with more precision, we also combined the fuzzy
partition matrix with the mean filter to detect breast can-
cer and reduce noise.
• To improve the performance of the EELM classifier, a
hybrid improved WCA-APSO optimization algorithm is
developed by incorporating parameter variations, and its
mathematical analysis is also presented. The improved
WCA-APSO optimization is employed to optimize the
weights of the EELM model.
• Further, to show the uniqueness of the improved WCA-
APSO hybrid algorithm, we have considered three differ-
ent benchmark functions for optimization. The results of
the improved WCA-APSO algorithm is compared with
metaheuristic algorithms such as the water cycle algo-
rithm (WCA), sine cosine algorithm (SCA), and artificial
bee colony (ABC) algorithms.
The remaining part of the paper is organized as follows:
Sect.2 presents related work of the research, Sect.3 presents

Int. j. inf. tecnol.
1 3
the materials and methods, which contains the research dia-
gram, and proposed IWCA-APSO-based EELM model,
Sect.4 presents the results and discussion; and Sect.5 pre-
sents the conclusion and reference.
2 Related work
Using computer-aided methods, Singh etal. [27] devel-
oped segmentation on k-means clustering. In addition, the
clustering with the MAIS dataset was upgraded using the
fuzzy intensification operator (INT). Velmurugan etal.
[28] suggested using k-Means and FCM techniques for
segmentation. Finally, compared the two approaches
and selected the most effective approach for analyz-
ing breast images. By combining Fuzzy C-Means with
the Chan-Vese model, Hmida etal. [29] created fuzzy
active contour model for segmenting masses utilizing the
regions of interest of mammographic images. The seg-
mented masses are then used to extract shape and margin
parameters that are used to categorize them as benign
or malignant. According to experimental findings on
regions of interest (ROIs) taken from the MIAS database,
the suggested strategy produces accurate mass segmenta-
tion and classification outcomes. A new graph cut based
segmentation algorithm was created by Zheng etal. [30]
to improve coarse manual segmentation for the identifi-
cation of tumor areas. Second, a spatio-temporal model
of segmented tumor is created to extract spatio-temporal
enhancement patterns by treating successive contrast-
enhanced images as a single spatio-temporal image
(STEPs). For instance, the proposed framework’s high
accuracy was confirmed through experiments that pro-
duced results like an area of 0.97 under the ROC curve.
The development of deep learning improves classifica-
tion accuracy, but model simulation requires a significant
amount of processing time. Table1 presents the literature
survey of some latest researches.
3 Materials andmethods
3.1 Proposed methodology
The proposed methodology in Fig.1 focuses on classifying
breast cancer by using machine learning and a soft comput-
ing hybrid model. In the first step, the mammogram images
are given to fuzzy factor improved FRFCM image segmenta-
tion and features are extracted by wavelet transform. In the
second step, the features are fed as input to the proposed
IWCA-APSO-EELM model, WCA-EELM model, WCA-
PSO-EELM model, and IWCA-APSO-EELM model. In the
third step, the classification comparison results are obtained
and presented. The Ensemble Extreme Learning Machine
model is a combination of ELM models. Each single ELM
model weight is optimized by the proposed IWCA-APSO
algorithm and ensemble all the outputs of all ELM. The
mean of all the ELM model outputs is selected. The detailed
diagram of the EELM model is presented in Fig.5.
Table 1 Literature survey of previous research
Sl no References Year Dataset used Model Accuracy in %
4 Hameed etal. [31] 2022 WSI Xception 97.33%
5 Maqsood etal. [32] 2022 DDSM Transferable texture convolutional neural net-
work (TTCNN) a deep learning model
97.49%
6 Joseph etal. [33] 2022 BreakHis dataset DNN 97.87%
11 Jabeen etal. [34] 2022 Breast Ultrasound
Images (BUSI)
Deep learning 99.1%
12 Ramesh etal. [35] 2022 MIAS dataset GoogLeNet 99.12%
13 Khozama etal. [36] 2022 BCSC dataset Ensemble Learning Model 91.33%
Fig. 1 Proposed methodology flow

Int. j. inf. tecnol.
1 3
3.1.1 Fuzzy factor improved fast androbust fuzzy C means
(FFI‑FRFCM) segmentation
The FCM method can store more visual evidence; how-
ever, detection accuracy is challenging. A fuzzy factor-
improved FRFCM method is proposed for detecting breast
cancer from mammogram images.
The objective function with local information [11] is
specified by
where the fuzzy aspect is given by
where
ukl
is the fuzzy partition matrix. The fuzzy partition
matrix is given by
And
where
vk
is the center. From Eq.(3), it is seen that the factor
Fkl
reduces the noise and preserve the image details, but time
for computation increases.
To improve the performance of the segmentation and
reduce the “computational” complexity, the “membership
partition matrix” is updated as
where
𝜌
is a constant, and
𝛾
is gray assessment of image and
“
𝜏
”is the smoothness factor. Further, using the dilation and
erosion operation on the image through the “morphological”
reconstruction operations, the new image is considered as
“
𝜉p
”, and is presented as
where
I
denotes an original image and
RC
b
is the “morpho-
logical closing” reconstruction. The membership partition
matrix is given by
(1)
J
FFI =
n
∑
l=1
c
∑
k=1
ukl
‖
‖
xl−vk
‖
‖
2+
n
∑
l=1
c
∑
k=1
F
kl
(2)
F
kl =
∑
k∈Nv
l≠k
1
dlk +1
(
1−ukl
)
m
‖
‖
xl−vk
‖
‖
2
(3)
u
kl =
1
c

j
=
1
xl−vk

2
+Fkl

xl−vj

2
+Fjl

1
m−1
(4)
v
k=
n
∑
k=1
um
klxl
n
∑
l=1
ukl
(5)
F
kl�=
∑
r∈Nv
l≠r
log
(
𝜌
𝜏+1
dlr
)
um
kr
‖
‖
xr−vk
‖
‖
2
(6)
𝜉p=Rc
b(I)
and
Now, applying the mean filter to the “membership sepa-
ration matrix”, the new “membership” partition matrix is
given by
With the application of mean filter the segmentation pro-
cess will provide a better detection of tumor from the breast
cancer images and improves the noise reduction capability.
3.1.2 Proposed hybrid IWCA‑APSO algorithm
In the particle swarm optimization (PSO) [23, 24] algorithm,
the velocity update equation is given by
And the position update equation is given by
where the learning factors β1 and β2 indicating the local and
global position weight coefficients,
C1,C2
are the random val-
ues taken in-between [0 1], and κ is inertia coefficient. The
complexity of the PSO has been reduced by reducing the
parameter variations and APSO [36] algorithm has evolved,
the velocity equations of the PSO are modified as
The position equation is given by
where
g∗
b
is the global best position parameter.
The WCA algorithm is based on how streams and rivers
flow, combined with the water cycle process to form the sea
proposed by Sadollah etal. [22]. Figure2 depicts the water
cycle algorithm, which begins with rainfall or precipitation
events by the formation of streams of population or design
variables [22, 23]. A new stream is selected when the stream
moves to a new location close to the sea, as seen in Fig.3.
The rivers are then chosen from the collection of streams
with the best match values. It is considered that streams
(7)
u
kp =
1
c

j=1
𝜉p−vk

2
+Fkp�

𝜉p−vj

2
+Fjp�

1
t−1
(8)
v
k=
c
∑
k=1
ut
kp𝜉
p
s
∑
p=1
ukp
(9)
U
=mean
[
U
kp]
(10)
v
i(l+1)=𝜅∗vi(l)+𝛽1C1∗

pbest
i−xi(l)

+𝛽2C2∗

pgbest
i−xi(l)

(11)
xi(l+1)=xi(l)+vi(l+1)
(12)
vi
(l+1)=v
i
(l)+𝛼∈
n
+𝛽
[
g
∗
b
−x
i
(l)
]
(13)
xi(l+1)=(1−𝛽)xi(l)+𝛽g∗
b+𝛼∈n

Int. j. inf. tecnol.
1 3
change positions and flow velocities as they proceed toward
rivers and the sea. Assuming the one-dimensional 1 × d array
to be a stream, the dimensional array for the solution and the
corresponding matrix is given by
(14)
RS
Totpop =
⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣
Sea
river −1
river −2
⋮
StreamSsr+1
StreamSsr+2
StreamSsr+3
⋮
StreamS
pop
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
=
⎡
⎢
⎢
⎢
⎢
⎣
x1
11 x1
12 ⋯x1
d(i,j+1)
x1
21 x2
22 ⋯x2
d(i+1,j+1)
⋮ ⋮⋯ ⋮
xspop
i+1,ixspop
i+1,j+1⋯xspop
d(i+n,j+n)
⎤
⎥
⎥
⎥
⎥
⎦
where the values of
Ssr
are taken as the sea and rivers with
the dimension of the matrix “
d
”.The total of number of riv-
ers and sea are presented as
Ssr
.
where
Spop
are the populations of stream, and the
Spop
streams
are created at the first stage of rain fall, then streams are cre-
ated. The rivers and sea are selected as the number of ideal
individuals minimum values
Ssr
. The stream is treated as the
sea when it has minimum value. Typically, water entering a
river goes through streams to the sea. Adding new rivers and
removing the surviving population as the stream flows into
the rivers depends on the amount of water flow.
By combining the two algorithms, improved water cycle
algorithm and accelerated particle swarm optimization and
ignoring the evaporation criteria, and taking into account the
position and velocity from the APSO algorithm, the stream
flow matrix of size
Spop ×D
, and the mapping of the posi-
tion and velocity equation to the stream flow, resulting in the
velocity of the flow update equation is given by
where,
𝜒
,
𝛼,𝜆1,𝜆2,and𝜆3
are the controlling parameter
of convergence and
vstr
i
(
l
+
1)
is the new stream velocity,
vriv
i
(l+1
)
is the new velocity of river. By considering the
velocity of stream and rivers, the new position update equa-
tion for stream and river is given by
The parameter
𝜒
is the controlling parameter for the
optimization, where x
str
i
(l+1
)
is the new stream position,
xriv
i
(l+1
)
new river position, and
𝛽
is the controlling coef-
ficient of the stream position.
3.2 Proposed IWCA‑APSO weight optimization
ofEELM Model
The extreme learning machine (ELM) [24] is a feed-forward
network that is known by its fast convergence. As the dataset
size grows, ELM suffers from overfitting. To improve the clas-
sification accuracy, we have proposed an IWCA-APSO hybrid
(15)
Ssr =No.of rivers +1(sea)
(16)
SStr =Spop −Ssr
(17)
vstr
i
(l+1)=𝜒∗v
str
i
(l)+𝛼∈
n
+𝜆
1
∗
(
x
sea
(l)−x
str
i
(l)
)
(18)
vstr
i
(l+1)=𝜒∗v
str
i
(l)+𝛼∈
n
+𝜆
2
∗
(
x
riv
(l)−x
str
i
(l)
)
(19)
vriv
i
(l+1)=𝜒∗v
str
i
(l)+𝛼∈
n
+𝜆
3
∗
(
x
sea
(l)−x
riv
i
(l)
)
(20)
x
str
i(l+1)=
{
𝜒∗(1−𝛽)x
str
i(l)+v
str
i(l+1),for sea >stream
𝜒∗(1−𝛽)xstr
i
(l)+vstr
i
(l+1),for river >
stream
(21)
xriver
i
(l+1)=𝜒∗(1−𝛽)x
str
i
(l)+v
riv
i
(l+1
)
Fig. 2 Water cycle algorithm [22]
Fig. 3 New positions of stream, flows to sea [22]

Int. j. inf. tecnol.
1 3
model for optimization of the weights of the Ensemble ELM
model. The Architecture of the proposed IWCA-APSO-based
EELM model is presented in Fig.4. First, we have taken single
ELM model shown in Fig.4 and optimized the weights by the
IWCA-APSO model, and the error is calculated, then ensem-
ble all other ELM errors and selected the average error. The
mathematical analysis is also presented step-wise to under-
stand the flow of algorithm (Fig.5).
3.2.1 Step‑1
According to the ELM architecture [24], the output is given by
where
q
(w,x)=
[
1, q
1(
w
1
,x
)
, ......., q
K(
w
K
,x
)]
is the hidden
layer and
𝛽
is the weight vector of all hidden neurons to
an output neuron to be analytically analyzed.
gk(
⋅
)
Which is
the activation function of hidden layer. Equation(8) can be
written as
where
Q
is the hidden layer matrix,
And
qL
w
K
;x
K
=

w
1
x
1
+w
1
x
1
.........w
K
x
K
.e

−

(xK−ci)
2
2𝜎2
k

.
Where
‖
‖
x
k
−c
i‖
‖
is the Euclidean distance between the
inputs and the function center.
Equation(9) is a linear equation, which can be solved by
where
Q†
is the “Moore–Penrose generalized inverse of
matrix” and
d
is the desired vector.
(22)
y
=
L
∑
k=0
𝛽kqk
(
wk;x
)
(23)
Q𝛽=y
(24)
Q
†=⋅
(
QTQ
)−1
QT
(25)

𝛽=Q
†
d,
Fig. 4 Architecture of the proposed IWCA-APSO-based EELM
model
Fig. 5 IWCA-APSO Based
ELM Model

Int. j. inf. tecnol.
1 3
3.2.2 Step‑2
The optimization takes place according to the

𝛽
. The error
for single ELM is given by
3.2.3 Step‑3
With the proposed weights
w
=
[
w
1
,w
2
....., w
L−1
, ...w
L]
of the
ELM model, the velocity equation is reformulated as
The position equation is given by
When river merged with sea, the weights are optimized
by the equation
The position equation is given by
3.2.4 Step‑4
Combining all ‘L’ ELMs, for the he
Lth
ELM, the error is
given by
where
y
ens =
1
L
L
∑
i=1
y
i
.
The expectation of the error is given by
(26)
e=d−y=d−Q
𝛽
(27)
wstr
i
(l+1)=𝜒∗w
str
i
(l)+𝛼∈
n
+𝜆
1
∗
(
x
sea
(l)−x
str
i
(l)
)
(28)
wstr
i
(l+1)=𝜒∗w
str
i
(l)+𝛼∈
n
+𝜆
2
∗
(
x
riv
(l)−x
str
i
(l)
)
(29)
xstr
i
(k+1)=𝜒∗(1−𝛽)x
str
i
(l)+w
str
i
(l+1
)
(30)
wriv
i
(k+1)=𝜒∗w
str
i
(k)+𝛼∈
n
+𝜆
3
∗
(
x
sea
(l)−x
riv
i
(l)
)
(31)
xriv
i
(l+1)=𝜒∗(1−𝛽)x
str
i
(l)+w
riv
i
(l+1
)
(32)
e
=d−y
ens
=d−Q

𝛽
ens
(33)
E
[
(
d
l
−y
)2
]=E
[
e2
l]
Now, the MSE of the ensemble model is
Therefore
The pseudo code for IWCA-APSO–EELM is presented
in Table1. Parameter values used for simulation in this
research are presented in the Table2.
3.2.5 Dataset
The INbreast database [37], which contains 410 mammo-
grams from 115 people, has been used in experiments. The
mammograms have two views such as cranial cardo (CC)
and mediolateral oblique (MLO). Depending on the compres-
sion plate that was utilized for the acquisition, the mammo-
gram’s size is either 4084 × 3328 or 3328 × 2560 pixels. The
INbresat database, which is open to the public, was used for
our tests. The sample image of the INbreast dataset is pre-
sented in Fig.6. We have selected the Morlet wavelet [24] and
extracted six features from 410 images, hence 410 × 6 = 2460
data are collected for each Wavelet. For our experiment, we
selected Morlet wavelet features after visualizing the col-
lected feature data. The Morlet wavelet function is given by
(34)
E
ens =E

1
L
L

i=1
E[e2
i]

2

=1
L2
L

i=1
E[e2
i
]
(35)
E
ens =
1
L
E
avg
(36)
𝜓
(t)=cos (1.75x)exp
(
−x2
2
)
Table 2 Values of the parameter used and its range
Parameters Values Bound range
𝜒
0.6 [0 1]
C1
0.9 [0 1]
C2
0.9 [0 1]
𝜆1,𝜆2,𝜆3
2[0 2]
𝛼
rand [0 1]
∈n
rand [0 1]
Fig. 6 The INbresat database
sample images [37]

Int. j. inf. tecnol.
1 3
4 Results anddiscussion
4.1 Validation results oftheproposed IWCA‑APSO
algorithm
To demonstrate the uniqueness of the new IWCA-APSO
algorithm, the proposed IWCA-APSO optimization tech-
nique has been compared to the current WCA and APSO
metaheuristic algorithms. The three benchmark functions,
such as Griewanks’s function, Sphere function, and Quar-
tic Function [25], are considered for optimization to dem-
onstrate the distinctiveness of the proposed IWCA-APSO
hybrid algorithm. In Table3, the benchmark functions
with their bound range and dimensions are presented. The
comparison results of validation are shown in Figs.7, 8,
and 9 in the results section. In order to show the unique-
ness of the proposed algorithm, each of the three functions
underwent optimization using APSO, WCA, WCA + PSO,
WCA + APSO, and IWCA + APSO optimization algorithms.
The validation of function F1 using the APSO, WCA,
WCA + PSO, WCA + APSO, and IWCA + APSO algorithms
is shown in Fig.7. Figure7 shows that the proposed IWCA-
APSO required only around 60 iterations, whereas APSO,
WCA, WCA + PSO, and WCA + APSO required about 600,
550, 450, and 120 iterations, respectively, to reach conver-
gence. For all benchmark function optimization,1000 itera-
tions are taken into account for simulation. The optimal
Table 3 Benchmark functions
for the validation of the
proposed IWCA-APSO
algorithm
Function Name of the function Details Dimension Bound regions
F1 Griewanks’s function
d
∑
i=1
x
2
i
4000 −
d
∏
i=1
cos
(
xi
√
i
)
+
1
30 [− 600,600]
F2 Sphere function
d
∑
i=1
x
2
i
30 [− 5.12,5.12]
F3 Quartic Function
d
∑
i=1
ix
4
i
30 [− 1.28,1.28]

Int. j. inf. tecnol.
1 3
values of functions F1, F2, and F3 are presented in Table5.
The validation of function F2 is shown in Fig.8.
The validation of function F3 is shown in Fig.9.
According to Fig. 9, the suggested IWCA-APSO
required less than 80 iterations, whereas APSO, WCA,
WCA + PSO, and WCA + APSO required more than
870 iterations, or 350 iterations, 280 iterations, and 100
iterations, respectively, to reach convergence. Further-
more, APSO, WCA, WCA + PSO, and WCA + APSO
all achieved ideal values of 0.8572, 0.6123, 0.5249, and
0.4913 for function F3, compared to the recommended
WCA-optimal APSO’s value of 0.3778.
Table4 shows the optimal values for APSO, WCA,
WCA + PSO, WCA + APSO, and IWCA + APSO algo-
rithms. When compared to APSO, WCA, WCA + PSO,
and WCA + APSO optimization algorithms, all
benchmark functions F1, F2, and F3 for the proposed
IWCA + APSO algorithm achieved good optimal values.
The comparison of optimal values are shown Fig.10.
0100 200 300 400 500 600700 800900 1000
No. Of Iteration
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Best fit
Function-F1
IWCA-APSO
WCA-PSO
WCA-APSO
WCA
APSO
Fig. 7 Validation of function F1 using APSO, WCA, WCA + PSO,
WCA + APSO and IWCA + APSO algorithms
0100 200 300 400 500 600 700 800 900 1000
Iteration
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Best fit
FUNCTION-F2
IWCA-APSO
WCA-PSO
WCA-APSO
WCA
APSO
Fig. 8 Validation of function F2 using APSO, WCA, WCA + PSO,
WCA + APSO and IWCA + APSO algorithms
0 100 200 300 400 500 600 700 800 900 1000
Iteration
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Best fit
Function-F3
IWCA-APSO
WCA-PSO
WCA-APSO
WCA
APSO
Fig. 9 Validation of function F3 using APSO, WCA, WCA + PSO,
WCA + APSO and IWCA + APSO algorithms
Table 4 Benchmark functions optimal value
Objective function optimal value
Optimization methods No. of Iterations F1 F2 F3
APSO 1000 0.8006 0.8039 0.8572
WCA 1000 0.4562 0.4782 0.6123
WCA-PSO 1000 0.4221 0.3435 0.5249
WCA + APSO 1000 0.3392 0.3279 0.4913
IWCA + APSO 1000 0.2851 0.2794 0.3778
Fig. 10 Optimal value comparison results of functions F1–F3 using
APSO, WCA, WCA + PSO, WCA + APSO and IWCA + APSO algo-
rithms

Int. j. inf. tecnol.
1 3
4.2 Segmentation results
The segmentation results were obtained by using EnFCM,
FLICM, NDFCM, FRFCM and proposed FFI-FRFCM
techniques. The segmentation accuracies are presented in
Table5. The Figs.11, 12, 13 and14 shows the different
image segmentation outputs.
The segmentation results by using EnFCM, FLICM,
NDFCM, FRFCM and proposed FFI-FRFCM techniques
are presented from Figs.11, 12, 13 and 14. It is observed
from the Fig.11 that the segmentation is not proper by using
EnFCM technique. Similarly, in FLICM technique, the noise
reduction capability is less and the segmentation accuracy is
95.65% and the segmentation result is presented in Fig.12.
It is found from Fig.13 that the FRFCM segmentation is
achieving better result in segmentation in the breast tumor.
But the detected tumor is not up to the requirement. The
proposed FFI-FRFCM segmentation shows 99.12% accu-
racy, which is shown in Fig.14, and shows good capability
of detection in terms of segmentation accuracy. The quality
measure PSNR value is 37.85dB and SSIM is 0.9253 in
case of proposed FFI-FRFCM segmentation respectively.
The higher value of PSNR and SSIM for FFI-FRFCM show
better signal-to noise ratio and noise reduction.
4.3 Classification performance results
Classification performance measurements are crucial to
identify the signals using machine learning models. The
terms "true positive ratio (TPR)," "true negative ratio
(TNR)," and "accuracy" are used to verify the classifier’s
performance analysis. Sensitivity is also referred to as the
"true positive ratio" (TPR). The K-fold cross-validation tech-
nique ensures that each subsample is trained and evaluated,
preventing overfitting issues and lowering generalization
errors. Results of the performance measure results are pre-
sented in Table6.
The MSE during classification is shown in Fig.15. In
contrast to the WCA-EELM, WCA-PSO-EELM, and WCA-
APSO-EELM, which required 95, 75, and 45 iterations,
respectively, the proposed IWCA-APSO-based ELM model
only required 25 iterations to reach convergence. According
Sensitivity
=TPR =
TP
TP +FN
Specificity
=TNR =
TN
TN +FP
Accuracy
=
TP +TN
TP +TN +FP +FN
to our analysis, the proposed IWCA-APSO-based EELM
model outperforms the WCA-EELM, WCA-PSO-EELM,
Table 5 Quality measures and Segmentation Accuracy
Bold value represents the comparison values of SSIM and PSNR.
Higher values of SSIM and PSNR show the better performance of
FFI-FRFCM
Algorithm Accuracy In % SSIM PSNR
En FCM 93.22 0.7985 27.31
FLICM 95.65 0.8524 29.55
NDFCM 97.17 0.8847 31.18
FRFCM 98.43 0.9013 35.29
FFI-FRFCM 99.12 0.9253 37.85
Input Image Tumor outline Detected Tumor
Fig. 11 Segmentation result of breast tumor using EnFCM technique
Input Image Tumor outline Detected Tumor
Fig. 12 Segmentation result of breast tumor using NDFCM tech-
nique
Input image
Tumor outline Detected Tumor
Fig. 13 Segmentation result of breast tumor using FRFCM technique
Input Image Tumor outline Detected Tumor
Fig. 14 Segmentation result of affected breast tissues using FFI-
FRFCM technique

Int. j. inf. tecnol.
1 3
and WCA-APSO-EELM models. The classification accu-
racy of the proposed model is achieved as 99.36%. The pro-
posed IWCA-APSO-based EELM model took 23.8751s less
than the other models, WCA-EELM, WCA-PSO-EELM,
and WCA-APSO-EELM models, which took 98.2462s,
65.1405s, and 34.0192s, respectively.
5 Conclusion
A hybrid IWCA-APSO algorithm-based EELM model was
proposed to classify cancerous and non-cancerous tissues
from the mammogram images. The proposed IWCA-PSO
algorithm optimized the weights of the EELM model to
enhance the classification performance. To assess the
robustness of the hybrid IWCA-APSO method, three bench-
mark functions, such as Griewanks’ function, Sphere func-
tion, and Quartic function, were considered for optimiza-
tion. The benchmark functions were optimized by APSO,
WCA, WCA + PSO, and WCA + APSO algorithms, and the
hybrid IWCA-APSO algorithm and comparison results were
presented. A fuzzy factor improved FRFCM segmentation
was proposed for detecting the breast cancer-affected tis-
sues from the mammogram images. The Morlet wavelet
transform was employed for feature extraction from the
segmented images. Six features were extracted and fed as
input to the IWCA-APSO-based EELM model for the clas-
sification of breast cancer. Compared to the WCA-EELM,
WCA-PSO-EELM, and WCA-APSO-EELM models, the
proposed IWCA-APSO-based EELM model yields better
classification results. The proposed IWCA-APSO-based
EELM model attains superior classification accuracy and
computational efficiency. Even though the computational
time is approximate to the WCA-APSO-EELM model, the
classification accuracy is better in the case of the proposed
IWCA-APSO-based EELM model. The proposed IWCA-
APSO-based EELM model has shown good capability for
classifying breast cancer mammogram images into can-
cerous and non-cancerous groups. The proposed IWCA-
APSO-based EELM models can be applied to liver tumor
datasets, and brain tumor image datasets. Since the deep
learning models are showing better results in classifica-
tion, but implementation of the models through the embed-
ded platform is difficult because of memory requirement,
high end processors and availability of peripheral hardware
accessories, which is not cost effective. The development of
the EELM model hybridization with Dove Swarm Optimi-
zation (DSO), Moth-flame optimization (MFO) and other
optimization technique, the proposed model’s implemen-
tation in an embedded platform with NVIDIA processor
and associated hardware for detection and classification of
breast cancer on real-time images in hospitals is the future
scope of the research.
Data availability The INbreast dataset is used in this research. The
dataset can be made available upon request to the corresponding author.
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