∎

11institutetext: N. Sinhababu 22institutetext: Subir Chowdhury School of
Quality and Reliability
IIT Kharagpur
Mobile: +91-8617826402
22email<EMAIL_ADDRESS>33institutetext: M. Sarma 44institutetext:
Subir Chowdhury School of Quality and Reliability
IIT Kharagpur
55institutetext: D.Samanta 66institutetext: Department of Computer Science and
Engineering
IIT Kharagpur

# Computational Intelligence Approach to Improve the Classification Accuracy
of Brain Neoplasm in MRI Data

Nilanjan Sinhababu  Monalisa Sarma  Debasis Samanta

###### Abstract

Automatic detection of brain neoplasm in Magnetic Resonance Imaging (MRI) is
gaining importance in many medical diagnostic applications. This report
presents two improvements for brain neoplasm detection in MRI data: an
advanced preprocessing technique is proposed to improve the area of interest
in MRI data and a hybrid technique using Convolutional Neural Network (CNN)
for feature extraction followed by Support Vector Machine (SVM) for
classification. The learning algorithm for SVM is modified with the addition
of cost function to minimize false positive prediction addressing the errors
in MRI data diagnosis. The proposed approach can effectively detect the
presence of neoplasm and also predict whether it is cancerous (malignant) or
non-cancerous (benign). To check the effectiveness of the proposed
preprocessing technique, it is inspected visually and evaluated using training
performance metrics. A comparison study between the proposed classification
technique and the existing techniques was performed. The result showed that
the proposed approach outperformed in terms of accuracy and can handle errors
in classification better than the existing approaches.

###### Keywords:

Medical imagingClassification of brain tumor dataBrain neoplasm diagnosisMRI
data classification

##  1 Introduction

Brain neoplasm is known as the deadliest of all forms of cancer. Any
abnormalities in the growth of neural cells within the brain skull or the
spinal cord lead to a brain neoplasm or more generally known as a brain tumor.
Around two-thirds of adults are diagnosed with aggressive brain cancer
resulting in death within 2 years of diagnosis chinot2014bevacizumab ;
gilbert2014randomized . The primary cause of death due to health-related
issues related to brain neoplasm is due to the unavailability of any special
cure after a certain stage aldape2019challenges . It is worth to mention that
any kind of neoplasm must be detected as early as possible. Diagnosis of any
brain tumor is done by a neurological test, for example, CT scan, Magnetic
Resonance Imaging (MRI)osborn2015diagnostic ; armstrong2004imaging , etc. MRI
is one of the advanced medical imaging techniques and is used to produce high-
quality images liang2000principles  to study tumors in soft tissues of the
brain. The need for a computationally intelligent approach for the
classification of brain neoplasm is required for the following reasons:

  * •

MRI provides the location and size of a tumor efficiently but has no way of
classifying its type aronen1994cerebral ; young2006brain .

  * •

For classification of the MRI, a biopsy is required, this process is painful,
time-consuming, and has limitations such as sampling error and variability in
interpretation aronen1994cerebral ; de1997proliferative .

  * •

Visual inspection and detection may result in misdiagnosis due to human errors
caused by visual fatigue de1997proliferative .

  * •

Daily reporting of a large number of new cases implies a high chance of
misdiagnosis due to the time limitations, interaction and doctor to patient
ratio ford1996doctor ; bagcchi2015india .

  * •

It is necessary to aid the medical fraternity to understand the tumor type
automatically and hence helps in reducing load and saving time.

  * •

Computerised analysis proven to be more superior and are being researched for
predicting cancerous cell in a brain MRI data.

To achieve the goal of developing an automatic brain neoplasm detection
system, various techniques are used in the literature. The three most
important stages present in these systems are data preprocessing, feature
optimization, and classification. Existing preprocessing techniques consider
noise removal while preserving texture information. Image preprocessing
techniques, such as cropping, size normalization, histogram equalization based
contrast enhancement amin2012brain , Gaussian filter-based noise removal
mahajanidetection , and Center Weighted Median(CWM) george2012mri  based
techniques are used. The Principal Component Analysis (PCA) amin2012brain ;
othman2011probabilistic ; singh2012classification  and Gray Level Co-
occurrence Matrix (GLCM) joshi2010classification ; mahajanidetection  based
techniques are used in majority of the works for feature extraction. Some of
the works kharrat2010hybrid  also used Spatial Gray Level Dependence Method
(SGLDM) to extract wavelet-based textures. Some of the methodologies used
manual intervention to extract texture and intensity features jafari2012hybrid
. For classification, the majority of the work use Multi-Layer Perceptron
(MLP), Probabilistic Neural Network (PNN), Support Vector Machine(SVM), etc.
amin2012brain ; singh2012classification ; othman2011probabilistic ;
kharrat2010hybrid . There exist works jafari2012hybrid ; mahajanidetection ,
which have combined multiple classifiers to improve the classification
accuracy, such as Back Propagation Neural Network(BPNN) and K-Nearest
Neighbours(KNN). Since, stacked MRI image slices can be used as a 3D
representation of the MRI data, few techniques use 3D-CNN for classification
of the neoplasm chen2018mri ; 6165309 .

After a detailed analysis of the existing techniques, the following issues are
found:

  * •

In the literature, very few preprocessing techniques have been used like noise
removal and contrast optimization. Further, many works in the literature skip
this phase.

  * •

Many approaches in the literature used techniques that extracts texture and
intensity-based features from MRI data to improve the classification
performance, but these techniques are used assuming that the feature
requirements are already known. Although these features provide improvement,
however, there is a possibility of unknown features that might not have been
considered.

  * •

PCA is a good feature selection algorithm as it tries to cover maximum
variance among the features in a dataset. However, incorrect selection of the
number of principal components can lead to information loss
uyeda2015comparative . Information loss in this domain can be costly and can
affect the overall model performance.

  * •

Classification algorithms are optimized for generalized performance, but due
to difference in the requirement of various domains, these generalized models
may not be suitable like in the case of brain neoplasm MRI data classification
pendharkar2003evolutionary .

  * •

Some of the papers in the literature used the 3D-CNN model for MRI data.
3D-CNN is good for 3D image classification, but CNN, in general, suffers when
the dataset size is not adequategal2017deep . Further, implementing an
additional CNN is computationally costly and may suffer from the drawbacks of
vanishing or exploding gradients. Identification of edge is a crucial task in
brain neoplasm MRI classification but 3D CNN based method has a severe over-
smoothing problem on edge boundariesDBLP:journals/corr/abs-1803-08669 .

  * •

Significance of model performance metrics are vastly different according to
the domain of the work and accuracy may not be the ultimate evaluating metric
for MRI data classification.

Preprocessing techniques in the literature consider noise removal, preserving
texture information but does not consider edge detection, a technique
considering edge is missing in the literature. The majority of the papers
published in these areas have extracted mainly textural and wavelet-based
features, but there is a possibility of other un-recognized features that may
improve model performance. Further, these techniques require manual
intervention and can be challenging when considering new data. Not many hybrid
techniques are used or compared in this field of research. For classification,
the majority of the papers have tried only to maximize accuracy assuming that
false positives and false negatives are equally bad. However, in the medical
domain, these two types of errors have very different costs associated.
Concerning these limitations, two main objectives are drawn:

  1. 1.

Propose a hybrid preprocessing stage to improve the area of interest in MRI
Image.

  2. 2.

Propose a CSVM model for harnessing the ability of CNN for feature extraction
and SVM for classification.

  3. 3.

Increasing model performances taking into consideration the different costs
associated with false positives and false negatives.

##  2 Related Work

In this section, a few important works related to brain neoplasm detection are
briefly surveyed.

###  2.1 Preprocessing techniques

MRI data may contain noise and defects that can hamper model performance. To
deal with such noisy data, various preprocessing techniques have been proposed
in the literature.

Amin and Mageed amin2012brain  proposed image preprocessing using image
cutting, image enhancement, and size normalization. They used histogram
equalization to increase the contrast range by increasing the dynamic range of
grey levels. They showed improvement in the distinction of features in the MRI
image.

Gadpayleand and Mahajani mahajanidetection  used Gaussian filter to remove
granular noise and resized the MRI data due to large size variations in the
used dataset. They used manual cropping for some MRI data for convenience.

George and Karnan george2012mri  used a modified Tracking Algorithm to remove
the film artifacts and then applying the Histogram Equalization and Center
Weighted Median (CWM) filter techniques separately to enhance the MRI images.

###  2.2 Feature optimization techniques

MRI data contains a large number of features and using all features not
necessarily increases the performance of a classification algorithm. Reducing
the number of features in the dataset usually improves accuracy as well as
training and testing time. An efficient way to select important features is
PCA ()Principle Component Analysis). PCA technique can remove
multicollinearity in the dataset, improves algorithm performance, and reduces
over-fitting. Further, the texture is an important aspect of MRI data, and to
extract the texture features, GLCM (Gray Level Co-occurrence Matrix) is widely
used, especially in medical image analysis.

Amin and Mageed amin2012brain  proposed a neural network and segmentation base
system to automatically detect the tumor in brain MRI images. In their
approach, PCA is used for feature extraction. Othman et al.
othman2011probabilistic  proposed a probabilistic neural network technique for
brain tumor classification. In their technique, features are extracted using
PCA. Daljit Singh et al. singh2012classification  proposed a hybrid technique
for automatic classification of an MRI image by extracting features using PCA
and GLCM. Joshi et al. joshi2010classification  proposed a brain tumor
detection and classification system in MR images by first extracting the tumor
portion from the brain image, then extracting the texture features of the
detected tumor using GLCM. Gadpayleand and Mahajani mahajanidetection
proposed a brain tumor detection and classification system. The tumor is
extracted using segmentation and then texture features are extracted using
GLCM.

Kharrat kharrat2010hybrid  proposes a hybrid approach for the classification
of brain tissues. The classification is based on a Genetic algorithm (GA) and
support vector machine (SVM). Features considered in their work are wavelet-
based texture features. They extracted features by spatial gray level
dependence method (SGLDM). The extracted features were given as input to the
SVM classifier.

###  2.3 Classification techniques

Many techniques are used in the literature for MRI brain neoplasm
classification. The objective in these approaches is to detect the presence
and/or severity of brain neoplasm.

Amin and Mageed amin2012brain  used Multi-Layer Perceptron (MLP) to classify
the extracted features of MRI brain images. The average recognition rate is
88.2% and the peak recognition rate is 96.7%. Othman et al.
othman2011probabilistic  performed brain tumor presence classification using
Probabilistic Neural Network (PNN). Daljit Singh et al.
singh2012classification  used a Support Vector Machine (SVM) classifier which
classifies the image to either normal or abnormal. Joshi et al.
joshi2010classification  detected the presence of brain tumor using the neuro-
fuzzy classifier. Gadpayleand and Mahajani mahajanidetection  combined the
BPNN and KNN classifiers to classify MRI brain images into the normal or
abnormal brain. The accuracy is 70% using the KNN classifier and 72.5% by
using the BPNN classifier. Kharrat kharrat2010hybrid  used the binary SVM
classifier with RBF kernel to detect the presence of a brain tumor with an
accuracy rate that varies from 94.44% to 98.14%. Jafari and Shafaghi
jafari2012hybrid  proposed a hybrid approach for brain tumor detection in MR
images based on Support Vector Machines(SVM). The accuracy of about 83.22% is
achieved and claimed their approach robust in detection.

##  3 Proposed Methodology

A computational intelligence approach is proposed to provide better and
reliable classifications of brain neoplasms in MRI data. An overview of the
proposed method is shown in Fig. 1. The major computational steps in the
proposed approach are image preprocessing, feature engineering, and
classification. The various steps in the approach are stated below:

  1. 1.

Preprocessing: The preprocessing step consists of two sub-steps. First, the
basic preprocessing techniques like resizing, noise removal, and contrast
optimization are performed. Next, a preprocessing technique is proposed based
on Sobel edge detection and contour to improve the area of interest in the MRI
image.

  2. 2.

Feature engineering: The proposed feature engineering includes feature
identification, feature extraction followed by feature optimization. We
propose an automatic approach to feature identification and extraction. The
convolution neural network model is built to generate important features
automatically for the brain neoplasm MRI data. Following this LASSO
regularization technique is used to remove unnecessary features and select the
suitable and most dominating features.

  3. 3.

Classification: We propose a two-stage classification approach. Two
classification models are used for the purpose. In the first stage of
classification, whether an input MRI data contains a tumor or not is
predicted. If an image contains a brain neoplasm, then the image is passed
through the second stage of the classifier. In the second stage of the
classification, the severity of the tumor is classified as benign or
malignant. In both stages of the classification, the SVM model with modified
cost optimization constraint is considered to minimize the false negative
classification.

In the following subsections, the above-mentioned three steps are discussed in
details.

Figure 1: Overview of the proposed brain neoplasm detection method.

###  3.1 Data preprocessing

There are two approaches to data preprocessing: regular data preprocessing and
specific preprocessing. The regular preprocessing task is to deal with poor
quality MR images. The improved quality MR image is used in the next level of
the preprocessing step to specify a region of interest. The next level of
preprocessing is proposed to improve the prediction accuracy.

####  3.1.1 Basic preprocessing

The basic preprocessing includes resizing, noise removal, and contrast
enhancement. The methodologies proposed for these activities are discussed in
the following section.

Resizing: It is the process of changing the scale of the images so that all
the samples in the training and testing data sets are of the same resolution.
This is required because, in the classification models, we must provide input
of the same size. The images are resized to $150\times 150$ pixels using the
using Numpy squeeze function for each MRI data, as shown in Fig. 2.

Figure 2: Example of resizing an MRI image.

Noise removal: Gaussian filter is a well-known method and is used to smooth a
noise by taking the average values surrounding a noise kumar2017noise . In
this experiment, the noise removal is performed using a Gaussian filter.
Essentially, a Gaussian filter is a low pass filter that is non-uniform. Also,
the kernel is symmetric in a Gaussian filter, which can reduce direction bias,
if any. Application of a Gaussian filter requires convolution of 2D Gaussian
distribution (see Eqn. 2) given an image input. It may be noted that 2D
Gaussian distribution is the product of two 1D Gaussian functions (see Eqn.
1). The kernel coefficients are sampled from Eqn. 2. An example showing the
noisy image and the same after the removal of noise is shown in Fig. 3.

$G\left(x\right)=\frac{1}{\sqrt[]{2\pi\sigma^{2}}}e^{-\frac{x^{2}}{2\sigma^{2}}}$
(1)
$G\left(x,y\right)=\frac{1}{2\pi\sigma^{2}}e^{-\frac{x^{2}+y^{2}}{2\sigma^{2}}}$
(2)

Figure 3: Example of noisy MR image and the image after noise removal.

Contrast enhancement: A Gaussian filter might hamper the image brightness and
contrast. Hence, a contrast optimization procedure is required. The contrast
of an image is the difference in the luminance of various sections in the
image. An optimal contrast-enhanced image will be able to show every object
present in the image. The need for contrast enhancement technique in medical
field images kotkar2013review  are of utmost importance. Local and global
transformation techniques kabir2010brightness  prove to be the best options in
this regard as they tend to maintain the mean brightness and does not inject
undesirable artifactskotkar2013review . Global Transformation Histogram
Equalization is used for contrast enhancement in this work. The global
transformation function formulated in Eqn. 3 is used for contrast enhancement.
Here, $T(g)$ being the global transformation function, where g denote its
intensity, $g_{min}$ and $g_{max}$ defines the lower and upper bounds of the
histogram partitions; here, x as intensity value, h(x) denotes the histogram
count.

$T\left(g\right)=g_{min}+\left(g_{max}-g_{min}\right)\left(\frac{\sum_{x=g_{min}}^{g}h\left(x\right)}{\sum_{x=g_{min}}^{g_{max}}h\left(x\right)}\right)$
(3)

An example showing the contrast enhancement using Global Transformation
Histogram Equalization is shown in Fig. 4.

Figure 4: Example of contrast enhancement in MRI image

####  3.1.2 Special preprocessing

Apart from the regular preprocessing techniques, an extra filtering mechanism
is proposed. The proposed technique is shown in Fig. 5. The proposed technique
starts with loading an MRI data which is already preprocessed using the basic
techniques described in Section 3.1.1. Then a contour plotting operation is
performed on the MRI data. In the next step, the Sobel edge detection
technique is used on the grayscale image to generate edges. Further, the Sobel
edge MRI data matrix is subtracted from the grayscale image data matrix. This
image is matched with the contour plot in the first step to preserve
brightness. Then the final image is stored in a grayscale format. This
preprocessing helped in reducing the already present artifacts and proved to
improved the features of the region of interest in MRI data. The contour plot,
Sobel edge detector, and the different functions are further described in
detail below.

Figure 5: The proposed Sobel edge detection based preprocessing.

Contour calibration: Regarding MRI images, it is desired to have a higher
contrast in the area of interest and lower on the rest. The images that are
analyzed till now are in gray scale, hence the different variations in
textures are not visible. To know the depth or height of a 3D plane contour
lines can be used. It is a function of two variables in a curve along which
the function has a constant value so that the curve joins points of equal
value. A gray-scale image can also be seen as a 3D representation of the
values ranging from 0 to 255 for each pixel of which contour can be
plottedkim2014relationship . In this experiment, the MRI has a size of 150
$\times$150 and the contour line can be used to define various colors to the
images with varying gray scale. An example showing the contour plot for an MRI
sample is shown in Fig. 6(a).

(a) Contour plot for gray scale MRI image.

(b) Sobel edge detection for gray scale MRI image.

(c) Difference contour for gray scale MRI image

Figure 6: An example of special preprocessing technique.

Sobel edge detection: Sobel edge detection technique is highly efficient in
the detection of edges in images if the image is free of granular noises.
Modified Sobel edge detection techniquesgao2010improved  proved to perform
superior in certain conditions. In this experiment, after the basic
preprocessing of the MRI, granular noise is certainly removed in the Gaussian
filtering process. Hence, we can proceed with the basic Sobel edge detection
technique vijayarani2013performance ; vincent2009descriptive for detection of
edges present in the MRI images. An example showing the Sobel edge detection
for an MRI sample is shown in Figure-6(b).

Differencing: In this phase, the matrices of grayscale MRI image is subtracted
from the Sobel edge MRI image are on a pixel by pixel basis. If different
contour intensity is present in original contour and Sobel edge contour then
take the higher value of intensity. This phase reduced the less oriented
regions and gave proper intensity uplifting in the regions of interest. An
example showing the contour matching operation over the difference image for
an MRI sample is shown in Fig. 6(c).

###  3.2 Feature engineering

Due to the lack of a huge amount of MRI data in a single place, it is very
difficult to analyze and classify images related to brain neoplasm. The
machine learning algorithms are optimized by using feature extraction
guyon2008feature  techniques to work with even a very low amount of data and
still performing quite well. Automatic feature extraction for brain neoplasm
MRI data is performed using a convolution feature extractor. Convolutional
neural networks are comprised of two parts, the first section performs
convolution using various kernels to extract features and then classification
is performed by dense layers. In a hybrid CSVM model, the first phase of a
normal CNN is used for feature extraction and the features are then fed to SVM
for further classification. Feature extraction using convolution neural
networks have been performed in various fields of research due to its flexible
and reliable results simard1999boxlets ; hammad2019novel . CNN model-based
feature extractors also prove to be superior in extracting textures from
imagesdewaele1988texture ; zhang2000all , which are a very important aspect in
MRI classifications as well. The convolution feature extractor model for
detecting the presence and severity of neoplasms in the MRI dataset is
discussed below.

Model: sequential
---
Layer Name_Type | Dimension | Parameters
Block-1_Conv-1 (Conv2D) | $(None,148,148,32)$ | 320
Block-1_MP-1 (MaxPooling2D) | $(None,74,74,32)$ | 0
Block-2_Conv-1 (Conv2D) | $(None,72,72,64)$ | 18496
Block-2_Conv-2 (Conv2D) | $(None,70,70,64)$ | 36928
Block-2_MP-1 (MaxPooling2D) | $(None,35,35,64)$ | 0
Block-3_Conv-1 (Conv2D) | $(None,33,33,96)$ | 55392
Block-3_MP-1 (MaxPooling2D) | $(None,16,16,96)$ | 0
Block-4_Conv-1 (Conv2D) | $(None,14,14,96)$ | 83040
Block-4_MP-1 (MaxPooling2D) | ($None,7,7,96)$ | 0
Block-5_Conv-1 (Conv2D) | $(None,5,5,64)$ | 55360
Block-5_MP-1 (MaxPooling2D) | $(None,2,2,64)$ | 0
Total params: 249,536 |  |
Trainable params: 249,536 |  |
Non$-$trainable params: 0 |  |

Table 1: Layer details of convolution model for feature extraction.

Training with the MRI dataset, which is made up of 150$\times$150 gray-scale
images, that is, each image is of shape (150,150,1) (Gray Scale = 1 channels).
The sequential convolution feature extraction model is provided in Table 1
containing layer names, dimension, and parameters. Further, note that the CNN
used in the experiment is also having the same architecture apart from the SVM
classifier, which is replaced using a fully connected neural network. An
example of the features extracted using a particular convolution layer on a
particular slice is given as an example in Fig. 7. The generated feature
vector will be used for the feature selection phase for reducing unnecessary
features. LASSO regularization is used to select the optimal set of features
and remove the features that may hamper the model performance. Convolutional
feature extractor provides 2,49,536 features based on the total input data
which has been significantly reduced to 5,240 features after LASSO feature
selection is performed.

Figure 7: Features extracted from a single slice in Block-1_Conv-1 layer.

###  3.3 MRI data classification

To understand the presence of a brain tumor or to classify the severity to
either benign or malignant is a binary classification problem. As per SVM
(Support Vector Machine) is concerned, it is a highly accepted binary
classifier for linear data and non-linear data(using special kernels). SVM
uses the concept of finding the best hyperplane that can separate the data
perfectly into two classes. SVM is a popular choice for classification
irrespective of the application domains, which varies from textnilanjan17  to
medical image classificationmachhale2015mri ; singh2012classification .
Further, SVM tends to perform well even on the small datasets huang2017svm
but deep learning requires a huge amount of datagal2017deep . The proposed
approach (CSVM) using CNN feature extraction and SVM classification is shown
in Fig. 8.

Figure 8: CSVM model for automatic feature extraction and classification.

SVM optimizes the hyperplane for the best classification of the classes
without considering the various cost associated with false positives and false
negatives. In general, this is not a problem as for many tasks there is no
significant cost imbalance for classes. But for a medical domain such as the
classification of brain MRI data for detection of neoplasm, the false
negatives have a higher cost associated when compared with false positives. To
deal with this issue of generalized SVM, the optimization function of the SVM
needs to be modified. The sample space is {$x_{i},y_{i}$},i = 1,2, . . . , m.
where, y${}_{\mathrm{\textrm{i}}}$ x${}_{\mathrm{\textrm{i}}}$$\mathrm{\in}$
$\mathrm{\\{}$F1, F2… Fn$\mathrm{\\}}$. The sample space has been separated
with a hyperplane given by g(x) = $w^{T}x_{i}+b$ = 0 where, w is a
n-dimensional coefficient vector that is normal to the hyperplane and b (bias)
is the offset.

Criteria for classification: Considering positive class indicates the presence
of neoplasm for the first classifier model and indicates malignant for the
severity classification model. The negative class on the other hand indicates
an absence of neoplasm for the first model and benign for the severity
classification of the neoplasm. Let $\boldsymbol{\mathrm{\textrm{C}}}_{s}$
denote the unequal misclassification costs associated with the false negative
class and xi is not perfectly separable with the hyperplane, then some samples
are allowed to be at a distance ${\mathrm{\xiup}}_{i}$ from their correct
margin boundary. The primal problem of SVM has been modified into solving the
following optimization task:

$f\left(x_{i},y_{i}\right)=min\frac{1}{2}{\left\|w\right\|}^{2}+C_{s}\sum_{i|y_{i}}{{\mathrm{\xiup}}_{i}}$

$subject\leavevmode\nobreak\ to,\leavevmode\nobreak\ \leavevmode\nobreak\
y_{i}\left[\left(w^{T}x_{i}+b\right)\right]\leavevmode\nobreak\ \geq
1\leavevmode\nobreak\ -{\mathrm{\xiup}}_{i}$ $where,\leavevmode\nobreak\
\leavevmode\nobreak\ i=1,2,\leavevmode\nobreak\ \dots,\leavevmode\nobreak\
m\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\ and\leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\ {\mathrm{\xiup}}_{i}\geq 0$

(4)

Considering C(penalty term) which controls the strength of penalty for
$\mathrm{\xiup}$. $C_{s}i|y_{i=+1}$ = C and $C_{s}i|y_{i=-1}$ = $C^{r}$.
Where, $C^{r}=\leavevmode\nobreak\ \frac{C_{s}}{C}$ provided $C_{s}>C$
implying, $C^{r}>0$. Since, $f\left(x_{i},y_{i}\right)$ is a constraint
optimization problem, $\mathrm{therefore,}$ converting this to un-constraint
optimization problem is done using Lagrangian Multiplier with
$\boldsymbol{\alpha}\leavevmode\nobreak\ ,\leavevmode\nobreak\
\leavevmode\nobreak\ \boldsymbol{\beta}$ as the Lagrange multipliers where
$\boldsymbol{\alpha}\boldsymbol{\geq}\boldsymbol{0}\leavevmode\nobreak\
and\leavevmode\nobreak\ \boldsymbol{\beta}\boldsymbol{\geq}\boldsymbol{0}$.

$\leavevmode\nobreak\ \mathrm{L(}\leavevmode\nobreak\
\mathrm{w,}\leavevmode\nobreak\ \mathrm{b,}\leavevmode\nobreak\
C_{i},\leavevmode\nobreak\ {\mathrm{\xiup}}_{i}\mathrm{)}=$

= $\frac{1}{2}{\left\|w\right\|}^{2}$ \+ $\sum{C_{i}{\mathrm{\xiup}}_{i}}$ \+
$\sum{{\alpha}_{i}}$ \-
$\sum{{\alpha}_{i}{\mathrm{\xiup}}_{i}}\leavevmode\nobreak\
-\leavevmode\nobreak\ \sum{{\alpha}_{i}y_{i}(w^{T}x_{i})}$ $-$
$\sum{{\alpha}_{i}y_{i}b}$ $-$ $\sum{{\beta}_{i}}{\mathrm{\xiup}}_{i}$

$C_{i}=\left\\{\begin{array}[]{c}C\leavevmode\nobreak\ \leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\
\leavevmode\nobreak\ y_{i}\in+1\\\ C^{r}*C\leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\
\leavevmode\nobreak\ y_{i}\in-1\end{array}\right.$

(5)

Optimization of the above Lagrangian (5) involves taking derivatives of the
Lagrangian with respect to w, b, $C_{i}$ and ${\mathrm{\xiup}}_{i}$ and set
the derivatives to zero to get the below equation:

$\mathrm{L}\leavevmode\nobreak\ \mathrm{(}\leavevmode\nobreak\
\mathrm{w,}\leavevmode\nobreak\ \mathrm{b,}\leavevmode\nobreak\
C_{i},\leavevmode\nobreak\
{\mathrm{\xiup}}_{i}\mathrm{)}=\sum_{i}{{\alpha}_{i}}-\sum_{i}{{\sum_{j}{{\alpha}_{i}}\alpha}_{j}y_{i}y_{j}K\left(x^{(i)},x^{(j)}\right)}$

$subject\leavevmode\nobreak\ to\leavevmode\nobreak\
\left\\{\begin{array}[]{c}{\sum_{i}{{\alpha}_{i}}y}_{i}=0\\\
0\leavevmode\nobreak\ \leq{\alpha}_{i}\leq C_{i}\end{array}\right.$ (6)

Considering MRI brain neoplasm classification ,
$\mathrm{\textrm{f}}:\mathrm{\textrm{X}}\mathrm{\to}\mathrm{\textrm{Y}}$ is a
nonlinear classification problem, SVM kernels needs to be used. Basically, a
kernel function maps the nonlinear data to an n-dimensional space where the
data is linearly separable by a hyperplane. SVM has many kernels to perform
the optimizations like linear, polynomial, and radial basis function(RBF). The
selection of a kernel proves to have significant variations in the performance
of the modelsscholkopf2002learning . RBF kernel maps the nonlinear vectors to
a high dimension space where the best hyper pane is drawn and it proves to be
the most preferred choice for image classification problems kharrat2010hybrid
; kuo2013kernel ; cao2008approximate ; scholkopf2002learning . Therefore, the
Radial Basis Function (RBF) kernel function is used for the experiment.

$K\left(x_{i},x_{j}\right)=exp\left(-g{\left\|x_{i}-x_{j}\right\|}^{2}\right)$

where, ${\left\|x_{i}-x_{j}\right\|}^{2}$ is two-norm distance and,

$\mathrm{g}$ is the kernel function parameter and $g=\leavevmode\nobreak\
\frac{1}{{2\sigma}^{2}}$

(7)

For an unknown feature vector ‘$x_{j}$’, the classification decision with RBF
Kernel (7) is represented as :

D(z) = $w\bullet z+b$ = $\sum^{m}_{i=1}{{\alpha}_{i}y_{i}}$K($x_{i}\bullet
x_{j}$) + b

(8)

The parameters, kernel function parameter ${}^{\prime}g^{\prime}$ and penalty
(C) needs to be tuned for the model to perform optimal throughout the dataset.
For tuning the SVM model parameters, the K-fold cross-validation technique
with the value of ‘k’ as 10 is used. Cross-validation provided the desired
value of parameters C and ${}^{\prime}g^{\prime}$ to be 13 and 2 for detecting
the presence of neoplasm and 9 and 3 for severity classification respectively,
which are used for the rest the experiment.

##  4 Experiments and Experimental Results

To establish the efficacy of the proposed approach, several experiments have
been carried out. In this section, the objectives of the experiments,
experimental environment, data sets used in the experiments, and results
observed are discussed.

###  4.1 Objectives of the experiments

Following are the objectives of our experiments:

  1. 1.

Effectiveness of the proposed preprocessing: Visual inspection and model
training evaluation of proposed preprocessing model.

  2. 2.

Effectiveness of the proposed cost optimization: Performance difference of
CSVM with and without cost-optimization.

  3. 3.

Classification accuracy: Performance evaluation of CSVM, CNN, SVM and Random
Forest on the MRI data considering cost imbalance of classes.

  4. 4.

Comparison with the existing approaches: Performance comparison of CSVM with
the existing works.

###  4.2 Experimental environment

The specification of the system used is as follows: O.S. - Windows 10
Professional, CPU - AMD® Ryzen™ 7-3700X Processor, RAM - 32GB DDR4, GPU -
NVIDIA GeForce® GTX 1080 Ti. The windows version of the
Python-64Bit10.5555/1593511  with editor IPython notebook PER-GRA:2007
throughout the experiment. Important modules used in the experiment include
tensorflow tensorflow2015-whitepaper , packages from NumPy oliphant2006guide ,
SciPy 2020SciPy-NMeth  and Matplotlib Hunter:2007 .

###  4.3 Dataset description

The objective of our work is to classify MRI images to predict the presence of
neoplasms and their severity. In this experiment, an MRI dataset is collected
from the online repository of The Whole Brain Atlasjohnson_becker . This
website is maintained by Harvard Medical School and has proved to be very
authentic in terms of medical imaging datasummers2003harvard . T2 weighted
images are used in the experiment as shown in Fig. 9. The types of the MRI for
malignant brain neoplasms in the dataset are glioma and sarcoma. And the
benign brain neoplasms are metastatic bronchogenic carcinoma(M.B.C.),
metastatic adenocarcinoma(M.A.) and meningioma. The shape of an MRI image is h
$\times$ w $\times$ n, where n is the number of slices in each image, h is
height and w is width, where h and w both equals to 256.

Figure 9: Example of stacked brain MRI slices

###  4.4 Results observed:

Vis-a-vis the objectives of the experiments, the results which we have
observed are presented in the following subsections.

####  4.4.1 Effectiveness of the proposed preprocessing

Visual inspection: An overview of the preprocessing for normal MRI can be seen
in Fig. 10. The preprocessing for benign MRI can be seen in the Fig. 11 and
malignant MRI can be seen in the Fig. 12.
To have a good demonstration of the preprocessing, three MRI images are
considered, one is normal which is shown in Fig. 10(a), that is, without any
neoplasm, the second one with benign neoplasm which is shown in Fig. 11(a) and
the third one with malignant neoplasm which is shown in Fig. 12(a).The contour
is plotted for three different MRI images, each for normal (see Fig.10(b)) ,
benign (see Fig.11(b)), and malignant (see Fig. 12(b)). Similar to contour,
Sobel egdes are shown for the three MRI images: normal ()in Fig. 10(c)),
benign (in Fig.11(c)), and malignant (in Fig. 12(c)). The final result after
taking difference is shown for the three MRI images, normal (Fig. 10(d)),
benign (Fig. 11(d)), and malignant (Fig. 12(d)).

(a) Normal GS

(b) Normal CT

(c) Normal SE

(d) Normal SD

Figure 10: Proposed preprocessing applied over normal MRI images.

To compare the preprocessed MRI images, visual inspection of image outline,
the colour of the various regions needs to be explored. The green colour
represents low intensity, yellow signifies higher intensity and brown lines
indicate higher variation in the intensities over that region. Figure-10 shows
a transition of the various stages of the proposed preprocessing for a normal
brain. The contour of the normal brain produces many yellow lines as seen in
Figure-10(b). But when compared with the difference contour, the regions are
equally coloured without any yellow lines. Further, no brown edge is seen in
the final image as seen in Figure-10(d). This means the proposed preprocessing
can normalize the lower ranges of intensity difference (yellow lines).

(a) Benign GS

(b) Benign CT

(c) Benign SE

(d) Benign SD

Figure 11: Proposed preprocessing applied over benign MRI images.

Figure 11 shows a transition of the various stages of the proposed
preprocessing for a benign brain neoplasm. The contour of the benign brain
produces many yellow regions as shown in Fig. 11(b). But when compared with
the difference contour, the less interesting regions are colored green with a
brown border. Further, a brown edge with yellow is is seen in the final image
where the benign neoplasm is present as seen in Fig. 11(d). This means the
proposed preprocessing can intensify the regions with benign neoplasm than the
other regions.

(a) Malignant GS

(b) Malignant CT

(c) Malignant SE

(d) Malignant SD

Figure 12: Proposed preprocessing applied over malignant MRI images.

Figure-12 shows a transition of the various stages of the proposed
preprocessing for a malignant brain neoplasm. The contour of the malignant
brain produces a centralized yellow region as seen in Fig. 12(b). But when
compared with the difference contour, the less interesting regions are colored
green with a brown border as previously seen with benign MRI. Further, a brown
edge with yellow is is seen in the final image where the malignant neoplasm is
present as seen in Fig. 12(d). The proposed preprocessing can outline the
portion with the brain tumor effectively, even if the tumor is discreetly
spaced. Further, many preprocessing techniques tend to over soften the image
during the noise removal process to get better accuracy, but this changes the
original image features. This proves to be beneficial when detecting the
presence of neoplasm but during the classification of the severity, this
process fails to get good results. But in the case of the proposed
preprocessing, the final output MRI image is free of over softness and hence
the features are preserved better.

Figure 13: CSVM: Accuracy versus training loss with and without proposed
preprocessing. Figure 14: CNN: Accuracy versus training loss with and without
proposed preprocessing.

Training evaluation: A loss function is used to optimize the machine learning
algorithm by calculating the loss on the training MRI dataset images. Its
interpretation is based on how well the model is performing for the dataset.
It is the sum of errors made for each data points in training. This value
implies how well or poor a model can perform after each iteration of
optimization also known as epochs. On the other hand, the training accuracy
metric is used to measure the algorithm’s performance based on the total
number of correctly classified data instances in terms of a probability value
during the training. For any model, our target is always to minimize the loss
while still having good accuracy. To check the benefit of the proposed
preprocessing technique over the models, four models are considered for the
experiment. The four models compared in this regard are the proposed CSVM
model, CNN, SVM, and Random Forest (RF). These models are chosen due to their
popularity in this field of research and these models tend to provide decent
results for image classification tasks. To test the effectiveness of the
proposed preprocessing technique, the models are trained on the same dataset
but one set with the proposed preprocessing applied and the other with the
application of only basic preprocessing steps. Also, it is important to keep a
note on the fact that the feature selection process in Section-3.2 only
applies to CSVM and not other models. Other models use the general image
features from the preprocessing step.

Figure 15: SVM: Accuracy versus training loss with and without proposed
preprocessing. Figure 16: RF:Accuracy versus training loss with and without
proposed preprocessing.

From the experimental results shown in Fig. 13, 14, 15, 16, it is observed
that the accuracy for training when using proposed preprocessing is
significantly better in most of the epochs compared to the same setting
without the proposed preprocessing step. As per the training loss is
concerned, the loss gets minimized much more with every epoch when the
proposed preprocessing is applied. In some of the epochs, the accuracy or loss
may be close but the final training accuracy with proposed preprocessing is
higher and the loss is lower. The superiority of the hybrid CSVM model can
also be seen in Fig. 13, as its training accuracy is consistently better than
the other models. Further, the introduction of the advanced proposed
preprocessing technique with all the models proves to be beneficial both in
maximizing the accuracy and minimizing the loss. The cause of the poor
performance of the CNN model is probably related to the very low number of
items in the dataset. Neural Network models perform better for a large
collection of data, in this case, prediction via hybrid CSVM proves the
capability of SVM in dealing with low data count but still producing
competitive results. For SVM without convolutional feature extraction, the
training accuracy is decreased. Random Forest performed worst in this case
with the lowest training accuracy. A more detailed comparison of the models is
performed for the test data in the later section. For the rest of the
experiment, the proposed preprocessing technique is considered regardless of
the models used.

####  4.4.2 Effect of the proposed cost optimization

From the experimental model of CSVM, confusion matrices are generated for each
case of classification, that is, for detecting the presence of neoplasm and
for classifying the type of neoplasm. An example confusion matrix is shown in
Figure-LABEL:fig:cmatrix. Confusion matrices by themselves do not provide much
insight into how a model performs. But rater, confusion matrices can provide a
fast at-a-glance insight about the classification. Further, lots of
performance metrics, like accuracy, precision, recall, F-measure is derived
from the confusion matrices. These metrics in turn provides a better
understanding of the model. For performance evaluation, the metrics used are
provided in Eqn. 9, 10, 11, 12.

$Accuracy(A)=\frac{TP+TN}{TP+TN+FP+FN}$ (9)

$Precision(P)=\frac{TP}{TP+FP}$ (10)

$Recall(R)=\frac{TP}{TP+FN}$ (11)

$F1-Score(F1)=2\times\frac{P\times R}{P+R}$ (12)

where:
True Positives(TP): Correct classification of presence of neoplasm/malignant,
True Negatives(TN): Correct classification of absence of neoplasm/benign,
False Positives(FP): Incorrect classification of absence of neoplasm/benign,
True Negatives(TN): Incorrect classification of presence of
neoplasm/malignant.

For detecting the presence of neoplasm, a false negative detection would mean,
some MRIs were detected as an absence of neoplasm when in fact there are
neoplasms present. So, there shall be no diagnosis involved, and could be
fatal. Whereas, false positive case there may be over-diagnosis but will not
be fatal. So, we shall try to analyze the results based on these conditions.
The confusion matrices for the detection of neoplasm in an MRI for CSVM
approaches with and without cost optimization are represented in Fig. 17. From
the confusion matrices, it is clear that the total false classifications of
CSVM with and without cost optimization are 3 and 2 respectively. Further, as
already discussed false positives are more tolerable than false negatives in
this situation. There are 2 false negative classifications via the CSVM model
without cost optimization and no false negative classifications in the case of
CSVM with cost optimization. It shows the advantage of the CSVM model with
cost optimization in this regard.

Figure 17: Confusion matrix for detecting presence of brain neoplasm.

For detecting the severity of neoplasm, a false negative detection would mean,
some MRIs were detected as benign when in fact it is malignant. In this case,
if the MRI is not re-evaluated quickly, there is a chance of fatality. False
positives in this case may suffer from sock but are still more acceptable than
the previous one. The confusion matrices for the detection of the severity of
the neoplasm in an MRI using CSVM approaches are represented in Fig. 18. From
the confusion matrices, it is clear that the total false classifications of
CSVM with and without cost optimization are 2 and 3 respectively. There are 2
false negative classifications via the CSVM model without cost optimization
and 1 false negative classification in the case of CSVM with cost
optimization. It again shows the advantage of cost optimized CSVM model over
the regular CSVM model for medical domain-specific data.

Figure 18: Confusion Matrix for Detecting Severity of Neoplasm

####  4.4.3 Classification accuracy

The MRI dataset of human brain images is split into 80:20 ratio for the
training and testing of the models and then the experiments are performed. The
experimental overview with the evaluation scores for detecting the presence of
neoplasms using CSVM, CNN, SVM, and Random Forest are presented in Table 2.
The training and testing columns have normal and neoplasm data points defined
as N and B+M. As seen from the result, CSVM achieved maximum scores in all the
aspects for detecting the presence of neoplasm.

| Number of MRI Images |
---|---|---
| Training | Testing | Evaluation Metrics
Classifier | Total Data | N | N+B | N | N+B | Accuracy | Precision | Recall | F1-Score
CSVM | 658 | 104 | 422 | 26 | 106 | 0.9848 | 0.9815 | 1 | 0.9907
CNN | 658 | 104 | 422 | 26 | 106 | 0.9242 | 0.9615 | 0.9434 | 0.9524
SVM | 658 | 104 | 422 | 26 | 106 | 0.8181 | 0.9271 | 0.8396 | 0.8812
RF | 658 | 104 | 422 | 26 | 106 | 0.6894 | 0.8652 | 0.7264 | 0.7898

Table 2: Evaluation scores for detecting presence of neoplasms.

The evaluation scores for detecting the severity of neoplasms are presented in
Table 3. The training and testing columns have benign and malignant data
points defined as B and M in the table. As seen from the result, CSVM again
achieved maximum scores in all the aspects for severity classification of
brain neoplasm. Further, cost optimization in the CSVM model has shown
significant improvement in recall score than other models.

| Number of MRI Images |
---|---|---
| Training | Testing | Evaluation Metrics
Classifier | Total Data | B | M | B | M | Accuracy | Precision | Recall | F1-Score
CSVM | 528 | 216 | 205 | 55 | 52 | 0.972 | 0.9623 | 0.9808 | 0.9714
CNN | 528 | 216 | 205 | 55 | 52 | 0.9346 | 0.9412 | 0.9231 | 0.932
SVM | 528 | 216 | 205 | 55 | 52 | 0.8598 | 0.8491 | 0.8654 | 0.8571
RF | 528 | 216 | 205 | 55 | 52 | 0.7477 | 0.7451 | 0.7308 | 0.7379

Table 3: Evaluation scores for severity classification.

####  4.4.4 Comparison with the existing approaches

To further evaluate the effectiveness of the CSVM approach, the final result
is compared with other procedures using the same MRI dataset. The compared
approaches omit the proposed preprocessing step and do not consider unequal
classification costs associated with the MRI Brain neoplasm classification.
The compared models use various techniques like Wavelet Transformation(WT),
Spatial Gray Level Dependence Method (SGLDM), Genetic Algorithm (GA), and
Principle Component Analysis(PCA). The result is shown in Table 4. From the
comparison, it is seen that CSVM performed best for both the classification
task i.e. neoplasm presence detection and severity classification from the
compared models. Detection of the presence of neoplasm is having a 15.26%
improvement over the compared technique. For severity detection, the CSVM
model is 1% and 3% more accurate than the compared procedures. As already
discussed, maximization of recall is necessary for this domain, we can see a
difference of 3.5% and 6.2% respectively from the compared procedures with
CSVM.

| Evaluation Metrics
---|---
Classifier | Classification Task | Accuracy | Precision | Recall | F1-Score
CSVM | Detect Neoplasm Presence | 0.9848 | 0.9815 | 1 | 0.9907
CSVM | Detect Neoplasm Severity | 0.9720 | 0.9623 | 0.9808 | 0.9714
| WT+SGLDM
---
+GA+SVM
Detect Neoplasm Severity | 0.9629 | N/A | 0.9460 | N/A
| SGLDM+GA
---
+SVM
Detect Neoplasm Severity | 0.9444 | N/A | 0.9187 | N/A
| PCA+GA
---
+SVM
Detect Neoplasm Presence | 0.8322 | N/A | N/A | N/A

Table 4: Comparison of proposed model with other procedures.

## Conclusions

A hybrid preprocessing using contour plot and Sobel edge is proposed and
results are observed by including and excluding this preprocessing step. The
results signify the benefit of using the proposed preprocessing technique, as
the model performance is increased in each case. Further, the proposed CSVM
performed better than a regular CNN, SVM, or Random Forest model every time in
classifying between normal and abnormal brain MRI and also for benign and
malignant. Cost optimization also helped in improving model performance and
reduced false negative predictions. Comparison with other procedures using the
same dataset also proves the efficacy of the overall proposed techniques.

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## Authors’ Biographies

Nilanjan Sinhababu received his B. Tech. degree in Computer Science &
Engineering from West Bengal Technical University, India. He is currently
pursuing his Master of Science (by research) degree Subir Chwdhury School of
Quality and Reliability, Indian Institute of Technology Kharagpur. His
research interests include recommendation system, data analytics, Machine
learning, deep learning, artificial intelligence, etc.

Monalisa Sarma received her Ph.D. degree in Computer Science & Engineering
from Indian Institute of Technology Kharagpur, India. She holds M.S. (by
research) and B. Tech. degrees both in Computer Science & Engineering from
Indian Institute of Technology Kharagpur, India, and North Hill University,
India, respectively. Presently, she is an assistant professor, Reliability
Engineering Centre, India Institute of Technology Kharagpur. Prior to joining
Indian Institute of Technology Kharagpur, she was working in the Department of
Computer Science & Engineering, Indian Institute of Technology Indore and
Siemens Research and Devolvement, Bangalore, India. Her current research
includes human reliability, big data security, biometric-based cryptography,
etc.

Debasis Samanta received his Ph.D. degree in Computer Science & Engineering
from Indian Institute of Technology Kharagpur, India. He holds M. Tech. and B.
Tech. degrees both in Computer Science & Engineering from Jadavpur University,
Kolkata, India and Calcutta University, India, respectively. Presently, he is
an Associate Professor, Department of Computer Science & Engineering, Indian
Institute of Technology Kharagpur. His current research includes Human
Computer Interaction, Brain Computing Interaction, Biometric-based System
Security, and Data Analytics.