# Comment on “Standard and non-standard Lagrangians for dissipative dynamical
systems with variable coefficientes”

Gabriel González  Cátedra CONCAYT–Universidad Autónoma de San Luis Potosí, San
Luis Potosí, 78000 MEXICO  Coordinación para la Innovación y la Aplicación de
la Ciencia y la Tecnología, Universidad Autónoma de San Luis Potosí,San Luis
Potosí, 78000 MEXICO

###### Abstract

Z.E. Musielak has reported in 2008 J. Phys. A: Math. Theor. 41 055205 methods
to obtain standard and non-standard Lagrangians and identify classes of
equations of motion that admit a Lagrangian description. In this comment we
show how to obtain new non-standard Lagrangians using the non-standard
Lagrangians previously found. In particular, it is demonstrated that for every
non-standard Lagrangian one can generate a new non-standard Lagrangian
associated to a new equation of motion.

Lagrangians are very useful because they can be used to formulate classical
and quantum theories, and can also be used to find a conservation law or to
estimate the solution of a differential equation.[1, 2]
Standard Lagrangians are quadratic forms with respect to $\dot{x}$, for the
one dimensional case the standard Lagrangian takes the form

$\mathcal{L}(x,\dot{x},t)=\frac{1}{2}P(x,t)\dot{x}^{2}+Q(x,t)\dot{x}+R(x,t)$
(1)

With a given Lagrangian we can obtain the equations of motion of the system by
using the Euler-Lagrange equations

$\frac{d}{dt}\left(\frac{\partial\mathcal{L}}{\partial\dot{x}}\right)-\frac{\partial\mathcal{L}}{\partial
x}=0$ (2)

Expanding the differentiation in equation (2) we get

$\ddot{x}\frac{\partial^{2}\mathcal{L}}{\partial\dot{x}^{2}}+\dot{x}\frac{\partial^{2}\mathcal{L}}{\partial\dot{x}\partial
x}+\frac{\partial^{2}\mathcal{L}}{\partial\dot{x}\partial
t}-\frac{\partial\mathcal{L}}{\partial x}=0$ (3)

If we differentiate equation (3) with respect to $\dot{x}$ we get the
following equation[3]

$\frac{\partial}{\partial\dot{x}}\left(\ddot{x}M\right)+x\frac{\partial
M}{\partial x}+\frac{\partial M}{\partial t}=0$ (4)

where $M(x,\dot{x},t)=\partial^{2}\mathcal{L}/\partial\dot{x}^{2}$. It is
important to note that for a standard Lagrangian
$\partial^{2}\mathcal{L}/\partial\dot{x}^{2}=M(x,,t)$, i.e. it does not depend
explicitly on $\dot{x}$, therefore if a non-standard Lagrangian exists then
the following condition most hold true, i.e.

$\frac{\partial M}{\partial\dot{x}}\neq 0$ (5)

Suppose now that we have the following equation of motion

$\ddot{x}=f_{0}(x,\dot{x},t)-\frac{g(x,t)}{M(x,\dot{x},t)}$ (6)

If we substitute equation (6) into equation (4) we obtain

$\frac{\partial}{\partial\dot{x}}\left(f_{0}M\right)+x\frac{\partial
M}{\partial x}+\frac{\partial M}{\partial t}=0$ (7)

Equation (7) tells us that if we know the non standard Lagrangian
$\mathcal{L}_{0}$ associated with the equation of motion given by

$\ddot{x}_{0}=f_{0}(x,\dot{x},t)$ (8)

then the non-standard Lagrangian associated with equation (6) can be
constructed by partially integrating
$\partial^{2}\mathcal{L}_{0}/\partial\dot{x}^{2}$, i.e.

$\mathcal{L}(x,\dot{x},t)=\int\int\frac{\partial^{2}\mathcal{L}_{0}}{\partial\dot{x}^{2}}d\dot{x}d\dot{x}+Q(x,t)\dot{x}+R(x,t)$
(9)

Proposition Suppose $\mathcal{L}_{0}$ is a non-standard Lagrangian for
$\ddot{x}_{0}$; then there exists a non-standard Lagrangian given by

$\mathcal{L}(x,\dot{x},t)=\mathcal{L}_{0}(x,\dot{x},t)-\int g(x,t)dx$ (10)

which describes the following equation of motion

$\ddot{x}=\ddot{x}_{0}-\frac{g(x,t)}{\frac{\partial^{2}\mathcal{L}_{0}}{\partial\dot{x}^{2}}}$
(11)

Proof We substitute the Lagrangian of equation (10) into the Euler-Lagrange
equation (see equation (2)) and after using equation (11) and the fact that
$\mathcal{L}_{0}$ describes the equation of motion $\ddot{x}_{0}$ we get an
identity which validates the proposition.

Let us now work out an example, the non-standard Lagrangian associated with
the standard harmonic oscillator, i.e. $\ddot{x}=-\omega^{2}x$, is given by[4]

$\mathcal{L}_{0}(x,\dot{x},t)=\frac{\dot{x}}{\omega
x}\arctan\left(\frac{\dot{x}}{\omega
x}\right)-\frac{1}{2}\ln\left(\dot{x}^{2}+\omega^{2}x^{2}\right)$ (12)

Using equation (12) we have

$\frac{\partial^{2}\mathcal{L}_{0}}{\partial\dot{x}^{2}}=\frac{1}{\omega^{2}x^{2}+\dot{x}^{2}}$
(13)

Now, suppose we want to obtain the non-standard Lagrangian of the following
equation of motion

$\ddot{x}=-\omega^{2}x-x\left(\omega^{2}x^{2}+\dot{x}^{2}\right)$ (14)

Equation (14) is of the Liénard type non-linear oscillator which shows very
unusual properties[5] and corresponds to the form of equation (11) by taking
$\ddot{x}_{0}=-\omega^{2}x$, $g(x,t)=x$ and
$\partial^{2}\mathcal{L}_{0}/\partial\dot{x}^{2}=\left(\omega^{2}x^{2}+\dot{x}^{2}\right)^{-1}$.
Using equation (10) we can obtain the following non-standard Lagrangian

$\mathcal{L}(x,\dot{x},t)=\frac{\dot{x}}{\omega
x}\arctan\left(\frac{\dot{x}}{\omega
x}\right)-\frac{1}{2}\ln\left(\dot{x}^{2}+\omega^{2}x^{2}\right)-\frac{x^{2}}{2}$
(15)

One can use this approach to generalized the non-standard Lagrangians obtained
by Z.E. Musielak, for example the equation of motion given by

$\ddot{x}+B(t)\dot{x}+\frac{2}{3}\left(\dot{B}(t)+\frac{1}{3}B(t)^{2}\right)x+g(x,t)\left(\dot{x}+\frac{2}{3}B(t)x\right)^{3}=0$
(16)

admits the following non-standard Lagrangian

$\mathcal{L}(x,\dot{x},t)=\frac{1}{\dot{x}+\frac{2}{3}B(t)x}-\int g(x,t)dx$
(17)

If $g(x,t)=0$ then que recover the non-standard Lagrangian obtained by
Musielak.[1]
In conclusion, once a non-standard Lagrangian has been found for a given
equation of motion, then it is possible to generate another non-standard
Lagrangian for a new equation of motion. A new result is that the forms of
equations with the new non-standard Lagrangian have linear, quadratic and
cubic dissipative terms.

## Acknowledgments

I would like to acknowledge support by the program Cátedras Conacyt through
project 1757 and from project A1-S-43579 of SEP-CONACYT Ciencia Básica and
Laboratorio Nacional de Ciencia y Tecnología de Terahertz.

## References

  * [1] Z E Musielak, Standard and non-standard Lagrangians for dissipative dynamical systems with variable coefficients, J. Phys. A: Math. Theor. 41 055205 (2008)
  * [2] Jan L Cieśliński and Tomasz Nikiciuk, A direct approach to the construction of standard and non-standard Lagrangians for dissipative dynamical systems with variable coefficients, J. Phys. A: Math. Theor. 43 175205 (2010)
  * [3] G. González, Lagrangians and Hamiltonians for One-Dimensional Autonomous Systems, International Journal of Theoretical Physics 43, 1885–1890 (2004)
  * [4] Havas, P. The range of application of the lagrange formalism — I. Nuovo Cim 5, 363–388 (1957)
  * [5] Chandrasekar, V. K. and Senthilvelan, M. and Lakshmanan, M., Unusual Liénard-type nonlinear oscillator, Phys. Rev. E 72, (6) (2005)


[1,3] MAHMOOD KHALSAN

These authors contributed equally to this work.

These authors contributed equally to this work.

[1]Advanced Technology Research Group, Faculty of Arts, Science and
Technology, The University of Northampton, UK

2]Centre for Physical Activity and Life Science, Faculty of Arts, Science and
Technology, The University of Northampton, UK, Country

3]Computer Science Department, University of Babylon, Iraq

# Fuzzy Gene Selection and Cancer Classification Based on Deep Learning Model

<EMAIL_ADDRESS>MU MU,(Member, IEEE)
<EMAIL_ADDRESS>EMAN SALIH AL-SHAMERY
<EMAIL_ADDRESS>LEE MACHADO
<EMAIL_ADDRESS>SURAJ AJIT<EMAIL_ADDRESS>MICHAEL
OPOKU AGYEMAN , (Senior Member, IEEE<EMAIL_ADDRESS>*  [  [

###### Abstract

Machine learning (ML) approaches have been used to develop highly accurate and
efficient applications in many fields including bio-medical science. However,
even with advanced ML techniques, cancer classification using gene expression
data is still complicated because of the high dimensionality of the datasets
employed. We developed a new fuzzy gene selection technique (FGS) to identify
informative genes to facilitate cancer classification and reduce the
dimensionality of the available gene expression data. Three feature selection
methods (Mutual Information, F-ClassIf, and Chi-squared) were evaluated and
employed to obtain the score and rank for each gene. Then, using Fuzzification
and Defuzzification methods to obtain the best single score for each gene,
which aids in the identification of significant genes. Our study applied the
fuzzy measures to six gene expression datasets including four Microarray and
two RNA-seq datasets for evaluating the proposed algorithm. With our FGS-
enhanced method, the cancer classification model achieved 96.5%,96.2%,96%, and
95.9% for accuracy, precision, recall, and f1-score respectively, which is
significantly higher than 69.2% accuracy, 57.8% precision, 66% recall, and
58.2% f1-score when standard MLP method was used. In examining the six
datasets that were used, the proposed model demonstrates its capacity to
classify cancer effectively.

###### keywords:

Gene expression, Classifier methods, Fuzzy gene selection, and Cancer
classification

##  1 Introduction

Cancer is the second leading cause of death worldwide and represents the
abnormal growth of cells and their frequent metastatic spread throughout the
body [1]. Cancer cells frequently proliferate independently of growth signals.
and neglect to respond to survival/death that instructs them to stop dividing
or to die (i.e. by apoptosis). This phenomenon occurs due to inherited or
environmental factors that cause DNA mutations or epigenetic modifications
that deregulate normal cellular gene expression programs [2]. For example, DNA
mutation is caused by harmful substances in the environment including
chemicals in tobacco smoke and ultraviolet radiation from the sun. Some cancer
genes are inherited (i.e. BRCA1/2) and have high penetrance due to their
fundamental role in cellular regulation. Therefore, the analysis of
deregulated gene expression programs in cancer cells may play an important
role in the early detection and treatment of cancer. Consequently, identifying
a specific set of genes (gene signatures) that aid classification may provide
an earlier diagnosis of cancer and provide personalized treatment options [2].
The tools (Microarray and RNA-seq technologies) that have been developed for
measuring the expression levels of genes in normal and cancer tissue have
opened the door for investigators to build and test a new mathematical and
statistical model for analyzing gene expression data. Those measurement tools
calculate the expression levels of thousands of genes across
hundreds/thousands of clinical samples.
Both (Microarray and RNA- seq technologies) measure transcriptome-wide gene
expressions and allow a comparison of cancerous and non-cancerous tissues.
Microarray methods measure the intensities of colored fluorescent probes
spotted on glass slides, which correspond to gene expression under different
conditions. Whereas RNA-Seq methods measures read counts as a proxy for
relative gene abundance [3]. RNA-seq methods have largely superseded
microarrays as they produce less noise and are more accurate in calculating
method gene expression abundance [4]. Researchers have developed a range of
mathematical and statistical techniques to analyze gene expression data for
various goals. This includes the identification of optimal gene signature
pathways, enhanced cancer classification, cancer prediction, drug discovery,
and improved personalized therapy. To achieve this, obstacles regarding the
high dimensionality and complexity of the publicly available gene expression
data remain. However, measurement tools for calculating gene expressions have
improved continuously. Artificial intelligence (AI) is now a powerful tool for
mitigating the time taken to analyze large cancer datasets. It has the
potential to improve the accuracy of cancer classification and/or cancer
prediction. AI is the broadest term used to classify machines that mimic human
intelligence. AI includes machine learning (ML) techniques including Support
Vector Machine (SVM), K-Nearest Neighbour (KNN), and Random Forest (RF)
approaches. ML also includes deep learning (DL) approaches that use
Convolutional Neural Networks (CNN), Long short-term memory (LSTM), and, MLP.

The present study provides significant contributions by attempting to address
a number of shortcomings.
First, a new fuzzy gene selection technique has been developed to make the
datasets on gene expression less dimensional.
Second, using a limited number of genes when using the FGS method prevents or
at least reduces overfitting problems when classifier approaches are applied.
Third: Reducing the amount of time required for a classifier model’s training
stage is made possible by a minimal number of biomarker genes that are
utilized as identifiers.
Fourth: The suggested paradigm enables early cancer detection and precise
cancer classification.
Fifth: Choosing a few useful informative genes to be employed.

The rest of the work is organized as follows: section II explores recent
studies analyzing gene expression data by using ML. Section III explains
theoretically the concepts of methods that have been used for developing the
fuzzy gene selection methods and classifier approaches that have been
employed. It also illustrated the repositories that have been used to download
the datasets employed for training and testing the proposed model. While
section IV explains practically the techniques that have been employed for
developing the proposed model (FGS and MLP). Section V discussed the results
that have been obtained from the proposed model (FGS and MLP) and compared the
other classifier approaches such as (i.e.SVM, KNN, and RF). Conclusions are
provided at the end of the paper.

##  2 Related Work

Sun et al. [5], suggested a new approach namely a multimodel deep neural
network (MDNN) that aims to improve the performance accuracy of breast cancer
classification. The proposed algorithm was trained and tested on publicly
available gene expression data that includes 24368 genes across 2509 breast
cancer and 548 normal samples [6]. The new model was compared with three
different machine learning methods (SVM, RF, and Logistic regression (LR)).
Minimum Redundancy Maximum Relevance (mRMR) was also employed as a feature
selection Technique to reduce the number of features (genes) to improve the
performance of classification accuracy. The accomplished accuracy was 82%,
80%, 79% and 76% for MDNN, SVM, RF, and LR respectively. However, recall
values were low in all classifier algorithms (45%, 36%, 22% and 18% for MDNN,
SVM, RF, and LR respectively) and precision was 95% for all classifier
approaches.

Although the suggested model’s performance accuracy was good, further accuracy
enhancement is necessary due to the cancer’s sensitivity. Furthermore, the
recall values were quite low, which had an impact on the performance of the
provided method. Typically, research use several datasets for different types
of cancer to validate the findings produced by applying their models, which
have been evaluated in this work where just one dataset was used.

Jing Xu et al. [7], proposed a novel Deep Neural Forest (DFNForest) algorithm
to classify subtypes of three different cancer types (Glioblastoma multiforme
(GBM)), Breast, and lung ). The system was tested by employing RNA-seq data
available from TCGA. The researcher used two feature selection techniques
(fisher ratio and neighborhood rough set) to reduce the dimensionality of the
publicly available data, addressed overfitting issues, and selected the genes
that significantly impacted the performance of the proposed model [8]. They
achieved an accuracy of 93% (breast), 88% (lung), and 84% (GBM).

Guillermo et al. [9], proposed CNN and transfer learning (TL) model for lung
tumor prediction. (10535) samples and the top 20k most expressed genes were
downloaded from TCGA for 33 different kinds of cancer but the proposed model
was tested only on the lung cancer dataset. The system compared the new model
against other classifier methods(densely connected multi-layer feed-forward
neural network (MLNN) and SVM) to evaluate the suggested model. The achieved
accuracy was 68%, 72%, and 69% for CNN, MLNN and SVM respectively. The
proposed model showed that low accuracy was accomplished, and it was tested
only on one type of cancer(lung) that may not achieve the same score of
accuracy for other types of cancer. The proposed model was not achieved better
accuracy than compared classifier methods that the investigator described in
this study (MLNN) was achieved better accuracy as illustrated previously.
Other evaluation measurements from this research were identified in Table1.

Table 1: Comparing the performance of CNN against MLNN and SVM Methods | AUC | Sensitivity | Specificity | Accuracy
---|---|---|---|---
CNN |  | 73%
---
| 67%
---
68% | 68%
MLNN |  | 70%
---
| 61%
---
73% | 72%
SVM |  | 70%
---
| 64%
---
69% | 69%

Yeganeh et al. [10], multiple machine learning methods with multiple gene
expression datasets of ovarian cancer employed for ovarian cancer prediction.
Seven GEO datasets(GSE12172, GSE14407, GSE9899, GSE37648, GSE18521, GSE38666,
and GSE10971) were obtained for training and testing the machine learning
approaches. The system used a 26-gene set panel for training different
classifier methods. The highest accomplished accuracy value was 0.89 when a
Random Forest pipeline was applied. Low accuracy achieved and imbalanced
datasets used were recorded as drawbacks in this work.

It concluded from this section that previous work requires developing a new
model for improving cancer classification and selecting a small number of
significant genes that would be used as identifiers for cancer classification.
More studies were discussed in our previous published work freely available
[30].

###  2.1 Publicly available datasets

Below are common data repositories that provided gene expression data from
normal and cancer-derived tissues used to train and test models for
classification or prediction purposes. Those repositories are further
described as follows.

####  2.1.1 Gene Expression Omnibus (GEO)

GEO [11] is a public functional genomics data repository supporting MIAME-
compliant data submissions. The repositories support RNA-seq and Microarray
data but GEO mostly provides Microarray data. The total number of samples that
are provided by GEO is 3635328 for different diseases. GEO is freely available
to download experiments and curated gene expression profiles by users or
researchers.

####  2.1.2 The Cancer Genome Atlas (TCGA)

TCGA [12] is a landmark cancer genomics program that is distinguished in
providing 84,031 samples from 33 different cancer types. The datasets that are
available on TCGA are measured by the RNA-seq and Microarray methods for
measuring expressed levels of gene activity for healthy and unhealthy tissues.

###  2.2 Feature selection

Feature Selection (FS) is a statistical method that aims to select an optimal
feature of a large number of original features for given a dataset [13]. The
goal is to choose the best subset of features with k features. FS approaches
have valuable benefits in reducing the training time, reducing the complexity
of the model, and are easy to interpret. Additionally, there are faster
responses with unseen data and powerful generalization that enhances the
performance of the model and avoids (or at least reduces) overfitting issues
[14]. This work has used three feature selection methods to identify the
optimal subset of genes that were employed later as identifiers for training
classifier methods. Those feature selection methods are explained below.

####  2.2.1 Mutual Information

Mutual information (MI) can be defined by how it gauges the amount of
information shared by two random variables. In the context of gene selection,
employs this definition to select a subset of important genes with respect to
the output vector [14]. It has two major benefits: it can be used as a
solution with different types of machine learning models, and it is a faster
solution for selecting features. Mathematically it can be defined as follows.
X represents the random variables(genes) and Y is the target (cancer types).

$I(X,Y)=\sum\sum p(X,Y)log\frac{p(x,y)}{p(x)p(y)}$ (1) $=H(Y)-H(Y/X)$ (2)

Where H(Y—X) is the conditional entropy of Y in the case of X is known.

####  2.2.2  F-ClassIF

F-class calculates the ratio between different values. In other words, it
calculates the variation between features/labels within the samples. This
method is called the ANOVA f-test [15]. F-test results in a score that
represents how far the feature is from other features. For example, calculate
a score for each feature between two classes and use this score for selecting
the important features. As shown in In Figure1, the red color presents class 1
and the blue color introduces class 2 and two features on the x and y axes.
The x feature is a better separator than y because if we project data on the
x-axis, two completely separated classes were obtained but when project data
onto y, two classes overlap in the middle of the axis. Based on that the
features which were got higher scores will be chosen as the best features for
a given dataset.

Figure 1: Illustration example of distributed Features to show up F-classif
work

####  2.2.3  Chi-squared

The chi-squared statistic is used to assess the independence of two
occurrences. To begin, compute the chi-squared between each gene and the
class. As a result, select the number of features based on the highest chi-
squared scores. The chi-squared formula is presented below [16]:

$\mathrm{X}_{\mathrm{c}}^{2}=\Sigma(\mathrm{O}_{\mathrm{i}^{-}}\mathrm{E}_{\mathrm{i}})^{2}/\mathrm{E}_{\mathrm{i}}$
(3)

Where: C = degrees of freedom, O = observed value(s), and E = expected
value(s)

###  2.3 Fuzzy gene selection (FGS)

The proposed new fuzzy gene selection method of selecting the best subset of
genes that were used as an identifier for the training classifier. The
proposed FGS can be summarized in four major steps as shown in Figure2. The
steps are illustrated as follows:

####  2.3.1 Pre-processing step

The process of preparing raw data for use by machine learning algorithms is
known as pre-possessing. Furthermore, it is the initial stage in data
cleansing prior to analysis procedures such as feature selection or
classification. The suggested algorithm employed three primary techniques of
pre-processing, which are as follows:
1\. Address the missing values: In general, missing values in a dataset have a
negative influence on classifier performance, hence there are multiple ways
for dealing with missing values (Eliminate Data Objects, Ignore the Missing
Value During Analysis, and Estimate Missing Values). There are no missing
values for a gene’s expressed level in gene expression data. However, certain
gene symbols are missing. As a result, this stage removed only the raw data
that does not contain the gene symbol.
2\. Handle the duplication: simply eliminating the duplicated gene symbols.
3\. Normalization is a procedure that is commonly used as part of data
preparation for ML, particularly inside neural network classifier approaches.
The primary goal of normalization is to modify the values of numeric columns
in the dataset to use a similar scale without distorting variance in value
ranges or losing information. The most common kind of normalization is min-max
normalization, which was applied in this study. The normalization value is
calculated using the equation below..

$V=\frac{v-\mathrm{min}_{\mathrm{A}}}{{\mathrm{max}_{\mathrm{A}}}-{\mathrm{min}_{\mathrm{A}}}}$
(4)

Where:
maxA is the maximum value of original values for a feature.
minA is the minimum value of original values for a feature.
and NmaxA,NminA are the maximum and minimum intervals of value.
V represents the feature value.

####  2.3.2 Vote step

Three feature selection approaches (MI,F-classif, and chi-squared) were used
to select informative genes. Depending on the step function (SF), each feature
selection approach chooses a different number of genes. The formula below has
been used to compute the step function. This algorithm is intended to avoid
using a limited number of selected genes, which may result in neglecting some
genes with the same score when using a fixed number of genes, such as the top
ten genes. It is also worth noting that using this formula gives more
flexibility to the step function value than using constant values such as 0.3.
If non- or small-selected features by a feature selection method have scored
equal to 0.3, we lose some essential features (genes) that could have been
selected by other feature selection methods.

$SF=max(FSS)*0.3$ (5)

Where SF is step function, FSS is the feature selection score for all genes.
max is the maximum score for all features scored by the feature selection
method.
The selected genes of this stage have scored either equal to the step function
or greater than the step function value that was calculated previously.

####  2.3.3 Fuzzification step

This is the process of changing crisp data into fuzzy data using membership
functions, with the goal of transforming the crisp data into data ranging
between (0-1). There are different types of membership functions, the
Triangular Membership Function was used in this work.

$Mf=\frac{\mathrm{W}_{\mathrm{i}}-a}{b-a}$ (6)

Where MF is the membership function.
W is the crisp value (score) for a gene.
a = lowest possible score (min).
b= highest possible score.
This membership function applied for the three feature selection methods which
means, there are MF1, MF2, and MF3 in this work.

####  2.3.4 Defuzzification step

This step is a process for converting the output data to crisp data. This step
is the final stage of the gene selection method that has been used to select
informative genes. The selected genes from these steps have been used as
identifiers for training the classifier approaches.

$ASG=\frac{\mathrm{MF}_{\mathrm{i}}+\mathrm{MF}_{\mathrm{i}}+\mathrm{MF}_{\mathrm{i}}}{N}$
(7)

Where ASG is the Average Score for a gene through the three feature selection
methods.
MF is the membership function for each gene. N is the number of feature
selection methods that have been employed. In this work (N equal 3).
The two preceding phases show that different filter feature selection
approaches provide different scores for the same gene. Fuzzification and
Defuzzification were used to get a single score for each gene. As a result, as
indicated in the equation below, using a step function for choosing the
optimal subset of genes that would be used as identifiers for cancer
classification.

$SF=max(FSS)*0.5$ (8)

Figure 2: Block Diagram of Proposed Fuzzy Gene selection Process

###  2.4 Classifier Approaches

####  2.4.1 Support Vector Machine(SVM)

It is applied for classification and regression challenges. However, SVM is
typically applied to a classification problem because it accomplished
outstanding performance in this area. SVM aims to create the best decision
boundary (Hyperplane) to segregate the input data in different spaces. The SVM
algorithm attempts to find the hyperplane in an n-dimensional space that
segregates different data points [17][18]. Although, SVM has been widely used.
However, it has some weaknesses. For example, SVM underperforms when the
datasets are largely comparing it to small datasets. SVM is not working well
with datasets containing noise data for instance target classes are
overlapping [19]. Additionally, it is not suited when the number of features
is larger than the number of samples. These disadvantages of SVM have a high
impact when applied to gene expression data because the gene expression data
is noisy, and the number of genes is greater than the number of samples.

####  2.4.2 K-Nearest Neighbors (KNN)

It works on the assumption that similar things are positioned near to one
another, making it more suitable for recommended system uses. To put it
another way, KNN calculates the distance between the new point and the
previously trained points (classes), so that the new point is predicted to the
nearest distance of trained classes in feature space if it has two classes
(Class A and Class B), as shown in Figure 3, and the ”star” in red color
represents the new class that requires prediction. Finding the best feature
space (K) in KNN is critical because there is no standard method [18]. It
often uses a large number of lists of integers to decide which one has the
highest accuracy. As a consequence of this, the finest K will be picked.
Although KNN is straightforward to use, there are several significant
drawbacks. It is prone to noisy and missing data, is inefficient with large
datasets, and contains data with high dimensionality.

Figure 3: KNN and its Hyperplane Selection

####  2.4.3 Decision Tree (DT)

A decision tree is a supervised machine-learning technique that is used for
both classification and regression challenges, however, it is mostly employed
as a solution for classification purposes [18]. DT works under the principle
that the data is continuously split according to a certain parameter. It is
easy to understand because it mimics the human process of making decisions and
it requires less clean data compared with other ML approaches. However, it is
complex compared with other algorithms because it consists of many layers and
may have overfitting issues.It is also computationally expensive as more class
data labels are applied. The procedure of DT working can be concluded in five
main steps as follows[21].
1.Step1: DT starts with an entire dataset, assume S, in a node is called the
root node.
2.Step2: Applying an attribute selection measure (ASM) to find the best
attribute for given a dataset.
3.Step3: Split the dataset into subsets that include the possible values for
finding the best attribute for the given dataset.
4\. Create the decision tress nodes, which have the best attribute.
5\. Repeat step 3 partitioning the dataset into subsets for making a new
decision tree, this process is continuously repeated until there is no
possibility of classifying nodes namely leaf nodes that each leaf node
presents one class or its probability [14].

####  2.4.4 Gaussian Naive Bayes (GNB)

Gaussian Naïve Bayes is supervised learning technique which relies on Bayes
theorem that is employed for classification challenge and specifically for
text classification because it is more suited to high dimensional training
datasets [22]. It is considered one of the top 10 classifier techniques in
data mining [23]. It is also characterized by faster prediction compared with
other classifier models , easy to build and most effective in classification
problems. However, GNB presumes that all features are independent which means
it misses the possibility to learn the relationship between features [24][22].
Another drawback of GNB is hardly identifying the conditional independence in
microarray data [25]. GNB works by taking each data point and assigning it to
whichever class is nearest to it. It disguised not only calculating the
distance by employing Euclidean distance between the new points and trained
class, but it also calculates how this compares to the class variance. For
each dimension, the z-score is calculated, and the distance from the mean is
divided by the standard deviation [26].

####  2.4.5 Multilayer Perceptron(MLP)

MLP is a type of feedforward neural network (ANN) that is vastly used in
pattern recognition, classification challenges, and prediction. It is mostly
employed to solve supervised learning problems [17]. MLP maps the input to the
output in a single direction of data and calculations. Generally, it consists
of three perceptron or layers, an input layer, an output layer and at least
one in between called a hidden layer[27]. Each layer in MLP is fully connected
with the next layer. The input layer is used to receive the signal from the
outside world to the network, hidden layers perform the arithmetic operations
from the input layer to the output layer while the output layer is responsible
of making the decision(prediction). As a result, the output layer aims to
transfer the information to the outside environment. Each layer in MLP is
composed of a number of nodes (neurons). Most importantly, MLP work can be
summarized in four main steps:
1) Step 1: propagating the input data forwarding from the input layer to the
output layer.
2) Step 2:MLP is learned by updating the connection weights between the
neurons to ensure a backpropagation algorithm is applied after input data of
each node in MLP is processed[27].
3) Step 3:Calculate the errors by finding the difference between the predicted
classes by MLP and the known classes and employ supervised learning to learn
MLP to reduce the calculated errors.
4) The previous three steps will be repeated over multiple iterations to learn
perfect weights.

###  2.5 Cross Validation

Cross Validation in ML is a statistical method that aims to minimize or avoid
overfitting issues in different classifier approaches. Rather than training a
model on one training dataset, Cross Validation method allows training the
model on many datasets. By splitting the dataset into multiple folds and
training the model on different folds [20]. As a result, the model achieves
generalization capabilities which is a good sign of a robust model. It also
assists to indicate a more accurate estimate of algorithm prediction
performance. The datasets split in kfold such as 5 as shown Figure4.

Figure 4: KFold Cross Validation Process with K=5

###  2.6 Evaluation Measurement Methods

This section is the evaluation tools that were used to evaluate the
performance of the proposed model against the other previous models or compare
the performance of classifier methods when the new fuzzy gene selection method
was employed against the classifier methods when the fuzzy gene selection was
not applied. As a result, these evaluation parameters are used for measuring
the performance of a model. There are four evaluation measurements that must
be explained to demonstrate that this proposed study outperformed the previous
studies. The evaluation measurements are as follows:
Accuracy (AC) is an evaluation measurement that is utilized to determine which
model is the best for a given dataset in AI. A ratio of correctly predicted
observations to the total observations is called as accuracy in AI. The
formula below is used to calculate it mathematically [28]:

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

Where TP is True Positive, TN is True Negative, FP is False Positive and FN is
False Negative.
A TP is the correctly predicted positive value which means that the value of
the actual class is cancer and the value of the predicted class is also
cancer.
A TN is an outcome where the model correctly predicts the negative class. A FP
is an outcome where the model incorrectly predicts the positive class. FN is
an outcome where the model incorrectly predicts the negative class .
Precision (Pre) is the ratio of correctly predicted positive observations to
the total predicted positive observations as described in [30]

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

A recall (Rec) is the fraction of retrieved instances among all relevant
instances. It is also known as sensitivity. The recall formula is illustrated
as [28]:

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

The F1 score (F1) has combined the precision and recall of a classifier into a
single metric by taking their harmonic mean, where a perfect F1 score has a
value of 1 and the worst score at 0 [28]:

$F1=2\times\frac{precision\times recall}{precision+recall}$ (12)

##  3 The proposed model

The proposed model may be divided into three basic stages of development.
These phases were completed in the following order:
1\. The Pre-processing stage is prior to machine learning included the removal
of the raw data that had missing or duplicate gene symbols. The data were
normalized by using a min-max normalization algorithm that aims to re-scale
the data between (0-1).
2\. The gene selection step, which was intended to select the optimal subset
of informative genes that would be used as identifiers for training classifier
algorithms, is the most significant stage of the proposed model. This stage
can be represented by the following two points: To begin, we used three
feature selection approaches (MI, F-classif, and chi-squared) with a step
function to select a subset (the determined step function was displayed in the
voting stage). Second, the developed fuzzy gene selection approach employed
fuzzy logic in a further analysis to choose fewer and more significant genes.
The suggested FGS employed Triangular Membership Function fuzzification and
center of gravity defuzzification with a step function (shown in the
defuzzification phase) to choose informative ones with a strong influence on
cancer classification.
3\. Classifier stage: the proposed algorithm used Multi-layer Perceptron
Classifier with three hidden layers. The output of the fuzzy gene selection
method(selected genes) was used as an input layer for MLP (node number of
input layer based on selected genes), three hidden layers were utilized
(300,200,100 nodes) and one output layer which is the output of the
classification(normal or malignant for binary classification and the class
name for multiclasses datasets).
Summary: The total number of layers for the proposed model fifteen layers
illustrated as follows: One input layer, three hidden layers for pre-
processing stage (missing values, duplication, and normalization),three
parallel hidden layers for filter feature selection methods. Two hidden layers
for fuzzification (Triangular Membership Function) and defuzzification (Center
of gravity). Three hidden layers for MLP classifier. Finally, one output
layer. The number of input nodes is flexible which is based on the number
features (number of genes) includes (the number of nodes when filter selection
methods employed and the number of nodes when the fuzzy logic applied).

Figure 5: The Proposed Model Structure

##  4 Results

###  4.1 Datasets used

Six gene expression datasets of different types of cancer were used for
training and testing the proposed model. The datasets comprised RNA-seq and
Microarray tools were used to evaluate the proposed fuzzy gene selection
algorithm with the two different measurement tools for measuring the expressed
level of gene activity. The datasets were obtained from TCGA and GEO
(GSE45827, GSE14520, GSE77314, GSE19804, TCGA, and GSE33630). The total number
of samples from the six datasets was 3,011 for multi and binary classes more
details were described in ( Table2). To avoid overfitting in the training
stage of the algorithm, the cross-validation method has been used with 5
Kfolds to split the datasets into multiple folds and train the algorithm on
different folds. In Table 2, KIRC stands for Kidney renal cell cancer, LUAD
stands for Lung adenocarcinoma, LUSC stands for Lung squamous cell carcinoma,
and UCEC is for Uterine corpus endometrial carcinoma.

Table 2: Summary of Datasets were Employed for Training and Testing The Proposed Model Dataset |  Tools |  N-samples |  N-Genes |  Cancer Types |  N-Class |  Reference
---|---|---|---|---|---|---
GSE45827 |  Microarray |  155 (Basal 41, Her2 30, Luminal B 30, Luminal A 29, CellLine 14, Normal 11 ) |  29873 |  Breast cancer subtypes |  6 |  [11]
GSE14520 |  Microarray |  445 ( Cancer 227, Normal 218) |  13425 |  Liver Cancer |  2 |  [11]
GSE77314 |  RNA-seq |  100 (Cancer 50, Normal 50) |  29087 |  Liver Cancer |  2 |  [11]
GSE19804 |  Microarray |  120 (Cancer 60, Normal 60) |  45782 |  Lung Cancer |  2 |  [11]
TCGA |  RNA-seq |  2086 ( BRCA 878, KIRC 537, UCEC 269, LUSC 240,LUAD 162) |  972 |  BRCA, KIRC, LUAD, LUSC, UCEC |  5 |  [29]
GSE33630 |  Microarray |  105 (PTC 49, Normal 45, ATC 11) |  23518 |  Thyroid |  3 |  [11]

###  4.2 Obtained results

This section investigates the usage of six datasets across five classifier
approaches, comparing the use of a fuzzy gene selection method and
demonstrating the benefits of using the suggested fuzzy gene selection
methodology. In this paper, we examine how FGS affects the performance of
cancer classification models. The full details are presented (Table 3 and
Table 4) of the datasets used for training and testing the models, cancer
types, and the achieved accuracy, precision, recall, and f1-score before the
fuzzy gene selection method was applied and after the fuzzy gene selection
method was used.

Table 3: Comparing five classifier approaches when applying and omitting FGS Dataset | Class Types | FS method | N-Genes | Classifier | Ac | Pre | Rec | F1
---|---|---|---|---|---|---|---|---
|  |  |  |  | DT.
---
| 90%
---
| 90.6%
---
| 88.9%
---
| 89.7%
---
|  |  |  |  | KNN.
---
| 94%
---
| 91%
---
| 97.6%
---
| 94%
---
| GSE14520
---
| Binary class
---
| No
---
| 13425
---
| SVM.
---
| 97%
---
| 96%
---
| 97.6%
---
| 97%
---
|  |  |  |  | GNB.
---
| 95%
---
| 95.6%
---
| 94%
---
| 94.8%
---
|  |  |  |  | MLP.
---
| 86.7%
---
| 76.5%
---
| 76.7%
---
| 76.5%
---
|  |  |  |  | DT.
---
| 96%
---
| 95%
---
| 97%
---
| 96%
---
|  |  |  |  | KNN.
---
| 96.6%
---
| 96%
---
| 97%
---
| 96.6%
---
| GSE14520
---
| Binary class
---
| FGS
---
| 23
---
| SVM.
---
| 96%
---
| 95.6%
---
| 96%
---
| 96%
---
|  |  |  |  | GNB.
---
| 96.6%
---
| 96%
---
| 97%
---
| 96.6%
---
|  |  |  |  | MLP.
---
| 96%
---
| 96%
---
| 96%
---
| 96%
---
|  |  |  |  | DT.
---
| 87.6%
---
| 77.6%
---
| 81%
---
| 79%
---
|  |  |  |  | KNN.
---
| 91%
---
| 87.7%
---
| 86.5%
---
| 86%
---
| GSE33630
---
| Multiclass
---
| No
---
| 23516
---
| SVM.
---
| 93%
---
| 95%
---
| 92%
---
| 92%
---
|  |  |  |  | GNB.
---
| 90%
---
| 93.7%
---
| 89.7%
---
| 90%
---
|  |  |  |  | MLP.
---
| 72%
---
| 55.6%
---
| 64.5%
---
| 58.5%
---
|  |  |  |  | DT.
---
| 93%
---
| 93%
---
| 93.5%
---
| 92.5%
---
|  |  |  |  | KNN.
---
| 94%
---
| 96%
---
| 92.8%
---
| 93%
---
| GSE33630
---
| Multiclass
---
| FGS
---
| 76
---
| SVM.
---
| 94%
---
| 96%
---
| 92.8%
---
| 93%
---
|  |  |  |  | GNB.
---
| 92%
---
| 88%
---
| 99.8%
---
| 88.8%
---
|  |  |  |  | MLP.
---
| 93%
---
| 95%
---
| 92%
---
| 92.5%
---
|  |  |  |  | DT.
---
| 91%
---
| 87%
---
| 85%
---
| 85.8%
---
|  |  |  |  | KNN.
---
| 88%
---
| 83%
---
| 81.5%
---
| 81.9%
---
| TCGA
---
| Multiclass
---
| No
---
| 971
---
| SVM.
---
| 95%
---
| 91.6%
---
| 91.8%
---
| 91.6%
---
|  |  |  |  | GNB.
---
| 94%
---
| 89.7%
---
| 92%
---
| 90.7%
---
|  |  |  |  | MLP.
---
| 94%
---
| 90.8%
---
| 89.8%
---
| 90%
---
|  |  |  |  | DT.
---
| 91.7%
---
| 88%
---
| 87%
---
| 86.5%
---
|  |  |  |  | KNN.
---
| 93.6%
---
| 89.8%
---
| 90%
---
| 89.6%
---
| TCGA
---
| Multiclass
---
| FGS
---
| 25
---
| SVM.
---
| 94 %
---
| 90.5%
---
| 90.7%
---
| 90.5%
---
|  |  |  |  | GNB.
---
| 92%
---
| 87.7%
---
| 90.8%
---
| 89%
---
|  |  |  |  | MLP.
---
| 95%
---
| 92%
---
| 91.6%
---
| 91.6%
---
Table 4: Comparing five classifier approaches when applying and omitting FGS Dataset | Class Types | FS method | N-Genes | Classifier | Ac | Pre | Rec | F1
---|---|---|---|---|---|---|---|---
|  |  |  |  | DT.
---
| 89%
---
| 90%
---
| 88%
---
| 90%
---
|  |  |  |  | KNN.
---
| 90.8%
---
| 88%
---
| 95%
---
| 91%
---
| GSE19804
---
| Binary class
---
| No
---
| 45782
---
| SVM.
---
| 95.8%
---
| 96.6%
---
| 95%
---
| 95.7%
---
|  |  |  |  | GNB.
---
| 92.5%
---
| 95%
---
| 90%
---
| 91.9%
---
|  |  |  |  | MLP.
---
| 50%
---
| 20%
---
| 40%
---
| 26.6%
---
|  |  |  |  | DT.
---
| 92.5%
---
| 93.6%
---
| 91.6%
---
| 92%
---
|  |  |  |  | KNN.
---
| 96.6%
---
| 96.7%
---
| 96.6%
---
| 96.6%
---
| GSE19804
---
| Binary class
---
| FGS
---
| 36
---
| SVM.
---
| 96.6%
---
| 97%
---
| 96.6%
---
| 96.6%
---
|  |  |  |  | GNB.
---
| 95.8%
---
| 96.7%
---
| 95%
---
| 95.7%
---
|  |  |  |  | MLP.
---
| 97.5%
---
| 97%
---
| 98%
---
| 97.5%
---
|  |  |  |  | DT.
---
| 95%
---
| 98%
---
| 91.9%
---
| 94%
---
|  |  |  |  | KNN.
---
| 88.9%
---
| 82%
---
| 100%
---
| 90%
---
| GSE77314
---
| Binary class
---
| No
---
| 29087
---
| SVM.
---
| 99%
---
| 98%
---
| 100%
---
| 99%
---
|  |  |  |  | GNB.
---
| 84%
---
| 100%
---
| 68%
---
| 80%
---
|  |  |  |  | MLP.
---
| 93%
---
| 98%
---
| 88%
---
| 91%
---
|  |  |  |  | DT.
---
| 97%
---
| 98%
---
| 96%
---
| 97%
---
|  |  |  |  | KNN.
---
| 99%
---
| 98%
---
| 100%
---
| 99%
---
| GSE77314
---
| Binary class
---
| FGS
---
| 12
---
| SVM.
---
| 99%
---
| 98%
---
| 100%
---
| 99%
---
|  |  |  |  | GNB.
---
| 97%
---
| 98%
---
| 96%
---
| 96.8%
---
|  |  |  |  | MLP.
---
| 99%
---
| 98%
---
| 100%
---
| 99%
---
|  |  |  |  | DT.
---
| 85.8%
---
| 83%
---
| 82.6%
---
| 81.5%
---
|  |  |  |  | KNN.
---
| 85%
---
| 87.9%
---
| 87.7%
---
| 87%
---
| GSE45827
---
| Multiclass
---
| No
---
| 29873
---
| SVM.
---
| 94.8%
---
| 96%
---
| 95.8%
---
| 95.8%
---
|  |  |  |  | GNB.
---
| 89%
---
| 92.7%
---
| 88.8%
---
| 89%
---
|  |  |  |  | MLP.
---
| 20.6%
---
| 6%
---
| 17%
---
| 7%
---
|  |  |  |  | DT
---
| 89.6%
---
| 90.9%
---
| 89.6%
---
| 88.8%
---
|  |  |  |  | KNN
---
| 95.48%
---
| 96.5%
---
| 96%
---
| 96%
---
| GSE45827
---
| Multiclass
---
| FGS
---
| 68
---
| SVM.
---
| 98.7%
---
| 99%
---
| 98.8%
---
| 98.9%
---
|  |  |  |  | GNB.
---
| 91.6%
---
| 94.5%
---
| 92%
---
| 92.8%
---
|  |  |  |  | MLP.
---
| 98.7%
---
| 99.3%
---
| 98.8%
---
| 98.9%
---

###  4.3 Results discussion

To show the differences between the results obtained by omitting and employing
the FGS technique with the five different classifier techniques, the accuracy
scores in 5 kfolds have been displayed on a bar chart. The two bar graphs (7
and 7) demonstrate the five-fold difference in accuracy ratings between
utilizing and ignoring FGS. The two bar graphs demonstrate how the usage of
FGS enhanced classifier model performance, notably with the MLP classifier.
The FGS method was also utilized to reduce the number of selected genes from
29873 to 68 genes. These results suggest that the development of the FGS
technique contributed to an improvement in accuracy, a reduction in the
training time for models, and the provision of early cancer detection by the
choice of instructive genes. Classifier models are also less complicated.

Figure 6: Accuracy scores for breast cancer (GSE45827) before employing FGS

Figure 7: Accuracy scores for breast cancer (GSE45827) when employing FGS

As shown in the two bar charts (9 and 9), a fuzzy gene selection strategy
significantly improved the performance of the five classifier approaches for
classifying lung cancer. In comparison to other classifier models, the
findings demonstrate that the MLP model offers predictions that are closer to
the ideal observed value. MLP earned an average accuracy score of 97.5 in 5
kfolds. Other classifiers, however, achieved average scores of 96.6, 96.6,
95.8, and 92.5 in 5 kfolds for SVM, KNN, GNB, and DT, respectively.
Additionally, only 36 genes out of 45782 genes were employed for training the
classifier models, a considerable decrease in the number of genes used.

Figure 8: Accuracy scores for lung cancer (GSE19804) without applying FGS

Figure 9: Accuracy scores for lung cancer (GSE19804) when FGS method applied

Although there is a slight improvement in the accuracy of most of the
classifiers used in this study to classify liver cancer datasets(GSE14520).
However, there is a significant enhancement in the MLP classifier when using
the FGS method, as it improved from 86.6 to 96 as an average accuracy score in
5 kfolds. More importantly, the FGS method reduced the number of genes used to
train models to 23 only out of 13425. The two bar charts (11 and 11) explain
the comparison accuracy scores with 5 kfolds for the five models when FGS
employed and omitted.

Figure 10: Accuracy scores for liver cancer (GSE14520 ) without applying FGS

Figure 11: Accuracy scores for liver cancer (GSE14520) when FGS method applied

Most classifier models used reached close to 100 where the average accuracy
score in 5 kfolds is 99% for the SVM, KNN, and MLP while 97% for GNB and DT
when fuzzy gene selection techniques are applied to the liver cancer dataset
(GSE77314). These remarkable enhancements in accuracy score are shown in (13
and 13). Moreover, the FGS method decreased the number of genes from 29087 to
only 12 genes that were used as identifiers for training the proposed model
and compared models. That leads to an increase in the model efficiency and
mitigates the time taken through algorithm training and provides early cancer
detection.

Figure 12: Accuracy score for liver cancer (GSE77314) in 5 kfolds without
using FGS

Figure 13: Accuracy score for liver cancer (GSE77314) in 5 kfolds when FGS
used

There was not a significant improvement in (TCGA) datasets because the number
of genes used was not large (971), so its use did not achieve a high level of
accuracy improvement. However, it improved the performance of the model by
reducing the number of selected genes that were used as identifiers to train
the technique. As a result, the FGS method decreased the number of genes from
971 to 25 genes only. In addition, a slight improvement in the accuracy as
well as the precision, we conclude that employing FGS in the worst cases will
give better accuracy and fewer genes, and that performed less time for
training the classifier models and provides early detection of cancer. The two
bar charts (15 and 15) illustrate the difference between the accuracy scores
in 5 kfolds when the classifier models were applied to the datasets with
omitting FGS and the accuracy score in 5 kfolds when the classifier applied to
the selected genes by FGS method.

Figure 14: Accuracy scores in 5 kfolds for the (TCGA) datasets without
applying FGS

Figure 15: Accuracy scores in 5 kfolds for the (TCGA) datasets when FGS
employed

For the majority of applied classifier models, and specifically, MLP, where
72% is the average accuracy score in 5 kfolds when omitting FGS, while 93%
when FGS is employed, good enhancement is obtained when the fuzzy gene
selection method is applied to thyroid cancer (GSE33630) datasets.
Additionally, the number of genes was reduced from 23516 to 76 genes, which
reduced the complexity, interpretability, and training time for algorithms as
well as enabled the early identification of cancer. The two bar graphs (17 and
17) show the differences in accuracy scores for five distinct classifier
models when the FGS approach is used in comparison to when it is not used.

Figure 16: Accuracy score in 5 kfolds for thyroid cancer (GSE33630) by
omitting FGS

Figure 17: Accuracy score in 5 kfolds for thyroid cancer (GSE33630) when FGS
used.

Briefly, multilayer perceptron achieved the highest average accuracy across
the six datasets when fuzzy gene selection was applied which was 96.5%. It
also, MLP has accomplished the highest improvement rate for the average
accuracy when the proposed fuzzy gene selection which was 27.3% . It can be
concluded that the highest improvement impact of fuzzy gene selection was when
a MLP classifier was employed and the accuracy improved from 69.2% before FGS
was applied while 96.5% when FGS was applied.
Based on the results that were explained previously, a full automated deep
neural network was proposed to analyze gene expression data as described in
(Figure 5). The proposed model attempted to achieve three main goals as
follows: The first goal, reducing the number of genes that would be used as
identifiers for training a classifier method in resulting that leads to reduce
the time consuming of training a model. Indeed, the proposed model succeeded
remarkably in reducing the number of genes as indicated in (Table 3 and Table
4). The second goal, enhancing the performance of the accuracy and other
evaluation measurement parameters and the aim was also accomplished where the
average accuracy was 96.5%. The third goal, selecting candidate genes as
putative targets for biologists to further investigate to determine whether
these genes simply useful for classification or are implicated in the
pathogenesis of these diseases.

##  5 Conclusion

In order to improve the machine learning performance for cancer
classification, this research introduces a novel fuzzy gene selection approach
for lowering the dimensionality (reducing the number of features) of gene
expression data. It also decreases the amount of time needed for algorithm
training. Using the commonly used measurement techniques ( Microarray and RNA-
seq) for estimating gene expression data, the proposed model was trained and
evaluated on six datasets obtained from TCGA and GEO. Three primary objectives
were accomplished by this work: to boost the effectiveness of classifier
techniques, help speed up the training process and cut down on the number of
chosen genes that are utilized as identifiers for the classifier training
model. The findings demonstrate that the suggested model (FGS-MLP) has the
best accuracy in the majority of the datasets studied, with accuracy levels
ranging from 93% at the lowest end to 99% at the top.

The average accuracy rating across six datasets is 96.5%. As a result, the
proposed model shows both the capacity to properly classify cancer and time
savings during the training phase. By more carefully choosing characteristics
(genes) from different cancer kinds, biologists can also benefit from the
selected genes in their study and early cancer detection. Furthermore, FGS may
also assist in reducing the complexity of a classifier method and avoiding or
at least mitigating the overfitting issue that typically arises when high
dimensionality datasets are used.

Regardless of the contributions and promising findings of this research, it
has some limitations. First, a limited number of datasets used that can more
datasets used for different cancer types especially RNA-seq data.
Additionally, no single classical ML classifier can continuously achieve the
best accuracy in all given datasets. Due to these limitations, future work
will make an effort to use more datasets for different cancer types and
propose a new classifier that can accurately and continuously classify gene
expression data.

## Declarations

  * •

Funding This research was partly funded by the Ministry of Higher Education
and Scientific Research in the Republic of Iraq, according to scholarship
number (22223) on (06/09/2017) to sponsor the first author to pursue his PhD
research.

  * •

Conflict of interest/Competing interests (check journal-specific guidelines
for which heading to use).
Not applicable

  * •

Ethics approval
Not applicable

  * •

Consent to participate

  * •

Consent for publication

  * •

Availability of data and materials. The original datasets that were employed
for cancer classification are freely available
at:https://github.com/mahmoodjasim/OrginalDataset. While the final datasets
that have been used after applying Fuzzy gene selection method are freely
available at:https://github.com/mahmoodjasim/Datasets-of-selected-genes

  * •

Code availability.
The codes used in this article are freely available
at:https://github.com/mahmoodjasim/Fuzzy-Gene-Selection-Code

  * •

Authors’ contributions

## References

  * [1] S. Shandilya and C. Chandankhede, ”Survey on recent cancer classification systems for cancer diagnosis,”International Conference on Wireless Communications, Signal Processing and Networking (WiSPNET), Chennai,2017, pp. 2590-2594, IEEE.
  * [2] J. Pati, ”Gene Expression Analysis for Early Lung Cancer Prediction Using Machine Learning Techniques: An Eco-Genomics Approach,” in IEEE Access, vol. 7, pp. 4232-4238, 2019.
  * [3] Wolff A, Bayerlová M, Gaedcke J, Kube D, Beißbarth T (2018) A comparative study of RNA-Seq and microarray data analysis on the two examples of rectal-cancer patients and Burkitt Lymphoma cells. PLOS ONE 13(5).
  * [4] Y. Piao and K. H. Ryu, ”Detection of differentially expressed genes using feature selection approach from RNA-Seq,” IEEE International Conference on Big Data and Smart Computing (BigComp), Jeju, 2017, pp. 304- 308\.
  * [5] D. Sun, M.Wang and A. Li, ”A Multimodal Deep Neural Network for Human Breast Cancer Prognosis Prediction by Integrating Multi-Dimensional Data,” in IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol.16, no.3, pp. 841-850,2019
  * [6] TCGA. (2012) The Somatic Mutation Profiles of 2,433 Breast Cancers Refines Their Genomic and Transcriptomic Landscapes.https://www.cbioportal.org
  * [7] ] J. Xu, P. Wu, Y. Chen, Q. Meng, H. Dawood and M. M. Khan, ”A Novel Deep Flexible Neural Forest Model for Classification of Cancer Subtypes Based on Gene Expression Data,” in IEEE Access, vol. 7, pp. 22086-22095, 2019.
  * [8] J. N. Weinstein et al., “The cancer genome atlas pan-cancer analysis project,” Nature Genet., vol. 45, no. 10, pp. 1113-1120, Sep. 2013.
  * [9] López-García G, Jerez JM, Franco L, Veredas FJ. Transfer learning with convolutional neural networks for cancer survival prediction using geneexpression data. PLoS One. 2020;15(3)
  * [10] P. N. Yeganeh and M. T. Mostafavi, ”Use of Machine Learning for Diagnosis of Cancer in Ovarian Tissues with a Selected mRNA Panel,” IEEE International Conference on Bioinformatics and Biomedicine (BIBM), Madrid, Spain, 2018, pp. 2429-2434
  * [11] Edgar R, Domrachev M, Lash AE. Gene Expression Omnibus: NCBI gene expression and hybridization array data repository, Nucleic Acids Res.,2002, vol. 30 (pg. 207-210).
  * [12] Weinstein, J.N., Collisson, E.A., Mills, G.B., Shaw, K.R.M., Ozenberger, B.A., Ellrott, K., Shmulevich, I., Sander, C., Stuart, J.M. and Cancer Genome Atlas Research Network, 2013. The cancer genome atlas pancancer analysis project. Nature genetics, 45(10), p.1113.
  * [13] J. Wu and C. Li, ”Feature Selection Based on Features Unit, ”International Conference on Information Science and Control Engineering (ICISCE), Changsha, 2017, pp. 330-333.
  * [14] Vergara, J.R.,review of feature selection methods based on mutual information. Neural Comput & Applic 24, 175–186 (2014).
  * [15] N. O. F. Elssied, O. Ibrahim, and A. H. Osman, “A novel feature selection based on one-way anova f-test for e-mail spam classification,” Research Journal of Applied Sciences, Engineering and Technology,vol. 7, no. 3, pp. 625–638, 2014.
  * [16] S. Ray, K. Alshouiliy, A. Roy, A. AlGhamdi and D. P. Agrawal, ” chi-squaredd Based Feature Selection for Stroke Prediction using AzureML,” 2020 Intermountain Engineering, Technology and Computing (IETC), 2020, pp. 1-6.
  * [17] Maharjan, Aashi, ”Machine Learning Approach for Predicting Cancer Using Gene Expression” (2020). UNLV Theses, Dissertations, Professional Papers, and Capstones. 3922.
  * [18] Alka Rani,Nishant K. Sinha, 2022. Support Vector Machine. [Online] Available at:https://www.sciencedirect.com/topics/computer-science/support-vector-machine
  * [19] Muhammad Ali Farooq, Peter Corcoran, Cosmin Rotariu, Waseem Shariff, ”Object Detection in Thermal Spectrum for Advanced Driver-Assistance Systems (ADAS)”, IEEE Access, vol.9, pp.156465-156481, 2021.
  * [20] C. Alippi and M. Roveri, ”Virtual k-fold cross validation: An effective method for accuracy assessment,” The 2010 International Joint Conference on Neural Networks (IJCNN), 2010, pp. 1-6.
  * [21] Yurong Zhong, ”The analysis of cases based on decision tree,”7th IEEE International Conference on Software Engineering and Service Science (ICSESS), 2016, pp. 142-147
  * [22] Hartatik, A. Purnomo, R. Hartono, and H. Nunawaro, “Naive Bayes Approach for Expert System Design of Children Skin Identification Based on Android,” IOP Conf. Ser. Mater. Sci. Eng., vol. 333, 2018.
  * [23] ] X. Wu, V. Kumar, J. R. Quinlan, J. Ghosh, Q. Yang, H. Motoda, G. J. McLachlan, A. Ng, B. Liu, S. Y. Philip et al., “Top 10 algorithms in data mining,” Knowledge and information systems, vol. 14, no. 1, pp. 1–37, 2008.
  * [24] A. H. Jahromi and M. Taheri, ”A non-parametric mixture of Gaussian naive Bayes classifiers based on local independent features,” 2017 Artificial Intelligence and Signal Processing Conference (AISP), 2017, pp. 209-212.
  * [25] Patil, T. R. Mrs. S. S. Sherekar.(2013): Performance Analysis of Naive Bayes and J48 Classification Algorithm for Data Classification. International Journal Of Computer Science And Applications, 6(2).
  * [26] Raizada RD, Lee YS. Smoothness without smoothing: why Gaussian naive Bayes is not naive for multi-subject searchlight studies. PLoS One. 2013;8(7)
  * [27] Xie, R., Wen, J., Quitadamo, A. et al. A deep auto-encoder model for gene expression prediction. BMC Genomics 18, 845 (2017).
  * [28] C. A. Ul Hassan, M. S. Khan and M. A. Shah, ”Comparison of Machine Learning Algorithms in Data classification,”International Conference on Automation and Computing (ICAC), Newcastle upon Tyne, United Kingdom,2018.
  * [29] K. N. C. Ferles and Y. Papanikolaou, “Cancer types: RNA sequencing values from tumor samples/tissues,” 2018. Distributed by Mendeley. [Online]. Available: https://data.mendeley.com/datasets/sf5n64hydt/1
  * [30] M. Khalsan et al., ”A Survey of Machine Learning Approaches Applied to Gene Expression Analysis for Cancer Prediction,” in IEEE Access, vol. 10, pp. 27522-27534, 2022.