<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.1 20151215//EN" "http://jats.nlm.nih.gov/publishing/1.1/JATS-journalpublishing1.dtd">
<article xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" article-type="research-article" dtd-version="1.1">
<front>
<journal-meta>
<journal-id journal-id-type="pmc">IASC</journal-id>
<journal-id journal-id-type="nlm-ta">IASC</journal-id>
<journal-id journal-id-type="publisher-id">IASC</journal-id>
<journal-title-group>
<journal-title>Intelligent Automation &#x0026; Soft Computing</journal-title>
</journal-title-group>
<issn pub-type="epub">2326-005X</issn>
<issn pub-type="ppub">1079-8587</issn>
<publisher>
<publisher-name>Tech Science Press</publisher-name>
<publisher-loc>USA</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">31039</article-id>
<article-id pub-id-type="doi">10.32604/iasc.2023.031039</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Smart Lung Tumor Prediction Using Dual Graph Convolutional Neural Network</article-title><alt-title alt-title-type="left-running-head">Smart Lung Tumor Prediction Using Dual Graph Convolutional Neural Network</alt-title><alt-title alt-title-type="right-running-head">Smart Lung Tumor Prediction Using Dual Graph Convolutional Neural Network</alt-title>
</title-group>
<contrib-group content-type="authors">
<contrib id="author-1" contrib-type="author" corresp="yes">
<name name-style="western"><surname>Alameen</surname><given-names>Abdalla</given-names></name><email>a.alameen@psau.edu.sa</email>
</contrib>
<aff id="aff-1"><institution>Department of Computer Science, College of Arts and Sciences, Prince Sattam Bin Abdulaziz University</institution>, <country>KSA</country></aff>
</contrib-group><author-notes><corresp id="cor1"><label>&#x002A;</label>Corresponding Author: Abdalla Alameen. Email: <email>a.alameen@psau.edu.sa</email></corresp></author-notes>
<pub-date pub-type="epub" date-type="pub" iso-8601-date="2022-08-24"><day>24</day>
<month>08</month>
<year>2022</year></pub-date>
<volume>36</volume>
<issue>1</issue>
<fpage>369</fpage>
<lpage>383</lpage>
<history>
<date date-type="received"><day>08</day><month>4</month><year>2022</year></date>
<date date-type="accepted"><day>21</day><month>6</month><year>2022</year></date>
</history>
<permissions>
<copyright-statement>&#x00A9; 2023 Alameen</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Alameen</copyright-holder>
<license xlink:href="https://creativecommons.org/licenses/by/4.0/">
<license-p>This work is licensed under a <ext-link ext-link-type="uri" xlink:type="simple" xlink:href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International License</ext-link>, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</license-p>
</license>
</permissions>
<self-uri content-type="pdf" xlink:href="TSP_IASC_31039.pdf"></self-uri>
<abstract>
<p>A significant advantage of medical image processing is that it allows non-invasive exploration of internal anatomy in great detail. It is possible to create and study 3D models of anatomical structures to improve treatment outcomes, develop more effective medical devices, or arrive at a more accurate diagnosis. This paper aims to present a fused evolutionary algorithm that takes advantage of both whale optimization and bacterial foraging optimization to optimize feature extraction. The classification process was conducted with the aid of a convolutional neural network (CNN) with dual graphs. Evaluation of the performance of the fused model is carried out with various methods. In the initial input Computer Tomography (CT) image, 150 images are pre-processed and segmented to identify cancerous and non-cancerous nodules. The geometrical, statistical, structural, and texture features are extracted from the preprocessed segmented image using various methods such as Gray-level co-occurrence matrix (GLCM), Histogram-oriented gradient features (HOG), and Gray-level dependence matrix (GLDM). To select the optimal features, a novel fusion approach known as Whale-Bacterial Foraging Optimization is proposed. For the classification of lung cancer, dual graph convolutional neural networks have been employed. A comparison of classification algorithms and optimization algorithms has been conducted. According to the evaluated results, the proposed fused algorithm is successful with an accuracy of 98.72&#x0025; in predicting lung tumors, and it outperforms other conventional approaches.</p>
</abstract>
<kwd-group kwd-group-type="author">
<kwd>CNN</kwd>
<kwd>dual graph convolutional neural network</kwd>
<kwd>GLCM</kwd>
<kwd>GLDM</kwd>
<kwd>HOG</kwd>
<kwd>image processing</kwd>
<kwd>lung tumor prediction</kwd>
<kwd>whale bacterial foraging optimization</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1">
<label>1</label>
<title>Introduction</title>
<p>Based on the structure of the cells, lung carcinoma is classified into small-cell carcinomas and non-small-cell carcinomas. More than 85&#x0025; of lung cancers are caused by long-term tobacco use&#x200E; [<xref ref-type="bibr" rid="ref-1">1</xref>]. There are 15&#x0025;&#x2013;20&#x0025; of lung tumors among people who have never smoked, as a result of factors such as air pollution, asbestos, radon gas, and secondhand smoke. According to the size and location of the lymph nodes on the tumor, lung cancer can be divided into I to IV categories. A timely diagnosis of this lung cancer may reduce the mortality rate, or else the chances of survival are high&#x200E; [<xref ref-type="bibr" rid="ref-2">2</xref>]. Radiology and CT are the traditional methods to detect lung tumors due to their lower distortion levels and the ability to detect malignant growths [<xref ref-type="bibr" rid="ref-3">3</xref>]. The CT image depicts a lung malignancy with irregular and regular lung structures.</p>
<p>An image is preprocessed by normalizing, enhancing quality, and reducing distortion. Various filters in both the frequency and spatial domains are applied to enhance the input image&#x200E; [<xref ref-type="bibr" rid="ref-4">4</xref>]. The adaptive median filter eliminates the noise issues associated with the median filter. In the Wiener filter, low pass filters are used to minimize noise and high pass filters are used for deconvolution on the CT image. In medical imaging, segmentation is considered the most dangerous task for locating the nodule region to extract its features. Different approaches are used for segmentation such as watershed edge-based approaches [<xref ref-type="bibr" rid="ref-5">5</xref>], thresholding [<xref ref-type="bibr" rid="ref-6">6</xref>], and region-based segmentation [<xref ref-type="bibr" rid="ref-7">7</xref>]. Thresholding and morphological operation are used to determine the tumor region from the segmented nodule. The lung nodule region is segmented and statistical, textual, geometric, and shape-based features are extracted [<xref ref-type="bibr" rid="ref-8">8</xref>]. There are several features present in medical neuroimaging, such as gray-level co-occurrence matrix (GLCM), gray level run length matrix (GLRLM), local binary pattern (LBP) and histogram, and gray level dependence matrix (GLDM)&#x200E; [<xref ref-type="bibr" rid="ref-9">9</xref>]. These feature sets are used to evaluate the decision-making process.</p>
<p>To reduce the dimension of the feature space, an evolutionary fusion technique referred to as Whale Optimization with Adaptive PSO (WASO-APSO) has been used to remove redundant features&#x200E; [<xref ref-type="bibr" rid="ref-10">10</xref>,<xref ref-type="bibr" rid="ref-11">11</xref>]. To improve the classification stage, the features are grouped using LDA (linear discriminate algorithm) [<xref ref-type="bibr" rid="ref-12">12</xref>,<xref ref-type="bibr" rid="ref-13">13</xref>]. In this study, the whale optimization approach is fused with bacterial foraging optimization to enhance the feature selection for the classification phase. The classification is a major step in determining parameters such as accuracy, sensitivity, and specificity of the classifier that aids in the diagnosis of lung cancer. In this study, support vector machines, convolutional neural networks, and dual graph convolutional neural networks are compared. Based on a linear function from statistical theory, a support vector machine is a multiclass model used to predict medical imaging results&#x200E; [<xref ref-type="bibr" rid="ref-14">14</xref>]. Recently, deep learning has been widely utilized in medical applications and problem-solving techniques. The convolutional neural network and its variants take into account the fully connected neurons with activation functions and use backpropagation to adjust weights&#x200E; [<xref ref-type="bibr" rid="ref-15">15</xref>].</p>
<p>Messay et al. developed a lung tumor detection system using thresholding and a rule-based approach&#x200E; [<xref ref-type="bibr" rid="ref-16">16</xref>]. Support Vector Machine (SVM) and rule-based approach have been implemented here to detect the false positive rate. Ant colony optimization approach has been used to find the edges and given as input to a circular neighbor algorithm to detect the lung nodule in. Bari et a. used a genetic algorithm to detect the relevant lung nodule feature for SVM classification [<xref ref-type="bibr" rid="ref-17">17</xref>]. Kumar et al. analyzed five algorithms for the detection of lung tumors [<xref ref-type="bibr" rid="ref-18">18</xref>]. The algorithms are k-means clustering, k-median clustering, inertia-weighted particle swarm optimization (IWPSO), particle swarm optimization (PSO), and guaranteed convergence particle swarm optimization (GCPSO). With the experimental analysis, they proved that for preprocessing adaptive median filter performs better and for classification GCPSO secured high accuracy of 95.89&#x0025;.</p>
<p>The remaining section of this smart lung cancer detection is structured as follows: Section 2 discusses the related literature. Section 3 discusses the materials and methods. Experimented results are discussed in Section 4 and Section 5 concludes the proposed lung tumor detection system with its future work.</p>
</sec>
<sec id="s2">
<label>2</label>
<title>Related Work</title>
<p>The early detection of cancer may increase the chance of a patient&#x2019;s survival. Researchers are rapidly developing computational intelligence techniques to detect disease patterns with medical imaging. In recent research on medical imaging, artificial intelligence [<xref ref-type="bibr" rid="ref-19">19</xref>,<xref ref-type="bibr" rid="ref-20">20</xref>], pattern recognition [<xref ref-type="bibr" rid="ref-21">21</xref>], and computer vision have been applied to data visualization concepts. To extract the abnormalities from CT images, computer-aided diagnosis is a challenging task for radiologists to take the necessary actions based on their decision-making. This section reviews relevant literature regarding lung tumor detection.</p>
<p>For lung CT image segmentation, Kumar et al. developed a hybrid 2D Otsu method with a modified artificial bee colony approach [<xref ref-type="bibr" rid="ref-18">18</xref>]. Uzelaltinbulat et al. applied thresholding and morphological operations to segment lung tumors [<xref ref-type="bibr" rid="ref-22">22</xref>]. Joon et al. utilized k-means clustering with fuzzy c-means to identify cancerous and non-cancerous lung nodules using texture and structural features [<xref ref-type="bibr" rid="ref-23">23</xref>]. Wang et al. used a multilevel image thresholding segmentation method and the best exponential k gravitational search method&#x200E; [<xref ref-type="bibr" rid="ref-24">24</xref>]. Prabukumar et al. developed a hybrid method for segmentation with texture, statistics, and geometrical features called Fuzzy C Mean with Region Growing Method&#x200E; [<xref ref-type="bibr" rid="ref-25">25</xref>]. The features have been enhanced by using a cuckoo search and an SVM classifier has been used to obtain an accuracy of 98.5&#x0025;. Recently, Naqi et al. proposed a hybrid method called Active Contour Model (ACM), combining 3D neighborhood connectivity with 3D geometric properties for nodule detection &#x200E; [<xref ref-type="bibr" rid="ref-26">26</xref>]. Comparative analysis with na&#x00EF;ve Bayes, SVM, and k-nearest neighbors (KNN) is performed., Zhou et al. proposed a novel computer-aided diagnosis method using the Convolutional Neural Network (CNN) for the detection of lung tumors on PET imaging [<xref ref-type="bibr" rid="ref-27">27</xref>]. The system has been evaluated for recall, precision, and F-score.</p>
<p>For lung CT image segmentation, Kumar et al. [<xref ref-type="bibr" rid="ref-18">18</xref>] developed a hybrid 2D Otsu method with a modified artificial bee colony approach. Uzelaltinbulat et al. applied thresholding and morphological operations to segment lung tumors [<xref ref-type="bibr" rid="ref-22">22</xref>]. Joon et al. utilized k-means clustering with fuzzy c-means to identify cancerous and non-cancerous lung nodules using texture and structural features [<xref ref-type="bibr" rid="ref-23">23</xref>]. Wang et al. used a multilevel image thresholding segmentation method and the best exponential k gravitational search method [<xref ref-type="bibr" rid="ref-24">24</xref>]. Prabukumar et al. developed a hybrid method for segmentation with texture, statistics, and geometrical features called Fuzzy C Mean with Region Growing Method &#x200E;[<xref ref-type="bibr" rid="ref-25">25</xref>]. The features have been enhanced by using a cuckoo search and an SVM classifier has been used to obtain an accuracy of 98.5&#x0025;. Recently, Naqi et al. proposed a hybrid method called Active Contour Model (ACM), combining 3D neighborhood connectivity with 3D geometric properties for nodule detection &#x200E;[<xref ref-type="bibr" rid="ref-26">26</xref>]. Comparative analysis with na&#x00EF;ve Bayes, SVM, and k-nearest neighbors (KNN) is performed. Zhou et al. proposed a novel computer-aided diagnosis method using the Convolutional Neural Network (CNN) for the detection of lung tumors on PET imaging [<xref ref-type="bibr" rid="ref-27">27</xref>].</p>
</sec>
<sec id="s3">
<label>3</label>
<title>Proposed Materials and Method Descriptions</title>
<p><xref ref-type="fig" rid="fig-1">Fig. 1</xref> illustrates the materials and proposed methodologies of the computer-aided diagnosis (CAD) system for the smart detection of lung tumors. This system has five steps, including CT image preprocessing, Image segmentation using thresholding methods and morphological operations, Feature extraction by using GLM, GLRLM, and HOG, optimization with W-BFOA and, Classification by using Dual Graph CNN (DGCNN).</p>
<fig id="fig-1">
<label>Figure 1</label>
<caption>
<title>Overview of proposed lung-tumor prediction system</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="IASC_31039-fig-1.png"/>
</fig>
<sec id="s3_1">
<label>3.1</label>
<title>Image Pre-Processing</title>
<p>Based on 150 CT images of tumorous lung and non-tumor patients obtained by the NCI Lung Cancer Database Consortium, the proposed CAD system called smart lung tumor detection has been implemented [<xref ref-type="bibr" rid="ref-28">28</xref>]. Preprocessing of the input image is considered a significant phase in research related to clinical applications of neuroimaging for improving image quality. In this paper, we perform preprocessing steps such as normalization, noise removal, image enhancement, and augmentation of the input image to produce an improved image,</p>
<p>It has been found that an adaptive median filter (AMF) coupled with a Wiener filter (WF) can be used to remove noise from a normalized input image with a minimum mean square error. An adaptive median filter can address some of the issues associated with the median filter (MF), including how it is only effective on salt and pepper noise, inefficient when the spatial density of the noise is high, and does not provide proper smoothing for large kernel sizes. Unlike MF, Adaptive MF employs a variable kernel size, and all pixels are not replaced with the median value. It consists of two steps, namely (I) identifying the median value for the kernel, and (II) determining whether the current pixel value is salt and pepper noise (impulse).</p>
<p>Using AMF, the denoise image is further improved using WF with minimum mean square error. In <xref ref-type="disp-formula" rid="eqn-1">Eq. (1)</xref>, WF is a statistical method to reduce image blurring and smoothen the image effect. <xref ref-type="fig" rid="fig-2">Fig. 2</xref> illustrates the enhanced CT image using AMF and WF.<disp-formula id="eqn-1"><label>(1)</label>
<mml:math id="mml-eqn-1" display="block"><mml:mi>F</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>m</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:msubsup><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mi>N</mml:mi></mml:msubsup><mml:mo>&#x2061;</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mi>w</mml:mi><mml:mo stretchy="false">[</mml:mo><mml:mrow><mml:mi>m</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>i</mml:mi></mml:mrow><mml:mo stretchy="false">]</mml:mo></mml:math>
</disp-formula></p>
<fig id="fig-2">
<label>Figure 2</label>
<caption>
<title>Filtered CT images</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="IASC_31039-fig-2.png"/>
</fig>
<p>To avoid the overfitting issue and satisfy the training process, network augmentation is being utilized. Image segmentation involves the process of separating images into parts based on objects or other relevant information. Using this method, the image becomes useful data for further analysis. Based on Shakeel et al., the purpose of image segmentation is to identify the boundaries and objects within the image &#x200E;[<xref ref-type="bibr" rid="ref-29">29</xref>]. The proposed work uses thresholding to segment CT images, while morphological operations are used to smooth the region of interest.</p>
<p>One of the simplest forms of segmentation is the threshold which segments grayscale images into binary images. If a pixel value is greater than the threshold value, that pixel is segmented as an object, otherwise as a boundary. Morphological mathematical operations are applied to the possible locating of a particular structuring element to smoothen the region of interest. Assume D is the binary image and B is the structuring element then the morphological operations such as Erosion, Dilation, Opening and Closing are depicted in <xref ref-type="disp-formula" rid="eqn-2">Eqs. (2)&#x2013;</xref><xref ref-type="disp-formula" rid="eqn-5">(5)</xref> respectively. <xref ref-type="fig" rid="fig-3">Fig. 3</xref> illustrates the thresholding-morphological operation-based segmentation.</p>
<fig id="fig-3">
<label>Figure 3</label>
<caption>
<title>Thresholding-morphological operation based segmentation</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="IASC_31039-fig-3.png"/>
</fig>
<p><disp-formula id="eqn-2"><label>(2)</label>
<mml:math id="mml-eqn-2" display="block"><mml:mi>E</mml:mi><mml:mi>r</mml:mi><mml:mi>o</mml:mi><mml:mi>s</mml:mi><mml:mi>i</mml:mi><mml:mi>o</mml:mi><mml:mi>n</mml:mi><mml:mo>&#x003A;</mml:mo><mml:mi>D</mml:mi><mml:mrow><mml:mspace width="thickmathspace" /><mml:mo>&#x2296;</mml:mo></mml:mrow><mml:mspace width="thickmathspace" /><mml:mi>B</mml:mi><mml:mo>=</mml:mo><mml:mo fence="false" stretchy="false">{</mml:mo><mml:mi>A</mml:mi><mml:mo fence="false" stretchy="false">|</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mi>B</mml:mi><mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mi>A</mml:mi></mml:msub><mml:mo>&#x2286;</mml:mo><mml:mi>D</mml:mi><mml:mo fence="false" stretchy="false">}</mml:mo></mml:math>
</disp-formula></p>
<p><disp-formula id="eqn-3"><label>(3)</label>
<mml:math id="mml-eqn-3" display="block"><mml:mi>D</mml:mi><mml:mi>i</mml:mi><mml:mi>l</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>i</mml:mi><mml:mi>o</mml:mi><mml:mi>n</mml:mi><mml:mo>&#x003A;</mml:mo><mml:mspace width="thinmathspace" /><mml:mspace width="thickmathspace" /><mml:mi>D</mml:mi><mml:mo>&#x2295;</mml:mo><mml:mi>B</mml:mi><mml:mo>=</mml:mo><mml:mo fence="false" stretchy="false">{</mml:mo><mml:mi>A</mml:mi><mml:mo fence="false" stretchy="false">|</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mi>B</mml:mi><mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mi>A</mml:mi></mml:msub><mml:mrow><mml:mo>&#x2229;</mml:mo></mml:mrow><mml:mo>&#x2061;</mml:mo><mml:mi>D</mml:mi><mml:mo>&#x2260;</mml:mo><mml:mi mathvariant="normal">&#x2205;</mml:mi><mml:mo fence="false" stretchy="false">}</mml:mo></mml:math>
</disp-formula></p>
<p><disp-formula id="eqn-4"><label>(4)</label>
<mml:math id="mml-eqn-4" display="block"><mml:mi>O</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi>g</mml:mi><mml:mo>&#x003A;</mml:mo><mml:mi>D</mml:mi><mml:mspace width="thickmathspace" /><mml:mrow><mml:mo>&#x2296;</mml:mo></mml:mrow><mml:mspace width="thickmathspace" /><mml:mi>B</mml:mi><mml:mo>=</mml:mo><mml:mi>D</mml:mi><mml:mrow><mml:mtext>&#xA0;</mml:mtext><mml:mo>&#x2296;</mml:mo><mml:mtext>&#xA0;</mml:mtext></mml:mrow><mml:mi>B</mml:mi><mml:mo>&#x2295;</mml:mo><mml:mi>D</mml:mi><mml:mi>B</mml:mi></mml:math>
</disp-formula></p>
<p><disp-formula id="eqn-5"><label>(5)</label>
<mml:math id="mml-eqn-5" display="block"><mml:mspace width="thickmathspace" /><mml:mi>C</mml:mi><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:mi>s</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi>g</mml:mi><mml:mo>&#x003A;</mml:mo><mml:mspace width="thinmathspace" /><mml:mi>D</mml:mi><mml:mrow><mml:mtext>&#xA0;</mml:mtext><mml:mo>&#x2296;</mml:mo><mml:mtext>&#xA0;</mml:mtext></mml:mrow><mml:mi>B</mml:mi><mml:mo>=</mml:mo><mml:mi>D</mml:mi><mml:mo>&#x2295;</mml:mo><mml:mi>B</mml:mi><mml:mo>&#x2295;</mml:mo><mml:mi>B</mml:mi></mml:math>
</disp-formula></p>
</sec>
<sec id="s3_2">
<label>3.2</label>
<title>Feature Extraction</title>
<p>After segmentation, lung nodule pattern information is obtained in the feature extraction phase. From each segmented nodule, this proposed feature extraction method extracts various geometrical, texture, statistical and structural features. The techniques such as GLCM, GLRLM, and HOG are used for feature extraction. GLCM is a second-order statistics approach that considers the relationship between couples of pixels. GLRLM obtains a higher-order statistical method that extracts the features with gray levels pixels that are occurring continuously. Metaheuristic approaches mimic the biological phenomenon of nature to solve the real work applications. In this study, whale optimization and bacterial foraging optimization are combined to select the optimal features to improve the prediction of lung tumor outcomes. Standard Whale Optimization Algorithm (WOA) simulates the behavior of predation by whales through swarm intelligence.</p>
<p>In the WOA approach, first, the prey&#x2019;s location and its surrounding are recognized by the whale. In some situations, the whale didn&#x2019;t find the prey&#x2019;s location. In that case, the current possible prey position is the target prey and the remaining individuals in the prey are moving to that optimal position. Once the best possible solution is found, other individuals also update their positions. This behavior is mathematically expressed as follows in <xref ref-type="disp-formula" rid="eqn-6">Eqs. (6)</xref> and <xref ref-type="disp-formula" rid="eqn-7">(7)</xref>.</p>
<p><disp-formula id="eqn-6"><label>(6)</label>
<mml:math id="mml-eqn-6" display="block"><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mi>X</mml:mi><mml:msup><mml:mspace width="thickmathspace" /><mml:mo>&#x2217;</mml:mo></mml:msup><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mi>P</mml:mi><mml:mo>.</mml:mo><mml:mi>D</mml:mi></mml:math>
</disp-formula></p>
<p><disp-formula id="eqn-7"><label>(7)</label>
<mml:math id="mml-eqn-7" display="block"><mml:mi>D</mml:mi><mml:mo>=</mml:mo><mml:mo fence="false" stretchy="false">|</mml:mo><mml:mrow><mml:mi>L</mml:mi><mml:mo>.</mml:mo><mml:mi>X</mml:mi><mml:msup><mml:mspace width="thickmathspace" /><mml:mo>&#x2217;</mml:mo></mml:msup><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo fence="false" stretchy="false">|</mml:mo></mml:math>
</disp-formula>where, <italic>t</italic>: current no. of iterations, <inline-formula id="ieqn-13">
<mml:math id="mml-ieqn-13"><mml:mi>X</mml:mi><mml:msup><mml:mspace width="thickmathspace" /><mml:mo>&#x2217;</mml:mo></mml:msup><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>
</inline-formula>: vector of prey current position, <italic>X(t)</italic>: vector of prey position, <italic>&#x007C; &#x007C;</italic>: an absolute value, and <italic>P</italic> and <italic>L</italic>-vectors representing the size of surroundings (or) coefficients. The vectors <italic>P</italic> and <italic>L</italic> are calculated as follows in the <xref ref-type="disp-formula" rid="eqn-8">Eqs. (8)</xref> and <xref ref-type="disp-formula" rid="eqn-9">(9)</xref>.</p>
<p><disp-formula id="eqn-8"><label>(8)</label>
<mml:math id="mml-eqn-8" display="block"><mml:mi>P</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mi>a</mml:mi><mml:mo>.</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>r</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>a</mml:mi></mml:math>
</disp-formula></p>
<p><disp-formula id="eqn-9"><label>(9)</label>
<mml:math id="mml-eqn-9" display="block"><mml:mi>L</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mi>r</mml:mi></mml:math>
</disp-formula>where, r: a random number in the range [0, 1], a: control parameter, and for the number of iterations it decreases the value in the range 2 to 0 as stated in <xref ref-type="disp-formula" rid="eqn-10">Eq. (10)</xref>, and <inline-formula id="ieqn-14">
<mml:math id="mml-ieqn-14"><mml:msub><mml:mi>T</mml:mi><mml:mi>m</mml:mi></mml:msub></mml:math>
</inline-formula>: maximum number of iterations.<disp-formula id="eqn-10"><label>(10)</label>
<mml:math id="mml-eqn-10" display="block"><mml:mi>a</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mn>2</mml:mn><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi>m</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math>
</disp-formula></p>
<p>The humpback whale&#x2019;s bubble net behavior is within the encirclement as shown in <xref ref-type="fig" rid="fig-4">Fig. 4</xref>, the whale is moving toward the prey along the spiral path. This behavior is mathematically modeled with two steps such as the shrinking inspiring method and spiral update position respectively.</p>
<fig id="fig-4">
<label>Figure 4</label>
<caption>
<title>Bubble-net foraging of the whale &#x200E;[<xref ref-type="bibr" rid="ref-30">30</xref>]</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="IASC_31039-fig-4.png"/>
</fig>
<p>In the first step, the convergence factor is reduced using the <xref ref-type="disp-formula" rid="eqn-8">Eqs. (8)&#x2013;</xref><xref ref-type="disp-formula" rid="eqn-10">(10)</xref>. The second step to updating the position is to calculate the distance from the individual whale to the current position. Simulate the whale to capture food in the spiral mathematically as in <xref ref-type="disp-formula" rid="eqn-11">Eq. (11)</xref>.</p>
<p><disp-formula id="eqn-11"><label>(11)</label>
<mml:math id="mml-eqn-11" display="block"><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:msup><mml:mi>D</mml:mi><mml:mn>1</mml:mn></mml:msup><mml:mo>.</mml:mo><mml:mspace width="thickmathspace" /><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>l</mml:mi></mml:mrow></mml:msup><mml:mo>.</mml:mo><mml:mi>cos</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mn>2</mml:mn><mml:mi>&#x03C0;</mml:mi><mml:mi>l</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo><mml:mi>X</mml:mi><mml:msup><mml:mspace width="thickmathspace" /><mml:mo>&#x2217;</mml:mo></mml:msup><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>
</disp-formula></p>
<p><disp-formula id="eqn-12"><label>(12)</label>
<mml:math id="mml-eqn-12" display="block"><mml:msup><mml:mi>D</mml:mi><mml:mn>1</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mo fence="false" stretchy="false">|</mml:mo><mml:mrow><mml:msup><mml:mi>X</mml:mi><mml:mo>&#x2217;</mml:mo></mml:msup><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo fence="false" stretchy="false">|</mml:mo></mml:math>
</disp-formula></p>
<p>where <italic>D<sup>1</sup></italic>: the distance between whale <italic>i</italic> to the current position, <italic>b</italic>: constant to define the spiral logarithmic form, <italic>l</italic>: a random number between [&#x2212;1, 1]. Spiral and contraction envelopment are performed with equal probability to obtain the synchronous model.</p>
<p>Randomly select the whale with the current position if <inline-formula id="ieqn-15">
<mml:math id="mml-ieqn-15"><mml:mo fence="false" stretchy="false">|</mml:mo><mml:mi>A</mml:mi><mml:mo fence="false" stretchy="false">|</mml:mo><mml:mo>&#x2265;</mml:mo><mml:mn>1</mml:mn></mml:math>
</inline-formula>. It will make the whale far away from the current target and global exploration characteristics are enhanced, it will find the best prey position to replace the current whale as stated in <xref ref-type="disp-formula" rid="eqn-13">Eq. (13)</xref></p>
<p><disp-formula id="eqn-13"><label>(13)</label>
<mml:math id="mml-eqn-13" display="block"><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:mi>P</mml:mi><mml:mo>.</mml:mo><mml:mi>L</mml:mi></mml:math>
</disp-formula></p>
<p><disp-formula id="eqn-14"><label>(14)</label>
<mml:math id="mml-eqn-14" display="block"><mml:mi>D</mml:mi><mml:mo>=</mml:mo><mml:mo fence="false" stretchy="false">|</mml:mo><mml:mrow><mml:mi>L</mml:mi><mml:mo>.</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo fence="false" stretchy="false">|</mml:mo></mml:math>
</disp-formula>where <italic>rnd</italic>: random number (vector) of the whale position.</p>
<p>The bacterial Foraging Optimization Algorithm (BFO) was proposed in 2002 to imitate the food searching attitude of a swarm of bacteria. Searching for the nutrients called global solution by bacteria in n-dimensional space. This will use three operations such as chemotaxis, reproduction, and elimination-dispersal events. The bacteria find the best solution with the help of the locomotive flagella linked to it. The swarm is defined that flagella rotation in a counter-clock direction that takes action to bacteria in a forwarding direction. If the flagella rotation is clockwise then each flagellum is behaving independently in a random direction. During the chemotactic progress, bacteria alternate the modes as tumble and run. Tumble is modeled as single chemotactic progress by a run. Among the total population called &#x2018;<italic>B</italic>&#x2019; bacteria, <italic>&#x03B8; (p, c, rp, e)</italic> denotes the current position of <italic>p<sup>th</sup></italic> bacteria during <italic>c<sup>th</sup></italic> chemotactic, <italic>rp<sup>th</sup></italic> reproduction, and e<sup>th</sup> elimination. The location of the succeeding bacteria is exhibited as in <xref ref-type="disp-formula" rid="eqn-15">Eq. (15)</xref>.</p>
<p><disp-formula id="eqn-15"><label>(15)</label>
<mml:math id="mml-eqn-15" display="block"><mml:mi>&#x03B8;</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>c</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>r</mml:mi><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>e</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mi>&#x03B8;</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>r</mml:mi><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>e</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo><mml:mi>C</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>c</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>.</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>&#x03D5;</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>c</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:msqrt><mml:msup><mml:mi>&#x03D5;</mml:mi><mml:mi>T</mml:mi></mml:msup><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>c</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>.</mml:mo><mml:mi>&#x03D5;</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>c</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:msqrt></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math>
</disp-formula></p>
<p>where <italic>C(p, c)</italic>: run-length unit of p<sup>th</sup> bacteria and <inline-formula id="ieqn-16">
<mml:math id="mml-ieqn-16"><mml:mi>&#x03D5;</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>c</mml:mi></mml:math>
</inline-formula>) : vector of random direction in the range [&#x2212;1, 1]. If <italic>p<sup>th</sup></italic> bacteria improve the fitness function <inline-formula id="ieqn-17">
<mml:math id="mml-ieqn-17"><mml:mi>J</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>r</mml:mi><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>e</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math>
</inline-formula> as the next step of chemotactic, the bacteria take a similar direction move or else bacteria tumble in a random direction to find the best possible solution. The number of runs is limited to the initialized count <italic>Nr</italic>. Nutrients searched for <italic>Nc</italic> chemotactic steps. After this bacteria move to the reproduction phase to work out each bacteria&#x2019;s health with its ability to locate the food during its life span. For each foraging bacteria&#x2019;s health is modeled as in <xref ref-type="disp-formula" rid="eqn-16">Eq. (16)</xref>.<disp-formula id="eqn-16"><label>(16)</label>
<mml:math id="mml-eqn-16" display="block"><mml:msubsup><mml:mi>E</mml:mi><mml:mrow><mml:mi>h</mml:mi><mml:mi>e</mml:mi><mml:mi>a</mml:mi><mml:mi>l</mml:mi><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow><mml:mi>p</mml:mi></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>N</mml:mi><mml:mi>c</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>&#x2061;</mml:mo><mml:mi>E</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>r</mml:mi><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>e</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math>
</disp-formula></p>
<p>All &#x2018;<italic>B</italic>&#x2019; bacteria are ordered based on their health value in ascending order. To make the population of bacteria constant, at least <italic>B/2</italic> healthy bacteria gets replaced with the remaining bacteria that are healthier. After <italic>Nrp</italic> reproduction steps, based on the probability of <italic>P<sub>ed</sub></italic><sub>,</sub> some of the bacteria are forcefully moved to a random search space which will avoid the local optimal solution to provide the best possible solution in the search area.</p>
<p>Fused WBFO is the novel optimization algorithm that works on both WO and BFO optimization algorithms. Based on WO&#x2019;s best possible solution finding strategy using the bubble net foraging approach, a globally optimal solution is found from the swam population. With this idea to give space to bacteria, the bacteria optimal solution is compared with the global optimal solution in chemotaxis iteration. The bacteria swim until the best possible solution is found. In BFO, the chemotaxis is the major step and WO is used here to update the arbitrary variables.</p>
<p>Based on the energy, bacteria are sorted in ascending order. Due to a lack of energy, some of the bacteria are dying. The remaining are inherited from the bacterial position of their parents. The bacteria are dispersed as per the <xref ref-type="disp-formula" rid="eqn-17">Eq. (17)</xref><disp-formula id="eqn-17"><label>(17)</label>
<mml:math id="mml-eqn-17" display="block"><mml:mi>S</mml:mi><mml:mi>e</mml:mi><mml:mi>t</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>B</mml:mi><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>i</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>B</mml:mi><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>i</mml:mi><mml:mi>a</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mi>E</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>B</mml:mi><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>i</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>B</mml:mi><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>i</mml:mi><mml:mi>a</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>B</mml:mi><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>i</mml:mi><mml:mi>a</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x2217;</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math>
</disp-formula></p>
<p>The workflow of the proposed optimization algorithm is shown in <xref ref-type="fig" rid="fig-5">Fig. 5</xref>. Until the maximum number of iterations is reached, the parameters, location, and fitness functions are updated. If the termination condition and elimination dispersion are reached then the best solution is returned. For chemotaxis count, check the parameter value of P, if it is greater than 1 then the current position and bacteria dispersion are calculated, or else the position of the whale is updated. The optimal feature subset using the proposed WBFO has been given as input to the classification phase for the detection of lung tumors.</p>
<fig id="fig-5">
<label>Figure 5</label>
<caption>
<title>Proposed WBFO workflow</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="IASC_31039-fig-5.png"/>
</fig>
<p>Each node of the NN graph is represented with the features extracted. The graph local and global consistency is considered by dual graph CNN with the implementation of two CNN. In Dual graph CNN, the dataset is represented as a matrix D <inline-formula id="ieqn-18">
<mml:math id="mml-ieqn-18"><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mi>R</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:math>
</inline-formula>, and data points are represented as <inline-formula id="ieqn-19">
<mml:math id="mml-ieqn-19"><mml:mi>D</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:msub><mml:mi>d</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:msub><mml:mi>d</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mspace width="thickmathspace" /><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mo>&#x2026;</mml:mo><mml:msub><mml:mi>d</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:math>
</inline-formula>. For the initial points, the label y is represented as <inline-formula id="ieqn-20">
<mml:math id="mml-ieqn-20"><mml:mi>y</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:msub><mml:mi>y</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mo>&#x2026;</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:math>
</inline-formula>. The structure of the graph is denoted as an adjacency matrix called <inline-formula id="ieqn-21">
<mml:math id="mml-ieqn-21"><mml:mi>A</mml:mi><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mi>R</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:math>
</inline-formula>. Dual graph CNN is constructed with local and global consistency (GL) and ensemble. Local consistency (LC) called <inline-formula id="ieqn-22">
<mml:math id="mml-ieqn-22"><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>l</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:math>
</inline-formula> is a type of feed-forward network. Feature matrix F and adjacency matrix A are the input of this model. The output of LC is z for hidden layer &#x2018;i&#x2019; is denoted in <xref ref-type="disp-formula" rid="eqn-18">Eq. (18)</xref>.<disp-formula id="eqn-18"><label>(18)</label>
<mml:math id="mml-eqn-18" display="block"><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>n</mml:mi><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>l</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mi>i</mml:mi></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mi>X</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:msup><mml:mi>z</mml:mi><mml:mi>i</mml:mi></mml:msup><mml:mo>=</mml:mo><mml:mi>&#x03C3;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mi>X</mml:mi><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:mrow></mml:mrow></mml:msup><mml:mrow><mml:mover><mml:mi>A</mml:mi><mml:mo stretchy="false">&#x00AF;</mml:mo></mml:mover></mml:mrow><mml:msup><mml:mi>X</mml:mi><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:mrow></mml:mrow></mml:msup><mml:msup><mml:mi>z</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:msup><mml:mi>w</mml:mi><mml:mi>i</mml:mi></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</disp-formula>where, <inline-formula id="ieqn-23">
<mml:math id="mml-ieqn-23"><mml:mrow><mml:mover><mml:mi>A</mml:mi><mml:mo stretchy="false">&#x00AF;</mml:mo></mml:mover></mml:mrow><mml:mo>=</mml:mo><mml:mi>A</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:math>
</inline-formula>, I-identity matrix, <inline-formula id="ieqn-24">
<mml:math id="mml-ieqn-24"><mml:mrow><mml:mover><mml:mi>A</mml:mi><mml:mo stretchy="false">&#x00AF;</mml:mo></mml:mover></mml:mrow></mml:math>
</inline-formula>&#x2013;adjacency matrix with self-loops, <italic>X</italic>-normalized adjacency matrix in normalized form, z-output, w-trainable parameter, and <inline-formula id="ieqn-25">
<mml:math id="mml-ieqn-25"><mml:mi>&#x03C3;</mml:mi></mml:math>
</inline-formula>-activation function. The node feature vector is represented with the addition of the neighboring node feature vector.</p>
<p>The frequency matrix <italic>f<sub>m</sub></italic> is calculated as follows: The random path is chosen from the sequence of nodes visited by the random user. If the random user on the node <italic>x<sub>i</sub></italic> at time <italic>t</italic>, the state is described as <italic>s(t&#x2009;)&#x2009;&#x003D;&#x2009;x<sub>i</sub>.</italic> The transition from one node to the neighbor <italic>x<sub>j</sub></italic> is declared as, <italic>r(s(t&#x2009;&#x002B;&#x2009;1)&#x2009;&#x003D;&#x2009;x<sub>j</sub>s(t)&#x2009;&#x003D;&#x2009;x<sub>i</sub>)</italic>. These transition states are assigned to the given adjacency matrix <italic>A</italic> as <xref ref-type="disp-formula" rid="eqn-19">Eq. (19)</xref>. The random walk used here is to calculate the similarity between the nodes.<disp-formula id="eqn-19"><label>(19)</label>
<mml:math id="mml-eqn-19" display="block"><mml:mi>r</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>s</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mrow><mml:mo fence="false" stretchy="false">|</mml:mo></mml:mrow><mml:mi>s</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:munder><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mi>j</mml:mi></mml:munder><mml:mo>&#x2061;</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math>
</disp-formula></p>
<p>The frequency matrix <italic>f<sub>m</sub></italic> is created using the <xref ref-type="disp-formula" rid="eqn-3">Eq. (3)</xref> for all the pairs of nodes. The path between the nodes is calculated using a random walk. Once the <italic>f<sub>m</sub></italic> is created, the <italic>i<sup>th</sup></italic> node of <italic>FM</italic> is the <italic>i<sup>th</sup></italic> row vector of <italic>f<sub>mi</sub></italic> and the <italic>j<sup>th</sup></italic> column of <italic>f<sub>m</sub></italic> is the <italic>j<sup>th</sup></italic> column vector of f<sub>mj.</sub> it is also called context <italic>c<sub>j</sub></italic>. the entry of the frequency the matrix <italic>f<sub>mi,j</sub></italic> is the number of times x<sub>i</sub> occurs in <italic>c</italic><sub>j</sub>. then the <italic>f<sub>m</sub></italic> has been used to calculate the PPMI matrix <inline-formula id="ieqn-26">
<mml:math id="mml-ieqn-26"><mml:mi>P</mml:mi><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mi>R</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:math>
</inline-formula> as in the <xref ref-type="disp-formula" rid="eqn-20">Eqs. (20)&#x2013;</xref><xref ref-type="disp-formula" rid="eqn-23">(23)</xref>.</p>
<p><disp-formula id="eqn-20"><label>(20)</label>
<mml:math id="mml-eqn-20" display="block"><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:mi mathvariant="normal">f</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">m</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mi mathvariant="normal">f</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">m</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math>
</disp-formula></p>
<p><disp-formula id="eqn-21"><label>(21)</label>
<mml:math id="mml-eqn-21" display="block"><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:msub><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mi>j</mml:mi></mml:msub><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mi mathvariant="normal">f</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">m</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2061;</mml:mo><mml:mi>F</mml:mi><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math>
</disp-formula></p>
<p><disp-formula id="eqn-22"><label>(22)</label>
<mml:math id="mml-eqn-22" display="block"><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:msub><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mi>i</mml:mi></mml:msub><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mi mathvariant="normal">f</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">m</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mi mathvariant="normal">f</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">m</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math>
</disp-formula></p>
<p><disp-formula id="eqn-23"><label>(23)</label>
<mml:math id="mml-eqn-23" display="block"><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">x</mml:mi></mml:mrow><mml:mo fence="false" stretchy="false">{</mml:mo><mml:mi>p</mml:mi><mml:mi>m</mml:mi><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mspace width="thickmathspace" /><mml:mn>0</mml:mn><mml:mo fence="false" stretchy="false">}</mml:mo></mml:mstyle></mml:math>
</disp-formula></p>
<p>where, <inline-formula id="ieqn-27">
<mml:math id="mml-ieqn-27"><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math>
</inline-formula>: the probability of node xi occurring in context <italic>cj</italic>, <inline-formula id="ieqn-28">
<mml:math id="mml-ieqn-28"><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msub></mml:math>
</inline-formula>: the probability of node <italic>xi</italic> and,<inline-formula id="ieqn-29">
<mml:math id="mml-ieqn-29"><mml:mspace width="thickmathspace" /><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math>
</inline-formula>: the probability of context <italic>cj</italic>.</p>
<p>As compared to the adjacency matrix, the <italic>PPMI</italic> matrix has reduced the hub nodes and increased the relationship among the data points. The global consistency convolution network <inline-formula id="ieqn-30">
<mml:math id="mml-ieqn-30"><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>v</mml:mi><mml:mi>G</mml:mi></mml:msub></mml:math>
</inline-formula> based on the <italic>PPMI</italic> matrix is denoted in <xref ref-type="disp-formula" rid="eqn-24">Eq. (24)</xref>.<disp-formula id="eqn-24"><label>(24)</label>
<mml:math id="mml-eqn-24" display="block"><mml:mi>C</mml:mi><mml:mi>o</mml:mi><mml:mi>n</mml:mi><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>g</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mi>i</mml:mi></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mi>D</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:msup><mml:mi>Z</mml:mi><mml:mi>i</mml:mi></mml:msup><mml:mo>=</mml:mo><mml:mi>&#x03C3;</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mi>X</mml:mi><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:mrow></mml:mrow></mml:msup><mml:mi>P</mml:mi><mml:msup><mml:mi>X</mml:mi><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:mrow></mml:mrow></mml:msup><mml:msup><mml:mi>z</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:msup><mml:mi>w</mml:mi><mml:mi>i</mml:mi></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:math>
</disp-formula>where, the <italic>P-PPMI</italic> matrix and <inline-formula id="ieqn-31">
<mml:math id="mml-ieqn-31"><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:munder><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mi>j</mml:mi></mml:munder><mml:mo>&#x2061;</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math>
</inline-formula></p>
<p>To combine the local and global consistency convolution for a dual graph convolutional network, a regularize is used. Loss function with the regularize is represented in <xref ref-type="disp-formula" rid="eqn-25">Eqs. (25)</xref> and <xref ref-type="disp-formula" rid="eqn-26">(26)</xref></p>
<p><disp-formula id="eqn-25"><label>(25)</label>
<mml:math id="mml-eqn-25" display="block"><mml:mi>L</mml:mi><mml:mi>o</mml:mi><mml:mi>s</mml:mi><mml:mi>s</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>C</mml:mi><mml:mi>o</mml:mi><mml:mi>n</mml:mi><mml:mi>v</mml:mi><mml:msub><mml:mspace width="thickmathspace" /><mml:mrow><mml:mi>l</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo><mml:mrow><mml:mi mathvariant="normal">&#x03BB;</mml:mi></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>C</mml:mi><mml:mi>o</mml:mi><mml:mi>n</mml:mi><mml:mi>v</mml:mi><mml:msub><mml:mspace width="thickmathspace" /><mml:mrow><mml:mi>l</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>C</mml:mi><mml:mi>o</mml:mi><mml:mi>n</mml:mi><mml:mi>v</mml:mi><mml:msub><mml:mspace width="thickmathspace" /><mml:mrow><mml:mi>g</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math>
</disp-formula></p>
<p><disp-formula id="eqn-26"><label>(26)</label>
<mml:math id="mml-eqn-26" display="block"><mml:msub><mml:mi>L</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>C</mml:mi><mml:mi>o</mml:mi><mml:mi>n</mml:mi><mml:mi>v</mml:mi><mml:msub><mml:mspace width="thickmathspace" /><mml:mrow><mml:mi>l</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mo fence="false" stretchy="false">|</mml:mo><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>L</mml:mi></mml:msub></mml:mrow><mml:mo fence="false" stretchy="false">|</mml:mo></mml:mrow></mml:mfrac></mml:mrow><mml:msub><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>l</mml:mi><mml:mi>&#x03F5;</mml:mi><mml:msub><mml:mi>y</mml:mi><mml:mi>L</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>&#x2061;</mml:mo><mml:msubsup><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>c</mml:mi></mml:msubsup><mml:mo>&#x2061;</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>l</mml:mi><mml:mo>.</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:msubsup><mml:mi>z</mml:mi><mml:mrow><mml:mi>l</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow><mml:mi>A</mml:mi></mml:msubsup></mml:mstyle></mml:math>
</disp-formula></p>
<p>where <inline-formula id="ieqn-32">
<mml:math id="mml-ieqn-32"><mml:msub><mml:mi>y</mml:mi><mml:mi>L</mml:mi></mml:msub></mml:math>
</inline-formula>&#x2013;labeled data for training and <inline-formula id="ieqn-33">
<mml:math id="mml-ieqn-33"><mml:mspace width="thickmathspace" /><mml:mi>Y</mml:mi><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mi>R</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:math>
</inline-formula></p>
</sec>
</sec>
<sec id="s4">
<label>4</label>
<title>Experimental Results and Analysis</title>
<p>The 150 lung CT images for tumor and non-tumor categories are collected from the lung cancer consortium for the proposed system evaluation. The input feature sets are split into a 7:3 ratio of training and testing datasets. The proposed system is implemented using python Sci-kit-learn and the results are compared with existing preprocessing filters, feature extraction methods, and classification systems in terms of accuracy, sensitivity, and specificity.</p>
<sec id="s4_1">
<label>4.1</label>
<title>Evaluation of Preprocessing</title>
<p>In the preprocessing stage, the filters such as Adaptive median and wiener filter combination are used in the proposed system. This is compared with other filters to prove the performance of the proposed preprocessing system in terms of the Speckle Suppression Index (<italic>SSI</italic>) and Speckle Suppression and Mean Preservation index (<italic>SMPI</italic>). <italic>SSI</italic> value is a linear minimum mean-square error filter value, and it can be reassessed similarity between pixels as shown in <xref ref-type="disp-formula" rid="eqn-27">Eq. (27)</xref>. <italic>SMPI</italic> value determines the lower values that give better performance of the filter in terms of mean preservation and noise reduction as shown in <xref ref-type="disp-formula" rid="eqn-28">Eqs. (28)</xref> and <xref ref-type="disp-formula" rid="eqn-29">(29)</xref>.</p>
<p><disp-formula id="eqn-27"><label>(27)</label>
<mml:math id="mml-eqn-27" display="block"><mml:mi>S</mml:mi><mml:mi>S</mml:mi><mml:mi>I</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:msqrt><mml:mi>V</mml:mi><mml:mi>a</mml:mi><mml:mi>r</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:msqrt></mml:mrow><mml:mrow><mml:mi>M</mml:mi><mml:mi>e</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mfrac></mml:mrow><mml:mspace width="thickmathspace" /><mml:mo>&#x2217;</mml:mo><mml:mspace width="thickmathspace" /><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>M</mml:mi><mml:mi>e</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>o</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:msqrt><mml:mi>V</mml:mi><mml:mi>a</mml:mi><mml:mi>r</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>o</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:msqrt></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:mstyle></mml:math>
</disp-formula></p>
<p><disp-formula id="eqn-28"><label>(28)</label>
<mml:math id="mml-eqn-28" display="block"><mml:mi>S</mml:mi><mml:mi>M</mml:mi><mml:mi>P</mml:mi><mml:mi>I</mml:mi><mml:mo>=</mml:mo><mml:mi>Q</mml:mi><mml:mo>&#x2217;</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:msqrt><mml:mi>V</mml:mi><mml:mi>a</mml:mi><mml:mi>r</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:msqrt></mml:mrow><mml:mrow><mml:msqrt><mml:mi>V</mml:mi><mml:mi>a</mml:mi><mml:mi>r</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>o</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:msqrt></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math>
</disp-formula></p>
<p><disp-formula id="eqn-29"><label>(29)</label>
<mml:math id="mml-eqn-29" display="block"><mml:mi>Q</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mo fence="false" stretchy="false">|</mml:mo><mml:mrow><mml:mi>M</mml:mi><mml:mi>e</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>o</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mi>M</mml:mi><mml:mi>e</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo fence="false" stretchy="false">|</mml:mo></mml:math>
</disp-formula></p>
<p>where <inline-formula id="ieqn-34">
<mml:math id="mml-ieqn-34"><mml:msub><mml:mi>I</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:math>
</inline-formula> is the filtered image and <inline-formula id="ieqn-35">
<mml:math id="mml-ieqn-35"><mml:msub><mml:mi>I</mml:mi><mml:mi>o</mml:mi></mml:msub></mml:math>
</inline-formula> is the noisy image. This SSI tends to be less than 1 if the filter performance is efficient in reducing the speckle noise. <xref ref-type="table" rid="table-1">Tab. 1</xref> shows the SSI and SMPI index values for sample 5 images in terms of filter results using proposed and existing filters. For image 3, the proposed combination of filters obtained SSI and SMPI values of 0.4141 and 0.5671 respectively. Other filters such as median, adaptive median, and Wiener filters obtained the SSI value as 0.5111, 0.5072, and 0.4901 respectively. SMPI values of these filters are 0.6401, 0.6721, and 0.6504 sequentially. The statistical measurements of the results prove that the proposed adaptive median with a Wiener filter obtained less value, which indicates the best filter to remove the noise compared to other filters.</p>
</sec>
<sec id="s4_2">
<label>4.2</label>
<title>Evaluation of Feature Extraction Method</title>
<p>The evaluation of the proposed feature extraction with optimization using WBFO is shown in <xref ref-type="table" rid="table-2">Tab. 2</xref>. The optimized threshold value obtained by WBFO is compared with the standard Whale optimization algorithm (WOA) and Bacterial foraging optimization (BFO). Based on the proposed WBFO optimization, we selected first-order texture features kurtosis, skewness, and uniformity, and for gray level matrix, we also selected Run-length Nonuniformity Low gray-level to run emphasis High gray-level run emphasis for Gray level run length matrix features.</p>
</sec>
<sec id="s4_3">
<label>4.3</label>
<title>Evaluation of Classification System</title>
<p>The proposed smart lung tumor detection using Dual graph CNN with an optimized feature set using WBFO has been evaluated with the parameters such as accuracy, sensitivity, and specificity. The proposed classification system with WBFO is compared with standard classification with traditional classifiers such as support vector machine (SVM), convolutional neural network (CNN), and Dual graph CNN without WBFO. The evaluated results are shown in <xref ref-type="table" rid="table-3 table-4 table-5 table-6">Tabs. 3&#x2013;6</xref>. The overall comparative analysis in terms of the accuracy of the classification system is shown in <xref ref-type="fig" rid="fig-6">Fig. 6</xref>.</p>
<fig id="fig-6">
<label>Figure 6</label>
<caption>
<title>Accuracy comparison of classifiers</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="IASC_31039-fig-6.png"/>
</fig>
<p>As a result of various evaluations, it has been demonstrated that the proposed lung cancer detection system is effective when the proposed WBFO-based optimization of feature selection is combined with a Dual Graph CNN classifier. Contrary to other classifiers such as SVM, CNN, and DGCNN without optimization, the proposed system ensured high accuracy. The accuracy of sample image 5 was determined by the machine learning approaches to be 83.11&#x0025;, 84.22&#x0025;, and 95.22&#x0025;, respectively. The proposed optimization approaches enhance the result of the Dual graph CNN classifier and increase the accuracy percentage to 98.72&#x0025;. Consequently, the proposed WBFO evolutionary approach improves the classification accuracy of the detection of lung tumors and non-lung tumor images.</p>
<p>The proposed DGCNN with WBFO secures the index percentage as shown in <xref ref-type="table" rid="table-5">Tab. 5</xref>. CNN achieved 87.91&#x0025;, 87.87&#x0025;, and 89.96&#x0025; for TPR, TNR, and AUC for the sample CT images number 1. Whereas SVM achieved 85.91&#x0025; 85.86&#x0025; and 89.96&#x0025; and DGCNN generated 92.9&#x0025;, 90.12&#x0025; and 96.02&#x0025; respectively. The sample result analysis for lung tumors is shown in <xref ref-type="table" rid="table-6">Tab. 6</xref>. Thus, the proposed WBFO improves the similarity index values, thereby proving the efficiency of the proposed system. In all types of statistical analyses, the proposed WBFO enhances the lung CT image feature selection and classification system for efficient lung tumor prediction.</p>
</sec>
</sec>
<sec id="s5">
<label>5</label>
<title>Conclusion</title>
<p>Early diagnosis of lung tumors is very important in determining the type of treatment that should be administered to the patient as well as taking preventative measures to lengthen the life of the patient. Using evolutionary and deep learning methods, we present a novel approach to the diagnosis of lung tumors. Preprocessed images are normalized and, adaptive median filters with wiener filters are applied to the input images. After the image has been normalized and enhanced, the tumor region is segmented using thresholding and morphological operations. To improve the accuracy of decision-making, the various features of lung CT images are extracted using GLCM, GLRLM, and HOG to obtain statistical information on the features. To enhance the feature selection process, the fused WFO method is used. With the proposed system, lung tumor detection accuracy was evaluated at 98.72&#x0025; using graph dual CNN. It is compared with support vector machines, standard CNNs, and DGCNNs without optimization. In comparison to existing algorithms, the proposed approach is shown to be effective through performance analysis using various metrics. To enhance the performance of the proposed system, various medical imaging and other meta-heuristic approaches will be added to the proposed work in the future.</p>
</sec>
</body>
<back>
<ack>
<p>The author thanks the Deanship of Research, Prince Sattam Bin Abdul-Aziz University, KSA, for providing an opportunity to conduct research.</p>
</ack><fn-group>
<fn fn-type="other">
<p><bold>Funding Statement:</bold> The author received no specific funding for this study.</p>
</fn>
<fn fn-type="conflict">
<p><bold>Conflicts of Interest:</bold> The author declares that he has no conflicts of interest to report regarding the present study.</p>
</fn>
</fn-group>
<ref-list content-type="authoryear">
<title>References</title>
<ref id="ref-1"><label>[1]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>M.</given-names> <surname>Kurkure</surname></string-name> and <string-name><given-names>A.</given-names> <surname>Thakare</surname></string-name></person-group>, &#x201C;<article-title>Introducing automated system for lung cancer detection using evolutionary approach</article-title>,&#x201D; <source>International Journal of Engineering and Computer Science</source>, vol. <volume>5</volume>, no. <issue>5</issue>, pp. <fpage>16736</fpage>&#x2013;<lpage>16739</lpage>, <year>2016</year>.</mixed-citation></ref>
<ref id="ref-2"><label>[2]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>S.</given-names> <surname>Makaju</surname></string-name>, <string-name><given-names>P.</given-names> <surname>Prasad</surname></string-name>, <string-name><given-names>A.</given-names> <surname>Alsadoon</surname></string-name>, <string-name><given-names>A. K.</given-names> <surname>Singh</surname></string-name> and <string-name><given-names>A.</given-names> <surname>Elchouemi</surname></string-name></person-group>, &#x201C;<article-title>Lung cancer detection using CT scan images</article-title>, &#x201D;<source>Procedia Computer Science</source>, vol. <volume>125</volume>, no. <issue>1</issue>, pp. <fpage>107</fpage>&#x2013;<lpage>104</lpage>, <year>2018</year>.</mixed-citation></ref>
<ref id="ref-3"><label>[3]</label><mixed-citation publication-type="conf-proc"><person-group person-group-type="author"><string-name><given-names>C.</given-names> <surname>Szegedy</surname></string-name>, <string-name><given-names>W.</given-names> <surname>Liu</surname></string-name>, <string-name><given-names>Y. Q.</given-names> <surname>Jia</surname></string-name>, <string-name><given-names>P.</given-names> <surname>Sermanet</surname></string-name>, <string-name><given-names>S.</given-names> <surname>Reed</surname></string-name> <etal>et al.,</etal></person-group> &#x201C;<article-title>Going deeper with convolutions</article-title>,&#x201D; in <conf-name>Proc. of the IEEE Conf. on Computer Vision and Pattern Recognition</conf-name>, <conf-loc>Boston, MA, USA</conf-loc>, pp. <fpage>1</fpage>&#x2013;<lpage>9</lpage>, <year>2015</year>.</mixed-citation></ref>
<ref id="ref-4"><label>[4]</label><mixed-citation publication-type="conf-proc"><person-group person-group-type="author"><string-name><given-names>N.</given-names> <surname>Mesanovic</surname></string-name>, <string-name><given-names>M.</given-names> <surname>Grgic</surname></string-name>, <string-name><given-names>H.</given-names> <surname>Huseinagic</surname></string-name>, <string-name><given-names>M.</given-names> <surname>Males</surname></string-name>, <string-name><given-names>E.</given-names> <surname>Skejic</surname></string-name> <etal>et al.,</etal></person-group> &#x201C;<article-title>Automatic CT image segmentation of the lungs with region growing algorithm</article-title>,&#x201D; in <conf-name>18th Int. Conf. on Systems, Signals and Image Processing-IWSSIP</conf-name>, Marlbor, Slovenia, pp. <fpage>395</fpage>&#x2013;<lpage>400</lpage>, <year>2011</year>.</mixed-citation></ref>
<ref id="ref-5"><label>[5]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>J.</given-names> <surname>John</surname></string-name> and <string-name><given-names>M. G.</given-names> <surname>Mini</surname></string-name></person-group>, &#x201C;<article-title>Multilevel thresholding based segmentation and feature extraction for pulmonary nodule detection</article-title>,&#x201D; <source>Procedia Technology</source>, vol. <volume>24</volume>, pp. <fpage>957</fpage>&#x2013;<lpage>963</lpage>, <year>2016</year>.</mixed-citation></ref>
<ref id="ref-6"><label>[6]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>A.</given-names> <surname>Humeau-Heurtier</surname></string-name></person-group>, &#x201C;<article-title>Texture feature extraction methods: A survey</article-title>,&#x201D; <source>IEEE Access</source>, vol. <volume>7</volume>, pp. <fpage>8975</fpage>&#x2013;<lpage>9000</lpage>, <year>2019</year>.</mixed-citation></ref>
<ref id="ref-7"><label>[7]</label><mixed-citation publication-type="conf-proc"><person-group person-group-type="author"><string-name><given-names>C.</given-names> <surname>Zu</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Wang</surname></string-name>, <string-name><given-names>L.</given-names> <surname>Zhou</surname></string-name>, <string-name><given-names>L.</given-names> <surname>Wang</surname></string-name> and <string-name><given-names>D.</given-names> <surname>Zhang</surname></string-name></person-group>, &#x201C;<article-title>Multi-modality feature selection with adaptive similarity learning for classification of Alzheimer&#x2019;s disease</article-title>,&#x201D; in <conf-name>2018 IEEE 15th Int. Symp. on Biomedical Imaging ISBI 2018</conf-name>, Washinton, USA, pp. <fpage>1542</fpage>&#x2013;<lpage>1545</lpage>, <year>2018</year>.</mixed-citation></ref>
<ref id="ref-8"><label>[8]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>J.</given-names> <surname>Nalepa</surname></string-name> and <string-name><given-names>M.</given-names> <surname>Kawulok</surname></string-name></person-group>, &#x201C;<article-title>Selecting training sets for support vector machines: A review</article-title>,&#x201D; <source>Artificial Intelligence Review</source>, vol. <volume>52</volume>, no. <issue>2</issue>, pp. <fpage>857</fpage>&#x2013;<lpage>900</lpage>, <year>2019</year>.</mixed-citation></ref>
<ref id="ref-9"><label>[9]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>D. C. R.</given-names> <surname>Novitasari</surname></string-name>, <string-name><given-names>A.</given-names> <surname>Lubab</surname></string-name>, <string-name><given-names>A.</given-names> <surname>Sawiji</surname></string-name> and <string-name><given-names>A. H.</given-names> <surname>Asyhar</surname></string-name></person-group>, &#x201C;<article-title>Application of feature extraction for breast cancer using one order statistic, GLCM, GLRLM, and GLDM</article-title>,&#x201D; <source>Advances in Science, Technology and Engineering Systems Journal (ASTESJ)</source>, vol. <volume>4</volume>,. no. <issue>4</issue>, pp. <fpage>115</fpage>&#x2013;<lpage>120</lpage>, <year>2019</year>.</mixed-citation></ref>
<ref id="ref-10"><label>[10]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>D.</given-names> <surname>Zhang</surname></string-name>, <string-name><given-names>J.</given-names> <surname>Hu</surname></string-name>, <string-name><given-names>F.</given-names> <surname>Li</surname></string-name>, <string-name><given-names>X.</given-names> <surname>Ding</surname></string-name>, <string-name><given-names>A. K.</given-names> <surname>Sangaiah</surname></string-name> <etal>et al.,</etal></person-group> &#x201C;<article-title>Small object detection via precise region-based fully convolutional networks</article-title>,&#x201D; <source>Computers, Materials and Continua</source>, vol. <volume>69</volume>, no. <issue>2</issue>, pp. <fpage>1503</fpage>&#x2013;<lpage>1517</lpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-11"><label>[11]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>J.</given-names> <surname>Zhang</surname></string-name>, <string-name><given-names>J.</given-names> <surname>Sun</surname></string-name>, <string-name><given-names>J.</given-names> <surname>Wang</surname></string-name> and <string-name><given-names>X. G.</given-names> <surname>Yue</surname></string-name></person-group>, &#x201C;<article-title>Visual object tracking based on residual network and cascaded correlation filters</article-title>,&#x201D; <source>Journal of Ambient Intelligence and Humanized Computing</source>, vol. <volume>12</volume>, no. <issue>8</issue>, pp. <fpage>8427</fpage>&#x2013;<lpage>8440</lpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-12"><label>[12]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>A.</given-names> <surname>Teramoto</surname></string-name>, <string-name><given-names>H.</given-names> <surname>Fujita</surname></string-name>, <string-name><given-names>O.</given-names> <surname>Yamamuro</surname></string-name> and <string-name><given-names>T.</given-names> <surname>Tamaki</surname></string-name></person-group>, &#x201C;<article-title>Automated detection of pulmonary nodules in PET/CT images: Ensemble false-positive reduction using a convolutional neural network technique</article-title>,&#x201D; <source>Medical Physics</source>, vol. <volume>43</volume>, no. <issue>6 Part 1</issue>, pp. <fpage>2821</fpage>&#x2013;<lpage>2827</lpage>, <year>2016</year>.</mixed-citation></ref>
<ref id="ref-13"><label>[13]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>N.</given-names> <surname>Zheng</surname></string-name>, <string-name><given-names>G.</given-names> <surname>Loizou</surname></string-name>, <string-name><given-names>X.</given-names> <surname>Jiang</surname></string-name>, <string-name><given-names>X.</given-names> <surname>Lan</surname></string-name> and <string-name><given-names>X.</given-names> <surname>Li</surname></string-name></person-group>, &#x201C;<article-title>Computer vision and pattern recognition</article-title>,&#x201D; <source>International Journal of Computer Mathematics</source>, vol. <volume>84</volume>, no. <issue>9</issue>, pp. <fpage>1265</fpage>&#x2013;<lpage>1266</lpage>, <year>2007</year>.</mixed-citation></ref>
<ref id="ref-14"><label>[14]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>S.</given-names> <surname>Vijh</surname></string-name>, <string-name><given-names>D.</given-names> <surname>Gaur</surname></string-name> and <string-name><given-names>S.</given-names> <surname>Kumar</surname></string-name></person-group>, &#x201C;<article-title>An intelligent lung tumor diagnosis system using whale optimization algorithm and support vector machine</article-title>,&#x201D; <source>International Journal of System Assurance Engineering and Management</source>, vol. <volume>11</volume>, no. <issue>2</issue>, pp. <fpage>374</fpage>&#x2013;<lpage>384</lpage>, <year>2020</year>.</mixed-citation></ref>
<ref id="ref-15"><label>[15]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>P.</given-names> <surname>Kavitha</surname></string-name> and <string-name><given-names>G.</given-names> <surname>Ayyappan</surname></string-name></person-group>, &#x201C;<article-title>Lung cancer detection at early stage by using SVM classifier techniques</article-title>,&#x201D; <source>Int J Pure Appl Math</source>, vol. <volume>119</volume>, no. <issue>12</issue>, pp. <fpage>3171</fpage>&#x2013;<lpage>3180</lpage>, <year>2018</year>.</mixed-citation></ref>
<ref id="ref-16"><label>[16]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>T.</given-names> <surname>Messay</surname></string-name>, <string-name><given-names>R. C.</given-names> <surname>Hardie</surname></string-name> and <string-name><given-names>S. K.</given-names> <surname>Rogers</surname></string-name></person-group>, &#x201C;<article-title>A new computationally efficient CAD system for pulmonary nodule detection in CT imagery</article-title>,&#x201D; <source>Medical Image Analysis</source>, vol. <volume>14</volume>, no. <issue>3</issue>, pp. <fpage>390</fpage>&#x2013;<lpage>406</lpage>, <year>2010</year>.</mixed-citation></ref>
<ref id="ref-17"><label>[17]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>M.</given-names> <surname>Bari</surname></string-name>, <string-name><given-names>A.</given-names> <surname>Ahmed</surname></string-name>, <string-name><given-names>M.</given-names> <surname>Sabir</surname></string-name> and <string-name><given-names>S.</given-names> <surname>Naveed</surname></string-name></person-group>, &#x201C;<article-title>Lung cancer detection using digital image processing techniques: A review</article-title>,&#x201D; <source>Mehran University Research Journal of Engineering &#x0026; Technology</source>, vol. <volume>38</volume>, no. <issue>2</issue>, pp. <fpage>351</fpage>&#x2013;<lpage>360</lpage>, <year>2019</year>.</mixed-citation></ref>
<ref id="ref-18"><label>[18]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>S.</given-names> <surname>Kumar</surname></string-name>, <string-name><given-names>T. K.</given-names> <surname>Sharma</surname></string-name>, <string-name><given-names>M.</given-names> <surname>Pant</surname></string-name> and <string-name><given-names>A. K.</given-names> <surname>Ray</surname></string-name></person-group>, &#x201C;<article-title>Adaptive artificial bee colony for segmentation of CT lung images</article-title>,&#x201D; <source>Int J Comp App iRAFIT</source>, vol. <volume>5</volume>, pp. <fpage>1</fpage>&#x2013;<lpage>5</lpage>, <year>2012</year>.</mixed-citation></ref>
<ref id="ref-19"><label>[19]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>G. T.</given-names> <surname>Herman</surname></string-name></person-group>, &#x201C;<article-title>Image reconstruction from projections</article-title>,&#x201D; <source>Real-Time Imaging</source>, vol. <volume>1</volume>, no. <issue>1</issue>, pp. <fpage>3</fpage>&#x2013;<lpage>18</lpage>. <year>1985</year>.</mixed-citation></ref>
<ref id="ref-20"><label>[20]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>U.</given-names> <surname>Reddy</surname></string-name>, <string-name><given-names>B.</given-names> <surname>Reddy</surname></string-name> and <string-name><given-names>B.</given-names> <surname>Reddy</surname></string-name></person-group>, &#x201C;<article-title>Recognition of lung cancer using machine learning mechanisms with fuzzy neural networks</article-title>, &#x201D;<source>Traitement du Signal</source>, vol. <volume>36</volume>, no. <issue>1</issue>, pp. <fpage>87</fpage>&#x2013;<lpage>91</lpage>, <year>2019</year>.</mixed-citation></ref>
<ref id="ref-21"><label>[21]</label><mixed-citation publication-type="book"><person-group person-group-type="author"><string-name><given-names>S.</given-names> <surname>Vijh</surname></string-name>, <string-name><given-names>S.</given-names> <surname>Sharma</surname></string-name> and <string-name><given-names>P.</given-names> <surname>Gaurav</surname></string-name></person-group>, &#x201C;<chapter-title>Brain tumor segmentation using OTSU embedded adaptive particle swarm optimization method and convolutional neural network</chapter-title>,&#x201D; in <source>Data Visualization and Knowledge Engineering</source>, <publisher-name>springer, Cham</publisher-name>, pp. <fpage>171</fpage>&#x2013;<lpage>194</lpage>, <year>2020</year>.</mixed-citation></ref>
<ref id="ref-22"><label>[22]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>S.</given-names> <surname>Uzelaltinbulat</surname></string-name> and <string-name><given-names>B.</given-names> <surname>Ugur</surname></string-name></person-group>, &#x201C;<article-title>Lung tumor segmentation algorithm</article-title>,&#x201D; <source>Procedia Computer Science</source>, vol. <volume>120</volume>, pp. <fpage>140</fpage>&#x2013;<lpage>147</lpage>, <year>2017</year>.</mixed-citation></ref>
<ref id="ref-23"><label>[23]</label><mixed-citation publication-type="book"><person-group person-group-type="author"><string-name><given-names>P.</given-names> <surname>Joon</surname></string-name>, <string-name><given-names>S. B.</given-names> <surname>Bajaj</surname></string-name> and <string-name><given-names>A.</given-names> <surname>Jatain</surname></string-name></person-group>, &#x201C;<chapter-title>Segmentation and detection of lung cancer using image processing and clustering techniques</chapter-title>,&#x201D; in <source>Progress in Advanced Computing and Intelligent Engineering</source>, <publisher-name>Springer</publisher-name>, <publisher-loc>Singapore</publisher-loc>, vol. <volume>713</volume>, pp. <fpage>13</fpage>&#x2013;<lpage>23</lpage>, <year>2019</year>.</mixed-citation></ref>
<ref id="ref-24"><label>[24]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>J.</given-names> <surname>Wang</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Wu</surname></string-name>, <string-name><given-names>S.</given-names> <surname>He</surname></string-name>, <string-name><given-names>P. K.</given-names> <surname>Sharma</surname></string-name>, <string-name><given-names>X.</given-names> <surname>Yu</surname></string-name> <etal>et al.,</etal></person-group> &#x201C;<article-title>Lightweight single image super-resolution convolution neural network in portable device</article-title>,&#x201D; <source>KSII Transactions on Internet and Information Systems (TIIS)</source>, vol. <volume>15</volume>, no. <issue>11</issue>, pp. <fpage>4065</fpage>&#x2013;<lpage>4083</lpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-25"><label>[25]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>M.</given-names> <surname>Prabukumar</surname></string-name>, <string-name><given-names>L.</given-names> <surname>Agilandeeswari</surname></string-name> and <string-name><given-names>K.</given-names> <surname>Ganesan</surname></string-name></person-group>, &#x201C;<article-title>An intelligent lung cancer diagnosis system using cuckoo search optimization and support vector machine classifier</article-title>,&#x201D; <source>Journal of Ambient Intelligence and Humanized Computing</source>, vol. <volume>10</volume>, no. <issue>1</issue>, pp. <fpage>267</fpage>&#x2013;<lpage>293</lpage>, <year>2019</year>.</mixed-citation></ref>
<ref id="ref-26"><label>[26]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>S. M.</given-names> <surname>Naqi</surname></string-name>, <string-name><given-names>M.</given-names> <surname>Sharif</surname></string-name> and <string-name><given-names>I. U.</given-names> <surname>Lali</surname></string-name></person-group>, &#x201C;<article-title>A 3D nodule candidate detection method supported by hybrid features to reduce false positives in lung nodule detection</article-title>,&#x201D; <source>Multimedia Tools and Applications</source>, vol. <volume>78</volume>, no. <issue>18</issue>, pp. <fpage>26287</fpage>&#x2013;<lpage>26311</lpage>, <year>2019</year>.</mixed-citation></ref>
<ref id="ref-27"><label>[27]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>S. R.</given-names> <surname>Zhou</surname></string-name> and <string-name><given-names>B.</given-names> <surname>Tan</surname></string-name></person-group>, &#x201C;<article-title>Electrocardiogram soft computing using hybrid deep learning CNN-ELM</article-title>,&#x201D; <source>Applied Soft Computing</source>, vol. <volume>86</volume>, pp. 1&#x2013;11, <year>2020</year>.</mixed-citation></ref>
<ref id="ref-28"><label>[28]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>C.</given-names> <surname>Bhuvaneswari</surname></string-name>, <string-name><given-names>P.</given-names> <surname>Aruna</surname></string-name> and <string-name><given-names>D.</given-names> <surname>Loganathan</surname></string-name></person-group>, &#x201C;<article-title>A new fusion model for classification of the lung diseases using genetic algorithm</article-title>,&#x201D; <source>Egyptian Informatics Journal</source>, vol. <volume>15</volume>, no. <issue>2</issue>, pp. <fpage>69</fpage>&#x2013;<lpage>77</lpage>, <year>2014</year>.</mixed-citation></ref>
<ref id="ref-29"><label>[29]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>P. M.</given-names> <surname>Shakeel</surname></string-name>, <string-name><given-names>M. A.</given-names> <surname>Burhanuddin</surname></string-name> and <string-name><given-names>M. I.</given-names> <surname>Desa</surname></string-name></person-group>, &#x201C;<article-title>Lung cancer detection from CT image using improved profuse clustering and deep learning instantaneously trained neural networks</article-title>,&#x201D; <source>Measurement</source>, vol. <volume>145</volume>, pp. <fpage>702</fpage>&#x2013;<lpage>712</lpage>, <year>2019</year>.</mixed-citation></ref>
<ref id="ref-30"><label>[30]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>Y. G.</given-names> <surname>Kim</surname></string-name>, <string-name><given-names>S. M.</given-names> <surname>Lee</surname></string-name>, <string-name><given-names>K. H.</given-names> <surname>Lee</surname></string-name>, <string-name><given-names>R.</given-names> <surname>Jang</surname></string-name>, <string-name><given-names>J.</given-names> <surname>Seo</surname></string-name> <etal>et al.,</etal></person-group> &#x201C;<article-title>Optimal matrix size of chest radiographs for computer-aided detection on lung nodule or mass with deep learning</article-title>,&#x201D; <source>European Radiology</source>, vol. <volume>30</volume>, no. <issue>9</issue>, pp. <fpage>4943</fpage>&#x2013;<lpage>4951</lpage>, <year>2020</year>. &#x200F;&#x200F;&#x200f;</mixed-citation></ref>
</ref-list><app-group id="appg1"><app id="app1">
<title>Appendix A:</title>
<table-wrap id="table-1"><label>Table 1</label>
<caption>
<title>Evaluation result for preprocessing noise removal filters</title></caption>
<table><colgroup><col align="left"/><col align="left"/><col align="left"/><col align="left"/><col align="left"/><col align="left"/><col align="left"/><col align="left"/><col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left" rowspan="2">Sample CT image number</th>
<th align="left" colspan="4">SSI</th>
<th align="left" colspan="4">SMPI</th>
</tr>
<tr>
<th align="left">Median filter</th>
<th align="left">Adaptive median filter</th>
<th align="left">Wiener filter</th>
<th align="left">Proposed adapt</th>
<th align="left">Median filter</th>
<th align="left">Adaptive median filter</th>
<th align="left">Wiener filter</th>
<th align="left">Proposed adaptive median</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">1</td>
<td align="left">0.6512</td>
<td align="left">0.6362</td>
<td align="left">0.6102</td>
<td align="left">0.5311</td>
<td align="left">0.7501</td>
<td align="left">0.7916</td>
<td align="left">0.7182</td>
<td align="left">0.6711</td>
</tr>
<tr>
<td align="left">2</td>
<td align="left">0.6321</td>
<td align="left">0.6282</td>
<td align="left">0.6121</td>
<td align="left">0.5311</td>
<td align="left">0.7621</td>
<td align="left">0.8036</td>
<td align="left">0.7302</td>
<td align="left">0.6891</td>
</tr>
<tr>
<td align="left">3</td>
<td align="left">0.5111</td>
<td align="left">0.5072</td>
<td align="left">0.4901</td>
<td align="left">0.4141</td>
<td align="left">0.6401</td>
<td align="left">0.6721</td>
<td align="left">0.6504</td>
<td align="left">0.5671</td>
</tr>
<tr>
<td align="left">4</td>
<td align="left">0.6712</td>
<td align="left">0.6672</td>
<td align="left">0.6501</td>
<td align="left">0.5641</td>
<td align="left">0.8011</td>
<td align="left">0.8326</td>
<td align="left">0.7692</td>
<td align="left">0.7261</td>
</tr>
<tr>
<td align="left">5</td>
<td align="left">0.6212</td>
<td align="left">0.6163</td>
<td align="left">0.7002</td>
<td align="left">0.5241</td>
<td align="left">0.7512</td>
<td align="left">0.7816</td>
<td align="left">0.7183</td>
<td align="left">0.6762</td>
</tr>
</tbody>
</table>
</table-wrap>

<table-wrap id="table-2"><label>Table 2</label>
<caption>
<title>Selected optimal feature subset using proposed WBFO optimization</title></caption>
<table><colgroup><col align="left"/><col align="left"/><col align="left"/><col align="left"/><col align="left"/><col align="left"/><col align="left"/><col align="left"/><col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left">Sum average</th>
<th align="left">Long run emphasis</th>
<th align="left">Run-length non-uniformity</th>
<th align="left">Low gray-level run emphasis</th>
<th align="left">High gray-level run emphasis</th>
<th align="left">Mean</th>
<th align="left">Skewness</th>
<th align="left">Kurtosis</th>
<th align="left">Class</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">2.31</td>
<td align="left">18231.12</td>
<td align="left">97.43</td>
<td align="left">101.332</td>
<td align="left">5782.123</td>
<td align="left">1.14</td>
<td align="left">2.10</td>
<td align="left">4.29</td>
<td align="left">0</td>
</tr>
<tr>
<td align="left">2.01</td>
<td align="left">27918.29</td>
<td align="left">162.38</td>
<td align="left">98.167</td>
<td align="left">5317.27</td>
<td align="left">1.06</td>
<td align="left">2.57</td>
<td align="left">8.26</td>
<td align="left">0</td>
</tr>
<tr>
<td align="left">2.13</td>
<td align="left">25262.22</td>
<td align="left">163.48</td>
<td align="left">99.267</td>
<td align="left">5318.37</td>
<td align="left">1.72</td>
<td align="left">3.67</td>
<td align="left">9.36</td>
<td align="left">0</td>
</tr>
<tr>
<td align="left">2.01</td>
<td align="left">30562.18</td>
<td align="left">80.27</td>
<td align="left">78.286</td>
<td align="left">4261.81</td>
<td align="left">1.02</td>
<td align="left">2.27</td>
<td align="left">11.27</td>
<td align="left">0</td>
</tr>
<tr>
<td align="left">3.21</td>
<td align="left">30563.38</td>
<td align="left">81.47</td>
<td align="left">79.486</td>
<td align="left">4263.01</td>
<td align="left">2.22</td>
<td align="left">3.47</td>
<td align="left">12.47</td>
<td align="left">0</td>
</tr>
<tr>
<td align="left">2.03</td>
<td align="left">30562.20</td>
<td align="left">80.29</td>
<td align="left">78.309</td>
<td align="left">4261.833</td>
<td align="left">1.05</td>
<td align="left">2.30</td>
<td align="left">11.30</td>
<td align="left">0</td>
</tr>
<tr>
<td align="left">2.10</td>
<td align="left">30562.27</td>
<td align="left">80.36</td>
<td align="left">78.379</td>
<td align="left">4261.903</td>
<td align="left">1.12</td>
<td align="left">2.37</td>
<td align="left">11.37</td>
<td align="left">0</td>
</tr>
<tr>
<td align="left">2.18</td>
<td align="left">110188.2</td>
<td align="left">198.27</td>
<td align="left">48.26</td>
<td align="left">2736.29</td>
<td align="left">1.08</td>
<td align="left">5.28</td>
<td align="left">26.26</td>
<td align="left">1</td>
</tr>
<tr>
<td align="left">2.09</td>
<td align="left">110188.0</td>
<td align="left">198.08</td>
<td align="left">48.07</td>
<td align="left">2736.1</td>
<td align="left">0.89</td>
<td align="left">5.09</td>
<td align="left">26.07</td>
<td align="left">1</td>
</tr>
<tr>
<td align="left">2.01</td>
<td align="left">1001298.</td>
<td align="left">196.06</td>
<td align="left">46.051</td>
<td align="left">2734.081</td>
<td align="left">1.02</td>
<td align="left">3.07</td>
<td align="left">24.05</td>
<td align="left">1</td>
</tr>
<tr>
<td align="left">2.01</td>
<td align="left">1223231.</td>
<td align="left">280.28</td>
<td align="left">27.187</td>
<td align="left">2461.18</td>
<td align="left">1.09</td>
<td align="left">7.28</td>
<td align="left">71.27</td>
<td align="left">1</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="table-3"><label>Table 3</label>
<caption>
<title>Classification result of SVM classifier</title></caption>
<table><colgroup><col align="left"/><col align="left"/><col align="left"/><col align="left"/><col align="left"/><col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left" colspan="6">SVM classification (&#x0025;)</th>
</tr>
<tr>
<th align="left">&#x0023;Sample CT image</th>
<th align="left">TPR (SN)</th>
<th align="left">TNR (SP)</th>
<th align="left">FPR</th>
<th align="left">FNR</th>
<th align="left">ACC</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">1</td>
<td align="left">85.91</td>
<td align="left">85.86</td>
<td align="left">8.54</td>
<td align="left">9.84</td>
<td align="left">89.96</td>
</tr>
<tr>
<td align="left">2</td>
<td align="left">88.31</td>
<td align="left">91.11</td>
<td align="left">10.88</td>
<td align="left">12.65</td>
<td align="left">90.08</td>
</tr>
<tr>
<td align="left">3</td>
<td align="left">84.28</td>
<td align="left">88.08</td>
<td align="left">11.41</td>
<td align="left">13.61</td>
<td align="left">86.03</td>
</tr>
<tr>
<td align="left">4</td>
<td align="left">82.01</td>
<td align="left">87.17</td>
<td align="left">11.98</td>
<td align="left">13.88</td>
<td align="left">84.28</td>
</tr>
<tr>
<td align="left">5</td>
<td align="left">84.29</td>
<td align="left">88.21</td>
<td align="left">12.02</td>
<td align="left">13.92</td>
<td align="left">83.11</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="table-4"><label>Table 4</label>
<caption>
<title>Classification result of CNN classifier</title></caption>
<table><colgroup><col align="left"/><col align="left"/><col align="left"/><col align="left"/><col align="left"/><col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left" colspan="6">CNN classification (&#x0025;)</th>
</tr>
<tr>
<th align="left">&#x0023;Sample CT image</th>
<th align="left">TPR (SN)</th>
<th align="left">TNR (SP)</th>
<th align="left">FPR</th>
<th align="left">FNR</th>
<th align="left">ACC</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">1</td>
<td align="left">87.91</td>
<td align="left">87.87</td>
<td align="left">7.54</td>
<td align="left">8.84</td>
<td align="left">89.96</td>
</tr>
<tr>
<td align="left">2</td>
<td align="left">89.31</td>
<td align="left">92.11</td>
<td align="left">9.88</td>
<td align="left">11.65</td>
<td align="left">91.08</td>
</tr>
<tr>
<td align="left">3</td>
<td align="left">85.28</td>
<td align="left">89.08</td>
<td align="left">10.41</td>
<td align="left">12.61</td>
<td align="left">87.03</td>
</tr>
<tr>
<td align="left">4</td>
<td align="left">83.01</td>
<td align="left">88.17</td>
<td align="left">10.98</td>
<td align="left">12.88</td>
<td align="left">85.28</td>
</tr>
<tr>
<td align="left">5</td>
<td align="left">85.39</td>
<td align="left">89.21</td>
<td align="left">11</td>
<td align="left">12.82</td>
<td align="left">84.22</td>
</tr>
</tbody>
</table>
</table-wrap><table-wrap id="table-5"><label>Table 5</label>
<caption>
<title>Classification result of Dual graph CNN with proposed WBFO optimization</title></caption>
<table><colgroup><col align="left"/><col align="left"/><col align="left"/><col align="left"/><col align="left"/><col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left" colspan="6">Dual graph CNN with proposed WBFO (&#x0025;)</th>
</tr>
<tr>
<th align="left">&#x0023;Sample CT image</th>
<th align="left">TPR (SN)</th>
<th align="left">TNR (SP)</th>
<th align="left">FPR</th>
<th align="left">FNR</th>
<th align="left">ACC</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">1</td>
<td align="left">92.9</td>
<td align="left">90.12</td>
<td align="left">0.012</td>
<td align="left">3.81</td>
<td align="left">96.02</td>
</tr>
<tr>
<td align="left">2</td>
<td align="left">91.32</td>
<td align="left">95.21</td>
<td align="left">0.021</td>
<td align="left">5.54</td>
<td align="left">96.2</td>
</tr>
<tr>
<td align="left">3</td>
<td align="left">93.81</td>
<td align="left">92.63</td>
<td align="left">0.018</td>
<td align="left">5.32</td>
<td align="left">96.91</td>
</tr>
<tr>
<td align="left">4</td>
<td align="left">95.02</td>
<td align="left">96.72</td>
<td align="left">0.0011</td>
<td align="left">3.72</td>
<td align="left">97.9</td>
</tr>
<tr>
<td align="left">5</td>
<td align="left">96.91</td>
<td align="left">95.022</td>
<td align="left">0.0001</td>
<td align="left">4.21</td>
<td align="left">98.72</td>
</tr>
</tbody>
</table>
</table-wrap><table-wrap id="table-6"><label>Table 6</label>
<caption>
<title>Sample lung nodule detection as tumor or non-tumor</title></caption>
<table><colgroup><col align="left"/><col align="left"/><col align="left"/><col align="left"/><col align="left"/><col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left">Input image</th>
<th align="left">Normalization</th>
<th align="left">Filters</th>
<th align="left">Thresholding</th>
<th align="left">Morphological opening &#x0026; closing</th>
<th align="left">Detection of lung nodule</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" colspan="6"><inline-graphic xlink:href="IASC_31039-inline-1.png"/></td>
</tr>
</tbody>
</table>
</table-wrap>
</app>
</app-group>
</back>
</article>