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<front>
<journal-meta>
<journal-id journal-id-type="pmc">CMC</journal-id>
<journal-id journal-id-type="nlm-ta">CMC</journal-id>
<journal-id journal-id-type="publisher-id">CMC</journal-id>
<journal-title-group>
<journal-title>Computers, Materials &#x0026; Continua</journal-title>
</journal-title-group>
<issn pub-type="epub">1546-2226</issn>
<issn pub-type="ppub">1546-2218</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">31037</article-id>
<article-id pub-id-type="doi">10.32604/cmc.2023.031037</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Optimal Deep Transfer Learning Based Colorectal Cancer Detection and Classification Model</article-title>
<alt-title alt-title-type="left-running-head">Optimal Deep Transfer Learning Based Colorectal Cancer Detection and Classification Model</alt-title>
<alt-title alt-title-type="right-running-head">Optimal Deep Transfer Learning Based Colorectal Cancer Detection and Classification Model</alt-title>
</title-group>
<contrib-group content-type="authors">
<contrib id="author-1" contrib-type="author" corresp="yes">
<name name-style="western"><surname>Ragab</surname><given-names>Mahmoud</given-names>
</name><xref ref-type="aff" rid="aff-1">1</xref>
<xref ref-type="aff" rid="aff-2">2</xref>
<xref ref-type="aff" rid="aff-3">3</xref><email>mragab@kau.edu.sa</email></contrib>
<contrib id="author-2" contrib-type="author">
<name name-style="western"><surname>Mahmoud</surname><given-names>Maged Mostafa</given-names>
</name><xref ref-type="aff" rid="aff-4">4</xref>
<xref ref-type="aff" rid="aff-5">5</xref>
<xref ref-type="aff" rid="aff-6">6</xref></contrib>
<contrib id="author-3" contrib-type="author">
<name name-style="western"><surname>Asseri</surname><given-names>Amer H.</given-names>
</name><xref ref-type="aff" rid="aff-2">2</xref>
<xref ref-type="aff" rid="aff-7">7</xref></contrib>
<contrib id="author-4" contrib-type="author">
<name name-style="western"><surname>Choudhry</surname><given-names>Hani</given-names>
</name><xref ref-type="aff" rid="aff-2">2</xref>
<xref ref-type="aff" rid="aff-7">7</xref></contrib>
<contrib id="author-5" contrib-type="author">
<name name-style="western"><surname>Yacoub</surname><given-names>Haitham A.</given-names>
</name><xref ref-type="aff" rid="aff-8">8</xref></contrib>
<aff id="aff-1"><label>1</label><institution>Information Technology Department, Faculty of Computing and Information Technology, King Abdulaziz University</institution>, <addr-line>Jeddah, 21589</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-2"><label>2</label><institution>Center for Artificial Intelligence in Precision Medicines, King Abdulaziz University</institution>, <addr-line>Jeddah, 21589</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-3"><label>3</label><institution>Department of Mathematics, Faculty of Science, Al-Azhar University</institution>, <addr-line>Naser City, 11884, Cairo</addr-line>, <country>Egypt</country></aff>
<aff id="aff-4"><label>4</label><institution>Cancer Biology Unit, King Fahd Medical Research Center</institution><institution>, King Abdulaziz University</institution>, <addr-line>Jeddah, 21589</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-5"><label>5</label><institution>Department of Medical Laboratory Sciences, Faculty of Applied Medical Sciences, King Abdulaziz University</institution>, <addr-line>Jeddah, 22252</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-6"><label>6</label><institution>Department of Molecular Genetics and Enzymology, Human Genetics and Genome Research Institute, National Research Centre</institution>, <addr-line>Cairo, 12622</addr-line>, <country>Egypt</country></aff>
<aff id="aff-7"><label>7</label><institution>Biochemistry Department, Faculty of Science, King Abdulaziz University</institution>, <addr-line>Jeddah, 21589</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-8"><label>8</label><institution>Cell Biology Department, Biotechnology Research Institute, National Research Centre</institution>, <addr-line>Giza, 12622</addr-line>, <country>Egypt</country></aff>
</contrib-group>
<author-notes>
<corresp id="cor1"><label>&#x002A;</label>Corresponding Author: Mahmoud Ragab. Email: <email>mragab@kau.edu.sa</email></corresp>
</author-notes>
<pub-date pub-type="epub" date-type="pub" iso-8601-date="2022-10-28"><day>28</day>
<month>10</month>
<year>2022</year></pub-date>
<volume>74</volume>
<issue>2</issue>
<fpage>3279</fpage>
<lpage>3295</lpage>
<history>
<date date-type="received">
<day>08</day>
<month>4</month>
<year>2022</year>
</date>
<date date-type="accepted">
<day>20</day>
<month>5</month>
<year>2022</year>
</date>
</history>
<permissions>
<copyright-statement>&#x00A9; 2023 Ragab et al.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Ragab et al.</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_CMC_31037.pdf"></self-uri>
<abstract>
<p>Colorectal carcinoma (CRC) is one such dispersed cancer globally and also prominent one in causing cancer-based death. Conventionally, pathologists execute CRC diagnosis through visible scrutinizing under the microscope the resected tissue samples, stained and fixed through Haematoxylin and Eosin (H&#x0026;E). The advancement of graphical processing systems has resulted in high potentiality for deep learning (DL) techniques in interpretating visual anatomy from high resolution medical images. This study develops a slime mould algorithm with deep transfer learning enabled colorectal cancer detection and classification (SMADTL-CCDC) algorithm. The presented SMADTL-CCDC technique intends to appropriately recognize the occurrence of colorectal cancer. To accomplish this, the SMADTL-CCDC model initially undergoes pre-processing to improve the input image quality. In addition, a dense-EfficientNet technique was employed to extract feature vectors from the pre-processed images. Moreover, SMA with Discrete Hopfield neural network (DHNN) method was applied for the recognition and classification of colorectal cancer. The utilization of SMA assists in appropriately selecting the parameters involved in the DHNN approach. A wide range of experiments was implemented on benchmark datasets to assess the classification performance. A comprehensive comparative study highlighted the better performance of the SMADTL-CDC model over the recent approaches.</p>
</abstract>
<kwd-group kwd-group-type="author">
<kwd>Colorectal cancer</kwd>
<kwd>deep transfer learning</kwd>
<kwd>slime mould algorithm</kwd>
<kwd>hyperparameter optimization</kwd>
<kwd>biomedical imaging</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1">
<label>1</label>
<title>Introduction</title>
<p>Colorectal cancer (CRC) is the second most typical reason for cancer death rate in America and Europe [<xref ref-type="bibr" rid="ref-1">1</xref>]. Pathological diagnosis was considered the most authorized technique for treating CRC that needs pathologist personnel to visibly scrutinize digital full scale whole slide images (WSI) [<xref ref-type="bibr" rid="ref-2">2</xref>]. The challenges stem from the difficulty of WSI comprising large images, histological alterations, textures, and complex shapes in nuclear staining [<xref ref-type="bibr" rid="ref-3">3</xref>]. In addition to this, lacking pathologists globally is in stark contrast to the fast collection of WSI data, and the daily work pressure of pathologists is intense which results in unintended misdiagnose because of exhaustion. Therefore, it is important to enhance diagnosing methodologies that are cost effective by using current artificial intelligence (AI) advancements [<xref ref-type="bibr" rid="ref-4">4</xref>].</p>
<p>Pathology slides offer a numerous quantity of data that was measured by traditional machine learning (ML) methods and digital pathology for years [<xref ref-type="bibr" rid="ref-5">5</xref>]. The earlier study was depending on ML methods for determining the cell classifier from the histological slides of tumor tissue. The categorization of histopathological images by using AI not only escalates the efficiency and preciseness of the classification but also allows doctors in taking prompt actions about clinical treatment [<xref ref-type="bibr" rid="ref-6">6</xref>]. But, many of the suggested simulation practices depends on manual feature labels, which consider the primary constraints of conventional textual analysis methods. Thus, in the past few years, deep learning (DL) was inaugurated for solving this issue and other restrictions [<xref ref-type="bibr" rid="ref-7">7</xref>].</p>
<p>DL is a new technology that acts as an advancement of machine learning, but then it utilizes various layers of neural network (NN) systems for learning and increasingly abstracts high level features to minimize the intervention of humans from the identification of distinct classes in the images [<xref ref-type="bibr" rid="ref-8">8</xref>]. Traditional neural networks (CNN) currently present proficient outcomes in classifying images in the domain of DL whereas a NN may have hundreds or dozens of layers for learning comprising images with distinct features [<xref ref-type="bibr" rid="ref-9">9</xref>]. A convolutional layer made up of a small sized kernel to produce enriched features implies weights to the input unit and instructs them via an activation function as the output unit. The primary benefit of utilizing CNN in comparison made to a classic NN is that it minimizes the model variables for better precise outcomes [<xref ref-type="bibr" rid="ref-10">10</xref>].</p>
<p>The researchers in [<xref ref-type="bibr" rid="ref-11">11</xref>] present a novel dynamic ensemble DL technique. Firstly, it produces a subset of methods according to the transfer learning approach in deep neural network (DNN). Next, the applicable set of methods is carefully chosen by the particle swarm optimization approach and integrated by averaging or voting systems. Sarwinda&#x00A0;et&#x00A0;al.&#x00A0;[<xref ref-type="bibr" rid="ref-12">12</xref>] examine a DL technique in image classification for detecting CRC using ResNet framework. The excellent achievement of a DL classifier method provokes scholars to perform them in medicinal images. The model trained to differentiate CRC into malignant and benign cancer. Mulenga&#x00A0;et&#x00A0;al.&#x00A0;[<xref ref-type="bibr" rid="ref-13">13</xref>] presented a feature augmentation method that groups data normalization method to prolong current feature of data. The projected technique integrates feature extension by augmenting information for improving CRC classifier accuracy of DNN architecture.</p>
<p>Ho&#x00A0;et&#x00A0;al.&#x00A0;[<xref ref-type="bibr" rid="ref-14">14</xref>] encompass a deep learning method based Fast Region related Convolution Neural Network (Fast-RCNN) structure for occurrence segmentation with a ResNet-101 feature extraction support which offers glandular segmentation, as well as traditional ML classification. Tsai&#x00A0;et&#x00A0;al.&#x00A0;[<xref ref-type="bibr" rid="ref-15">15</xref>] presented the optimal classifier method based selected optimizer and adapted the parameter of CNN method. Next, we employed DL method for differentiating between diseased and healthy large intestine tissues. Initially, we trained a NN and related the network structure optimizer. Next, it can be adapted the parameter of the network layer to augment the better structure. At last, we compared the highly trained DL method on two distinct histological image open data sets.</p>
<p>This study develops a slime mould algorithm with deep transfer learning enabled colorectal cancer detection and classification (SMADTL-CCDC) approach. The presented SMADTL-CCDC technique undergoes pre-processing to improve the input image quality. In addition, a dense-EfficientNet method was employed to extract feature vectors from the pre-processed images. Moreover, SMA with Discrete Hopfield neural network (DHNN) approach was applied for the recognition and classification of CRC. The utilization of SMA assists in appropriately selecting the parameters involved in the DHNN approach. A wide range of experiments was applied to benchmark datasets for assessing the classification performances.</p>
<p>The rest of the paper is provided as follows. Section 2 offers the proposed model and Section 3 provides performance validation. Lastly, Section 4 concludes the work.</p>
</sec>
<sec id="s2">
<label>2</label>
<title>The Proposed Model</title>
<p>In this study, a new SMADTL-CCDC model has been developed to appropriately recognize the occurrence of CRC. The SMADTL-CCDC model originally undergoes pre-processing to improve the input image quality. Followed by, a dense-EfficientNet model is employed to extract feature vectors in the pre-processed images. Moreover, SMA with DHNN model is applied for the recognition and classification of CRC. <xref ref-type="fig" rid="fig-1">Fig. 1</xref> illustrates the work flow of SMADTL-CCDC technique.</p>
<fig id="fig-1">
<label>Figure 1</label>
<caption>
<title>Work flow of SMADTL-CCDC technique</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31037-fig-1.png"/>
</fig>
<sec id="s2_1">
<label>2.1</label>
<title>Feature Extraction</title>
<p>Once the medical image is preprocessed, the next step is for deriving a set of feature vectors using the dense EfficientNet model. CNN contains a group of layers implemented from the finding of image features. One of the important layers is pooling, convolution, activation, and batch normalization (BN) layers. Primary, the convolution layer is considered that needed unit from the CNN frameworks. The layer has contained a group of filters for discovering the existence of specific features which is executed from the image characterized as edge and texture called feature maps. Afterward, the activation layer is utilized for processing non-linear transformation for determining the result of prior convolution layer with application of activation function, for instance, Rectified Linear Unit (ReLU). The ReLU has generally utilized the activation function as it offers fast processing and demonstrations no problem with exploding problems. The ReLU is formulated as:</p>
<p><disp-formula id="eqn-1"><label>(1)</label><mml:math id="mml-eqn-1" display="block"><mml:mrow><mml:mtext>F</mml:mtext></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mtext>x</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mo movablelimits="true" form="prefix">max</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mrow><mml:mtext>x</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>.</mml:mo></mml:math></disp-formula>whereas the gradient for input is determined as:</p>
<p><disp-formula id="eqn-2"><label>(2)</label><mml:math id="mml-eqn-2" display="block"><mml:mfrac><mml:mrow><mml:mi mathvariant="normal">&#x2202;</mml:mi><mml:mrow><mml:mtext>F</mml:mtext></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mtext>x</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2202;</mml:mi><mml:mrow><mml:mtext>x</mml:mtext></mml:mrow></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mml:mtr><mml:mtd><mml:mn>0</mml:mn><mml:mrow><mml:mtext>&#xA0;if</mml:mtext></mml:mrow><mml:mspace width="1em" /><mml:mrow><mml:mi mathvariant="normal">x</mml:mi></mml:mrow><mml:mo>&#x2264;</mml:mo><mml:mn>0</mml:mn></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mn>1</mml:mn><mml:mrow><mml:mtext>&#xA0;if</mml:mtext></mml:mrow><mml:mspace width="1em" /><mml:mrow><mml:mi mathvariant="normal">x</mml:mi></mml:mrow><mml:mo>&#x003E;</mml:mo><mml:mn>0</mml:mn></mml:mtd></mml:mtr></mml:mtable><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>The BN layer tries for minimizing the amount of trained epochs that are needed from the network trained. It also improves the function by rescaling all the scalar features <inline-formula id="ieqn-1"><mml:math id="mml-ieqn-1"><mml:msub><mml:mrow><mml:mtext>x</mml:mtext></mml:mrow><mml:mrow><mml:mrow><mml:mtext>u</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> with restricted mini-batch <inline-formula id="ieqn-2"><mml:math id="mml-ieqn-2"><mml:mrow><mml:mtext>B</mml:mtext></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:msub><mml:mrow><mml:mtext>x</mml:mtext></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mrow><mml:mtext>m</mml:mtext></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:math></inline-formula> dependent upon <xref ref-type="disp-formula" rid="eqn-3">Eq. (3)</xref></p>
<p><disp-formula id="eqn-3"><label>(3)</label><mml:math id="mml-eqn-3" display="block"><mml:msub><mml:mrow><mml:mover><mml:mrow><mml:mtext>x</mml:mtext></mml:mrow><mml:mo stretchy="false">&#x005E;</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mrow><mml:mtext>u</mml:mtext></mml:mrow></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mrow><mml:mtext>x</mml:mtext></mml:mrow><mml:mrow><mml:mrow><mml:mtext>u</mml:mtext></mml:mrow></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>&#x03BC;</mml:mi><mml:mrow><mml:mrow><mml:mtext>B</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:msqrt><mml:msubsup><mml:mi>&#x03C3;</mml:mi><mml:mrow><mml:mrow><mml:mtext>B</mml:mtext></mml:mrow></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:mi>&#x03B5;</mml:mi></mml:msqrt></mml:mfrac></mml:math></disp-formula></p>
<p>In which <inline-formula id="ieqn-3"><mml:math id="mml-ieqn-3"><mml:mi>&#x03B5;</mml:mi></mml:math></inline-formula> signifies the smaller positive value for terminating the division by 0, <inline-formula id="ieqn-4"><mml:math id="mml-ieqn-4"><mml:msub><mml:mi>&#x03BC;</mml:mi><mml:mrow><mml:mrow><mml:mtext>B</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> represents the mini-batch mean that is defined with utilize of <xref ref-type="disp-formula" rid="eqn-4">Eq. (4)</xref>, and <inline-formula id="ieqn-5"><mml:math id="mml-ieqn-5"><mml:msubsup><mml:mi>&#x03C3;</mml:mi><mml:mrow><mml:mrow><mml:mtext>B</mml:mtext></mml:mrow></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup></mml:math></inline-formula> stands for the mini-batch variance that is evaluated by <xref ref-type="disp-formula" rid="eqn-5">Eq. (5)</xref>.</p>
<p><disp-formula id="eqn-4"><label>(4)</label><mml:math id="mml-eqn-4" display="block"><mml:msub><mml:mi>&#x03BC;</mml:mi><mml:mrow><mml:mrow><mml:mtext>B</mml:mtext></mml:mrow></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mtext>m</mml:mtext></mml:mrow></mml:mfrac><mml:munderover><mml:mo>&#x2211;</mml:mo><mml:mrow><mml:mrow><mml:mtext>u</mml:mtext></mml:mrow><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mrow><mml:mtext>m</mml:mtext></mml:mrow></mml:mrow></mml:munderover><mml:msub><mml:mrow><mml:mtext>x</mml:mtext></mml:mrow><mml:mrow><mml:mrow><mml:mtext>v</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></disp-formula></p>
<p><disp-formula id="eqn-5"><label>(5)</label><mml:math id="mml-eqn-5" display="block"><mml:msubsup><mml:mi>&#x03C3;</mml:mi><mml:mrow><mml:mrow><mml:mtext>B</mml:mtext></mml:mrow></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mtext>m</mml:mtext></mml:mrow></mml:mfrac><mml:munderover><mml:mo>&#x2211;</mml:mo><mml:mrow><mml:mrow><mml:mtext>u</mml:mtext></mml:mrow><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mrow><mml:mtext>m</mml:mtext></mml:mrow></mml:mrow></mml:munderover><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mrow><mml:mtext>x</mml:mtext></mml:mrow><mml:mrow><mml:mrow><mml:mtext>u</mml:mtext></mml:mrow></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>&#x03BC;</mml:mi><mml:mrow><mml:mrow><mml:mtext>B</mml:mtext></mml:mrow></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:math></disp-formula></p>
<p>But the implementing BN, 2 new elements, &#x03B3;, and &#x03B2; are commonly contained for allowing scaling and shifting-generalized inputs dependent upon <xref ref-type="disp-formula" rid="eqn-6">Eq. (6)</xref>. Such elements were learned with network features.</p>
<p><disp-formula id="eqn-6"><label>(6)</label><mml:math id="mml-eqn-6" display="block"><mml:msub><mml:mi>&#x03B3;</mml:mi><mml:mrow><mml:mrow><mml:mtext>u</mml:mtext></mml:mrow></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>&#x03B3;</mml:mi><mml:msub><mml:mrow><mml:mover><mml:mrow><mml:mtext>x</mml:mtext></mml:mrow><mml:mo stretchy="false">&#x005E;</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mrow><mml:mtext>u</mml:mtext></mml:mrow></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi>&#x03B2;</mml:mi></mml:math></disp-formula></p>
<p>The pooling layer concentrate on decreasing the perimeter of feature map for deciding on an essential and viable feature for minimizing the amount of parameters and processing of networks.</p>
<p>In this article, a novel dense CNN architecture has been proposed that is a mixture of pre-trained EfficientNetB0 with dense layer. EfficientB0 contains 7 MBConv blocks and 230 layers [<xref ref-type="bibr" rid="ref-16">16</xref>]. It features a thick block structure comprising four closely connected layers with a growth rate of 4. All the layers in this model make use of the output feature map of the previous level as the input feature map. The dense block is comprised of convolutional layers of similar size to the input feature map in EfficientNet. Dense block uses previous convolutional layer output feature map for generating additional feature maps with less convolutional kernel. This CNN method retrieves 150 &#x00D7; 150 improved image data. The dense EfficientNet architecture has alternative drop-out and dense layers. A dense layer is a primary layer that feeds each output from the preceding layer to each neuron, all the neurons provide single output to the following layer. The drop-out layer is utilized for reducing the capacity or thins the network during the training process and avoids over-fitting. We start by adding a pooling layer, three drop-out layers, and four dense layers to ensure the model function properly. The number of neurons in the dense unit is 720, 360, 360, and 180, correspondingly. The drop-out value is 0.25, 0.25, and 0.5, correspondingly. At last, the researchers have utilized a dense layer comprised of four fully connected neurons along with a classification layer to classify and compute the possible score for all the classes.</p>
</sec>
<sec id="s2_2">
<label>2.2</label>
<title>DHNN Based Classification</title>
<p>To classify CRC, the DHNN model has been exploited. Assume that the output value of DHNN is <inline-formula id="ieqn-6"><mml:math id="mml-ieqn-6"><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:math></inline-formula> or 1, which is recorded as the excitation and inhibition states of neuron, correspondingly. The provided mark is shown in the following [<xref ref-type="bibr" rid="ref-17">17</xref>]:
<list list-type="bullet">
<list-item>
<p><inline-formula id="ieqn-7"><mml:math id="mml-ieqn-7"><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> indicates an external input value.</p></list-item>
<list-item>
<p><inline-formula id="ieqn-8"><mml:math id="mml-ieqn-8"><mml:mi>b</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> denotes a threshold of the <inline-formula id="ieqn-9"><mml:math id="mml-ieqn-9"><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> neuron.</p></list-item>
<list-item>
<p><inline-formula id="ieqn-10"><mml:math id="mml-ieqn-10"><mml:msub><mml:mi>&#x03C9;</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> represents the connection weight among two neurons, <inline-formula id="ieqn-11"><mml:math id="mml-ieqn-11"><mml:msub><mml:mi>&#x03C9;</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>&#x03C9;</mml:mi><mml:mrow><mml:mi>j</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>.</mml:mo></mml:math></inline-formula></p></list-item>
<list-item>
<p><inline-formula id="ieqn-12"><mml:math id="mml-ieqn-12"><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> signifies a binary neuron, <inline-formula id="ieqn-13"><mml:math id="mml-ieqn-13"><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mo>&#x2211;</mml:mo><mml:msub><mml:mi>&#x03C9;</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>.</mml:mo></mml:math></inline-formula></p></list-item>
<list-item>
<p><inline-formula id="ieqn-14"><mml:math id="mml-ieqn-14"><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> characterizes an output value, <inline-formula id="ieqn-15"><mml:math id="mml-ieqn-15"><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mml:mtr><mml:mtd><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x003C;</mml:mo><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mn>1</mml:mn><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2265;</mml:mo><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo></mml:mrow></mml:math></inline-formula></p></list-item>
<list-item>
<p><inline-formula id="ieqn-16"><mml:math id="mml-ieqn-16"><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> implies the <inline-formula id="ieqn-17"><mml:math id="mml-ieqn-17"><mml:mi>j</mml:mi></mml:math></inline-formula> neuron and shows the state of node jth at time <inline-formula id="ieqn-18"><mml:math id="mml-ieqn-18"><mml:mi>t</mml:mi><mml:mo>.</mml:mo></mml:math></inline-formula></p></list-item>
</list></p>
<p><inline-formula id="ieqn-19"><mml:math id="mml-ieqn-19"><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> denotes the state of node jth at time <inline-formula id="ieqn-20"><mml:math id="mml-ieqn-20"><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math></inline-formula>:</p>
<p><disp-formula id="eqn-7"><label>(7)</label><mml:math id="mml-eqn-7" display="block"><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mml:mtr><mml:mtd><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo></mml:mtd><mml:mtd><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x003C;</mml:mo><mml:mn>0</mml:mn></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mn>1</mml:mn><mml:mo>,</mml:mo></mml:mtd><mml:mtd><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2265;</mml:mo><mml:mn>0</mml:mn></mml:mtd></mml:mtr></mml:mtable><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mi>f</mml:mi><mml:mi>i</mml:mi><mml:mi>s</mml:mi><mml:mi>a</mml:mi><mml:mrow><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">l</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">e</mml:mi><mml:mi mathvariant="italic">a</mml:mi><mml:mi mathvariant="italic">r</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="italic">f</mml:mi><mml:mi mathvariant="italic">u</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">t</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">n</mml:mi></mml:mrow><mml:mo>.</mml:mo></mml:math></disp-formula></p>
<list list-type="bullet">
<list-item>
<p><inline-formula id="ieqn-21"><mml:math id="mml-ieqn-21"><mml:mi>Y</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mo stretchy="false">[</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><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>y</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">]</mml:mo></mml:math></inline-formula> represent an <inline-formula id="ieqn-22"><mml:math id="mml-ieqn-22"><mml:mi>n</mml:mi></mml:math></inline-formula> dimension vector.</p></list-item>
</list>
<p>The primary model of the DHNN is comprised of six neurons. Assume the operational mode of the Hopfield architecture to serial mode. Here, the Lyapunov function is the energy function, also it can be determined in the following:</p>
<p><disp-formula id="eqn-8"><label>(8)</label><mml:math id="mml-eqn-8" display="block"><mml:mi>E</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac><mml:munderover><mml:mo>&#x2211;</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:munderover><mml:munderover><mml:mo>&#x2211;</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:munderover><mml:msub><mml:mi>&#x03C9;</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:munderover><mml:mo>&#x2211;</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:munderover><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>.</mml:mo></mml:math></disp-formula></p>
<p>In our method, the outer-product technique is utilized for designing the Hopfield network, and the training objective preserves K <inline-formula id="ieqn-23"><mml:math id="mml-ieqn-23"><mml:mi>n</mml:mi></mml:math></inline-formula>-dimension attractor. <xref ref-type="fig" rid="fig-2">Fig. 2</xref> illustrates the structure of Boltzmann machine and Hopfield network.</p>
<fig id="fig-2">
<label>Figure 2</label>
<caption>
<title>(a) Boltzmann machine (b) Hop field network</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31037-fig-2.png"/>
</fig>
<p><disp-formula id="ueqn-9"><mml:math id="mml-ueqn-9" display="block"><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:msubsup><mml:mi>c</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:msubsup><mml:mi>c</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msubsup><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msubsup><mml:mo>]</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:math></disp-formula></p>
<p><disp-formula id="eqn-9"><label>(9)</label><mml:math id="mml-eqn-9" display="block"><mml:msub><mml:mi>&#x03C9;</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mml:mtr><mml:mtd><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:mn>1</mml:mn><mml:mi>a</mml:mi></mml:mfrac><mml:munderover><mml:mrow><mml:mo>&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>K</mml:mi></mml:mrow></mml:munderover><mml:mo>&#x2061;</mml:mo><mml:msubsup><mml:mi>c</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msubsup><mml:msubsup><mml:mi>c</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:mspace width="1em" /><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mi>n</mml:mi></mml:mstyle></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mi>j</mml:mi></mml:mtd></mml:mtr></mml:mtable><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo></mml:mrow></mml:math></disp-formula>whereas <inline-formula id="ieqn-24"><mml:math id="mml-ieqn-24"><mml:mi>a</mml:mi></mml:math></inline-formula> indicates the adjusting ratio; take <inline-formula id="ieqn-25"><mml:math id="mml-ieqn-25"><mml:mi>a</mml:mi><mml:mo>=</mml:mo><mml:mi>n</mml:mi><mml:mo>.</mml:mo></mml:math></inline-formula> The process is given in the following:</p>
<p><bold>Step 1:</bold> Initializing the network.</p>
<p><bold>Step 2:</bold> The ith neuron is arbitrarily chosen in the networks.</p>
<p><bold>Step 3:</bold> Evaluate the input value <inline-formula id="ieqn-26"><mml:math id="mml-ieqn-26"><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> for i-th neuron.</p>
<p><bold>Step 4:</bold> Evaluate the output value <inline-formula id="ieqn-27"><mml:math id="mml-ieqn-27"><mml:msub><mml:mi>&#x03BD;</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> for i-th neuron. Now, the output of other neurons in the network remains same.</p>
<p><bold>Step 5:</bold> to define either the network is stable or not: when it can be stable or meet the provided condition, it stops; or else, return to step 2.</p>
<p>Here, The steady state can be determined by <inline-formula id="ieqn-28"><mml:math id="mml-ieqn-28"><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="normal">&#x0394;</mml:mi><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mi>&#x03BD;</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>, <inline-formula id="ieqn-29"><mml:math id="mml-ieqn-29"><mml:mi mathvariant="normal">&#x0394;</mml:mi><mml:mi>t</mml:mi><mml:mo>&#x003E;</mml:mo><mml:mn>0.</mml:mn></mml:math></inline-formula></p>
</sec>
<sec id="s2_3">
<label>2.3</label>
<title>Hyperparameter Optimization</title>
<p>In this work, the utilization of SMA assists in appropriately selecting the parameters involved in the DHNN approach [<xref ref-type="bibr" rid="ref-18">18</xref>]. The steps involved in SMA are given as follows.</p>
<p><bold>Step 1:</bold> During this step, mathematics to the slime mold performance was created and subsequent rule was allocated for determining upgraded place in searching for food. The condition for this is dependent on <inline-formula id="ieqn-30"><mml:math id="mml-ieqn-30"><mml:mi>r</mml:mi></mml:math></inline-formula> and <inline-formula id="ieqn-31"><mml:math id="mml-ieqn-31"><mml:mi>p</mml:mi></mml:math></inline-formula>. It can be contraction mode of mold:</p>
<p><disp-formula id="eqn-10"><label>(10)</label><mml:math id="mml-eqn-10" display="block"><mml:mrow><mml:mover><mml:mrow><mml:mi>X</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>&#x2192;</mml:mo></mml:mover></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mml:mtr><mml:mtd><mml:mover><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>+</mml:mo><mml:mover><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>&#x22C5;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mover><mml:mi>W</mml:mi><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>&#x22C5;</mml:mo><mml:mover><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>A</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>&#x2212;</mml:mo><mml:mover><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>B</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>)</mml:mo></mml:mrow><mml:mi>r</mml:mi><mml:mo>&#x003C;</mml:mo><mml:mi>p</mml:mi></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mover><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>&#x22C5;</mml:mo><mml:mover><mml:mrow><mml:mi>X</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mi>r</mml:mi><mml:mo>&#x2265;</mml:mo><mml:mi>p</mml:mi></mml:mtd></mml:mtr></mml:mtable><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:math></disp-formula></p>
<p>In which <inline-formula id="ieqn-32"><mml:math id="mml-ieqn-32"><mml:mrow><mml:mover><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow></mml:math></inline-formula> signifies the parameter with range of <inline-formula id="ieqn-33"><mml:math id="mml-ieqn-33"><mml:mstyle displaystyle="false" scriptlevel="0"><mml:mtext>--</mml:mtext></mml:mstyle><mml:mi>a</mml:mi></mml:math></inline-formula> and <inline-formula id="ieqn-34"><mml:math id="mml-ieqn-34"><mml:mi>a</mml:mi><mml:mo>,</mml:mo></mml:math></inline-formula> <inline-formula id="ieqn-35"><mml:math id="mml-ieqn-35"><mml:mrow><mml:mover><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow></mml:math></inline-formula> signifies the parameter that methods linearly nearby 0. &#x2018;<inline-formula id="ieqn-36"><mml:math id="mml-ieqn-36"><mml:mi>t</mml:mi></mml:math></inline-formula>&#x2019; implies the existing iteration, <inline-formula id="ieqn-37"><mml:math id="mml-ieqn-37"><mml:mrow><mml:mover><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow></mml:math></inline-formula> signifies the place of all the particles from the region whereas odor is maximal, <inline-formula id="ieqn-38"><mml:math id="mml-ieqn-38"><mml:mrow><mml:mover><mml:mi>X</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow></mml:math></inline-formula> refers to the mold place, <inline-formula id="ieqn-39"><mml:math id="mml-ieqn-39"><mml:msub><mml:mrow><mml:mover><mml:mi>X</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>A</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-40"><mml:math id="mml-ieqn-40"><mml:msub><mml:mrow><mml:mover><mml:mi>X</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>B</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> represents the arbitrarily chosen variables in the swarm, <inline-formula id="ieqn-41"><mml:math id="mml-ieqn-41"><mml:mrow><mml:mover><mml:mi>W</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow></mml:math></inline-formula> signifies the measured of the weighted of masses. The maximal limit of <inline-formula id="ieqn-42"><mml:math id="mml-ieqn-42"><mml:mi>p</mml:mi></mml:math></inline-formula> is given as follows:</p>
<p><disp-formula id="eqn-11"><label>(11)</label><mml:math id="mml-eqn-11" display="block"><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mi>tan</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mi>h</mml:mi><mml:mi>S</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>i</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mi>D</mml:mi><mml:mi>F</mml:mi><mml:mi>F</mml:mi><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:math></disp-formula>whereas <inline-formula id="ieqn-43"><mml:math id="mml-ieqn-43"><mml:mi>i</mml:mi><mml:mo>&#x2208;</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mo>,</mml:mo></mml:math></inline-formula> <inline-formula id="ieqn-44"><mml:math id="mml-ieqn-44"><mml:mi>S</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>i</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo></mml:math></inline-formula> fitness of <inline-formula id="ieqn-45"><mml:math id="mml-ieqn-45"><mml:mrow><mml:mover><mml:mi>X</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow><mml:mo>,</mml:mo></mml:math></inline-formula> <inline-formula id="ieqn-46"><mml:math id="mml-ieqn-46"><mml:mi>D</mml:mi><mml:mi>F</mml:mi><mml:mo>=</mml:mo></mml:math></inline-formula> entire fitness in each step. The formula of <inline-formula id="ieqn-47"><mml:math id="mml-ieqn-47"><mml:mrow><mml:mover><mml:mi>v</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow></mml:math></inline-formula> as follows:</p>
<p><disp-formula id="eqn-12"><label>(12)</label><mml:math id="mml-eqn-12" display="block"><mml:mrow><mml:mover><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>a</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p><disp-formula id="eqn-13"><label>(13)</label><mml:math id="mml-eqn-13" display="block"><mml:mi>a</mml:mi><mml:mo>=</mml:mo><mml:mi>arctan</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mi>h</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mfrac><mml:mi>t</mml:mi><mml:mrow><mml:munder><mml:mo movablelimits="true" form="prefix">max</mml:mo><mml:mrow><mml:mo>&#x2212;</mml:mo></mml:mrow></mml:munder><mml:mi>t</mml:mi></mml:mrow></mml:mfrac><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>.</mml:mo></mml:math></disp-formula></p>
<p>The formula of <inline-formula id="ieqn-48"><mml:math id="mml-ieqn-48"><mml:mrow><mml:mover><mml:mi>W</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow></mml:math></inline-formula> is listed as:</p>
<p><disp-formula id="eqn-14"><label>(14)</label><mml:math id="mml-eqn-14" display="block"><mml:mrow><mml:mover><mml:mrow><mml:mi>W</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">m</mml:mi><mml:mi mathvariant="italic">e</mml:mi><mml:mi mathvariant="italic">l</mml:mi><mml:mi mathvariant="italic">l</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">d</mml:mi><mml:mi mathvariant="italic">e</mml:mi><mml:mi mathvariant="italic">x</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mml:mtr><mml:mtd><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mi>r</mml:mi><mml:mo>&#x22C5;</mml:mo><mml:mi>log</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:mrow><mml:mi>b</mml:mi><mml:mi>F</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>S</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>b</mml:mi><mml:mi>F</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>w</mml:mi><mml:mi>F</mml:mi></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mstyle><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mspace width="1em" /><mml:mrow><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">d</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">t</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">n</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mi>r</mml:mi><mml:mo>&#x22C5;</mml:mo><mml:mi>log</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:mrow><mml:mi>b</mml:mi><mml:mi>F</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>S</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>b</mml:mi><mml:mi>F</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>w</mml:mi><mml:mi>F</mml:mi></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mstyle><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mspace width="1em" /><mml:mrow><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">t</mml:mi><mml:mi mathvariant="italic">h</mml:mi><mml:mi mathvariant="italic">e</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">s</mml:mi></mml:mrow></mml:mtd></mml:mtr></mml:mtable><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:math></disp-formula></p>
<p><disp-formula id="eqn-15"><label>(15)</label><mml:math id="mml-eqn-15" display="block"><mml:mrow><mml:mi mathvariant="italic">S</mml:mi><mml:mi mathvariant="italic">m</mml:mi><mml:mi mathvariant="italic">e</mml:mi><mml:mi mathvariant="italic">l</mml:mi><mml:mi mathvariant="italic">l</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="italic">I</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">d</mml:mi><mml:mi mathvariant="italic">e</mml:mi><mml:mi mathvariant="italic">x</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mi>s</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>t</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>S</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:math></disp-formula>whereas <inline-formula id="ieqn-49"><mml:math id="mml-ieqn-49"><mml:mi>S</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>i</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> ranks first half of populations, <inline-formula id="ieqn-50"><mml:math id="mml-ieqn-50"><mml:mi>r</mml:mi></mml:math></inline-formula> signifies the arbitrary value from the interval of zero and one<inline-formula id="ieqn-51"><mml:math id="mml-ieqn-51"><mml:mo>,</mml:mo></mml:math></inline-formula> <inline-formula id="ieqn-52"><mml:math id="mml-ieqn-52"><mml:mi>b</mml:mi><mml:mi>F</mml:mi></mml:math></inline-formula> denotes the optimum fitness reached from the existing iterative procedure, <inline-formula id="ieqn-53"><mml:math id="mml-ieqn-53"><mml:mi>w</mml:mi><mml:mi>F</mml:mi></mml:math></inline-formula> refers to the worse fitness value reached from the iterative procedure, and <inline-formula id="ieqn-54"><mml:math id="mml-ieqn-54"><mml:mi>S</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>t</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>s</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> function sort fitness value.</p>
<p><bold>Step 2:</bold> The formula to upgrade the places of agents (that is, to wrap food) is provided as:</p>
<p><disp-formula id="eqn-16"><label>(16)</label><mml:math id="mml-eqn-16" display="block"><mml:mover><mml:msup><mml:mi>X</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mml:mtr><mml:mtd><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mo>&#x22C5;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mi>U</mml:mi><mml:mi>B</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>L</mml:mi><mml:mi>B</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>L</mml:mi><mml:mi>B</mml:mi><mml:mo>,</mml:mo><mml:mspace width="1em" /><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mo>&#x003C;</mml:mo><mml:mi>z</mml:mi></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mover><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>+</mml:mo><mml:mover><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>&#x22C5;</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mi>W</mml:mi><mml:mo>&#x22C5;</mml:mo><mml:mover><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>A</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>&#x2212;</mml:mo><mml:mover><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>B</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>,</mml:mo><mml:mspace width="1em" /><mml:mi>r</mml:mi><mml:mo>&#x003C;</mml:mo><mml:mi>p</mml:mi><mml:mo>,</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mover><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>&#x22C5;</mml:mo><mml:mover><mml:mrow><mml:mi>X</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>,</mml:mo><mml:mspace width="1em" /><mml:mi>r</mml:mi><mml:mo>&#x2265;</mml:mo><mml:mi>p</mml:mi></mml:mtd></mml:mtr></mml:mtable><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>In which, <inline-formula id="ieqn-55"><mml:math id="mml-ieqn-55"><mml:mi>L</mml:mi><mml:mi>B</mml:mi></mml:math></inline-formula> and <inline-formula id="ieqn-56"><mml:math id="mml-ieqn-56"><mml:mi>U</mml:mi><mml:mi>B</mml:mi></mml:math></inline-formula> indicate the searching limits, and <inline-formula id="ieqn-57"><mml:math id="mml-ieqn-57"><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:math></inline-formula> and <inline-formula id="ieqn-58"><mml:math id="mml-ieqn-58"><mml:mi>r</mml:mi></mml:math></inline-formula> signify the arbitrary values.</p>
<p><bold>Step 3:</bold> Using the up gradation from the searching procedure, the value of <inline-formula id="ieqn-59"><mml:math id="mml-ieqn-59"><mml:mrow><mml:mover><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow></mml:math></inline-formula> vibrantly variations among <inline-formula id="ieqn-60"><mml:math id="mml-ieqn-60"><mml:mstyle displaystyle="false" scriptlevel="0"><mml:mtext>--</mml:mtext></mml:mstyle><mml:mi>a</mml:mi></mml:math></inline-formula> and <inline-formula id="ieqn-61"><mml:math id="mml-ieqn-61"><mml:mi>a</mml:mi></mml:math></inline-formula>, and <inline-formula id="ieqn-62"><mml:math id="mml-ieqn-62"><mml:mrow><mml:mover><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow></mml:math></inline-formula> differs amongst &#x2212;1 and 1, and finally shrinks to 0. It can be recognized that &#x2018;grabbling of food&#x2019;.</p>
</sec>
</sec>
<sec id="s3">
<label>3</label>
<title>Results and Discussion</title>
<p>In this section, the experimental validation of the SMADTL-CCDC model is tested using Warwick-QU dataset (<uri xlink:href="https://www.warwick.ac.uk/fac/sci/dcs/research/tia/glascontest/download">www.warwick.ac.uk/fac/sci/dcs/research/tia/glascontest/download</uri>). It comprises 165 images with two class labels namely benign and malignant [<xref ref-type="bibr" rid="ref-19">19</xref>]. A few sample images of Colorectal Cancer are demonstrated in <xref ref-type="fig" rid="fig-3">Fig. 3</xref>.</p>
<fig id="fig-3">
<label>Figure 3</label>
<caption>
<title>Sample images of colorectal cancer</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31037-fig-3.png"/>
</fig>
<p><xref ref-type="fig" rid="fig-4">Fig. 4</xref> showcases the set of confusion matrices produced by the SMADTL-CCDC model on distinct sizes of training/testing (TR/TS) data. On 90% of TR data, the SMADTL-CCDC model has recognized 61 images into benign and 84 images into malignant. Also, on 80% of TR data, the SMADTL-CCDC approach has recognized 58 images into benign and 69 images into malignant. Besides, on 70% of TR data, the SMADTL-CCDC methodology has recognized 61 images into benign and 84 images into malignant.</p>
<fig id="fig-4">
<label>Figure 4</label>
<caption>
<title>Confusion matrix of SMADTL-CCDC technique on distinct sizes of TR/TS data</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31037-fig-4.png"/>
</fig>
<p><xref ref-type="table" rid="table-1">Tab. 1</xref> provides a detailed CRC classifier result of the SMADTL-CCDC model on TR/TS data of 90:10. The obtained values indicated that the SMADTL-CCDC model has accomplished improved performance in both cases. For instance, with 90% of TR data, the SMADTL-CCDC model has offered an average <inline-formula id="ieqn-63"><mml:math id="mml-ieqn-63"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-64"><mml:math id="mml-ieqn-64"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-65"><mml:math id="mml-ieqn-65"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-66"><mml:math id="mml-ieqn-66"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, and <inline-formula id="ieqn-67"><mml:math id="mml-ieqn-67"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> of 97.97%, 98.28%, 97.66%, 97.66%, and 97.92% respectively. At the same time, with 10% of TS data, the SMADTL-CCDC system has offered an average <inline-formula id="ieqn-68"><mml:math id="mml-ieqn-68"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-69"><mml:math id="mml-ieqn-69"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-70"><mml:math id="mml-ieqn-70"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-71"><mml:math id="mml-ieqn-71"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, and <inline-formula id="ieqn-72"><mml:math id="mml-ieqn-72"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> of 94.12%, 93.75%, 95%, 95%, and 94.04% correspondingly.</p>
<table-wrap id="table-1">
<label>Table 1</label>
<caption>
<title>Result analysis of SMADTL-CCDC method with various measures on TR/TS data of 90:10</title>
</caption>
<table frame="hsides" >
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th colspan="2">Training/Testing (90:10)</th>
</tr>
<tr>
<th>Class label</th>
<th>Accuracy</th>
<th>Precision</th>
<th>Recall</th>
<th>Specificity</th>
<th>F-score</th>
</tr>
</thead>
<tbody>
<tr>
<td>Training phase</td>
</tr>
<tr>
<td>Benign</td>
<td>97.97</td>
<td>100</td>
<td>95.31</td>
<td>100</td>
<td>97.6</td>
</tr>
<tr>
<td>Malignant</td>
<td>97.97</td>
<td>96.55</td>
<td>100</td>
<td>95.31</td>
<td>98.25</td>
</tr>
<tr>
<td>Average</td>
<td>97.97</td>
<td>98.28</td>
<td>97.66</td>
<td>97.66</td>
<td>97.92</td>
</tr>
<tr>
<td>Testing phase</td>
</tr>
<tr>
<td>Benign</td>
<td>94.12</td>
<td>100.00</td>
<td>90.00</td>
<td>100.00</td>
<td>94.74</td>
</tr>
<tr>
<td>Malignant</td>
<td>94.12</td>
<td>87.50</td>
<td>100.00</td>
<td>90.00</td>
<td>93.33</td>
</tr>
<tr>
<td>Average</td>
<td>94.12</td>
<td>93.75</td>
<td>95.00</td>
<td>95.00</td>
<td>94.04</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The training accuracy (TA) and validation accuracy (VA) attained by the SMADTL-CCDC model on TR/TS data of 90:10 is demonstrated in <xref ref-type="fig" rid="fig-5">Fig. 5</xref>. The experimental outcomes implied that the ICSOA-DLPEC model has gained maximum values of TA and VA. In specific, the VA is seemed to be higher than TA.</p>
<fig id="fig-5">
<label>Figure 5</label>
<caption>
<title>TA and VA analysis of SMADTL-CCDC model on TR/TS data of 90:10</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31037-fig-5.png"/>
</fig>
<p>The training loss (TL) and validation loss (VL) achieved by the SMADTL-CCDC model on TR/TS data of 90:10 is established in <xref ref-type="fig" rid="fig-6">Fig. 6</xref>. The experimental outcomes inferred that the ICSOA-DLPEC model has accomplished least values of TL and VL. In specific, the VL is seemed to be lower than TL.</p>
<fig id="fig-6">
<label>Figure 6</label>
<caption>
<title>TL and VL analysis of SMADTL-CCDC model on TR/TS data of 90:10</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31037-fig-6.png"/>
</fig>
<p><xref ref-type="table" rid="table-2">Tab. 2</xref> offers a detailed CRC classifier result of the SMADTL-CCDC model on TR/TS data of 80:20. The obtained values referred that the SMADTL-CCDC approach has accomplished improved performance in both cases. For instance, with 80% of TR data, the SMADTL-CCDC model has offered an average <inline-formula id="ieqn-73"><mml:math id="mml-ieqn-73"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-74"><mml:math id="mml-ieqn-74"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-75"><mml:math id="mml-ieqn-75"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-76"><mml:math id="mml-ieqn-76"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, and <inline-formula id="ieqn-77"><mml:math id="mml-ieqn-77"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> of 96.21%, 96.41%, 96.06%, 96.06%, and 96.19% respectively. Eventually, with 20% of TS data, the SMADTL-CCDC methodology has offered an average <inline-formula id="ieqn-78"><mml:math id="mml-ieqn-78"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-79"><mml:math id="mml-ieqn-79"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-80"><mml:math id="mml-ieqn-80"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-81"><mml:math id="mml-ieqn-81"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, and <inline-formula id="ieqn-82"><mml:math id="mml-ieqn-82"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> of 96.97%, 97.73%, 95.83%, 95.83%, and 96.66% correspondingly.</p>
<table-wrap id="table-2">
<label>Table 2</label>
<caption>
<title>Result analysis of SMADTL-CCDC method with various measures on TR/TS data of 80:20</title>
</caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th colspan="2">Training/Testing (80:20)</th>
</tr>
<tr>
<th>Class label</th>
<th>Accuracy</th>
<th>Precision</th>
<th>Recall</th>
<th>Specificity</th>
<th>F-score</th>
</tr>
</thead>
<tbody>
<tr>
<td>Training phase</td>
</tr>
<tr>
<td>Benign</td>
<td>96.21</td>
<td>98.31</td>
<td>93.55</td>
<td>98.57</td>
<td>95.87</td>
</tr>
<tr>
<td>Malignant</td>
<td>96.21</td>
<td>94.52</td>
<td>98.57</td>
<td>93.55</td>
<td>96.50</td>
</tr>
<tr>
<td>Average</td>
<td>96.21</td>
<td>96.41</td>
<td>96.06</td>
<td>96.06</td>
<td>96.19</td>
</tr>
<tr>
<td>Testing phase</td>
</tr>
<tr>
<td>Benign</td>
<td>96.97</td>
<td>100.00</td>
<td>91.67</td>
<td>100.00</td>
<td>95.65</td>
</tr>
<tr>
<td>Malignant</td>
<td>96.97</td>
<td>95.45</td>
<td>100.00</td>
<td>91.67</td>
<td>97.67</td>
</tr>
<tr>
<td>Average</td>
<td>96.97</td>
<td>97.73</td>
<td>95.83</td>
<td>95.83</td>
<td>96.66</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The TA and VA attained by the SMADTL-CCDC model on TR/TS data of 80:20 are demonstrated in <xref ref-type="fig" rid="fig-7">Fig. 7</xref>. The experimental outcomes implied that the ICSOA-DLPEC model has gained maximal values of TA and VA. In specific, the VA is seemed that higher than TA.</p>
<fig id="fig-7">
<label>Figure 7</label>
<caption>
<title>TA and VA analysis of SMADTL-CCDC model on TR/TS data of 80:20</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31037-fig-7.png"/>
</fig>
<p>The TL and VL achieved by the SMADTL-CCDC technique on TR/TS data of 80:20 are established in <xref ref-type="fig" rid="fig-8">Fig. 8</xref>. The experimental outcomes inferred that the ICSOA-DLPEC model has accomplished least values of TL and VL. In specific, the VL has appeared that lower than TL.</p>
<fig id="fig-8">
<label>Figure 8</label>
<caption>
<title>TL and VL analysis of SMADTL-CCDC model on TR/TS data of 80:20</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31037-fig-8.png"/>
</fig>
<p><xref ref-type="table" rid="table-3">Tab. 3</xref> gives a detailed CRC classifier result of the SMADTL-CCDC system on TR/TS data of 70:30. The obtained values indicated that the SMADTL-CCDC approach has accomplished enhanced performance in both cases. For instance, with 70% of TR data, the SMADTL-CCDC algorithm has offered an average <inline-formula id="ieqn-83"><mml:math id="mml-ieqn-83"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-84"><mml:math id="mml-ieqn-84"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-85"><mml:math id="mml-ieqn-85"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-86"><mml:math id="mml-ieqn-86"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, and <inline-formula id="ieqn-87"><mml:math id="mml-ieqn-87"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> of 99.13%, 99.07%, 99.19%, 99.19%, and 99.13% respectively. In addition, with 30% of TS data, the SMADTL-CCDC system has offered an average <inline-formula id="ieqn-88"><mml:math id="mml-ieqn-88"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-89"><mml:math id="mml-ieqn-89"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-90"><mml:math id="mml-ieqn-90"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-91"><mml:math id="mml-ieqn-91"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, and <inline-formula id="ieqn-92"><mml:math id="mml-ieqn-92"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> of 98%, 97.73%, 98.28%, 98.28%, and 97.96% correspondingly.</p>
<table-wrap id="table-3">
<label>Table 3</label>
<caption>
<title>Result analysis of SMADTL-CCDC method with various measures on TR/TS data of 70:30</title>
</caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th colspan="2">Training/Testing (70:30)</th>
</tr>
<tr>
<th>Class label</th>
<th>Accuracy</th>
<th>Precision</th>
<th>Recall</th>
<th>Specificity</th>
<th>F-score</th>
</tr>
</thead>
<tbody>
<tr>
<td>Training phase</td>
</tr>
<tr>
<td>Benign</td>
<td>99.13</td>
<td>98.15</td>
<td>100.00</td>
<td>98.39</td>
<td>99.07</td>
</tr>
<tr>
<td>Malignant</td>
<td>99.13</td>
<td>100.00</td>
<td>98.39</td>
<td>100.00</td>
<td>99.19</td>
</tr>
<tr>
<td>Average</td>
<td>99.13</td>
<td>99.07</td>
<td>99.19</td>
<td>99.19</td>
<td>99.13</td>
</tr>
<tr>
<td>Testing phase</td>
</tr>
<tr>
<td>Benign</td>
<td>98.00</td>
<td>95.45</td>
<td>100.00</td>
<td>96.55</td>
<td>97.67</td>
</tr>
<tr>
<td>Malignant</td>
<td>98.00</td>
<td>100.00</td>
<td>96.55</td>
<td>100.00</td>
<td>98.25</td>
</tr>
<tr>
<td>Average</td>
<td>98.00</td>
<td>97.73</td>
<td>98.28</td>
<td>98.28</td>
<td>97.96</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The TA and VA attained by the SMADTL-CCDC algorithm on TR/TS data of 70:30 are demonstrated in <xref ref-type="fig" rid="fig-9">Fig. 9</xref>. The experimental outcomes implied that the ICSOA-DLPEC model has gained maximum values of TA and VA. In specific, the VA is appeared to be higher than TA.</p>
<fig id="fig-9">
<label>Figure 9</label>
<caption>
<title>TA and VA analysis of SMADTL-CCDC model on TR/TS data of 70:30</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31037-fig-9.png"/>
</fig>
<p>The TL and VL achieved by the SMADTL-CCDC model on TR/TS data of 70:30 are established in <xref ref-type="fig" rid="fig-10">Fig. 10</xref>. The experimental outcomes inferred that the ICSOA-DLPEC technique has accomplished least values of TL and VL. In specific, the VL is seemed to be lower than TL.</p>
<fig id="fig-10">
<label>Figure 10</label>
<caption>
<title>TL and VL analysis of SMADTL-CCDC model on TR/TS data of 70:30</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31037-fig-10.png"/>
</fig>
<p><xref ref-type="fig" rid="fig-11">Fig. 11</xref> provides a comparative <inline-formula id="ieqn-93"><mml:math id="mml-ieqn-93"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> examination of the SMADTL-CCDC model with existing models [<xref ref-type="bibr" rid="ref-20">20</xref>&#x2013;<xref ref-type="bibr" rid="ref-23">23</xref>]. The figure reported that the ResNet-18 (60-40), ResNet-50 (60-40), and DL-CP models have attained lower <inline-formula id="ieqn-94"><mml:math id="mml-ieqn-94"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> values of 66.29%, 61.69%, and 70.93% respectively. In addition, the ResNet-18 (80-20), ResNet-50 (75-25), ResNet-50 (80-20), and DL-SC Models have obtained slightly increased <inline-formula id="ieqn-95"><mml:math id="mml-ieqn-95"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> values of 84.67%, 90.78%, 94.79%, and 84.80% respectively. Though the ResNet-18 (75-25) model has accomplished reasonably <inline-formula id="ieqn-96"><mml:math id="mml-ieqn-96"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 98.26%, the SMADTL-CCDC model has resulted in superior <inline-formula id="ieqn-97"><mml:math id="mml-ieqn-97"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 98.28%.</p>
<fig id="fig-11">
<label>Figure 11</label>
<caption>
<title><inline-formula id="ieqn-108"><mml:math id="mml-ieqn-108"><mml:mi>S</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> analysis of SMADTL-CCDC approach with recent methodologies</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31037-fig-11.png"/>
</fig>
<p><xref ref-type="fig" rid="fig-12">Fig. 12</xref> offers a comparative <inline-formula id="ieqn-98"><mml:math id="mml-ieqn-98"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> analysis of the SMADTL-CCDC model with existing models. The figure exposed that the ResNet-18 (75.25), DL-CP, and DL-SC models have attained lower <inline-formula id="ieqn-99"><mml:math id="mml-ieqn-99"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> values of 65.30%, 73.04%, and 82.82% correspondingly. Also, the ResNet-18 (60-40), ResNet-50 (80-20), ResNet-18 (75-25), and ResNet-18 (80-20) Models have obtained somewhat improved <inline-formula id="ieqn-100"><mml:math id="mml-ieqn-100"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> values of 84.71%, 85.42%, 89.10%, and 89.11% correspondingly. But the ResNet-50 (60-40) approach has accomplished reasonably <inline-formula id="ieqn-101"><mml:math id="mml-ieqn-101"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 94.35%, the SMADTL-CCDC model has resulted in superior <inline-formula id="ieqn-102"><mml:math id="mml-ieqn-102"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 98.28%.</p>
<fig id="fig-12">
<label>Figure 12</label>
<caption>
<title><inline-formula id="ieqn-109"><mml:math id="mml-ieqn-109"><mml:mi>S</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> analysis of SMADTL-CCDC approach with recent methodologies</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31037-fig-12.png"/>
</fig>
<p><xref ref-type="fig" rid="fig-13">Fig. 13</xref> gives a comparative <inline-formula id="ieqn-103"><mml:math id="mml-ieqn-103"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> examination of the SMADTL-CCDC model with existing models. The figure reported that the DL-CP, ResNet-18 (60-40), and ResNet-50 (60-40) approaches have attained lower <inline-formula id="ieqn-104"><mml:math id="mml-ieqn-104"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> values of 72.28%, 74.76%, and 7.23% correspondingly. Morover, the ResNet-18 (75-25), DL-SC, ResNet-18 (80-20), and ResNet-50 (75-25) Models have obtained slightly increased <inline-formula id="ieqn-105"><mml:math id="mml-ieqn-105"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> values of 83.19%, 83.47%, 87.56%, and 89.70% correspondingly. At last, the ResNet-50 (80-20) algorithm has accomplished reasonably <inline-formula id="ieqn-106"><mml:math id="mml-ieqn-106"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 90.25%, the SMADTL-CCDC approach has resulted in higher <inline-formula id="ieqn-107"><mml:math id="mml-ieqn-107"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 98%.</p>
<fig id="fig-13">
<label>Figure 13</label>
<caption>
<title><inline-formula id="ieqn-110"><mml:math id="mml-ieqn-110"><mml:mi>A</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> analysis of SMADTL-CCDC approach with recent methodologies</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31037-fig-13.png"/>
</fig>
<p>From the detailed results and discussion, it can be evident that the SMADTL-CCDC model has gained maximum performance over the other methods.</p>
</sec>
<sec id="s4">
<label>4</label>
<title>Conclusion</title>
<p>In this study, a new SMADTL-CCDC model has been developed to appropriately recognize the occurrence of CRC. The SMADTL-CCDC model originally undergoes pre-processing to improve the input image quality. Followed by, a dense-EfficientNet approach was employed to extract feature vectors in the pre-processed images. Moreover, SMA with DHNN technique was executed for the recognition and classification of CRC. The utilization of SMA assists in appropriately selecting the parameters contained in the DHNN approach. A wide range of experiments is applied to benchmark datasets to assess the classification performance. A comprehensive comparative study highlighted the better performance of the SMADTL-CDC technique on the recent approaches. In future, hybrid DL models can be employed to perform classification processes.</p>
</sec>
</body>
<back>
<fn-group>
<fn fn-type="other"><p><bold>Funding Statement:</bold> This work was funded by the Deanship of Scientific Research (DSR) at King AbdulAziz University (KAU), Jeddah, Saudi Arabia, under grant no. (DF-497-141-1441). The authors, therefore, gratefully acknowledge DSR for technical and financial support.</p>
</fn>
<fn fn-type="conflict"><p><bold>Conflicts of Interest:</bold> The authors declare that they have no conflicts of interest to report regarding the present study.</p>
</fn>
</fn-group>
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