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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">26715</article-id>
<article-id pub-id-type="doi">10.32604/cmc.2022.026715</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Automated Artificial Intelligence Empowered Colorectal Cancer Detection and Classification Model</article-title>
<alt-title alt-title-type="left-running-head">Automated Artificial Intelligence Empowered Colorectal Cancer Detection and Classification Model</alt-title>
<alt-title alt-title-type="right-running-head">Automated Artificial Intelligence Empowered 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>Albukhari</surname><given-names>Ashwag</given-names></name><xref ref-type="aff" rid="aff-2">2</xref>
<xref ref-type="aff" rid="aff-4">4</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>Centre of Artificial Intelligence for 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>Mathematics Department, 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>Biochemistry Department, Faculty of Science, King Abdulaziz University</institution>, <addr-line>Jeddah, 21589</addr-line>, <country>Saudi Arabia</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="2022-04-20"><day>20</day>
<month>04</month>
<year>2022</year></pub-date>
<volume>72</volume>
<issue>3</issue>
<fpage>5577</fpage>
<lpage>5591</lpage>
<history>
<date date-type="received"><day>03</day><month>1</month><year>2022</year></date>
<date date-type="accepted"><day>18</day><month>3</month><year>2022</year></date>
</history>
<permissions>
<copyright-statement>&#x00A9; 2022 Ragab and Albukhari</copyright-statement>
<copyright-year>2022</copyright-year>
<copyright-holder>Ragab and Albukhari</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_26715.pdf"></self-uri>
<abstract>
<p>Colorectal cancer is one of the most commonly diagnosed cancers and it develops in the colon region of large intestine. The histopathologist generally investigates the colon biopsy at the time of colonoscopy or surgery. Early detection of colorectal cancer is helpful to maintain the concept of accumulating cancer cells. In medical practices, histopathological investigation of tissue specimens generally takes place in a conventional way, whereas automated tools that use Artificial Intelligence (AI) techniques can produce effective results in disease detection performance. In this background, the current study presents an Automated AI-empowered Colorectal Cancer Detection and Classification (AAI-CCDC) technique. The proposed AAI-CCDC technique focuses on the examination of histopathological images to diagnose colorectal cancer. Initially, AAI-CCDC technique performs pre-processing in three levels such as gray scale transformation, Median Filtering (MF)-based noise removal, and contrast improvement. In addition, Nadam optimizer with EfficientNet model is also utilized to produce meaningful feature vectors. Furthermore, Glowworm Swarm Optimization (GSO) with Stacked Gated Recurrent Unit (SGRU) model is used for the detection and classification of colorectal cancer. The proposed AAI-CCDC technique was experimentally validated using benchmark dataset and the experimental results established the supremacy of the proposed AAI-CCDC technique over conventional approaches.</p>
</abstract>
<kwd-group kwd-group-type="author">
<kwd>Colorectal cancer</kwd>
<kwd>medical data classification</kwd>
<kwd>noise removal</kwd>
<kwd>data classification</kwd>
<kwd>artificial intelligence</kwd>
<kwd>biomedical images</kwd>
<kwd>deep learning</kwd>
<kwd>optimizers</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1"><label>1</label><title>Introduction</title>
<p>Cancer grading is a procedure that determines the extent of malignancy and it is a major criteria utilized in medical settings to plan the treatment and inform the patient about disease prognosis [<xref ref-type="bibr" rid="ref-1">1</xref>]. However, it is challenging to attain high accuracy in cancer grading process in pathology practice. At the time of diagnosis, the tumors exhibit high levels of heterogeneity since the cancerous cells are capable enough to produce different levels of angiogenesis, host inflammatory response, and tumor necrosis among other factors included in tumor growth [<xref ref-type="bibr" rid="ref-2">2</xref>]. Also, the spatial preparation of heterogeneous cell types is proved that it has an association with cancer grading [<xref ref-type="bibr" rid="ref-3">3</xref>]. Thus, both quantitative and qualitative analyses of distinct types of cancer cells can assist in tumor stratification which in turn helps in determining the most effective therapeutic options [<xref ref-type="bibr" rid="ref-4">4</xref>]. Genomic architecture and cancer-specific markers can be used to classify tumors and identify different types of cells within the tumor. However, this scenario requires extensive characterization, time and experimental validation of tumor cells to identify useful markers [<xref ref-type="bibr" rid="ref-5">5</xref>].</p>
<p>In Colorectal Cancer (CRC), the morphology of intestinal gland includes gland formation whereas architectural appearance is a primary criterion for cancer grading. Glands are significant histological structures in almost all organs of the body with a primary purpose to achieve i.e., to secret carbohydrates and proteins [<xref ref-type="bibr" rid="ref-6">6</xref>]. Human colon contains masses of glands in it. Intestinal gland originates in the epithelial layer that is composed of single sheet of columnar epithelium. This epithelium forms a tubular shaped finger which expands the internal surface of colon to baseline connecting tissues [<xref ref-type="bibr" rid="ref-7">7</xref>]. Intestinal glands are responsible for the absorption of nutrients and water, mucus secretion to protect the epithelium in hostile mechanical and chemical environments and provide a niche for epithelial cells to redevelop. Because of its hostile environments, epithelial layers are one of the fastest and continually redeveloping structures in human body. This rapid renewal process of the cells needs coordination among cell apoptosis, proliferation, and differentiation processes [<xref ref-type="bibr" rid="ref-8">8</xref>]. When there is a loss in integrity among these processes, in the regeneration of epithelial cells, colorectal cancer i.e., colorectal adenocarcinoma develops and it is one of the common types of cancer. It is challenging to segment the gland images manually. Automatic gland segmentation allows the extraction of quantitative features related to gland morphology in digitalized image of CRC tissues. The effective segmentation of glands paves the way towards increasing the accuracy of cancer grading and computer-enabled grading of CRC. However, effective segmentation of glands, to differentiate cancer grading, remains a challenging problem [<xref ref-type="bibr" rid="ref-9">9</xref>]. At present, medical imaging is an effective mechanism in the diagnosis of different diseases including the presence of solid tumors. Machine Learning (ML) device is used in medical image processing to resolve medical images and pattern recognition [<xref ref-type="bibr" rid="ref-10">10</xref>].</p>
<p>Bychkov et al. [<xref ref-type="bibr" rid="ref-11">11</xref>] combined recurrent and convolution structures to train a deep network and forecast the CRC result based on the images of tumour tissue samples. The novelty of this method is that it straightforwardly predicts the patient outcomes without intermediate tissue classification. Vorontsov et al. [<xref ref-type="bibr" rid="ref-12">12</xref>] estimated the agreement, efficiency, and the performance of Fully Convolutional Network (FCN) for liver lesion detection and segmentation during CT scan examination in patients with Colorectal Liver Metastases (CLM). This retrospective analysis examined an automated model in which the proposed FCN was tested, trained, and validated with 26, 115, and 15 contrast materials while the CT examination contained 105, 261, and 22 tumors respectively. In general, manual segmentation and tumor detection by a radiotherapist remain the standard reference. The implementation of fully automatic and user-corrected segmentation is compared with manual segmentation. The communication period of automatic, inter-user agreement and user-corrected segmentation have been evaluated earlier.</p>
<p>Zhou et al. [<xref ref-type="bibr" rid="ref-13">13</xref>] developed an approach in which global labels were utilized to attain Whole Slide Images (WSIs) after which localization and classification of carcinoma was done by integrating the features in distinct magnifications of WSI. The method was tested and trained by 1346 CRC WSI. Xu et al. [<xref ref-type="bibr" rid="ref-14">14</xref>] presented a Deep Learning (DL)-based model in CRC detection and segmentation using the images of digitalized H&#x0026;E-stained histology slides. Based on the assumption that this method is an excellent performer on standard slides, the NN algorithm can be used further as an appropriate screening method that can save time of the pathologists in finding the tumor region. Also, their technique is recommended as an effective supporter of CRC diagnosis. Ito et al. [<xref ref-type="bibr" rid="ref-15">15</xref>] focused on using deep DL software and Convolutional Neural Network (CNN) to help in cT1b diagnoses. Recessed, Protruding, and flat lesions were investigated in this study. Caffe and AlexNet were employed for ML methods. Data Finetuning which increases the number of images, was implemented. Over-sampling was carried out for training image to avoid impartialities in image number and learning was conducted.</p>
<p>The current research work presents an Automated AI-empowered Colorectal Cancer Detection and Classification (AAI-CCDC) technique. Primarily, the proposed AAI-CCDC technique performs pre-processing in three levels namely, gray scale transformation, Median Filtering (MF)-based noise removal, and contrast improvement. In addition, Nadam optimizer with EfficientNet model is also utilized to produce meaningful feature vectors. Furthermore, Glowworm Swarm Optimization (GSO) with Stacked Gated Recurrent Unit (SGRU) model is used in the detection and classification of CRC. The proposed AAI-CCDC technique was validated for its performance using benchmark dataset and the results were assessed under different metrics.</p>
</sec>
<sec id="s2"><label>2</label><title>Design of AAI-CCDC Technique</title>
<p>In current study, an effective AAI-CCDC technique is developed for the examination of histopathological images to diagnose CRC. The presented AAI-CCDC technique encompasses pre-processing, EfficientNet-based feature extraction, Nadam-based parameter tuning, SGRU-based classification, and GSO-based hyperparameter tuning. The usage of Nadam and GSO algorithms is for improving the detection and classification efficiency of CRC. <xref ref-type="fig" rid="fig-1">Fig. 1</xref> is the overall block diagram of the proposed AAI-CCDC technique.</p>
<fig id="fig-1"><label>Figure 1</label><caption><title>Block diagram of AAI-CCDC technique</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_26715-fig-1.png"/></fig>
<sec id="s2_1"><label>2.1</label><title>Stage I: Pre-Processing</title>
<p>In this initial stage of AAI-CCDC technique, pre-processing of the image is executed in three levels namely, gray scale transformation, MF-based noise removal, and contrast improvement. At first, the color images are converted into grayscale form. Followed by, the noise is removed with the help of MF technique. This results in <inline-formula id="ieqn-1"><mml:math id="mml-ieqn-1"><mml:mi>m</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>n</mml:mi></mml:math></inline-formula> neighborhood while every neighborhood is assembled in the rising order. Then, the median value of the arranged series is elected and the intermediate pixel is substituted [<xref ref-type="bibr" rid="ref-16">16</xref>]. It can be defined using <xref ref-type="disp-formula" rid="eqn-1">Eq. (1)</xref>:
<disp-formula id="eqn-1"><label>(1)</label><mml:math id="mml-eqn-1" display="block"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mi>m</mml:mi><mml:mi>e</mml:mi><mml:mi>d</mml:mi><mml:mi>i</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>j</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2208;</mml:mo><mml:mi>C</mml:mi></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:math></disp-formula>where <italic>C</italic> implies the neighboring value. Thirdly, CLAHE model is used for contrast enhancement procedure.</p>
</sec>
<sec id="s2_2"><label>2.2</label><title>Stage II: EfficientNet Based Feature Extraction</title>
<p>After image pre-processing, extraction of features is the next stage in which EfficientNet model is used [<xref ref-type="bibr" rid="ref-17">17</xref>]. The authors utilized EfficientNetB4 technique to Transfer Learning (TL) procedure and global_average_pooling2d layer to minimize the over fitting issues by decreasing the entire number of parameters. In the same way, an order of three inner dense layers with RELU activation function and dropout layer are additionally used. Overall, a 30&#x0025; dropout rate is selected arbitrarily so as to avoid over-fitting. At last, one resultant dense layer has two resultant units against binary classification, and three resultant units for multi-class classification with softmax activation function which is for creating the presented automated detection method. Open source materials such as software and library materials are only used for the current study. In order to reproduce the outcomes, the reader utilizes Google Colab Notebook with the help of GPU runtime type. This software i2 is utilized at no costs, as it is offered by Google for research purposes. This software utilizes a Tesla K80 GPU of 12 GB. EfficientNet techniques were used for pre-training while scaled CNN technique was utilized in TL from image classification issues. ImageDataAugmentor is a custom image data generator to Keras that supports augmentation components.</p>
<p>The authors utilized three distinct important libraries for the technique presented in this study. These libraries contain EfficientNet, Albumentation, and ImageDataAugmentor modules. Accordingly, EfficientNet techniques are dependent upon easy and extremely-effective compound scaling techniques. This technique allows the scale up baseline ConvNet for some target resource constraint, but the model&#x2019;s efficacy is continued and utilized in TL dataset. In general, EfficientNet technique attains a combination of superior accuracy and optimum efficacy on the present CNN&#x2019;s namely MobileNetV2, ImageNet, AlexNet, and GoogleNet. No similar analysis is conducted so far utilizing EfficientNet to TL regarding COVID-19 classification to optimum updating of author skill. EfficientNet contains B0 to B7 techniques while everyone has distinct parameters in the range of 5.3&#x2005;M to 66&#x2005;M. The authors, in this study, utilized EfficentNetB4 which has 19&#x2005;M parameter and it is an appropriate model which can be justified based on its resource and resolve.</p>
</sec>
<sec id="s2_3"><label>2.3</label><title>Stage III: Nadam Optimizer</title>
<p>Nadam optimizer can be utilized as per the literature [<xref ref-type="bibr" rid="ref-18">18</xref>] to fine tune the hyperparameters of EfficientNet model. NAdam is more of Nesterov momentum to adaptive moment estimation (Adam). In order to consider the DBN method for optimization of normal charging voltage as instance, the upgrade rules of Adam are attained as follows
<disp-formula id="eqn-2"><label>(2)</label><mml:math id="mml-eqn-2" display="block"><mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi mathvariant="normal">&#x2207;</mml:mi><mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03B8;</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mi>J</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03B8;</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula>
<disp-formula id="eqn-3"><label>(3)</label><mml:math id="mml-eqn-3" display="block"><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow></mml:math></disp-formula>
<disp-formula id="eqn-4"><label>(4)</label><mml:math id="mml-eqn-4" display="block"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:msubsup><mml:mi>g</mml:mi><mml:mi>t</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:math></disp-formula>
<disp-formula id="eqn-5"><label>(5)</label><mml:math id="mml-eqn-5" display="block"><mml:mrow><mml:msub><mml:mrow><mml:mover><mml:mi>m</mml:mi><mml:mo>&#x005E;</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mtext>t</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mi>&#x03B2;</mml:mi><mml:mn>1</mml:mn><mml:mi>t</mml:mi></mml:msubsup></mml:mrow></mml:mfrac></mml:math></disp-formula>
<disp-formula id="eqn-6"><label>(6)</label><mml:math id="mml-eqn-6" display="block"><mml:mrow><mml:msub><mml:mrow><mml:mover><mml:mi>v</mml:mi><mml:mo stretchy="false">&#x005E;</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mtext>t</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mi>&#x03B2;</mml:mi><mml:mn>2</mml:mn><mml:mi>t</mml:mi></mml:msubsup></mml:mrow></mml:mfrac></mml:math></disp-formula>
<disp-formula id="eqn-7"><label>(7)</label><mml:math id="mml-eqn-7" display="block"><mml:mrow><mml:msub><mml:mi>&#x03B8;</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>&#x03B8;</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mfrac><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:msqrt><mml:mrow><mml:mover><mml:mi>v</mml:mi><mml:mo stretchy="false">&#x005E;</mml:mo></mml:mover></mml:mrow></mml:msqrt><mml:mo>+</mml:mo><mml:mi>&#x03B5;</mml:mi></mml:mrow></mml:mfrac><mml:mrow><mml:msub><mml:mrow><mml:mover><mml:mi>m</mml:mi><mml:mo>&#x005E;</mml:mo></mml:mover></mml:mrow><mml:mi>t</mml:mi></mml:msub></mml:mrow><mml:mspace width="thickmathspace" /></mml:math></disp-formula>where <inline-formula id="ieqn-2"><mml:math id="mml-ieqn-2"><mml:mi>&#x03B8;</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03B8;</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mtext>&#xA0;</mml:mtext></mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03B8;</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mtext>&#xA0;</mml:mtext></mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03B8;</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mtext>&#xA0;</mml:mtext></mml:mrow><mml:mo>&#x22EF;</mml:mo><mml:mrow><mml:msub><mml:mi>&#x03B8;</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:math></inline-formula> implies the parameter of normal charging voltage of DBN technique; <inline-formula id="ieqn-3"><mml:math id="mml-ieqn-3"><mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> signifies the gradient vector in normal charging voltage of trained DBN technique; <inline-formula id="ieqn-4"><mml:math id="mml-ieqn-4"><mml:mi>&#x03B7;</mml:mi></mml:math></inline-formula> refers to the rate of learning the normal charging voltage of trained DBN technique; <inline-formula id="ieqn-5"><mml:math id="mml-ieqn-5"><mml:mi>J</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03B8;</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> indicates the partition function of RBM from normal charging voltage of DBN technique, <inline-formula id="ieqn-6"><mml:math id="mml-ieqn-6"><mml:mrow><mml:msub><mml:mi mathvariant="normal">&#x2207;</mml:mi><mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03B8;</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> denotes the partial derivative of <inline-formula id="ieqn-7"><mml:math id="mml-ieqn-7"><mml:mi>J</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03B8;</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> whereas <inline-formula id="ieqn-8"><mml:math id="mml-ieqn-8"><mml:mi>&#x03B8;</mml:mi><mml:mo>,</mml:mo><mml:mspace width="thinmathspace" /><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, and <inline-formula id="ieqn-9"><mml:math id="mml-ieqn-9"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> denote the 1<sup>st</sup>-order moment (mean) and 2<sup>nd</sup>-order moment (variance) of gradient under the trained DBN approach with normal charging voltage; <inline-formula id="ieqn-10"><mml:math id="mml-ieqn-10"><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula id="ieqn-11"><mml:math id="mml-ieqn-11"><mml:mrow><mml:mover><mml:mi>v</mml:mi><mml:mo stretchy="false">&#x005E;</mml:mo></mml:mover></mml:mrow></mml:math></inline-formula> stand for deviation corrections of <inline-formula id="ieqn-12"><mml:math id="mml-ieqn-12"><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula id="ieqn-13"><mml:math id="mml-ieqn-13"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> which are used for offsetting the deviations; <inline-formula id="ieqn-14"><mml:math id="mml-ieqn-14"><mml:mrow><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula id="ieqn-15"><mml:math id="mml-ieqn-15"><mml:mrow><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> define the exponential decomposition rates of <inline-formula id="ieqn-16"><mml:math id="mml-ieqn-16"><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula id="ieqn-17"><mml:math id="mml-ieqn-17"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mspace width="thinmathspace" /><mml:mi>&#x03B5;</mml:mi></mml:math></inline-formula> demonstrates the correction parameter which ensures that the denominator has non-zero; <italic>t</italic> signifies the amount of iterations from the trained DBN approach with normal charging voltage.
<disp-formula id="eqn-8"><label>(8)</label><mml:math id="mml-eqn-8" display="block"><mml:mrow><mml:msub><mml:mi>&#x03B8;</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>&#x03B8;</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mfrac><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:msqrt><mml:mrow><mml:mover><mml:mi>v</mml:mi><mml:mo stretchy="false">&#x005E;</mml:mo></mml:mover></mml:mrow><mml:mo>+</mml:mo><mml:mi>&#x03B5;</mml:mi></mml:msqrt></mml:mrow></mml:mfrac><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mi>&#x03B2;</mml:mi><mml:mn>1</mml:mn><mml:mi>t</mml:mi></mml:msubsup></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mi>&#x03B2;</mml:mi><mml:mn>1</mml:mn><mml:mi>t</mml:mi></mml:msubsup></mml:mrow></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p><inline-formula id="ieqn-18"><mml:math id="mml-ieqn-18"><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mi>&#x03B2;</mml:mi><mml:mn>1</mml:mn><mml:mi>t</mml:mi></mml:msubsup></mml:math></inline-formula> inside the bracket denotes the deviation correction value, evaluated for momentum vector, at the preceding moment of DBN technique with normal charging voltage. This value is attained by exchanging <inline-formula id="ieqn-19"><mml:math id="mml-ieqn-19"><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> as follows.
<disp-formula id="eqn-9"><label>(9)</label><mml:math id="mml-eqn-9" display="block"><mml:mrow><mml:msub><mml:mi>&#x03B8;</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>&#x03B8;</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mfrac><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:msqrt><mml:mrow><mml:mover><mml:mi>v</mml:mi><mml:mo stretchy="false">&#x005E;</mml:mo></mml:mover></mml:mrow><mml:mo>+</mml:mo><mml:mi>&#x03B5;</mml:mi></mml:msqrt></mml:mrow></mml:mfrac><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mrow><mml:mover><mml:mi>m</mml:mi><mml:mo stretchy="false">&#x005E;</mml:mo></mml:mover></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mtext>t</mml:mtext></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mi>&#x03B2;</mml:mi><mml:mn>1</mml:mn><mml:mi>t</mml:mi></mml:msubsup></mml:mrow></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>In case at present Nesterov momentum, the deviation correction evaluates the <inline-formula id="ieqn-20"><mml:math id="mml-ieqn-20"><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of present momentum vector in the DBN technique with normal charging voltage. This value is directly utilized to replace the deviation-corrected evaluate <inline-formula id="ieqn-21"><mml:math id="mml-ieqn-21"><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> of the preceding momentum that results in the upgradation rule of NAdam of DBN technique with normal charging voltage.
<disp-formula id="eqn-10"><label>(10)</label><mml:math id="mml-eqn-10" display="block"><mml:mrow><mml:msub><mml:mi>&#x03B8;</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>&#x03B8;</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mfrac><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:msqrt><mml:mrow><mml:mover><mml:mi>v</mml:mi><mml:mo stretchy="false">&#x005E;</mml:mo></mml:mover></mml:mrow><mml:mo>+</mml:mo><mml:mi>&#x03B5;</mml:mi></mml:msqrt></mml:mrow></mml:mfrac><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:mover><mml:mi>m</mml:mi><mml:mo stretchy="false">&#x005E;</mml:mo></mml:mover></mml:mrow><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mi>&#x03B2;</mml:mi><mml:mn>1</mml:mn><mml:mi>t</mml:mi></mml:msubsup></mml:mrow></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>The typical momentum technique has a drawback i.e., its rate of learning cannot be altered from the trained method and it utilizes a single rate of learning to update the weight.</p>
</sec>
<sec id="s2_4"><label>2.4</label><title>Stage IV: SGRU Based Classification</title>
<p>In this final stage, SGRU model is exploited to determine the class labels for CRC detection. Traditional ML method deals with time series problems; all the moments of a sample are considered as a distinct independent arbitrary parameter. Further, it is also given to the neural network or regression method for training purposes. But, the current model assumes that the information at distinct moments is independent of each other. So, their time sequence is taken into account [<xref ref-type="bibr" rid="ref-19">19</xref>]. RNN model is presented for capturing the temporal relation by utilizing ML method. GRU is an adapted RNN-based LSTM model. Once the error signal is propagated backwards through time in traditional RNN, the signal tends to blow up or go vanish. These two cases result in network failure to learn from the information. GRU has the capacity to avoid the abovementioned problems and minimize the difficulty of the model without any loss of effective learning capacity.</p>
<p>GRU cell forms every step in the GRU model. In this regard, both reset and update gates are FC layers with sigmoid activation and are utilized for memory control. The preceding hidden layers preserve the historical memory while the update gates control the addition of candidate hidden layer to the hidden layer. The reset gates know how to integrate the input with historical memory so that it becomes a candidate hidden layer. At last, the candidate hidden layer, which is previously a hidden layer, and the output of update gate constitute the existing output and hidden layers. GRU cell is formulated based on the equations given below.
<disp-formula id="ueqn-1">
<mml:math id="mml-ueqn-1" display="block"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mi>&#x03C3;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msup><mml:mi>W</mml:mi><mml:mi>z</mml:mi></mml:msup></mml:mrow><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:msup><mml:mi>U</mml:mi><mml:mi>z</mml:mi></mml:msup></mml:mrow><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:msup><mml:mi>b</mml:mi><mml:mi>z</mml:mi></mml:msup></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:math></disp-formula>
<disp-formula id="eqn-11"><label>(11)</label><mml:math id="mml-eqn-11" display="block"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mi>&#x03C3;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msup><mml:mi>W</mml:mi><mml:mi>r</mml:mi></mml:msup></mml:mrow><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:msup><mml:mi>U</mml:mi><mml:mi>r</mml:mi></mml:msup></mml:mrow><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:msup><mml:mi>b</mml:mi><mml:mi>r</mml:mi></mml:msup></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mspace width="thickmathspace" /><mml:mspace width="thickmathspace" /><mml:mspace width="thickmathspace" /><mml:mspace width="thickmathspace" /></mml:math></disp-formula>
<disp-formula id="ueqn-2">
<mml:math id="mml-ueqn-2" display="block"><mml:mrow><mml:mover><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow><mml:mo>&#x007E;</mml:mo></mml:mover></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mtext>  tanh&#xA0;</mml:mtext></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>W</mml:mi><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mi>U</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow><mml:mo>&#x2299;</mml:mo><mml:mspace width="thickmathspace" /><mml:mspace width="thickmathspace" /><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>b</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:math></disp-formula>
<disp-formula id="ueqn-3">
<mml:math id="mml-ueqn-3" display="block"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2299;</mml:mo><mml:mrow><mml:mover><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow><mml:mo>&#x007E;</mml:mo></mml:mover></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow><mml:mo>&#x2299;</mml:mo><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>,</mml:mo></mml:math></disp-formula></p>
<p>Here, <inline-formula id="ieqn-22"><mml:math id="mml-ieqn-22"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> represents the hidden layer at <inline-formula id="ieqn-23"><mml:math id="mml-ieqn-23"><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:math></inline-formula> and <inline-formula id="ieqn-24"><mml:math id="mml-ieqn-24"><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mspace width="thinmathspace" /><mml:mspace width="thinmathspace" /><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula id="ieqn-25"><mml:math id="mml-ieqn-25"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mspace width="thinmathspace" /><mml:mspace width="thinmathspace" /><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, and <inline-formula id="ieqn-26"><mml:math id="mml-ieqn-26"><mml:mrow><mml:mover><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow><mml:mo>&#x007E;</mml:mo></mml:mover></mml:mrow></mml:math></inline-formula> denote the inputs of GRU cell, output of update gate, output of reset gate, candidate hidden layer, and hidden layer at <italic>t</italic>, correspondingly. <italic>W</italic> and <italic>U</italic> indicate the weight matrices of FC layer, and <italic>b</italic> indicates the bias vector. <inline-formula id="ieqn-27"><mml:math id="mml-ieqn-27"><mml:mi>&#x03C3;</mml:mi></mml:math></inline-formula> and<inline-formula id="ieqn-28"><mml:math id="mml-ieqn-28"><mml:mrow><mml:mtext>  tanh&#xA0;</mml:mtext></mml:mrow></mml:math></inline-formula>denote sigmoid and<inline-formula id="ieqn-29"><mml:math id="mml-ieqn-29"><mml:mrow><mml:mtext>  tanh</mml:mtext></mml:mrow></mml:math></inline-formula> activation functions correspondingly. <inline-formula id="ieqn-30"><mml:math id="mml-ieqn-30"><mml:mo>&#x2299;</mml:mo></mml:math></inline-formula> signifies element-wise products between two matrices of a similar size. In order to improve the learning capacity, several GRU cells are stacked with input and output direction. Further, the output of GRU cell at every step is utilized as the input of following GRU cell at respective step.</p>
</sec>
<sec id="s2_5"><label>2.5</label><title>Stage V: GSO Based Hyperparameter Tuning</title>
<p>In order to improve the detection outcomes of SGRU model, GSO algorithm is utilized. In the presented approach, all the glowworms have a local visibility range and a luciferin level. The local visibility range identifies the neighboring glowworm that is visible to them whereas the luciferin level of glowworm defines its light intensity [<xref ref-type="bibr" rid="ref-20">20</xref>]. The glowworm probabilistically selects a neighbor with high luciferin level than itself and flies towards the neighbor as it get attracted towards the light.&#x00A0;The local visibility range is dynamic so as to maintain a large number of neighbors. The GSO simulates the&#x00A0;glowworm behavior and contains three stages. In luciferin update stage, the luciferin level of all the glowworms is estimated based on the decay of its luminescence and the merits of its novel location after carrying out the movement with an evolution cycle <italic>t</italic>. The luciferin level of glowworm <italic>i</italic> is upgraded as follows.
<disp-formula id="eqn-12"><label>(12)</label><mml:math id="mml-eqn-12" display="block"><mml:msubsup><mml:mi>l</mml:mi><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo stretchy="false">&#x2190;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mi>&#x03C1;</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:msubsup><mml:mi>l</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:msubsup><mml:mo>+</mml:mo><mml:mi>&#x03C4;</mml:mi><mml:msubsup><mml:mi>f</mml:mi><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:math></disp-formula></p>
<p>Whereas <inline-formula id="ieqn-31"><mml:math id="mml-ieqn-31"><mml:mi>&#x03C1;</mml:mi></mml:math></inline-formula> represents the decay ratio of glowworm luminescence and <inline-formula id="ieqn-32"><mml:math id="mml-ieqn-32"><mml:mi>&#x03C4;</mml:mi></mml:math></inline-formula> denotes the enhancement constant. The initial term is the persistent substance of luminescence, due to decay with time whereas the next term is the additive luminescence as a function of <inline-formula id="ieqn-33"><mml:math id="mml-ieqn-33"><mml:msubsup><mml:mi>f</mml:mi><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:math></inline-formula> that represents the objective values evaluated at glowworm novel location (now, without losing the generality, the objective function is considered to be increased).</p>
<p>In the movement stage of evolution cycle, all the glowworms in a swarm should implement a movement. This is done by flying towards a neighbor with high luciferin level than the incumbent glowworm and is situated within the local visibility neighborhood i.e., radius <inline-formula id="ieqn-34"><mml:math id="mml-ieqn-34"><mml:msubsup><mml:mi>r</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:msubsup></mml:math></inline-formula>. The probability of glowworm <italic>i</italic> being attracted towards a brighter glowworm <italic>j</italic> in the evolution cycle <italic>t</italic> is as follows.
<disp-formula id="eqn-13"><label>(13)</label><mml:math id="mml-eqn-13" display="block"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msubsup><mml:mi>l</mml:mi><mml:mi>j</mml:mi><mml:mi>t</mml:mi></mml:msubsup><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mi>l</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:msubsup></mml:mrow><mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="normal">&#x03A3;</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mo>&#x2208;</mml:mo><mml:msubsup><mml:mi>N</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:msubsup></mml:mrow></mml:msub></mml:mrow><mml:msubsup><mml:mi>l</mml:mi><mml:mi>k</mml:mi><mml:mi>t</mml:mi></mml:msubsup><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mi>l</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:msubsup></mml:mrow></mml:mfrac></mml:math></disp-formula></p>
<p>Here, <inline-formula id="ieqn-35"><mml:math id="mml-ieqn-35"><mml:msubsup><mml:mi>N</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:msubsup></mml:math></inline-formula> represents the set of glowworms within the visibility neighborhood of glowworm <italic>i</italic> during evolution cycle <italic>t</italic>. After choosing a neighbor, say glowworm <italic>i</italic>, the existing glowworm <italic>i</italic> moves towards the neighbor and upgrades its location as shown in <xref ref-type="fig" rid="fig-2">Fig. 2</xref>, the flowchart for GSO technique.
<disp-formula id="eqn-14"><label>(14)</label><mml:math id="mml-eqn-14" display="block"><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo stretchy="false">&#x2190;</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:msubsup><mml:mo>+</mml:mo><mml:mi>s</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:msubsup><mml:mi>x</mml:mi><mml:mi>j</mml:mi><mml:mi>t</mml:mi></mml:msubsup><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:msubsup></mml:mrow><mml:mrow><mml:mrow><mml:mo>|</mml:mo><mml:mrow><mml:mrow><mml:mo>|</mml:mo><mml:mrow><mml:msubsup><mml:mi>x</mml:mi><mml:mi>j</mml:mi><mml:mi>t</mml:mi></mml:msubsup><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:msubsup></mml:mrow><mml:mo>|</mml:mo></mml:mrow></mml:mrow><mml:mo>|</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<fig id="fig-2"><label>Figure 2</label><caption><title>Flowchart of GSO technique</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_26715-fig-2.png"/></fig>
<p>whereas <italic>s</italic> denotes the movement distance and <inline-formula id="ieqn-36"><mml:math id="mml-ieqn-36"><mml:mo stretchy="false">&#x2225;</mml:mo><mml:mo>&#x2219;</mml:mo><mml:mo stretchy="false">&#x2225;</mml:mo></mml:math></inline-formula> shows the length of the referred vector. Generally, glowworm <italic>i</italic> moves in <italic>s</italic> unit of distance towards glowworm <inline-formula id="ieqn-37"><mml:math id="mml-ieqn-37"><mml:mi>j</mml:mi><mml:mo>.</mml:mo><mml:mrow><mml:mtext>&#xA0;</mml:mtext></mml:mrow></mml:math></inline-formula>The visibility range upgrades the stage dynamically and it tunes the visibility radius of all the glowworms to preserve an ideal number of neighbors, <inline-formula id="ieqn-38"><mml:math id="mml-ieqn-38"><mml:mrow><mml:msup><mml:mi>N</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. Hence, the existing number of neighbors, <inline-formula id="ieqn-39"><mml:math id="mml-ieqn-39"><mml:mrow><mml:mo>|</mml:mo><mml:mrow><mml:msubsup><mml:mi>N</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:msubsup></mml:mrow><mml:mo>|</mml:mo></mml:mrow></mml:math></inline-formula> is compared with <inline-formula id="ieqn-40"><mml:math id="mml-ieqn-40"><mml:mrow><mml:msup><mml:mi>N</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> and the visibility radius <inline-formula id="ieqn-41"><mml:math id="mml-ieqn-41"><mml:msubsup><mml:mi>r</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:msubsup></mml:math></inline-formula> is tuned as follows.
<disp-formula id="eqn-15"><label>(15)</label><mml:math id="mml-eqn-15" display="block"><mml:msubsup><mml:mi>r</mml:mi><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo stretchy="false">&#x2190;</mml:mo><mml:mrow><mml:mtext>  min&#xA0;</mml:mtext></mml:mrow><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mrow><mml:mtext>  max</mml:mtext></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mtext>  max&#xA0;</mml:mtext></mml:mrow><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mrow><mml:mtext>&#xA0;</mml:mtext></mml:mrow><mml:msubsup><mml:mi>r</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:msubsup><mml:mo>+</mml:mo><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msup><mml:mi>N</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mi>N</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:math></disp-formula>whereas <inline-formula id="ieqn-42"><mml:math id="mml-ieqn-42"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mrow><mml:mtext>  max&#xA0;</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> denotes the maximal visibility radius and <inline-formula id="ieqn-43"><mml:math id="mml-ieqn-43"><mml:mi>&#x03B7;</mml:mi></mml:math></inline-formula> represents the scaling variable to tune <inline-formula id="ieqn-44"><mml:math id="mml-ieqn-44"><mml:msubsup><mml:mi>N</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:msubsup></mml:math></inline-formula>. Hence, the value of <inline-formula id="ieqn-45"><mml:math id="mml-ieqn-45"><mml:msubsup><mml:mi>r</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:msubsup></mml:math></inline-formula> is improved, when <inline-formula id="ieqn-46"><mml:math id="mml-ieqn-46"><mml:msubsup><mml:mi>N</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:msubsup><mml:mo>&#x003C;</mml:mo><mml:mrow><mml:msup><mml:mi>N</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, and it gets reduced when <inline-formula id="ieqn-47"><mml:math id="mml-ieqn-47"><mml:msubsup><mml:mi>N</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:msubsup><mml:mo>&#x003E;</mml:mo><mml:mrow><mml:msup><mml:mi>N</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. The possible range of <inline-formula id="ieqn-48"><mml:math id="mml-ieqn-48"><mml:msubsup><mml:mi>r</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:msubsup></mml:math></inline-formula> is limited between <inline-formula id="ieqn-49"><mml:math id="mml-ieqn-49"><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mrow><mml:mtext>&#xA0;</mml:mtext></mml:mrow><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mrow><mml:mtext>  max&#xA0;</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:math></inline-formula>. The phenomenon of <inline-formula id="ieqn-50"><mml:math id="mml-ieqn-50"><mml:msubsup><mml:mi>r</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:msubsup><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:math></inline-formula> shows that various glowworms resort to the location of existing glowworms, whereas <inline-formula id="ieqn-51"><mml:math id="mml-ieqn-51"><mml:msubsup><mml:mi>r</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:msubsup><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mrow><mml:mtext>  max&#xA0;</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> discloses the situation in which the glowworm exists at a large distance than almost all the glowworms.</p>
</sec>
</sec>
<sec id="s3"><label>3</label><title>Experimental Validation</title>
<p>The proposed AAI-CCDC technique was experimentally validated using the publicly available Warwick-QU dataset for its performance [<xref ref-type="bibr" rid="ref-21">21</xref>]. The data contains 165 colorectal histopathological images obtained from 74 patients with benign tumors and 91 patients with malignant tumors [<xref ref-type="bibr" rid="ref-22">22</xref>]. This data was captured using Zeiss MIRAX MIDI Scanner by relating an image data weight range of 716 kilobytes, 1.187 kilobytes, and image data resolution range of 567 &#x00D7; 430 pixels to 775 &#x00D7; 522 pixels with all pixels maintaining a distance of 0.6&#x2005;&#x03BC;m in the actual distance. The representative sample images of CRC are shown in <xref ref-type="fig" rid="fig-3">Fig. 3</xref>.</p>
<fig id="fig-3"><label>Figure 3</label><caption><title>Representative histopathological images from patients with benign and malignant Colorectal Cancer</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_26715-fig-3.png"/></fig>
<p><xref ref-type="fig" rid="fig-4">Fig. 4</xref> showcases ten confusion matrices generated by AAI-CCDC technique under distinct epochs. With 200 epochs, the proposed AAI-CCDC technique stratified 73 images as benign tumors and 88 images as malignant tumors. With 400 epochs, AAI-CCDC technique stratified 73 images as benign tumors and 90 images as malignant tumors. Further, for 1400 epochs, the proposed AAI-CCDC technique stratified 74 images as benign tumors and 87 images as malignant tumors. Eventually, with 1800 epochs, AAI-CCDC technique classified 73 images as benign tumors and 88 images as malignant tumors. Lastly, with 2000 epochs, the presented AAI-CCDC technique identified 71 images as benign tumors and 87 images as malignant tumors.</p>
<fig id="fig-4"><label>Figure 4</label><caption><title>Confusion matrix of AAI-CCDC technique under distinct epochs</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_26715-fig-4.png"/></fig>
<p><xref ref-type="table" rid="table-1">Tab. 1</xref> depicts the results of overall analysis of AAI-CCDC technique under distinct epochs. The results show that the proposed AAI-CCDC technique produced effective outcomes under all epochs. For instance, with 200 epochs, AAI-CCDC technique offered an <inline-formula id="ieqn-52"><mml:math id="mml-ieqn-52"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of 97.58&#x0025;, <inline-formula id="ieqn-53"><mml:math id="mml-ieqn-53"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of 98.65&#x0025;, <inline-formula id="ieqn-54"><mml:math id="mml-ieqn-54"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of 96.70&#x0025;, <inline-formula id="ieqn-55"><mml:math id="mml-ieqn-55"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of 96.05&#x0025;, and an <inline-formula id="ieqn-56"><mml:math id="mml-ieqn-56"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> of 97.33&#x0025;. Besides, with 600 epochs, the proposed AAI-CCDC technique obtained an <inline-formula id="ieqn-57"><mml:math id="mml-ieqn-57"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of 98.79&#x0025;, <inline-formula id="ieqn-58"><mml:math id="mml-ieqn-58"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of 100&#x0025;, <inline-formula id="ieqn-59"><mml:math id="mml-ieqn-59"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of 97.80&#x0025;, <inline-formula id="ieqn-60"><mml:math id="mml-ieqn-60"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of 97.37&#x0025;, and an <inline-formula id="ieqn-61"><mml:math id="mml-ieqn-61"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> of 98.67&#x0025;. In line with this, with 1200 epochs, AAI-CCDC technique achieved an <inline-formula id="ieqn-62"><mml:math id="mml-ieqn-62"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of 96.36&#x0025;, <inline-formula id="ieqn-63"><mml:math id="mml-ieqn-63"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of 97.30&#x0025;, <inline-formula id="ieqn-64"><mml:math id="mml-ieqn-64"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of 95.60&#x0025;, <inline-formula id="ieqn-65"><mml:math id="mml-ieqn-65"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of 94.74&#x0025;, and an <inline-formula id="ieqn-66"><mml:math id="mml-ieqn-66"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> of 96&#x0025;. Moreover, with 2000 epochs, AAI-CCDC technique accomplished an <inline-formula id="ieqn-67"><mml:math id="mml-ieqn-67"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of 95.76&#x0025;, <inline-formula id="ieqn-68"><mml:math id="mml-ieqn-68"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of 95.95&#x0025;, <inline-formula id="ieqn-69"><mml:math id="mml-ieqn-69"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of 95.60&#x0025;, <inline-formula id="ieqn-70"><mml:math id="mml-ieqn-70"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of 94.67&#x0025;, and an <inline-formula id="ieqn-71"><mml:math id="mml-ieqn-71"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> of 95.30&#x0025;. <xref ref-type="fig" rid="fig-5">Fig. 5</xref> demonstrates the results of average analysis accomplished by AAI-CCDC technique against existing techniques. The figure reports that the proposed AAI-CCDC technique produced a high average <inline-formula id="ieqn-72"><mml:math id="mml-ieqn-72"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of 97.40&#x0025;, <inline-formula id="ieqn-73"><mml:math id="mml-ieqn-73"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of 98.52&#x0025;, <inline-formula id="ieqn-74"><mml:math id="mml-ieqn-74"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of 96.48&#x0025;, <inline-formula id="ieqn-75"><mml:math id="mml-ieqn-75"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of 95.81&#x0025;, and an <inline-formula id="ieqn-76"><mml:math id="mml-ieqn-76"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> of 97.14&#x0025;.</p>
<table-wrap id="table-1"><label>Table 1</label><caption><title>Results of the analysis of AAI-CCDC technique with different measures</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">No. of Epochs</th>
<th align="left">Accuracy</th>
<th align="left">Sensitivity</th>
<th align="left">Specificity</th>
<th align="left">Precision</th>
<th align="left">F-Score</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">Epoch-200</td>
<td align="left">97.58</td>
<td align="left">98.65</td>
<td align="left">96.70</td>
<td align="left">96.05</td>
<td align="left">97.33</td>
</tr>
<tr>
<td align="left">Epoch-400</td>
<td align="left">98.79</td>
<td align="left">98.65</td>
<td align="left">98.90</td>
<td align="left">98.65</td>
<td align="left">98.65</td>
</tr>
<tr>
<td align="left">Epoch-600</td>
<td align="left">98.79</td>
<td align="left">100.00</td>
<td align="left">97.80</td>
<td align="left">97.37</td>
<td align="left">98.67</td>
</tr>
<tr>
<td align="left">Epoch-800</td>
<td align="left">96.97</td>
<td align="left">98.65</td>
<td align="left">95.60</td>
<td align="left">94.81</td>
<td align="left">96.69</td>
</tr>
<tr>
<td align="left">Epoch-1000</td>
<td align="left">97.58</td>
<td align="left">98.65</td>
<td align="left">96.70</td>
<td align="left">96.05</td>
<td align="left">97.33</td>
</tr>
<tr>
<td align="left">Epoch-1200</td>
<td align="left">96.36</td>
<td align="left">97.30</td>
<td align="left">95.60</td>
<td align="left">94.74</td>
<td align="left">96.00</td>
</tr>
<tr>
<td align="left">Epoch-1400</td>
<td align="left">97.58</td>
<td align="left">100.00</td>
<td align="left">95.60</td>
<td align="left">94.87</td>
<td align="left">97.37</td>
</tr>
<tr>
<td align="left">Epoch-1600</td>
<td align="left">96.97</td>
<td align="left">98.65</td>
<td align="left">95.60</td>
<td align="left">94.81</td>
<td align="left">96.69</td>
</tr>
<tr>
<td align="left">Epoch-1800</td>
<td align="left">97.58</td>
<td align="left">98.65</td>
<td align="left">96.70</td>
<td align="left">96.05</td>
<td align="left">97.33</td>
</tr>
<tr>
<td align="left">Epoch-2000</td>
<td align="left">95.76</td>
<td align="left">95.95</td>
<td align="left">95.60</td>
<td align="left">94.67</td>
<td align="left">95.30</td>
</tr>
<tr>
<td align="left">Average</td>
<td align="left">97.40</td>
<td align="left">98.52</td>
<td align="left">96.48</td>
<td align="left">95.81</td>
<td align="left">97.14</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="fig-5"><label>Figure 5</label><caption><title>Average analysis results of AAI-CCDC technique under different measures</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_26715-fig-5.png"/></fig>
<p>The overall accuracy outcome analysis results accomplished by the proposed AAI-CCDC technique on test data is portrayed in <xref ref-type="fig" rid="fig-6">Fig. 6</xref>. The results exhibit that the presented AAI-CCDC technique accomplished an improved validation accuracy than the training accuracy. It is also observed that the accuracy values got saturated at an epoch count of 1000.</p>
<fig id="fig-6"><label>Figure 6</label><caption><title>Accuracy graph analysis results of AAI-CCDC technique</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_26715-fig-6.png"/></fig>
<p>The overall loss outcome analysis results of the proposed AAI-CCDC algorithm on test data are shown in <xref ref-type="fig" rid="fig-7">Fig. 7</xref>. The figure reveals that the proposed AAI-CCDC system achieved a low validation loss compared to training loss. It is additionally noticed that the loss values got saturated at the epoch count of 1000.</p>
<fig id="fig-7"><label>Figure 7</label><caption><title>Loss graph analysis results of AAI-CCDC technique</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_26715-fig-7.png"/></fig>
<p><xref ref-type="fig" rid="fig-8">Fig. 8</xref> demonstrates the comparative <inline-formula id="ieqn-77"><mml:math id="mml-ieqn-77"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> analysis results achieved by AAI-CCDC technique over recent methods [<xref ref-type="bibr" rid="ref-23">23</xref>,<xref ref-type="bibr" rid="ref-24">24</xref>]. The results show that ResNet-18(60&#x2013;40), ResNet-50(60&#x2013;40), and SC-CNN techniques produced lower <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:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values such as 73&#x0025;, 77&#x0025;, and 69.95&#x0025; respectively. In addition, ResNet-18(75&#x2013;25), ResNet-18(80&#x2013;20), and SC-CNN techniques obtained moderately closer <inline-formula id="ieqn-79"><mml:math id="mml-ieqn-79"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values such as 81&#x0025;, 85&#x0025;, and 81.65&#x0025; respectively. Though ResNet-50(75&#x2013;25) and ResNet-50 (80&#x2013;20) techniques accomplished closer <inline-formula id="ieqn-80"><mml:math id="mml-ieqn-80"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values like 81&#x0025; and 85&#x0025; respectively, the presented AAI-CCDC technique achieved a maximum <inline-formula id="ieqn-81"><mml:math id="mml-ieqn-81"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of 97.40&#x0025;.</p>
<fig id="fig-8"><label>Figure 8</label><caption><title>Accuracy analysis results of AAI-CCDC technique with recent algorithms</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_26715-fig-8.png"/></fig>
<p><xref ref-type="fig" rid="fig-9">Fig. 9</xref> depicts the results for comparative <inline-formula id="ieqn-82"><mml:math id="mml-ieqn-82"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> analysis, attained by AAI-CCDC approach on recent algorithms. The outcomes demonstrate that ResNet-50(60&#x2013;40), ResNet-18(60&#x2013;40), and CP-CNN methods produced lesser <inline-formula id="ieqn-83"><mml:math id="mml-ieqn-83"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mtext>&#xA0;</mml:mtext></mml:mrow></mml:math></inline-formula>values such as 60&#x0025;, 64&#x0025;, and 68.70&#x0025; correspondingly. Besides, SC-CNN, ResNet-18(80&#x2013;20), and ResNet-50(75&#x2013;25) methods gained moderately closer <inline-formula id="ieqn-84"><mml:math id="mml-ieqn-84"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values like 82.70&#x0025;, 83&#x0025;, and 89&#x0025; correspondingly. However, ResNet-50(80&#x2013;20) and ResNet-18(75&#x2013;25) methodologies accomplished closer <inline-formula id="ieqn-85"><mml:math id="mml-ieqn-85"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> outcomes such as 93&#x0025; and 96&#x0025; correspondingly. Eventually, the presented AAI-CCDC technique produced a superior <inline-formula id="ieqn-86"><mml:math id="mml-ieqn-86"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of 98.52&#x0025;.</p>
<fig id="fig-9"><label>Figure 9</label><caption><title>Sensitivity analysis of AAI-CCDC technique with recent algorithms</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_26715-fig-9.png"/></fig>
<p><xref ref-type="fig" rid="fig-10">Fig. 10</xref> portrays the comparative <inline-formula id="ieqn-87"><mml:math id="mml-ieqn-87"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> analysis results, achieved by the proposed AAI-CCDC technique over recent methods. The outcomes demonstrate that ResNet-18(75&#x2013;25), CP-CNN, and SC-CNN techniques produced low <inline-formula id="ieqn-88"><mml:math id="mml-ieqn-88"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mtext>&#xA0;</mml:mtext></mml:mrow></mml:math></inline-formula>values such as 63&#x0025;, 71.20&#x0025;, and 80.60&#x0025; respectively. Followed by, ResNet-18(60&#x2013;40), ResNet-50(80&#x2013;20), and ResNet-18(80&#x2013;20) techniques obtained moderately closer <inline-formula id="ieqn-89"><mml:math id="mml-ieqn-89"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values such as 83&#x0025;, 83&#x0025;, and 87&#x0025; respectively. Though ResNet-50(75&#x2013;25) and ResNet-50 (60&#x2013;40) approaches accomplished nearby <inline-formula id="ieqn-90"><mml:math id="mml-ieqn-90"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> results such as 87&#x0025; and 92&#x0025; respectively, the proposed AAI-CCDC system produced a superior <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:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mtext>&#xA0;</mml:mtext></mml:mrow></mml:math></inline-formula>of 96.48&#x0025;. From the above-mentioned tables and figures, it is clear that the presented AAI-CCDC technique has accomplished effectual outcomes over other techniques and is a promising candidate for examining histopathological images to diagnose CRC.</p>
<fig id="fig-10"><label>Figure 10</label><caption><title>Specificity analysis of AAI-CCDC technique with recent algorithms</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_26715-fig-10.png"/></fig>
</sec>
<sec id="s4"><label>4</label><title>Conclusion</title>
<p>In current study, an effective AAI-CCDC technique is developed to assess the histopathological images so as to diagnose and classify CRC. The presented AAI-CCDC technique encompasses preprocessing, EfficientNet-based feature extraction, Nadam-based parameter tuning, SGRU-based classification, and GSO-based hyperparameter tuning. Nadam and GSO algorithms are used to improve the detection and classification efficiency of CRC. The proposed AAI-CCDC technique was experimentally validated against benchmark dataset and the experimental results infer that AAI-CCDC technique is superior to recent approaches in terms of performance. It achieved the maximum <inline-formula id="ieqn-92"><mml:math id="mml-ieqn-92"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of 97.40&#x0025;. Therefore, AAI-CCDC technique can be applied as a novel tool in detection and classification of CRC. In future, hybrid DL models can be used to boost the outcomes of AAI-CCDC technique.</p>
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<p>This work was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under Grant No. (D-398&#x2013;247&#x2013;1443). The authors, therefore, gratefully acknowledge DSR technical and financial support.</p>
</ack>
<fn-group>
<fn fn-type="other"><p><bold>Funding Statement:</bold> This work was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under Grant No. (D-398&#x2013;247&#x2013;1443).</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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