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<front>
<journal-meta>
<journal-id journal-id-type="pmc">CSSE</journal-id>
<journal-id journal-id-type="nlm-ta">CSSE</journal-id>
<journal-id journal-id-type="publisher-id">CSSE</journal-id>
<journal-title-group>
<journal-title>Computer Systems Science &#x0026; Engineering</journal-title>
</journal-title-group>
<issn pub-type="ppub">0267-6192</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">30556</article-id>
<article-id pub-id-type="doi">10.32604/csse.2023.030556</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Sailfish Optimization with Deep Learning Based Oral Cancer Classification Model</article-title><alt-title alt-title-type="left-running-head">Sailfish Optimization with Deep Learning Based Oral Cancer Classification Model</alt-title><alt-title alt-title-type="right-running-head">Sailfish Optimization with Deep Learning Based Oral Cancer 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>Duhayyim</surname><given-names>Mesfer Al</given-names></name>
<xref ref-type="aff" rid="aff-1">1</xref><email>m.alduhayyim@psau.edu.sa</email>
</contrib>
<contrib id="author-2" contrib-type="author">
<name name-style="western"><surname>Malibari</surname><given-names>Areej A.</given-names></name>
<xref ref-type="aff" rid="aff-2">2</xref>
</contrib>
<contrib id="author-3" contrib-type="author">
<name name-style="western"><surname>Dhahbi</surname><given-names>Sami</given-names></name>
<xref ref-type="aff" rid="aff-3">3</xref>
</contrib>
<contrib id="author-4" contrib-type="author">
<name name-style="western"><surname>Nour</surname><given-names>Mohamed K.</given-names></name>
<xref ref-type="aff" rid="aff-4">4</xref>
</contrib>
<contrib id="author-5" contrib-type="author">
<name name-style="western"><surname>Al-Turaiki</surname><given-names>Isra</given-names></name>
<xref ref-type="aff" rid="aff-5">5</xref>
</contrib>
<contrib id="author-6" contrib-type="author">
<name name-style="western"><surname>Obayya</surname><given-names>Marwa</given-names></name>
<xref ref-type="aff" rid="aff-6">6</xref>
</contrib>
<contrib id="author-7" contrib-type="author">
<name name-style="western"><surname>Mohamed</surname><given-names>Abdullah</given-names></name>
<xref ref-type="aff" rid="aff-7">7</xref>
</contrib>
<aff id="aff-1"><label>1</label><institution>Department of Computer Science, College of Sciences and Humanities-Aflaj, Prince Sattam bin Abdulaziz University</institution>, <addr-line>Al-Kharj, 16278</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-2"><label>2</label><institution>Department of Industrial and Systems Engineering, College of Engineering, Princess Nourah bint Abdulrahman University</institution>, <addr-line>Riyadh, 11671</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-3"><label>3</label><institution>Department of Computer Science, College of Science &#x0026; Art at Mahayil, King Khalid University</institution>, <addr-line>Abha, 62529</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-4"><label>4</label><institution>Department of Computer Science, College of Computing and Information System, Umm Al-Qura University</institution>, <addr-line>Mecca, 24382</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-5"><label>5</label><institution>Department of Information Technology, College of Computer and Information Sciences, King Saud University</institution>, <addr-line>Riyadh, 4545</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-6"><label>6</label><institution>Department of Biomedical Engineering, College of Engineering, Princess Nourah bint Abdulrahman University</institution>, <addr-line>Riyadh, 11671</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-7"><label>7</label><institution>Research Centre, Future University in Egypt</institution>, <addr-line>New Cairo, 11845</addr-line>, <country>Egypt</country></aff>
</contrib-group><author-notes><corresp id="cor1"><label>&#x002A;</label>Corresponding Author: Mesfer Al Duhayyim. Email: <email>m.alduhayyim@psau.edu.sa</email></corresp></author-notes>
<pub-date pub-type="epub" date-type="pub" iso-8601-date="2022-08-04"><day>04</day>
<month>08</month>
<year>2022</year></pub-date>
<volume>45</volume>
<issue>1</issue>
<fpage>753</fpage>
<lpage>767</lpage>
<history>
<date date-type="received"><day>29</day><month>3</month><year>2022</year></date>
<date date-type="accepted"><day>30</day><month>4</month><year>2022</year></date>
</history>
<permissions>
<copyright-statement>&#x00A9; 2023 Duhayyim et al.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Duhayyim 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_CSSE_30556.pdf"></self-uri>
<abstract>
<p>Recently, computer aided diagnosis (CAD) model becomes an effective tool for decision making in healthcare sector. The advances in computer vision and artificial intelligence (AI) techniques have resulted in the effective design of CAD models, which enables to detection of the existence of diseases using various imaging modalities. Oral cancer (OC) has commonly occurred in head and neck globally. Earlier identification of OC enables to improve survival rate and reduce mortality rate. Therefore, the design of CAD model for OC detection and classification becomes essential. Therefore, this study introduces a novel Computer Aided Diagnosis for OC using Sailfish Optimization with Fusion based Classification (CADOC-SFOFC) model. The proposed CADOC-SFOFC model determines the existence of OC on the medical images. To accomplish this, a fusion based feature extraction process is carried out by the use of VGGNet-16 and Residual Network (ResNet) model. Besides, feature vectors are fused and passed into the extreme learning machine (ELM) model for classification process. Moreover, SFO algorithm is utilized for effective parameter selection of the ELM model, consequently resulting in enhanced performance. The experimental analysis of the CADOC-SFOFC model was tested on Kaggle dataset and the results reported the betterment of the CADOC-SFOFC model over the compared methods with maximum accuracy of 98.11%. Therefore, the CADOC-SFOFC model has maximum potential as an inexpensive and non-invasive tool which supports screening process and enhances the detection efficiency.</p>
</abstract>
<kwd-group kwd-group-type="author">
<kwd>Oral cancer</kwd>
<kwd>computer aided diagnosis</kwd>
<kwd>deep learning</kwd>
<kwd>fusion model</kwd>
<kwd>seagull optimization</kwd>
<kwd>classification</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1">
<label>1</label>
<title>Introduction</title>
<p>Oral cancer (OC) is a lethal disease highly related to mortality and morbidity, and it comes under the neck and head sections [<xref ref-type="bibr" rid="ref-1">1</xref>]. Numerous image processing systems are widely utilized for the earlier diagnosis of OC that results in increased cancer survival rate and greater treatment efficiency. Medical imaging method, computer-aided detection, and diagnosis makes potential change in cancer treatment, now it can be diagnosed in the earlier stage by analyzing magnetic resonance imaging (MRI) scans, X-ray and computed tomography (CT) images. It helps to easily examine the anatomical structure of oral cavity and allows to precisely extract healthy regions from tumor areas. Defining the accurate class of OC at earlier stages is a considerably difficult task [<xref ref-type="bibr" rid="ref-2">2</xref>]. Thus, computer aided application would be extremely advantageous as it helps the medical doctor to offer a comprehensive treatment process and has a classification of diseases in healthcare diagnosis process.</p>
<p>Conventionally, cancer treatment mainly depends upon the grading of tumors. But the grading and discrepancy have added to imprecise prognosis in OC patients [<xref ref-type="bibr" rid="ref-3">3</xref>]. Despite the rising amount of predictive markers, the entire disease prediction remains same [<xref ref-type="bibr" rid="ref-4">4</xref>]. It is due to the challenge in the incorporation of this marker in the present staging scheme [<xref ref-type="bibr" rid="ref-5">5</xref>]. Better diagnostic and prognostic accuracy assists the clinician in making decisions based on the proper treatment for survival [<xref ref-type="bibr" rid="ref-6">6</xref>]. Eventually, machine learning (ML) technique (shallow learning) has been reported to provide better prognostication of OC. Note that, the usage of ML technique has been reported to offer a better prognostication when compared to the conventional statistical analysis [<xref ref-type="bibr" rid="ref-7">7</xref>]. The ML technique can exhibit promising outcomes since it can discern the complicated relations among the variables included in the dataset [<xref ref-type="bibr" rid="ref-8">8</xref>]. Considering the touted feasibility and advantage of the ML approaches in cancer prognostication, the application has gained considerable interest over the last few decades. Because of that, it is poised to help the clinician in taking decisions thus promoting and improving good management of patient health. Interestingly, the advanced technology has resulted in the alteration of shallow ML to deep ML. Deep learning (DL) technique has been touted to increases better management of cancer [<xref ref-type="bibr" rid="ref-9">9</xref>,<xref ref-type="bibr" rid="ref-10">10</xref>].</p>
<p>Song et al. [<xref ref-type="bibr" rid="ref-11">11</xref>] present for addressing this shortcoming by employing a Bayesian deep network able to evaluate uncertainty for assessing OC image classifier reliability. It can be estimated the method utilizes a huge intraoral cheek mucosa image data set captured utilizing our customized device in high-risk populations for demonstrating that meaningful uncertainty data is created. Tanriver et al. [<xref ref-type="bibr" rid="ref-12">12</xref>] discovered the potential application of computer vision and DL approaches from the OC field in the scope of photographic image and examined the prospect of automated model to identify oral potentially malignant disorder with 2-stage pipeline. Camalan et al. [<xref ref-type="bibr" rid="ref-13">13</xref>] established a DL approach for classifying images as &#x201C;suspicious&#x201D; and &#x201C;normal&#x201D; and for highlighting the region of image most probably that contained from decision-making with creating automated heat map. The author has established a model for classifying images as healthy and abnormal with executing transfer learning (TL) on Inception-ResNet-V2 and created automated heat map for highlighting the area of image most probable that contained from the decision making.</p>
<p>Lim et al. [<xref ref-type="bibr" rid="ref-14">14</xref>] established a new DL structure called as D&#x2019;OraCa for classifying oral lesions utilizing photographic images. It can be primary for developing a mouth landmark recognition method to the oral image and integrating it as to the oral lesion classifier method as guidance for improving the classifier accuracy. It can be measured the efficacy of 5 distinct deep convolutional neural network (DCNN) and MobileNetV2 is selected as the feature extracting to presented mouth landmark recognition method. Lin et al. [<xref ref-type="bibr" rid="ref-15">15</xref>] projected an effectual smartphone based image analysis approach, influenced by a DL technique, for addressing the challenge of automatic recognition of oral disease. Primary, an easy yet effectual centered rule image capture method has been presented to gather oral cavity images. Afterward, dependent upon this approach, a medium-sized oral data set with 5 categories of diseases has been generated, and resampling approach has been projected to lessen the result of images variability in hand held smartphones camera. At last, an existing DL network (HRNet) has been established for evaluating the performance of our approach for OC recognition.</p>
<p>This study introduces a novel Computer Aided Diagnosis for OC using Sailfish Optimization with Fusion based Classification (CADOC-SFOFC) model. The proposed CADOC-SFOFC model performs fusion based feature extraction process using VGGNet-16 and Residual Network (ResNet) model. Besides, feature vectors are fused and passed into the extreme learning machine (ELM) model for classification process. Moreover, SFO algorithm is utilized for effective parameter selection of the ELM model, consequently resulting in enhanced performance. The experimental analysis of the CADOC-SFOFC model was tested on Kaggle dataset and the results reported the betterment of the CADOC-SFOFC model over the compared methods.</p>
</sec>
<sec id="s2">
<label>2</label>
<title>Materials and Methods</title>
<p>In this study, a novel CADOC-SFOFC model has been devised to determine the existence of OC on medical images. Initially, the CADOC-SFOFC model carried out the fusion based feature extraction procedure using VGGNet-16 and ResNet model. In addition, feature vectors are fused and passed into the ELM model for classification process. Finally, the SFO algorithm is utilized for effective parameter selection of the ELM model as illustrated in <xref ref-type="fig" rid="fig-1">Fig. 1</xref>.</p>
<fig id="fig-1">
<label>Figure 1</label>
<caption>
<title>Block diagram of CADOC-SFOFC model</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CSSE_30556-fig-1.png"/>
</fig>
<sec id="s2_1">
<label>2.1</label>
<title>Dataset Used</title>
<p>The performance validation of the CADOC-SFOFC model on OC classification is performed using a benchmark dataset from Kaggle repository (available at <uri xlink:href="https://www.kaggle.com/shivam17299/oral-cancer-lips-and-tongue-images">https://www.kaggle.com/shivam17299/oral-cancer-lips-and-tongue-images</uri>). The dataset includes lip and tongue images with two class labels. A total of 87 images come under cancer class and 44 images under non-cancer class. <xref ref-type="fig" rid="fig-2">Fig. 2</xref> depicts a sample set of tongue images.</p>
<fig id="fig-2">
<label>Figure 2</label>
<caption>
<title>Sample images</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CSSE_30556-fig-2.png"/>
</fig>
</sec>
<sec id="s2_2">
<label>2.2</label>
<title>Image Pre-Processing</title>
<p>Gabor filter (GF) is initially employed to preprocess the input images. It is an oriented complicated sinusoidal grating modified using 2-D Gaussian envelope. For a 2-D coordinate <inline-formula id="ieqn-1">
<mml:math id="mml-ieqn-1"><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>b</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> model, the GF comprises real as well as imaginary components, as given in <xref ref-type="disp-formula" rid="eqn-1">Eq. (1)</xref>:</p>
<p><disp-formula id="eqn-1"><label>(1)</label>
<mml:math id="mml-eqn-1" display="block"><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>&#x03B4;</mml:mi><mml:mo>,</mml:mo><mml:mi>&#x03B8;</mml:mi><mml:mo>,</mml:mo><mml:mi>&#x03C8;</mml:mi><mml:mo>,</mml:mo><mml:mi>&#x03C3;</mml:mi><mml:mo>,</mml:mo><mml:mi>&#x03B3;</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>b</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mspace width="thickmathspace" /><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">x</mml:mi><mml:mi mathvariant="normal">p</mml:mi><mml:mspace width="thickmathspace" /></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:msup><mml:mi>a</mml:mi><mml:mrow><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mo>&#x2032;</mml:mo></mml:msup></mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:msup><mml:mi>&#x03B3;</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:msup><mml:mi>b</mml:mi><mml:mrow><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mo>&#x2032;</mml:mo></mml:msup></mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mrow><mml:msup><mml:mi>&#x03C3;</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mrow><mml:mspace width="thickmathspace" /><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">x</mml:mi><mml:mi mathvariant="normal">p</mml:mi><mml:mspace width="thickmathspace" /></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>2</mml:mn><mml:mi>&#x03C0;</mml:mi><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msup></mml:mrow><mml:mi>&#x03B4;</mml:mi></mml:mfrac></mml:mrow><mml:mo>+</mml:mo><mml:mi>&#x03C8;</mml:mi></mml:mstyle></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</disp-formula></p>
<p>where</p>
<p><disp-formula id="eqn-2"><label>(2)</label>
<mml:math id="mml-eqn-2" display="block"><mml:msup><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mi>a</mml:mi><mml:mrow><mml:mspace width="thickmathspace" /><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mspace width="thickmathspace" /></mml:mrow><mml:mi>&#x03B8;</mml:mi><mml:mo>+</mml:mo><mml:mi>b</mml:mi><mml:mrow><mml:mspace width="thickmathspace" /><mml:mi mathvariant="normal">s</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mspace width="thickmathspace" /></mml:mrow><mml:mi>&#x03B8;</mml:mi></mml:math>
</disp-formula></p>
<p><disp-formula id="eqn-3"><label>(3)</label>
<mml:math id="mml-eqn-3" display="block"><mml:msup><mml:mrow><mml:mi>b</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mi>a</mml:mi><mml:mrow><mml:mspace width="thickmathspace" /><mml:mi mathvariant="normal">s</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mspace width="thickmathspace" /></mml:mrow><mml:mi>&#x03B8;</mml:mi><mml:mo>+</mml:mo><mml:mi>b</mml:mi><mml:mrow><mml:mspace width="thickmathspace" /><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mspace width="thickmathspace" /></mml:mrow><mml:mi>&#x03B8;</mml:mi></mml:math>
</disp-formula></p>
<p>where <inline-formula id="ieqn-2">
<mml:math id="mml-ieqn-2"><mml:mi>&#x03B4;</mml:mi></mml:math>
</inline-formula> indicates wavelength and <inline-formula id="ieqn-3">
<mml:math id="mml-ieqn-3"><mml:mi>&#x03B8;</mml:mi></mml:math>
</inline-formula> implies orientation separation angle of Gabor kernel, <inline-formula id="ieqn-4">
<mml:math id="mml-ieqn-4"><mml:mi>&#x03C8;</mml:mi></mml:math>
</inline-formula> denotes phase offset, <inline-formula id="ieqn-5">
<mml:math id="mml-ieqn-5"><mml:mi>&#x03C3;</mml:mi></mml:math>
</inline-formula> represents standard derivation of Gaussian envelope, and <inline-formula id="ieqn-6">
<mml:math id="mml-ieqn-6"><mml:mi>&#x03B3;</mml:mi></mml:math>
</inline-formula> is the spatial aspects ratio.</p>
</sec>
<sec id="s2_3">
<label>2.3</label>
<title>Feature Extraction</title>
<p>In this study, two feature vectors namely Visual Geometry Group (VGG16) and ResNet models are applied [<xref ref-type="bibr" rid="ref-16">16</xref>,<xref ref-type="bibr" rid="ref-17">17</xref>].</p>
</sec>
<sec id="s2_4">
<label>2.4</label>
<title>Feature Fusion and Classification</title>
<p>At this stage, the fusion of features is carried out into a matrix by the use of partial least square (PLS) based fusion model [<xref ref-type="bibr" rid="ref-18">18</xref>]. Assume <inline-formula id="ieqn-7">
<mml:math id="mml-ieqn-7"><mml:mrow><mml:msub><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>w</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> and <inline-formula id="ieqn-8">
<mml:math id="mml-ieqn-8"><mml:mrow><mml:msub><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>w</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> denotes a pair of chosen feature vectors of dimension <inline-formula id="ieqn-9">
<mml:math id="mml-ieqn-9"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mi>K</mml:mi></mml:math>
</inline-formula> and <inline-formula id="ieqn-10">
<mml:math id="mml-ieqn-10"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mi>K</mml:mi></mml:math>
</inline-formula>. Assume <inline-formula id="ieqn-11">
<mml:math id="mml-ieqn-11"><mml:mrow><mml:msub><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>w</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>j</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> as a fused vector of dimensions <inline-formula id="ieqn-12">
<mml:math id="mml-ieqn-12"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mi>K</mml:mi></mml:math>
</inline-formula>. Besides, the central parameters <inline-formula id="ieqn-13">
<mml:math id="mml-ieqn-13"><mml:mrow><mml:mover><mml:mi>U</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow></mml:math>
</inline-formula> and <inline-formula id="ieqn-14">
<mml:math id="mml-ieqn-14"><mml:mrow><mml:mover><mml:mi>V</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow></mml:math>
</inline-formula> indicates zero mean, where <inline-formula id="ieqn-15">
<mml:math id="mml-ieqn-15"><mml:mrow><mml:mover><mml:mi>U</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow><mml:mo>&#x2208;</mml:mo><mml:mrow><mml:msub><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>w</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> and <inline-formula id="ieqn-16">
<mml:math id="mml-ieqn-16"><mml:mrow><mml:mover><mml:mi>V</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow><mml:mo>&#x2208;</mml:mo><mml:mrow><mml:msub><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>w</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> . Consider <inline-formula id="ieqn-17">
<mml:math id="mml-ieqn-17"><mml:mrow><mml:msub><mml:mi>&#x03B4;</mml:mi><mml:mrow><mml:mi>u</mml:mi><mml:mi>v</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mover><mml:mi>U</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mover><mml:mi>V</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow></mml:math>
</inline-formula> and <inline-formula id="ieqn-18">
<mml:math id="mml-ieqn-18"><mml:mrow><mml:msub><mml:mi>&#x03B4;</mml:mi><mml:mrow><mml:mi>v</mml:mi><mml:mi>u</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:msubsup><mml:mi>&#x03B4;</mml:mi><mml:mrow><mml:mi>u</mml:mi><mml:mi>v</mml:mi></mml:mrow><mml:mi>T</mml:mi></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mi>n</mml:mi></mml:mfrac></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mstyle></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03B4;</mml:mi><mml:mrow><mml:mi>u</mml:mi><mml:mi>v</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> represents set covariance amongst vectors <inline-formula id="ieqn-19">
<mml:math id="mml-ieqn-19"><mml:mrow><mml:mover><mml:mi>U</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow></mml:math>
</inline-formula> and <inline-formula id="ieqn-20">
<mml:math id="mml-ieqn-20"><mml:mrow><mml:mover><mml:mi>V</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow></mml:math>
</inline-formula>. The PLS holds correlated features to fuse them. The fusion procedure via PLS reduces the number of predictors. The decomposition model between <inline-formula id="ieqn-21">
<mml:math id="mml-ieqn-21"><mml:mrow><mml:mover><mml:mi>U</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow></mml:math>
</inline-formula> and <inline-formula id="ieqn-22">
<mml:math id="mml-ieqn-22"><mml:mrow><mml:mover><mml:mi>V</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow></mml:math>
</inline-formula> can be represented using <xref ref-type="disp-formula" rid="eqn-4">Eqs. (4)</xref> and <xref ref-type="disp-formula" rid="eqn-5">(5)</xref>:</p>
<p><disp-formula id="eqn-4"><label>(4)</label>
<mml:math id="mml-eqn-4" display="block"><mml:mrow><mml:mover><mml:mi>U</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow><mml:mo>=</mml:mo><mml:munderover><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo></mml:mrow><mml:mi>d</mml:mi></mml:munderover><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:msub><mml:mi>&#x03B7;</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>w</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mi>i</mml:mi><mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mi>T</mml:mi></mml:msup></mml:mrow><mml:mo>=</mml:mo><mml:mi>E</mml:mi></mml:math>
</disp-formula></p>
<p><disp-formula id="eqn-5"><label>(5)</label>
<mml:math id="mml-eqn-5" display="block"><mml:mrow><mml:mover><mml:mi>V</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow><mml:mo>=</mml:mo><mml:munderover><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo></mml:mrow><mml:mi>d</mml:mi></mml:munderover><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:msub><mml:mi>&#x03B7;</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>w</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mi>i</mml:mi><mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mi>T</mml:mi></mml:msup></mml:mrow><mml:mo>=</mml:mo><mml:mi>F</mml:mi></mml:math>
</disp-formula></p>
<p>In case of using PLS, two directions amongst <inline-formula id="ieqn-23">
<mml:math id="mml-ieqn-23"><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> and <inline-formula id="ieqn-24">
<mml:math id="mml-ieqn-24"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> are obtained as given below:</p>
<p><disp-formula id="eqn-6"><label>(6)</label>
<mml:math id="mml-eqn-6" display="block"><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mo>}</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:munder><mml:mrow><mml:mrow><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">x</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:msup><mml:mi>u</mml:mi><mml:mi>T</mml:mi></mml:msup></mml:mrow><mml:mi>u</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:msup><mml:mi>v</mml:mi><mml:mi>T</mml:mi></mml:msup></mml:mrow><mml:mi>v</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:munder><mml:mo>&#x2061;</mml:mo><mml:mi>C</mml:mi><mml:mi>o</mml:mi><mml:mi>v</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mover><mml:mi>U</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow></mml:mrow><mml:mi>T</mml:mi></mml:msup></mml:mrow><mml:mi>u</mml:mi><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thickmathspace" /></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mover><mml:mi>V</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow></mml:mrow><mml:mi>T</mml:mi></mml:msup></mml:mrow><mml:mi>v</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</disp-formula></p>
<p><disp-formula id="eqn-7"><label>(7)</label>
<mml:math id="mml-eqn-7" display="block"><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mo>}</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mspace width="thickmathspace" /></mml:mrow><mml:munder><mml:mrow><mml:mrow><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">x</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:msup><mml:mi>u</mml:mi><mml:mi>T</mml:mi></mml:msup></mml:mrow><mml:mi>u</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:msup><mml:mi>v</mml:mi><mml:mi>T</mml:mi></mml:msup></mml:mrow><mml:mi>v</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:munder><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mspace width="thickmathspace" /></mml:mrow><mml:mrow><mml:msup><mml:mi>u</mml:mi><mml:mi>T</mml:mi></mml:msup></mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03B4;</mml:mi><mml:mrow><mml:mi>u</mml:mi><mml:mi>v</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mi>v</mml:mi><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thickmathspace" /></mml:mrow><mml:mi>f</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mrow><mml:mspace width="thickmathspace" /></mml:mrow><mml:mi>i</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:mn>3</mml:mn><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thickmathspace" /></mml:mrow><mml:mo>&#x2026;</mml:mo><mml:mi>d</mml:mi><mml:mrow><mml:mspace width="thickmathspace" /><mml:mspace width="thickmathspace" /></mml:mrow><mml:mi>a</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math>
</disp-formula></p>
<p>They are integrated into single matrix and resultant vector was gained with <inline-formula id="ieqn-25">
<mml:math id="mml-ieqn-25"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mi>K</mml:mi></mml:math>
</inline-formula> dimension. The fused vector can be denoted as <inline-formula id="ieqn-26">
<mml:math id="mml-ieqn-26"><mml:mrow><mml:msub><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>w</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>j</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> . Then, they are fed into the ELM model to classify them. It can be formulated as follows. The structure of ELM is shown in <xref ref-type="fig" rid="fig-3">Fig. 3</xref>. Consider <inline-formula id="ieqn-27">
<mml:math id="mml-ieqn-27"><mml:mi>L</mml:mi></mml:math>
</inline-formula> hidden layer nodes, the activation function <inline-formula id="ieqn-28">
<mml:math id="mml-ieqn-28"><mml:mi>g</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> can be denoted as follows [<xref ref-type="bibr" rid="ref-19">19</xref>]:</p>
<p><disp-formula id="eqn-8"><label>(8)</label>
<mml:math id="mml-eqn-8" display="block"><mml:munderover><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>L</mml:mi></mml:munderover><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:munderover><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>L</mml:mi></mml:munderover><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mi>g</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>.</mml:mo><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</disp-formula></p>
<p><disp-formula id="eqn-9"><label>(9)</label>
<mml:math id="mml-eqn-9" display="block"><mml:mrow><mml:msup><mml:mi>&#x03B2;</mml:mi><mml:mi>T</mml:mi></mml:msup></mml:mrow><mml:mo>=</mml:mo><mml:mi>O</mml:mi></mml:math>
</disp-formula></p>
<p>where <inline-formula id="ieqn-29">
<mml:math id="mml-ieqn-29"><mml:mi>L</mml:mi></mml:math>
</inline-formula> signifies hidden layer, <inline-formula id="ieqn-30">
<mml:math id="mml-ieqn-30"><mml:mrow><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> indicates output weight vector, <inline-formula id="ieqn-31">
<mml:math id="mml-ieqn-31"><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> represents input weight vector approaching hidden layer, <inline-formula id="ieqn-32">
<mml:math id="mml-ieqn-32"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> implies offset value, <inline-formula id="ieqn-33">
<mml:math id="mml-ieqn-33"><mml:mi>H</mml:mi></mml:math>
</inline-formula> denotes output hidden layer node, <inline-formula id="ieqn-34">
<mml:math id="mml-ieqn-34"><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>.</mml:mo><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> represents inner product of <inline-formula id="ieqn-35">
<mml:math id="mml-ieqn-35"><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula>, and <inline-formula id="ieqn-36">
<mml:math id="mml-ieqn-36"><mml:mi>O</mml:mi></mml:math>
</inline-formula> implies predicted outcome. <xref ref-type="disp-formula" rid="eqn-19">Eq. (19)</xref> can be rewritten as follows:</p>
<p><disp-formula id="eqn-10"><label>(10)</label>
<mml:math id="mml-eqn-10" display="block"><mml:mrow><mml:mover><mml:mi>&#x03B2;</mml:mi><mml:mo stretchy="false">&#x005E;</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi mathvariant="normal">E</mml:mi><mml:mi mathvariant="normal">L</mml:mi><mml:mi mathvariant="normal">M</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mspace width="thickmathspace" /></mml:mrow><mml:munder><mml:mrow><mml:mrow><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mspace width="thickmathspace" /><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">n</mml:mi></mml:mrow></mml:mrow><mml:mi>&#x03B2;</mml:mi></mml:munder><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo></mml:mrow><mml:mrow><mml:msup><mml:mi>&#x03B2;</mml:mi><mml:mi>T</mml:mi></mml:msup></mml:mrow><mml:mi>H</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>O</mml:mi><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo></mml:mrow></mml:math>
</disp-formula></p>
<p>For enhancing the stableness of the ELM model, the minimization function can be provided using <xref ref-type="disp-formula" rid="eqn-11">Eq. (11)</xref>:</p>
<p><disp-formula id="eqn-11"><label>(11)</label>
<mml:math id="mml-eqn-11" display="block"><mml:munder><mml:mrow><mml:mo form="prefix">min</mml:mo></mml:mrow><mml:mi>w</mml:mi></mml:munder><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:mrow><mml:mrow><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo></mml:mrow><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:mrow><mml:mi>c</mml:mi><mml:mrow><mml:mspace width="thickmathspace" /></mml:mrow><mml:munderover><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>N</mml:mi></mml:munderover><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03F5;</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mtext>&#xA0;</mml:mtext><mml:mrow><mml:mi mathvariant="normal">s</mml:mi><mml:mo>.</mml:mo><mml:mi mathvariant="normal">t</mml:mi><mml:mo>.</mml:mo></mml:mrow><mml:mtext>&#xA0;</mml:mtext><mml:mrow><mml:msup><mml:mi>&#x03B2;</mml:mi><mml:mi>T</mml:mi></mml:msup></mml:mrow><mml:mi>h</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mstyle></mml:mstyle></mml:math>
</disp-formula></p>
<p>where <inline-formula id="ieqn-37">
<mml:math id="mml-ieqn-37"><mml:mrow><mml:msub><mml:mi>&#x03F5;</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> signifies training error, <inline-formula id="ieqn-38">
<mml:math id="mml-ieqn-38"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> specifies equivalent labels to the samples <inline-formula id="ieqn-39">
<mml:math id="mml-ieqn-39"><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula>, and <inline-formula id="ieqn-40">
<mml:math id="mml-ieqn-40"><mml:mi>c</mml:mi></mml:math>
</inline-formula> represents penalty variable.</p>
<fig id="fig-3">
<label>Figure 3</label>
<caption>
<title>Structure of ELM model</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CSSE_30556-fig-3.png"/>
</fig>
</sec>
<sec id="s2_5">
<label>2.5</label>
<title>Parameter Tuning</title>
<p>At the final stage, the SFO algorithm is utilized for effective parameter selection of the ELM model, consequently resulting in enhanced performance. The SFO is a new nature-inspired metaheuristic approach which is demonstrated once a set of hunting sailfish (SF) [<xref ref-type="bibr" rid="ref-20">20</xref>]. It demonstrates optimal efficacy associated with common metaheuristic approach. In the SFO approach, it is considered as SF is candidate solution and the place of SF in the exploration region signifies the parameter of issue. The position of <inline-formula id="ieqn-41">
<mml:math id="mml-ieqn-41"><mml:mrow><mml:msup><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>
</inline-formula> SF from the <inline-formula id="ieqn-42">
<mml:math id="mml-ieqn-42"><mml:mrow><mml:msup><mml:mi>k</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>
</inline-formula> searching iteration is characterized as <inline-formula id="ieqn-43">
<mml:math id="mml-ieqn-43"><mml:mi>S</mml:mi><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>
</inline-formula>, and the corresponding fitness is estimated by <inline-formula id="ieqn-44">
<mml:math id="mml-ieqn-44"><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>S</mml:mi><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula>. The sardines are also crucial contributors to the SFO method. It is regarded as school of sardines which move from the searching region. The location of <inline-formula id="ieqn-45">
<mml:math id="mml-ieqn-45"><mml:mrow><mml:msup><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>
</inline-formula> sardine was illustrated as <inline-formula id="ieqn-46">
<mml:math id="mml-ieqn-46"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula>, and the corresponding fitness was calculated by <inline-formula id="ieqn-47">
<mml:math id="mml-ieqn-47"><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula>. In the SFO method, the SF possesses the optimal location that has been selected as leading SF that affects the acceleration and manoeuvrability of sardines under attack. Moreover, the position of injured sardine in each round is selected as an optimal location for cooperative hunting in SF. The algorithm aims at avoiding beforehand removal solution. injured sardines and Elite SF are <inline-formula id="ieqn-48">
<mml:math id="mml-ieqn-48"><mml:msubsup><mml:mi>Y</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mi>S</mml:mi><mml:mi>F</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mi>i</mml:mi></mml:msubsup></mml:math>
</inline-formula> denoted in the following equation:</p>
<p><disp-formula id="eqn-12"><label>(12)</label>
<mml:math id="mml-eqn-12" display="block"><mml:msubsup><mml:mi>Y</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mi>S</mml:mi><mml:mi>F</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mi>i</mml:mi></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>l</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>S</mml:mi><mml:mi>F</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mi>i</mml:mi></mml:msubsup><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:msub><mml:mi>&#x03BB;</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mi>o</mml:mi><mml:mi>m</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:msubsup><mml:mi>Y</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>l</mml:mi><mml:mi>i</mml:mi><mml:mi>&#x03C4;</mml:mi><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>S</mml:mi><mml:mi>F</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mi>i</mml:mi></mml:msubsup><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi>j</mml:mi><mml:mi>u</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mi>S</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mi>i</mml:mi></mml:msubsup></mml:mrow><mml:mn>2</mml:mn></mml:mfrac></mml:mrow></mml:mstyle></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mi>u</mml:mi><mml:mi>r</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mi>S</mml:mi><mml:mi>F</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mi>i</mml:mi></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</disp-formula></p>
<p>whereas <inline-formula id="ieqn-49">
<mml:math id="mml-ieqn-49"><mml:msubsup><mml:mi>Y</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mi>u</mml:mi><mml:mi>r</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>S</mml:mi><mml:mi>F</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mi>i</mml:mi></mml:msubsup></mml:math>
</inline-formula> indicates the existing location of SF and arbitrary <inline-formula id="ieqn-50">
<mml:math id="mml-ieqn-50"><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> denotes the random value ranges within [0&#x2013;1].</p>
<p>The parameter <inline-formula id="ieqn-51">
<mml:math id="mml-ieqn-51"><mml:mrow><mml:msub><mml:mi>&#x03BB;</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> describes the coefficient from the <inline-formula id="ieqn-52">
<mml:math id="mml-ieqn-52"><mml:mrow><mml:msup><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>
</inline-formula> iteration and values are given by:</p>
<p><disp-formula id="eqn-13"><label>(13)</label>
<mml:math id="mml-eqn-13" display="block"><mml:mrow><mml:msub><mml:mi>&#x03BB;</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mo>&#x00D7;</mml:mo><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mi>S</mml:mi><mml:mi>D</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>S</mml:mi><mml:mi>D</mml:mi></mml:math>
</disp-formula></p>
<p>In which <inline-formula id="ieqn-53">
<mml:math id="mml-ieqn-53"><mml:mi>S</mml:mi><mml:mi>D</mml:mi></mml:math>
</inline-formula> represents the sardine density that indicates the quantity of sardines in each iteration. The parameter <inline-formula id="ieqn-54">
<mml:math id="mml-ieqn-54"><mml:mi>S</mml:mi><mml:mi>D</mml:mi></mml:math>
</inline-formula> is given by:</p>
<p><disp-formula id="eqn-14"><label>(14)</label>
<mml:math id="mml-eqn-14" display="block"><mml:mi>S</mml:mi><mml:mi>D</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>S</mml:mi><mml:mi>F</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>S</mml:mi><mml:mi>F</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi>S</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</disp-formula></p>
<p>Here <inline-formula id="ieqn-55">
<mml:math id="mml-ieqn-55"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>S</mml:mi><mml:mi>F</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>
</inline-formula> and <inline-formula id="ieqn-56">
<mml:math id="mml-ieqn-56"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi>S</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> signifies the quantity of SF and sardines. At first, the hunt, SF is energetic, in addition, sardines aren&#x2019;t injured or tired. The sardines are quickly escaped. However, with nonstop hunting, the strength of SF attack was reduced gradually. Meanwhile, the sardines are tired, and also the alertness of the position of SF is minimized. Therefore, the outcomes, the sardines are hunted. As per the algorithmic process, a novel location of sardine <inline-formula id="ieqn-57">
<mml:math id="mml-ieqn-57"><mml:msubsup><mml:mi>Y</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi>S</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mi>i</mml:mi></mml:msubsup></mml:math>
</inline-formula> denoted in the following:</p>
<p><disp-formula id="eqn-15"><label>(15)</label>
<mml:math id="mml-eqn-15" display="block"><mml:msubsup><mml:mi>Y</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi>S</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mi>i</mml:mi></mml:msubsup><mml:mo>=</mml:mo><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mi>o</mml:mi><mml:mi>m</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msubsup><mml:mi>Y</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>l</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>S</mml:mi><mml:mi>F</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mi>i</mml:mi></mml:msubsup><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mrow><mml:mi>o</mml:mi><mml:mi>l</mml:mi><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mi>S</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mi>i</mml:mi></mml:msubsup><mml:mo>+</mml:mo><mml:mi>A</mml:mi><mml:mi>T</mml:mi><mml:mi>P</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</disp-formula></p>
<p>Now <inline-formula id="ieqn-58">
<mml:math id="mml-ieqn-58"><mml:msubsup><mml:mi>Y</mml:mi><mml:mrow><mml:mi>o</mml:mi><mml:mi>l</mml:mi><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mi>S</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mi>i</mml:mi></mml:msubsup></mml:math>
</inline-formula> denotes the older location of sardine and arbitrary <inline-formula id="ieqn-59">
<mml:math id="mml-ieqn-59"><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> characterizes the arbitrary value ranges within [0&#x2013;1]. <inline-formula id="ieqn-60">
<mml:math id="mml-ieqn-60"><mml:mi>A</mml:mi><mml:mi>T</mml:mi><mml:mi>P</mml:mi></mml:math>
</inline-formula> indicates the SF attack power. The parameter <inline-formula id="ieqn-61">
<mml:math id="mml-ieqn-61"><mml:mi>A</mml:mi><mml:mi>T</mml:mi><mml:mi>P</mml:mi></mml:math>
</inline-formula> is evaluated by:</p>
<p><disp-formula id="eqn-16"><label>(16)</label>
<mml:math id="mml-eqn-16" display="block"><mml:mi>A</mml:mi><mml:mi>T</mml:mi><mml:mi>P</mml:mi><mml:mo>=</mml:mo><mml:mi>B</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>2</mml:mn><mml:mo>&#x00D7;</mml:mo><mml:mi>l</mml:mi><mml:mi>t</mml:mi><mml:mi>r</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>&#x03F5;</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</disp-formula></p>
<p>whereas <inline-formula id="ieqn-62">
<mml:math id="mml-ieqn-62"><mml:mi>B</mml:mi></mml:math>
</inline-formula> and <inline-formula id="ieqn-63">
<mml:math id="mml-ieqn-63"><mml:mi>&#x03F5;</mml:mi></mml:math>
</inline-formula> indicate the coefficient that is employed for minimizing the attack power within [B-0] and <inline-formula id="ieqn-64">
<mml:math id="mml-ieqn-64"><mml:mi>I</mml:mi><mml:mi>t</mml:mi><mml:mi>r</mml:mi></mml:math>
</inline-formula> indicates the amount of iterations. While the attack power of SF minimized the hunting time, this decreases the convergence rate. When <inline-formula id="ieqn-65">
<mml:math id="mml-ieqn-65"><mml:mi>A</mml:mi><mml:mi>T</mml:mi><mml:mi>P</mml:mi></mml:math>
</inline-formula> is high, that is, greater than 0.5, the location of each sardine is upgraded. On the other hand, <inline-formula id="ieqn-66">
<mml:math id="mml-ieqn-66"><mml:mi>&#x03B1;</mml:mi></mml:math>
</inline-formula> sardines with <inline-formula id="ieqn-67">
<mml:math id="mml-ieqn-67"><mml:mi>&#x03B2;</mml:mi></mml:math>
</inline-formula> variable upgrade their locations. The amount of sardines upgraded the location is described by:</p>
<p><disp-formula id="eqn-17"><label>(17)</label>
<mml:math id="mml-eqn-17" display="block"><mml:mi>&#x03B1;</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi>S</mml:mi></mml:msub></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mi>A</mml:mi><mml:mi>T</mml:mi><mml:mi>P</mml:mi></mml:math>
</disp-formula></p>
<p>Then, <inline-formula id="ieqn-68">
<mml:math id="mml-ieqn-68"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi>S</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> shows the amount of sardines in each iteration. The amount of parameters of the sardines upgraded the place can be accomplished by:</p>
<p><disp-formula id="eqn-18"><label>(18)</label>
<mml:math id="mml-eqn-18" display="block"><mml:mi>&#x03B2;</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mi>A</mml:mi><mml:mi>T</mml:mi><mml:mi>P</mml:mi></mml:math>
</disp-formula></p>
<p>In which <inline-formula id="ieqn-69">
<mml:math id="mml-ieqn-69"><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> characterizes the amount of parameters from the <inline-formula id="ieqn-70">
<mml:math id="mml-ieqn-70"><mml:mrow><mml:msup><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>
</inline-formula> iteration. When the sardine was hunted, the fitness is greater than the SF. Here, the location of SF <inline-formula id="ieqn-71">
<mml:math id="mml-ieqn-71"><mml:msubsup><mml:mi>Y</mml:mi><mml:mrow><mml:mi>S</mml:mi><mml:mi>F</mml:mi></mml:mrow><mml:mi>i</mml:mi></mml:msubsup></mml:math>
</inline-formula> is upgraded by newest location of hunted sardine <inline-formula id="ieqn-72">
<mml:math id="mml-ieqn-72"><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>S</mml:mi><mml:mi>i</mml:mi></mml:msubsup></mml:math>
</inline-formula> for hunting novel sardine. It can be expressed by:</p>
<p><disp-formula id="eqn-19"><label>(19)</label>
<mml:math id="mml-eqn-19" display="block"><mml:msubsup><mml:mi>Y</mml:mi><mml:mrow><mml:mi>S</mml:mi><mml:mi>F</mml:mi></mml:mrow><mml:mi>i</mml:mi></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>S</mml:mi><mml:mi>i</mml:mi></mml:msubsup><mml:mrow><mml:mspace width="thickmathspace" /></mml:mrow><mml:mi>i</mml:mi><mml:mi>f</mml:mi><mml:mrow><mml:mspace width="thickmathspace" /></mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&lt;</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>S</mml:mi><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</disp-formula></p>
<p>For adjusting the ELM parameters, the SFO algorithm computes a fitness function for accomplishing maximum classifier results. It derives a fitness function using the error rate and the fitness value should be as low as possible. It can be defined as follows.</p>
<p><disp-formula id="eqn-20"><label>(20)</label>
<mml:math id="mml-eqn-20" display="block"><mml:mi>f</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mi>s</mml:mi><mml:mi>s</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>C</mml:mi><mml:mi>l</mml:mi><mml:mi>a</mml:mi><mml:mi>s</mml:mi><mml:mi>s</mml:mi><mml:mi>i</mml:mi><mml:mi>f</mml:mi><mml:mi>i</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>E</mml:mi><mml:mi>r</mml:mi><mml:mi>r</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>R</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>n</mml:mi><mml:mi>u</mml:mi><mml:mi>m</mml:mi><mml:mi>b</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mrow><mml:mspace width="thickmathspace" /></mml:mrow><mml:mi>o</mml:mi><mml:mi>f</mml:mi><mml:mrow><mml:mspace width="thickmathspace" /></mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>s</mml:mi><mml:mi>c</mml:mi><mml:mi>l</mml:mi><mml:mi>a</mml:mi><mml:mi>s</mml:mi><mml:mi>s</mml:mi><mml:mi>i</mml:mi><mml:mi>f</mml:mi><mml:mi>i</mml:mi><mml:mi>e</mml:mi><mml:mi>d</mml:mi><mml:mrow><mml:mspace width="thickmathspace" /></mml:mrow><mml:mi>s</mml:mi><mml:mi>a</mml:mi><mml:mi>m</mml:mi><mml:mi>p</mml:mi><mml:mi>l</mml:mi><mml:mi>e</mml:mi><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mi>T</mml:mi><mml:mi>o</mml:mi><mml:mi>t</mml:mi><mml:mi>a</mml:mi><mml:mi>l</mml:mi><mml:mrow><mml:mspace width="thickmathspace" /></mml:mrow><mml:mi>n</mml:mi><mml:mi>u</mml:mi><mml:mi>m</mml:mi><mml:mi>b</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mrow><mml:mspace width="thickmathspace" /></mml:mrow><mml:mi>o</mml:mi><mml:mi>f</mml:mi><mml:mrow><mml:mspace width="thickmathspace" /></mml:mrow><mml:mi>s</mml:mi><mml:mi>a</mml:mi><mml:mi>m</mml:mi><mml:mi>p</mml:mi><mml:mi>l</mml:mi><mml:mi>e</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:mfrac></mml:mrow><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow><mml:mn>100</mml:mn></mml:mstyle></mml:math>
</disp-formula></p>
</sec>
</sec>
<sec id="s3">
<label>3</label>
<title>Results and Discussion</title>
<p>In this section, the experimental validation of the CADOC-SFOFC model is performed using benchmark dataset from Kaggle repository. A set of four confusion matrices achieved by the CADOC-SFOFC model on distinct sizes of training/testing (TR/TS) data is illustrated in <xref ref-type="fig" rid="fig-4">Fig. 4</xref>. With TR/TS data of 90:10, the CADOC-SFOFC model has recognized 4 instances under cancer and 9 instances under non-cancer classes.</p>
<fig id="fig-4">
<label>Figure 4</label>
<caption>
<title>Confusion matrices of CADOC-SFOFC model</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CSSE_30556-fig-4.png"/>
</fig>
<p>At the same time, with TR/TS data of 80:20, the CADOC-SFOFC model has recognized 18 instances under cancer and 8 instances under non-cancer classes. Followed by, with TR/TS data of 70:30, the CADOC-SFOFC model has recognized 25 instances under cancer and 13 instances under non-cancer classes. Lastly, with TR/TS data of 60:40, the CADOC-SFOFC model has recognized 38 instances under cancer and 14 instances under non-cancer classes.</p>
<p><xref ref-type="table" rid="table-1">Tab. 1</xref> and <xref ref-type="fig" rid="fig-5">Fig. 5</xref> exhibits detailed OC classification outcomes of the CADOC-SFOFC model on distinct sizes of TR/TS data. The experimental outcomes implied that the CADOC-SFOFC model has gained effectual outcomes on various TR/TS data.</p>
<table-wrap id="table-1"><label>Table 1</label>
<caption>
<title>Overall classification outcomes of CADOC-SFOFC model</title></caption>
<table><colgroup>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Class Labels</th>
<th>Accuracy</th>
<th>Precision</th>
<th>Recall</th>
<th>Specificity</th>
<th>F-Score</th>
</tr>
</thead>
<tbody>
<tr>
<td colspan="6">Training/Testing (90:10)</td>
</tr>
<tr>
<td>&#x2003;Cancer</td>
<td>92.86</td>
<td>100.00</td>
<td>80.00</td>
<td>100.00</td>
<td>88.89</td>
</tr>
<tr>
<td>&#x2003;Non-Cancer</td>
<td>92.86</td>
<td>90.00</td>
<td>100.00</td>
<td>80.00</td>
<td>94.74</td>
</tr>
<tr>
<td>&#x2003;Average</td>
<td>92.86</td>
<td>95.00</td>
<td>90.00</td>
<td>90.00</td>
<td>91.81</td>
</tr>
<tr>
<td colspan="6">Training/Testing (80:20)</td>
</tr>
<tr>
<td>&#x2003;Cancer</td>
<td>96.30</td>
<td>94.74</td>
<td>100.00</td>
<td>88.89</td>
<td>97.30</td>
</tr>
<tr>
<td>&#x2003;Non-Cancer</td>
<td>96.30</td>
<td>100.00</td>
<td>88.89</td>
<td>100.00</td>
<td>94.12</td>
</tr>
<tr>
<td>&#x2003;Average</td>
<td>96.30</td>
<td>97.37</td>
<td>94.44</td>
<td>94.44</td>
<td>95.71</td>
</tr>
<tr>
<td colspan="6">Training/Testing (70:30)</td>
</tr>
<tr>
<td>&#x2003;Cancer</td>
<td>95.00</td>
<td>100.00</td>
<td>92.59</td>
<td>100.00</td>
<td>96.15</td>
</tr>
<tr>
<td>&#x2003;Non-Cancer</td>
<td>95.00</td>
<td>86.67</td>
<td>100.00</td>
<td>92.59</td>
<td>92.86</td>
</tr>
<tr>
<td>&#x2003;Average</td>
<td>95.00</td>
<td>93.33</td>
<td>96.30</td>
<td>96.30</td>
<td>94.51</td>
</tr>
<tr>
<td colspan="6">Training/Testing (60:40)</td>
</tr>
<tr>
<td>&#x2003;Cancer</td>
<td>98.11</td>
<td>97.44</td>
<td>100.00</td>
<td>93.33</td>
<td>98.70</td>
</tr>
<tr>
<td>&#x2003;Non-Cancer</td>
<td>98.11</td>
<td>100.00</td>
<td>93.33</td>
<td>100.00</td>
<td>96.55</td>
</tr>
<tr>
<td>&#x2003;Average</td>
<td>98.11</td>
<td>98.72</td>
<td>96.67</td>
<td>96.67</td>
<td>97.63</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="fig-5">
<label>Figure 5</label>
<caption>
<title>OC classification of CADOC-SFOFC model under distinct TR/TS data</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CSSE_30556-fig-5.png"/>
</fig>
<p>For instance, with TR/TS of 90:10, the CADOC-SFOFC model has classified cancer images with <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: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>, <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:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></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:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:mrow></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:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thickmathspace" /></mml:mrow></mml:math>
</inline-formula>and <inline-formula id="ieqn-77">
<mml:math id="mml-ieqn-77"><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 92.86%, 100%, 80%, 100% and 88.89% respectively. In line with, under TR/TS of 80:20, the CADOC-SFOFC model has classified cancer images with <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: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>, <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:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></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:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:mrow></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:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thickmathspace" /></mml:mrow></mml:math>
</inline-formula>and <inline-formula id="ieqn-82">
<mml:math id="mml-ieqn-82"><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 96.30%, 94.74%, 100%, 88.% and 88.89% respectively. Moreover, with TR/TS of 70:30, the CADOC-SFOFC model has classified cancer images with <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: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>, <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:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></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:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:mrow></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:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thickmathspace" /></mml:mrow></mml:math>
</inline-formula>and <inline-formula id="ieqn-87">
<mml:math id="mml-ieqn-87"><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%, 100%, 92.59%, 100% and 96.15% respectively. At last, with TR/TS of 60:40, the CADOC-SFOFC model has classified cancer images with <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: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>, <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:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></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:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:mrow></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:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thickmathspace" /></mml:mrow></mml:math>
</inline-formula>and <inline-formula id="ieqn-92">
<mml:math id="mml-ieqn-92"><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 98.11%, 97.44%, 100%, 93.33% and 98.70% respectively. Moreover, with TR/TS of 80:20, the CADOC-SFOFC model has provided average <inline-formula id="ieqn-93">
<mml:math id="mml-ieqn-93"><mml:mi>a</mml:mi><mml:mi>c</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>, <inline-formula id="ieqn-94">
<mml:math id="mml-ieqn-94"><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>, <inline-formula id="ieqn-95">
<mml:math id="mml-ieqn-95"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula>, <inline-formula id="ieqn-96">
<mml:math id="mml-ieqn-96"><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:mo>,</mml:mo><mml:mrow><mml:mspace width="thickmathspace" /></mml:mrow></mml:math>
</inline-formula>and <inline-formula id="ieqn-97">
<mml:math id="mml-ieqn-97"><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 96.30%, 97.37%, 94.44%, 94.44% and 95.71% respectively. Furthermore, with TR/TS of 70:30, the CADOC-SFOFC model has provided average <inline-formula id="ieqn-98">
<mml:math id="mml-ieqn-98"><mml:mi>a</mml:mi><mml:mi>c</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>, <inline-formula id="ieqn-99">
<mml:math id="mml-ieqn-99"><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>, <inline-formula id="ieqn-100">
<mml:math id="mml-ieqn-100"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula>, <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:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thickmathspace" /></mml:mrow></mml:math>
</inline-formula>and <inline-formula id="ieqn-102">
<mml:math id="mml-ieqn-102"><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%, 93.33%, 96.30%, 96.30% and 95.71% respectively.</p>
<p><xref ref-type="fig" rid="fig-6">Fig. 6</xref> demonstrates a clear training and validation accuracies of the CADOC-SFOFC model on test dataset. The training and validation accuracies are measured under varying numbers of epochs. It is exhibited that the CADOC-SFOFC model has gained increased values of training and validation accuracies.</p>
<fig id="fig-6">
<label>Figure 6</label>
<caption>
<title>Training and validation accuracies of CADOC-SFOFC model</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CSSE_30556-fig-6.png"/>
</fig>
<p><xref ref-type="fig" rid="fig-7">Fig. 7</xref> validates the training and validation losses of the CADOC-SFOFC model on test dataset. The training and validation losses can be determined with a rising number of epochs. It is displayed that the CADOC-SFOFC model has extended reduced values of training and validation losses.</p>
<fig id="fig-7">
<label>Figure 7</label>
<caption>
<title>Training and validation losses of CADOC-SFOFC model</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CSSE_30556-fig-7.png"/>
</fig>
<p><xref ref-type="fig" rid="fig-8">Fig. 8</xref> highlights the ROC curves of the CADOC-SFOFC model obtained under distinct sizes of TR/TS data. The figures reported that the CADOC-SFOFC model has accomplished effectual OC classification under two classes namely cancer and non-cancer. It is also noticed that the CADOC-SFOFC model has gained maximum ROC values under two classes.</p>
<fig id="fig-8">
<label>Figure 8</label>
<caption>
<title>Precision-recall curves of CADOC-SFOFC model under distinct TR/TS data</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CSSE_30556-fig-8.png"/>
</fig>
<p><xref ref-type="fig" rid="fig-9">Fig. 9</xref> demonstrates the precision-recall curves of the CADOC-SFOFC model attained under dissimilar sizes of TR/TS data. The results represented that the CADOC-SFOFC model has reached maximum OC classification under two classes namely cancer and non-cancer. It is observed that the CADOC-SFOFC model has showcased improved precision-recall values under two classes.</p>
<fig id="fig-9">
<label>Figure 9</label>
<caption>
<title>ROC of CADOC-SFOFC model under distinct TR/TS data</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CSSE_30556-fig-9.png"/>
</fig>
<p>For assessing the enhanced outcomes of the CADOC-SFOFC model, a comparison study with recent models [<xref ref-type="bibr" rid="ref-21">21</xref>&#x2013;<xref ref-type="bibr" rid="ref-23">23</xref>] is made in <xref ref-type="table" rid="table-2">Tab. 2</xref> and <xref ref-type="fig" rid="fig-10">Fig. 10</xref>. The results implied that the ADCO-DL, Inception-v4, and DenseNet models have reached lower OC classification results. Followed by, the artificial neural network (ANN)-support vector machine (SVM) and C-Net models have tried to showcase moderately improved classification outcomes. Though the random forest (RF) model has accomplished reasonable OC classification results with <inline-formula id="ieqn-103">
<mml:math id="mml-ieqn-103"><mml:mi>a</mml:mi><mml:mi>c</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>, <inline-formula id="ieqn-104">
<mml:math id="mml-ieqn-104"><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>, <inline-formula id="ieqn-105">
<mml:math id="mml-ieqn-105"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula>, and <inline-formula id="ieqn-106">
<mml:math id="mml-ieqn-106"><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 97.09%, 92.34%, 93.86%, and 94.09%, the CADOC-SFOFC model has surpassed existing methodologies with maximum <inline-formula id="ieqn-107">
<mml:math id="mml-ieqn-107"><mml:mi>a</mml:mi><mml:mi>c</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>, <inline-formula id="ieqn-108">
<mml:math id="mml-ieqn-108"><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>, <inline-formula id="ieqn-109">
<mml:math id="mml-ieqn-109"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula>, and <inline-formula id="ieqn-110">
<mml:math id="mml-ieqn-110"><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 98.11%, 98.72%, 96.67%, and 97.63% respectively.</p>
<table-wrap id="table-2"><label>Table 2</label>
<caption>
<title>Comparison study of CADOC-SFOFC model with existing models</title></caption>
<table><colgroup>
<col/>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Methods</th>
<th>Accuracy</th>
<th>Precision</th>
<th>Recall</th>
<th>F-Score</th>
</tr>
</thead>
<tbody>
<tr>
<td>ADCOL-DL</td>
<td>85.69</td>
<td>91.32</td>
<td>90.92</td>
<td>85.90</td>
</tr>
<tr>
<td>Inception-v4 Model</td>
<td>87.85</td>
<td>92.36</td>
<td>85.78</td>
<td>85.69</td>
</tr>
<tr>
<td>DenseNet Model</td>
<td>88.78</td>
<td>91.40</td>
<td>83.69</td>
<td>83.98</td>
</tr>
<tr>
<td>RF Model</td>
<td>97.09</td>
<td>92.34</td>
<td>93.86</td>
<td>94.09</td>
</tr>
<tr>
<td>ANN-SVM Model</td>
<td>95.12</td>
<td>93.59</td>
<td>92.62</td>
<td>90.97</td>
</tr>
<tr>
<td>C-Net Model</td>
<td>96.89</td>
<td>90.41</td>
<td>90.18</td>
<td>94.67</td>
</tr>
<tr>
<td>CADOC-SFOFC</td>
<td>98.11</td>
<td>98.72</td>
<td>96.67</td>
<td>97.63</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="fig-10">
<label>Figure 10</label>
<caption>
<title>Comparative analysis of CADOC-SFOFC model with recent approaches</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CSSE_30556-fig-10.png"/>
</fig>
<p>The enhanced performance of the CADOC-SFOFC model is due to the inclusion of SFO based parameter optimization process. After investigating the above mentioned results and discussion, it can be ensured that the CADOC-SFOFC model has the ability to outperform the other methods with improved OC classification outcomes.</p>
</sec>
<sec id="s4">
<label>4</label>
<title>Conclusion</title>
<p>In this study, a novel CADOC-SFOFC model has been devised to determine the existence of OC on medical images. Initially, the CADOC-SFOFC model carried out the fusion based feature extraction procedure using VGGNet-16 and ResNet model. In addition, feature vectors are fused and passed into the ELM model for classification process. Finally, the SFO algorithm is utilized for effective parameter selection of the ELM model, consequently resulting in enhanced performance. The experimental analysis of the CADOC-SFOFC model was tested on Kaggle dataset and the results reported the betterment of the CADOC-SFOFC model over the compared methods. Therefore, the CADOC-SFOFC model has maximum potential as an inexpensive and non-invasive tool which supports screening process and enhances the detection efficiency. In future, the detection efficiency can be improvised by the design of advanced DL based classifier models.</p><fn-group>
<fn fn-type="other">
<p><bold>Funding Statement:</bold> The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work under grant number (RGP 2/142/43). Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2022R151), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia. The authors would like to thank the Deanship of Scientific Research at Umm Al-Qura University for supporting this work by Grant Code: 22UQU4310373DSR13. This research project was supported by a grant from the Research Center of the Female Scientific and Medical Colleges, Deanship of Scientific Research, King Saud University.</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>
</sec>
</body>
<back>
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