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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">32729</article-id>
<article-id pub-id-type="doi">10.32604/cmc.2023.032729</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Automated Autism Spectral Disorder Classification Using Optimal Machine Learning Model</article-title>
<alt-title alt-title-type="left-running-head">Automated Autism Spectral Disorder Classification Using Optimal Machine Learning Model</alt-title>
<alt-title alt-title-type="right-running-head">Automated Autism Spectral Disorder Classification Using Optimal Machine Learning Model</alt-title>
</title-group>
<contrib-group content-type="authors">
<contrib id="author-1" contrib-type="author">
<name name-style="western"><surname>Mengash</surname><given-names>Hanan Abdullah</given-names></name><xref ref-type="aff" rid="aff-1">1</xref></contrib>
<contrib id="author-2" contrib-type="author">
<name name-style="western"><surname>Alqahtani</surname><given-names>Hamed</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>Maray</surname><given-names>Mohammed</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>Marzouk</surname><given-names>Radwa</given-names></name><xref ref-type="aff" rid="aff-1">1</xref></contrib>
<contrib id="author-6" contrib-type="author">
<name name-style="western"><surname>Al-Hagery</surname><given-names>Mohammed Abdullah</given-names></name><xref ref-type="aff" rid="aff-5">5</xref></contrib>
<contrib id="author-7" contrib-type="author">
<name name-style="western"><surname>Mohsen</surname><given-names>Heba</given-names></name><xref ref-type="aff" rid="aff-6">6</xref></contrib>
<contrib id="author-8" 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-7">7</xref><email>m.alduhayyim@psau.edu.sa</email></contrib>
<aff id="aff-1"><label>1</label><institution>Department of Information Systems, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University</institution>, <addr-line>P.O. Box 84428</addr-line>, <addr-line>Riyadh, 11671</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-2"><label>2</label><institution>Department of Information Systems, College of Computer Science, Center of Artificial Intelligence and Unit of Cybersecurity, King Khalid University</institution>, <addr-line>Abha</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-3"><label>3</label><institution>Department of Information Systems, College of Computer Science, King Khalid University</institution>, <addr-line>Abha</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-4"><label>4</label><institution>Department of Computer Sciences, College of Computing and Information System, Umm Al-Qura University</institution>, <country>Saudi Arabia</country></aff>
<aff id="aff-5"><label>5</label><institution>Department of Computer Science, College of Computer, Qassim University</institution>, <country>Saudi Arabia</country></aff>
<aff id="aff-6"><label>6</label><institution>Department of Computer Science, Faculty of Computers and Information Technology, Future University in Egypt, New Cairo</institution>, <addr-line>11835</addr-line>, <country>Egypt</country></aff>
<aff id="aff-7"><label>7</label><institution>Department of Computer Science, College of Sciences and Humanities-Aflaj, Prince Sattam bin Abdulaziz University</institution>, <country>Saudi Arabia</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 publication-format="print" date-type="pub" iso-8601-date="2022-12-15"><day>15</day>
<month>12</month>
<year>2022</year></pub-date>
<volume>74</volume>
<issue>3</issue>
<fpage>5251</fpage>
<lpage>5265</lpage>
<history>
<date date-type="received"><day>27</day><month>5</month><year>2022</year></date>
<date date-type="accepted"><day>29</day><month>6</month><year>2022</year></date>
</history>
<permissions>
<copyright-statement>&#x00A9; 2023 Mengash et al.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Mengash et al.</copyright-holder>
<license xlink:href="https://creativecommons.org/licenses/by/4.0/">
<license-p>This work is licensed under a <ext-link ext-link-type="uri" xlink:type="simple" xlink:href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International License</ext-link>, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</license-p>
</license>
</permissions>
<self-uri content-type="pdf" xlink:href="TSP_CMC_32729.pdf"></self-uri>
<abstract>
<p>Autism Spectrum Disorder (ASD) refers to a neuro-disorder where an individual has long-lasting effects on communication and interaction with others. Advanced information technology which employs artificial intelligence (AI) model has assisted in early identify ASD by using pattern detection. Recent advances of AI models assist in the automated identification and classification of ASD, which helps to reduce the severity of the disease. This study introduces an automated ASD classification using owl search algorithm with machine learning (ASDC-OSAML) model. The proposed ASDC-OSAML model majorly focuses on the identification and classification of ASD. To attain this, the presented ASDC-OSAML model follows min-max normalization approach as a pre-processing stage. Next, the owl search algorithm (OSA)-based feature selection (OSA-FS) model is used to derive feature subsets. Then, beetle swarm antenna search (BSAS) algorithm with Iterative Dichotomiser 3 (ID3) classification method was implied for ASD detection and classification. The design of BSAS algorithm helps to determine the parameter values of the ID3 classifier. The performance analysis of the ASDC-OSAML model is performed using benchmark dataset. An extensive comparison study highlighted the supremacy of the ASDC-OSAML model over recent state of art approaches.</p>
</abstract>
<kwd-group kwd-group-type="author">
<kwd>Autism spectral disorder</kwd>
<kwd>machine learning</kwd>
<kwd>owl search algorithm</kwd>
<kwd>feature selection</kwd>
<kwd>id3 classifier</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1"><label>1</label><title>Introduction</title>
<p>Autism Spectrum Disorder (ASD) was a neuro-developmental ailment that makes persistent deficiency in social interaction behavior and skills of children. According to Diagnostic and Statistical Manual of Mental Disorders 5 (DSM-5) [<xref ref-type="bibr" rid="ref-1">1</xref>], social communication skills have been defined as 1) deficits in non-verbal interactive behavior, 2) deficits in understanding, developing, and maintaining relations 3) deficits in social emotional reciprocity [<xref ref-type="bibr" rid="ref-2">2</xref>]. Moreover, deficits in conduct were described as limited and repeated behaviour patterns and fixated interest between children having autism, which mentioned firstly repeated motor movements or stereotyping; secondly insistence on sameness, problems having variations in rigid outlines of nonverbal or verbal behavior or routine; thirdly fixated interest and finally unusual reply to sensory prospects [<xref ref-type="bibr" rid="ref-3">3</xref>]. Children having sensory problems might contain hypo sensitiveness or hyper sensitiveness to an extensive array of senses namely smells, sights, tastes, touch, sounds, body awareness, and balance. As an instance, children undergoing hypersensitiveness to noises may discover sounds which arise from air-coolers as disturbing [<xref ref-type="bibr" rid="ref-4">4</xref>,<xref ref-type="bibr" rid="ref-5">5</xref>]. Also, other problems habitually refer to sensory problems were swinging back and forth, flailing of the arms or hands, self-harm, and walking on tiptoes.</p>
<p>Autism diagnosis needs substantial amount of cost and time. Detection of autism at an initial stage could be very helpful for the victim counselling patients with correct treatment in the initial level [<xref ref-type="bibr" rid="ref-6">6</xref>]. This actually prevents the condition of patient from worsening and will aid in reducing long-term charges related with deferred prognosis. Hence timely, correct and simple screening test tools are highly necessary that will forecast autism traits in person and detect whether they no need or need complete autism valuation [<xref ref-type="bibr" rid="ref-7">7</xref>,<xref ref-type="bibr" rid="ref-8">8</xref>]. For improving the process of diagnosis of ASD, authors currently initiated implementing machine learning (ML) intellectual approaches. The main goal of such ML works on ASD is enhancing diagnosing period for providing faster accessibility to medical services, enriching accuracy of prognosis, and diminishing dimension of the input data because for identifying the ASDs highest ranked features [<xref ref-type="bibr" rid="ref-9">9</xref>,<xref ref-type="bibr" rid="ref-10">10</xref>]. ML can be referred to a research domain which complies artificial intelligence (AI) search approaches, mathematics, and other sciences for extracting precise prediction methods from datasets. ML approaches namely decision tree (DT), neural network (NN), rule-based classifier, and support vector machine (SVM), were automatic tools that usually need minimum human interference at the time of data processing [<xref ref-type="bibr" rid="ref-11">11</xref>&#x2013;<xref ref-type="bibr" rid="ref-13">13</xref>].</p>
<p>In [<xref ref-type="bibr" rid="ref-14">14</xref>], the authors focused on revealing the pattern between normal and autistic children by using electroencephalogram (EEG) through the deep learning (DL) technique. The brain signal dataset utilized pattern detection where the extracted feature undergoes the multilayer perceptron (MLP) network for the classification technique. The authors in [<xref ref-type="bibr" rid="ref-15">15</xref>], developed DL method for prognosis of ASD from functional brain network built using brain functional magnetic resonance imaging (fMRI) dataset. The whole Autism Brain Imaging Dataset Exchange 1 (ABIDE 1) is applied for investigating the efficiency of the presented technique. Firstly, we constructed the brain network from brain fMRI image and determines the raw feature according to brain network. Next, we applied an autoencoder (AE) for learning the advanced feature from the raw feature. Then, they study trained a deep neural network (DNN) using the advanced features.</p>
<p>In [<xref ref-type="bibr" rid="ref-16">16</xref>], three AI techniques have been introduced such as ML, DL, and hybrid techniques among themselves, for earlier diagnoses of autism. In [<xref ref-type="bibr" rid="ref-17">17</xref>], the researchers presented deep multi-modal models that learn a joint description from two kinds of datasets provided using fMRI scans. Integrating two functional imaging modalities in an automatic end-to-end autism diagnoses technique provides widespread images of the neural action, and thus allows for precise diagnosis. The researchers in [<xref ref-type="bibr" rid="ref-18">18</xref>] employ a DL technique from convolutional neural network (CNN) variant to identify the patient is ASD or non-ASD and extracts the strong features from neuro-images in fMRI. Next, it explains the efficiency of pre-processed images through accuracy for classifying the neural pattern.</p>
<p>This study introduces an automated ASD classification using owl search algorithm with machine learning (ASDC-OSAML) model. The proposed ASDC-OSAML model majorly focuses on the identification and classification of ASD. To attain this, the presented ASDC-OSAML model follows min-max normalization approach as a pre-processing stage. Next, the owl search algorithm-based feature selection (OSA-FS) model is used to derive feature subsets. Then, beetle swarm antenna search (BSAS) algorithm with Iterative Dichotomiser 3 (ID3) classification technique was implied for ASD detection and classification. The performance analysis of the ASDC-OSAML model is performed using benchmark dataset.</p>
</sec>
<sec id="s2"><label>2</label><title>The Proposed ASD Model</title>
<p>In this study, a new ASDC-OSAML approach was advanced for the identification and classification of ASD. The presented ASDC-OSAML model follows min-max normalization approach as a pre-processing stage. Next, the OSA-FS model is used to derive feature subsets. Then, BSAS algorithm with ID3 classification technique has been implemented for ASD detection and classification. <xref ref-type="fig" rid="fig-1">Fig. 1</xref> depicts the overall block diagram of ASDC-OSAML approach.</p>
<fig id="fig-1"><label>Figure 1</label><caption><title>Overall block diagram of ASDC-OSAML approach</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_32729-fig-1.png"/></fig>
<sec id="s2_1"><label>2.1</label><title>Stage 1: Process Involved in OSA-FS Model</title>
<p>At the initial stage, the OSA-FS model is used to derive feature subsets. Like other nature-inspired population related techniques, OSA initiates the optimization technique using an initialized solution set that characterizes the initial location of owls in forest <inline-formula id="ieqn-1"><mml:math id="mml-ieqn-1"><mml:mo stretchy="false">(</mml:mo><mml:mi>d</mml:mi></mml:math></inline-formula> dimension searching space) [<xref ref-type="bibr" rid="ref-19">19</xref>].</p>
<p>When <italic>n</italic> number of owls in the forest, then the arbitrary location has been stored in <inline-formula id="ieqn-2"><mml:math id="mml-ieqn-2"><mml:mi>n</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>d</mml:mi></mml:math></inline-formula> matrixes in the following:
<disp-formula id="eqn-1"><label>(1)</label><mml:math id="mml-eqn-1" display="block"><mml:mi>O</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mtable columnalign="left left left left left" rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:msub><mml:mi>O</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:msub><mml:mi>O</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:mo>&#x2026;</mml:mo></mml:mtd><mml:mtd><mml:mo>&#x2026;</mml:mo></mml:mtd><mml:mtd><mml:msub><mml:mi>O</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mi>O</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:msub><mml:mi>O</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:mo>&#x22EF;</mml:mo></mml:mtd><mml:mtd><mml:mo>&#x22EF;</mml:mo></mml:mtd><mml:mtd><mml:msub><mml:mi>O</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>&#x22EE;</mml:mo></mml:mtd><mml:mtd><mml:mo>&#x22EE;</mml:mo></mml:mtd><mml:mtd><mml:mo>&#x22EE;</mml:mo></mml:mtd><mml:mtd><mml:mo>&#x22EE;</mml:mo></mml:mtd><mml:mtd><mml:mo>&#x22EE;</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>&#x22EE;</mml:mo></mml:mtd><mml:mtd><mml:mo>&#x22EE;</mml:mo></mml:mtd><mml:mtd><mml:mo>&#x22EE;</mml:mo></mml:mtd><mml:mtd><mml:mo>&#x22EE;</mml:mo></mml:mtd><mml:mtd><mml:mo>&#x22EE;</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mi>O</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:msub><mml:mi>O</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:mo>&#x22EF;</mml:mo></mml:mtd><mml:mtd><mml:mo>&#x22EF;</mml:mo></mml:mtd><mml:mtd><mml:msub><mml:mi>O</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable><mml:mo>]</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-1">Eq. (1)</xref>, matrix component <inline-formula id="ieqn-3"><mml:math id="mml-ieqn-3"><mml:msub><mml:mi>O</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> signifies the <inline-formula id="ieqn-4"><mml:math id="mml-ieqn-4"><mml:msup><mml:mi>j</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> parameter of <inline-formula id="ieqn-5"><mml:math id="mml-ieqn-5"><mml:msup><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> owl. A uniform distribution is utilized for allocating the initialized position of all the owls in the forest.
<disp-formula id="eqn-2"><label>(2)</label><mml:math id="mml-eqn-2" display="block"><mml:msub><mml:mi>O</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>O</mml:mi><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi>U</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>O</mml:mi><mml:mrow><mml:mi>U</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>O</mml:mi><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-2">Eq. (2)</xref>, <inline-formula id="ieqn-6"><mml:math id="mml-ieqn-6"><mml:msub><mml:mi>O</mml:mi><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-7"><mml:math id="mml-ieqn-7"><mml:msub><mml:mi>O</mml:mi><mml:mrow><mml:mi>U</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> indicates lower and upper limits correspondingly, of <inline-formula id="ieqn-8"><mml:math id="mml-ieqn-8"><mml:msup><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> owl <inline-formula id="ieqn-9"><mml:math id="mml-ieqn-9"><mml:msub><mml:mi>O</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> in <inline-formula id="ieqn-10"><mml:math id="mml-ieqn-10"><mml:msup><mml:mi>j</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> parameter and <inline-formula id="ieqn-11"><mml:math id="mml-ieqn-11"><mml:mi>U</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>O</mml:mi><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is arbitrary value lies within [0, 1]. The fitness of all the owl&#x2019;s positions in the forest can be calculated by the objective function and saved in the subsequent matrixes:
<disp-formula id="eqn-3"><label>(3)</label><mml:math id="mml-eqn-3" display="block"><mml:mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mml:mtr><mml:mtd><mml:mi>f</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mtable rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:msub><mml:mi>O</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>O</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2026;</mml:mo><mml:msub><mml:mi>O</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mo>]</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:msub><mml:mi>O</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>O</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2026;</mml:mo><mml:msub><mml:mi>O</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mo>]</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>&#x22EE;</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>&#x22EE;</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:msub><mml:mi>O</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>O</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2026;</mml:mo><mml:msub><mml:mi>O</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mo>]</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable><mml:mo>]</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula></p>
<p>Here, it can be considered that fitness value of all the owl locations straightforwardly refers the intensity data get by the ears. Therefore, better owl receives <inline-formula id="ieqn-12"><mml:math id="mml-ieqn-12"><mml:mrow><mml:mtext>&#xA0;max&#xA0;</mml:mtext></mml:mrow></mml:math></inline-formula> intensity (for maximizing problem) since it can be closer to vole. The normalized intensity data of <inline-formula id="ieqn-13"><mml:math id="mml-ieqn-13"><mml:msup><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> owl was applied for updating the location and it is evaluated by the following equation:
<disp-formula id="eqn-4"><label>(4)</label><mml:math id="mml-eqn-4" display="block"><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:mi>w</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>w</mml:mi></mml:mrow></mml:mfrac></mml:mstyle></mml:math></disp-formula>where
<disp-formula id="eqn-5"><label>(5)</label><mml:math id="mml-eqn-5" display="block"><mml:mi>b</mml:mi><mml:mo>=</mml:mo><mml:munder><mml:mo movablelimits="true" form="prefix">max</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mi>&#x03F5;</mml:mi><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:munder><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:math></disp-formula>
<disp-formula id="eqn-6"><label>(6)</label><mml:math id="mml-eqn-6" display="block"><mml:mi>w</mml:mi><mml:mo>=</mml:mo><mml:munder><mml:mo movablelimits="true" form="prefix">min</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mi>&#x03F5;</mml:mi><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:munder><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:math></disp-formula></p>
<p>The distance of prey and owl can be evaluated as follows:
<disp-formula id="eqn-7"><label>(7)</label><mml:math id="mml-eqn-7" display="block"><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo><mml:msub><mml:mi>O</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>V</mml:mi><mml:msub><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math></disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-7">Eq. (7)</xref>, <italic>V</italic> indicates the position of prey that is accomplished using the fittest owl. Also, it was considered that one vole (global optimal) in the forest was there. Owl takes silent flight when moving to the prey. Therefore, they receive changed intensity following the inverse square law of sound intensity:
<disp-formula id="eqn-8"><label>(8)</label><mml:math id="mml-eqn-8" display="block"><mml:mi>I</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:msubsup><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:mrow><mml:mtext>Random noise</mml:mtext></mml:mrow></mml:math></disp-formula></p>
<p>Here, <inline-formula id="ieqn-14"><mml:math id="mml-ieqn-14"><mml:msubsup><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup></mml:math></inline-formula> is utilized rather than <inline-formula id="ieqn-15"><mml:math id="mml-ieqn-15"><mml:mn>4</mml:mn><mml:mi>&#x03C0;</mml:mi><mml:msubsup><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup></mml:math></inline-formula> and noise of environment is assumed for making the arithmetical model. Here, vole is active, and therefore the movement forces the owl to change the existing location silently. Here, the movement of prey was intended by utilizing probability and therefore novel position of owl is attained by:
<disp-formula id="eqn-9"><label>(9)</label><mml:math id="mml-eqn-9" display="block"><mml:mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mml:mtr><mml:mtd><mml:msubsup><mml:mrow><mml:mi>O</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mml:mtr><mml:mtd><mml:msubsup><mml:mrow><mml:mi>O</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:mi>&#x03B2;</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>I</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>&#x00D7;</mml:mo><mml:mrow><mml:mo>|</mml:mo><mml:mi>&#x03B1;</mml:mi><mml:mi>V</mml:mi><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mrow><mml:mi>O</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:mo>|</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mi>i</mml:mi><mml:mi>f</mml:mi><mml:mspace width="thinmathspace" /><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>v</mml:mi><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo>&#x003C;</mml:mo><mml:mn>0.5</mml:mn></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msubsup><mml:mrow><mml:mi>O</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:mo>&#x2212;</mml:mo><mml:mi>&#x03B2;</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>I</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>&#x00D7;</mml:mo><mml:mrow><mml:mo>|</mml:mo><mml:mi>&#x03B1;</mml:mi><mml:mi>V</mml:mi><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mrow><mml:mi>O</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:mo>|</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mi>i</mml:mi><mml:mi>f</mml:mi><mml:mspace width="thinmathspace" /><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>v</mml:mi><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2265;</mml:mo><mml:mn>0.5</mml:mn></mml:mtd></mml:mtr></mml:mtable><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-9">Eq. (9)</xref>, <inline-formula id="ieqn-16"><mml:math id="mml-ieqn-16"><mml:mi>P</mml:mi><mml:mi>v</mml:mi><mml:mi>m</mml:mi></mml:math></inline-formula> denotes the probability of vole movements, <inline-formula id="ieqn-17"><mml:math id="mml-ieqn-17"><mml:mi>&#x03B1;</mml:mi></mml:math></inline-formula> refers to a random integer within <inline-formula id="ieqn-18"><mml:math id="mml-ieqn-18"><mml:mrow><mml:mo>[</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>0.5</mml:mn><mml:mo>]</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula id="ieqn-19"><mml:math id="mml-ieqn-19"><mml:mi>&#x03B2;</mml:mi></mml:math></inline-formula> was a linearly reducing constant from 1.9 to 0. <inline-formula id="ieqn-20"><mml:math id="mml-ieqn-20"><mml:mi>&#x03B2;</mml:mi></mml:math></inline-formula> present larger changes and promote the exploration of searching space. Since the model progress, the variation is decreased for encouraging exploitation. The presented technique has only one user determined variable <inline-formula id="ieqn-21"><mml:math id="mml-ieqn-21"><mml:mrow><mml:mo>(</mml:mo><mml:mi>&#x03B2;</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> where genetic algorithm (GA), particle swarm optimization (PSO), bat algorithm (BA), and so on, have larger amount of parametric settings. <xref ref-type="fig" rid="fig-2">Fig. 2</xref> depicts the steps involved in OSA.</p>
<fig id="fig-2"><label>Figure 2</label><caption><title>Steps involved in OSA</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_32729-fig-2.png"/></fig>
<p>The fitness function of the OSA-FS model was devised to maintain a balance among the quantity of features which was chosen in every solution (minimal) and the classification accuracy (maximal) acquired with the help of such selected features, <xref ref-type="disp-formula" rid="eqn-10">Eq. (10)</xref> denotes the fitness function for evaluating resolutions.
<disp-formula id="eqn-10"><label>(10)</label><mml:math id="mml-eqn-10" display="block"><mml:mrow><mml:mtext mathvariant="italic">Fitness</mml:mtext></mml:mrow><mml:mo>=</mml:mo><mml:mi>&#x03B1;</mml:mi><mml:msub><mml:mi>&#x03B3;</mml:mi><mml:mrow><mml:mi>R</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>D</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>&#x03B2;</mml:mi><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:mrow><mml:mo>|</mml:mo><mml:mi>R</mml:mi><mml:mo>|</mml:mo></mml:mrow><mml:mrow><mml:mo>|</mml:mo><mml:mi>C</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:mfrac></mml:mstyle></mml:math></disp-formula>where <inline-formula id="ieqn-22"><mml:math id="mml-ieqn-22"><mml:msub><mml:mi>&#x03B3;</mml:mi><mml:mrow><mml:mi>R</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> signifies the classifier error rate of a presented classifier (the ID3 classifier was utilized). <inline-formula id="ieqn-23"><mml:math id="mml-ieqn-23"><mml:mrow><mml:mo>|</mml:mo><mml:mi>R</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:math></inline-formula> refers the cardinality of selected subset and <inline-formula id="ieqn-24"><mml:math id="mml-ieqn-24"><mml:mrow><mml:mo>|</mml:mo><mml:mi>C</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:math></inline-formula> means aggregate number of features in datasets, <inline-formula id="ieqn-25"><mml:math id="mml-ieqn-25"><mml:mi>&#x03B1;</mml:mi></mml:math></inline-formula> and <inline-formula id="ieqn-26"><mml:math id="mml-ieqn-26"><mml:mi>&#x03B2;</mml:mi></mml:math></inline-formula> were 2 parameters respective to the significance of classifier quality and subsets length. &#x2208; [1, 0] and <inline-formula id="ieqn-27"><mml:math id="mml-ieqn-27"><mml:mi>&#x03B2;</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mi>&#x03B1;</mml:mi><mml:mo>.</mml:mo></mml:math></inline-formula></p>
</sec>
<sec id="s2_2"><label>2.2</label><title>Stage 2: ASD Classification Model</title>
<p>Once the features are chosen, the ID3 classification model is applied for ASD detection and classification. The ID3 approach chooses testing components with relating and computing their information gain (IG). Consider <italic>S</italic> indicate the group of data instances. The <italic>C</italic> class component has <italic>m</italic> dissimilar values that indicate <italic>m</italic> class labels <inline-formula id="ieqn-28"><mml:math id="mml-ieqn-28"><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><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:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. Given that <inline-formula id="ieqn-29"><mml:math id="mml-ieqn-29"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> be the number of samples from class <inline-formula id="ieqn-30"><mml:math id="mml-ieqn-30"><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><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:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. The predicted data amount for categorizing <italic>S</italic> as follows:
<disp-formula id="eqn-11"><label>(11)</label><mml:math id="mml-eqn-11" display="block"><mml:mi>I</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mrow><mml:mo>&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msubsup><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>log</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2061;</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-11">Eq. (11)</xref>, <inline-formula id="ieqn-31"><mml:math id="mml-ieqn-31"><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> indicates the possibility of instance from <italic>S</italic> suitable for class <inline-formula id="ieqn-32"><mml:math id="mml-ieqn-32"><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>. <inline-formula id="ieqn-33"><mml:math id="mml-ieqn-33"><mml:mi>I</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> indicates the average required data amount for recognizing the class labels to all the instances from S.</p>
<p>Consider the component <italic>A</italic> has <italic>v</italic> dissimilar values <inline-formula id="ieqn-34"><mml:math id="mml-ieqn-34"><mml:mrow><mml:mo>{</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>&#x03BD;</mml:mi></mml:mrow></mml:msub><mml:mo>}</mml:mo></mml:mrow></mml:math></inline-formula> from the S trainable dataset. Once <italic>A</italic> is a nominal component, then, the component splits <italic>S</italic> as <italic>v</italic> subset so that <inline-formula id="ieqn-35"><mml:math id="mml-ieqn-35"><mml:mrow><mml:mo>{</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>&#x03BD;</mml:mi></mml:mrow></mml:msub><mml:mo>}</mml:mo></mml:mrow></mml:math></inline-formula>, in that <inline-formula id="ieqn-36"><mml:math id="mml-ieqn-36"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> describes the set of <italic>S</italic> where samples from <inline-formula id="ieqn-37"><mml:math id="mml-ieqn-37"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> has the comparable component values <inline-formula id="ieqn-38"><mml:math id="mml-ieqn-38"><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> on <italic>A</italic>. However, sample from <inline-formula id="ieqn-39"><mml:math id="mml-ieqn-39"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> might have different class labels. Consider <inline-formula id="ieqn-40"><mml:math id="mml-ieqn-40"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> indicates the group of samples that class labels are <inline-formula id="ieqn-41"><mml:math id="mml-ieqn-41"><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> from the set of <inline-formula id="ieqn-42"><mml:math id="mml-ieqn-42"><mml:mo fence="false" stretchy="false">{</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo fence="false" stretchy="false">|</mml:mo><mml:mi>A</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mspace width="thinmathspace" /><mml:mi>j</mml:mi><mml:mo>&#x2208;</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mspace width="thinmathspace" /><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mspace width="thinmathspace" /><mml:mi>&#x03BD;</mml:mi><mml:mo>,</mml:mo><mml:mspace width="thinmathspace" /><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2208;</mml:mo><mml:mi>S</mml:mi><mml:mo fence="false" stretchy="false">}</mml:mo></mml:math></inline-formula> wherein component <inline-formula id="ieqn-43"><mml:math id="mml-ieqn-43"><mml:mi>A</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>. The required amount of information to split the trainable dataset <italic>S</italic> was evaluated as follows:</p>
<p><disp-formula id="eqn-12"><label>(12)</label><mml:math id="mml-eqn-12" display="block"><mml:mi>E</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msubsup><mml:mrow><mml:mo>&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>&#x03BD;</mml:mi></mml:mrow></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>+</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mi>s</mml:mi></mml:mfrac></mml:mstyle><mml:mo>&#x00D7;</mml:mo><mml:mi>I</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>The minimal data amount required, an additional purity of sub dataset can be
<disp-formula id="eqn-13"><label>(13)</label><mml:math id="mml-eqn-13" display="block"><mml:mi>I</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mrow><mml:mo>&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msubsup><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>log</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-13">Eq. (13)</xref>, <inline-formula id="ieqn-44"><mml:math id="mml-ieqn-44"><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> denotes the probability of instance from <inline-formula id="ieqn-45"><mml:math id="mml-ieqn-45"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> based on class <inline-formula id="ieqn-46"><mml:math id="mml-ieqn-46"><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>. <inline-formula id="ieqn-47"><mml:math id="mml-ieqn-47"><mml:mi>I</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> denotes the average dataset amount required for recognizing the class label to all the instances from&#x00A0;<inline-formula id="ieqn-48"><mml:math id="mml-ieqn-48"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>.
<disp-formula id="eqn-14"><label>(14)</label><mml:math id="mml-eqn-14" display="block"><mml:mrow><mml:mtext mathvariant="italic">InfoGain</mml:mtext></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>I</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>E</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>Especially, the amount of data needed (based on the class) minus the amount of novel dataset needed (depends on component <inline-formula id="ieqn-49"><mml:math id="mml-ieqn-49"><mml:mi>A</mml:mi></mml:math></inline-formula>). Selection of the component using maximal <inline-formula id="ieqn-50"><mml:math id="mml-ieqn-50"><mml:mrow><mml:mtext mathvariant="italic">InfoGain</mml:mtext></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> as testing component that is assigned to internal nodes from DT. Here, the amount of data needed to categorize sample is minimal.</p>
</sec>
<sec id="s2_3"><label>2.3</label><title>Stage 3: Parameter Tuning</title>
<p>In this study, the design of BSAS algorithm helps to determine the parameter values [<xref ref-type="bibr" rid="ref-20">20</xref>&#x2013;<xref ref-type="bibr" rid="ref-22">22</xref>] of the ID3 classifier. The original beetle antenna search (BAS) involves searching and detecting behaviors [<xref ref-type="bibr" rid="ref-23">23</xref>]. In every timestep, beetles move in a random direction. Thus, a random unit vector <inline-formula id="ieqn-51"><mml:math id="mml-ieqn-51"><mml:mover><mml:mi>b</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> is utilized for describing the direction. The coordinate of right-and left-hand sides of the beetle antennae as follows,
<disp-formula id="eqn-15"><label>(15)</label><mml:math id="mml-eqn-15" display="block"><mml:mtable columnalign="left" rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mi>x</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mi>d</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:mover><mml:mi>b</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mo>,</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mi>x</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:mo>&#x2212;</mml:mo><mml:msup><mml:mi>d</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:mover><mml:mi>b</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-15">Eq. (15)</xref>, the subscript <inline-formula id="ieqn-52"><mml:math id="mml-ieqn-52"><mml:mi>r</mml:mi><mml:mo>,</mml:mo><mml:mspace width="thinmathspace" /><mml:mi>l</mml:mi></mml:math></inline-formula> characterizes the right- and left- hand sides correspondingly, the superscript <italic>t</italic> characterizes certain moments. <italic>d</italic> are behalf of distance from the antenna to the centroid of the beetle. Especially, <inline-formula id="ieqn-53"><mml:math id="mml-ieqn-53"><mml:msup><mml:mi>d</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> signifies beetle searching region at a specific moment, and the region will attenuate over time. <inline-formula id="ieqn-54"><mml:math id="mml-ieqn-54"><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> guarantees that <inline-formula id="ieqn-55"><mml:math id="mml-ieqn-55"><mml:msup><mml:mi>d</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> won&#x2019;t decrease to zero. Moreover, magnitude of <inline-formula id="ieqn-56"><mml:math id="mml-ieqn-56"><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> based on the scaling of certain problems. The beetle detection behavior is defined by,
<disp-formula id="eqn-16"><label>(16)</label><mml:math id="mml-eqn-16" display="block"><mml:msup><mml:mi>x</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:msup><mml:mi>x</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mi>&#x03B4;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:mover><mml:mi>b</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mi>s</mml:mi><mml:mi>i</mml:mi><mml:mi>g</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-16">Eq. (16)</xref>, <inline-formula id="ieqn-57"><mml:math id="mml-ieqn-57"><mml:msup><mml:mi>&#x03B4;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> indicates the step size that reduces over time as follows. The updating rule of <italic>d</italic> and <inline-formula id="ieqn-58"><mml:math id="mml-ieqn-58"><mml:mi>&#x03B4;</mml:mi></mml:math></inline-formula> are given as follows,
<disp-formula id="eqn-17"><label>(17)</label><mml:math id="mml-eqn-17" display="block"><mml:msup><mml:mi>d</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:msub><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mi>d</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math></disp-formula>
<disp-formula id="eqn-18"><label>(18)</label><mml:math id="mml-eqn-18" display="block"><mml:msup><mml:mi>&#x03B4;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:msub><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:mi>&#x03B4;</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mi>&#x03B4;</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x03B4;</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>.</mml:mo></mml:math></disp-formula></p>
<p>From the expression, <inline-formula id="ieqn-59"><mml:math id="mml-ieqn-59"><mml:msub><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-60"><mml:math id="mml-ieqn-60"><mml:msub><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:mi>&#x03B4;</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> indicates attenuation coefficient of antennae length <italic>d</italic> and step size <inline-formula id="ieqn-61"><mml:math id="mml-ieqn-61"><mml:mi>&#x03B4;</mml:mi></mml:math></inline-formula> correspondingly. The presetting of <italic>d</italic> and <inline-formula id="ieqn-62"><mml:math id="mml-ieqn-62"><mml:mi>&#x03B4;</mml:mi></mml:math></inline-formula> parameters seriously influences the performance of BAS.</p>
<p>Generally, BAS technique has two major disadvantages. Firstly, beetles move in one random direction. It could not assurance that the move of beetle will make the objective function better. Similarly, we enhance the searching behavior of BAS technique by using <italic>k</italic> beetle to move in <italic>k</italic> direction, which improves the probability to search best location for beetles. Next, all the movements of beetle cause a step size and update of the position. Indeed, when the objective function is better, the location of beetle must be upgraded when the step size not. As a result, we designed a feedback-based location and step-size update approach. Additionally, a <inline-formula id="ieqn-63"><mml:math id="mml-ieqn-63"><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>&#x03B4;</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> probability constant is presented for measuring the effect of random direction. In another word, we assume there is a <inline-formula id="ieqn-64"><mml:math id="mml-ieqn-64"><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>&#x03B4;</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> smaller probability that <italic>k</italic> beetle will miss the best position (variable subset) for objective function at the present step size. Thus, we produce a random value lies within <inline-formula id="ieqn-65"><mml:math id="mml-ieqn-65"><mml:mrow><mml:mo>[</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>]</mml:mo></mml:mrow></mml:math></inline-formula> and compared them to <inline-formula id="ieqn-66"><mml:math id="mml-ieqn-66"><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>&#x03B4;</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>. Consequently, when <italic>k</italic> beetle could not find small objective function value, BSAS approach assumes there is no best location at existing step size and it should be upgraded. In some instances, the approach assumes there are still few locations to fulfill beetle requirement for minimizing the objective, however, the beetle could find it due to limited beetle number <inline-formula id="ieqn-67"><mml:math id="mml-ieqn-67"><mml:mi>k</mml:mi><mml:mo>.</mml:mo></mml:math></inline-formula> Hence, sensing length <italic>d</italic> and step-size <inline-formula id="ieqn-68"><mml:math id="mml-ieqn-68"><mml:mi>&#x03B4;</mml:mi></mml:math></inline-formula> remains unchanged when the arbitrary number is lesser than <inline-formula id="ieqn-69"><mml:math id="mml-ieqn-69"><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>&#x03B4;</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>.</p>
</sec>
</sec>
<sec id="s3"><label>3</label><title>Experimental Validation</title>
<p>The proposed model is simulated using Python tool. The experimental validation of the ASDC-OSAML model is tested using three datasets, as given in <xref ref-type="table" rid="table-1">Table 1</xref>.</p>
<table-wrap id="table-1"><label>Table 1</label><caption><title>Dataset description</title></caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left">No.</th>
<th align="left">Dataset name</th>
<th align="left">Sources</th>
<th align="left">Number of attributes</th>
<th align="left">Number of instances</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">1</td>
<td align="left">ASD-Children dataset</td>
<td align="left">UCI</td>
<td align="left">21</td>
<td align="left">292</td>
</tr>
<tr>
<td align="left">2</td>
<td align="left">ASD-Adolescent dataset</td>
<td align="left">UCI</td>
<td align="left">21</td>
<td align="left">104</td>
</tr>
<tr>
<td align="left">3</td>
<td align="left">ASD-Adult dataset</td>
<td align="left">UCI</td>
<td align="left">21</td>
<td align="left">704</td>
</tr>
</tbody>
</table>
</table-wrap>
<p><xref ref-type="fig" rid="fig-3">Fig. 3</xref> shows the best cost inspection of the OSA-FS with other FS models. The figure implied that the OSA-FS model has resulted in effectual outcomes over other FS models with minimal best cost.</p>
<fig id="fig-3"><label>Figure 3</label><caption><title>Best cost analysis of OSA-FS approach with other FS models</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_32729-fig-3.png"/></fig>
<p><xref ref-type="fig" rid="fig-4">Fig. 4</xref> highlights the confusion matrices formed by the ASDC-OSAML model on the test data. With ASD-children dataset, the ASDC-OSAML model has recognized 140 samples into Yes class and 151 samples into No class. Meanwhile, with ASD-adolescent dataset, the ASDC-OSAML approach has recognized 62 samples into Yes class and 41 samples into No class. Eventually, with ASD-adult dataset, the ASDC-OSAML technique has recognized 189 samples into Yes class and 506 samples into No class.</p>
<fig id="fig-4"><label>Figure 4</label><caption><title>Confusion matrices of ASDC-OSAML approach (a) ASD-children dataset, (b) ASD-adolescent dataset, and (c) ASD-adult dataset</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_32729-fig-4.png"/></fig>
<p><xref ref-type="table" rid="table-2">Table 2</xref> provides an overall ASD classification outcomes of the ASDC-OSAML model on test data.</p>
<table-wrap id="table-2"><label>Table 2</label><caption><title>Result analysis of ASDC-OSAML approach with distinct measures</title></caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left">Class name</th>
<th align="left">Accuracy</th>
<th align="left">Sensitivity</th>
<th align="left">Specificity</th>
<th align="left">F-Score</th>
<th align="left">AUPR score</th>
</tr>
</thead>
<tbody>
<tr>
<td align="center" colspan="6">ASD-Children dataset</td>
</tr>
<tr>
<td align="left">Yes</td>
<td align="left">99.66</td>
<td align="left">99.29</td>
<td align="left">100.00</td>
<td align="left">99.64</td>
<td align="left">99.65</td>
</tr>
<tr>
<td align="left">No</td>
<td align="left">99.66</td>
<td align="left">100.00</td>
<td align="left">99.29</td>
<td align="left">99.67</td>
<td align="left">99.65</td>
</tr>
<tr>
<td align="left">Average</td>
<td align="left">99.66</td>
<td align="left">99.65</td>
<td align="left">99.65</td>
<td align="left">99.66</td>
<td align="left">99.65</td>
</tr>
<tr>
<td align="center" colspan="6">ASD-Adolescent dataset</td>
</tr>
<tr>
<td align="left">Yes</td>
<td align="left">99.04</td>
<td align="left">98.41</td>
<td align="left">100.00</td>
<td align="left">99.20</td>
<td align="left">99.21</td>
</tr>
<tr>
<td align="left">No</td>
<td align="left">99.04</td>
<td align="left">100.00</td>
<td align="left">98.41</td>
<td align="left">98.80</td>
<td align="left">99.21</td>
</tr>
<tr>
<td align="left">Average</td>
<td align="left">99.04</td>
<td align="left">99.21</td>
<td align="left">99.21</td>
<td align="left">99.00</td>
<td align="left">99.21</td>
</tr>
<tr>
<td align="center" colspan="6">ASD-Adult dataset</td>
</tr>
<tr>
<td align="left">Yes</td>
<td align="left">98.72</td>
<td align="left">100.00</td>
<td align="left">98.25</td>
<td align="left">97.67</td>
<td align="left">99.13</td>
</tr>
<tr>
<td align="left">No</td>
<td align="left">98.72</td>
<td align="left">98.25</td>
<td align="left">100.00</td>
<td align="left">99.12</td>
<td align="left">99.13</td>
</tr>
<tr>
<td align="left">Average</td>
<td align="left">98.72</td>
<td align="left">99.13</td>
<td align="left">99.13</td>
<td align="left">98.40</td>
<td align="left">99.13</td>
</tr>
</tbody>
</table>
</table-wrap>
<p><xref ref-type="fig" rid="fig-5">Fig. 5</xref> reports a brief result analysis of the ASDC-OSAML model on the test ASD_childern dataset. The ASDC-OSAML model has identified Yes class with <inline-formula id="ieqn-70"><mml:math id="mml-ieqn-70"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 99.66&#x0025;, <inline-formula id="ieqn-71"><mml:math id="mml-ieqn-71"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 99.29&#x0025;, <inline-formula id="ieqn-72"><mml:math id="mml-ieqn-72"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 100&#x0025;, <inline-formula id="ieqn-73"><mml:math id="mml-ieqn-73"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">score</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> of 99.64&#x0025;, and area under the precision-recall curve (AUPR) of 99.65&#x0025;. Also, the ASDC-OSAML algorithm has identified No class with <inline-formula id="ieqn-74"><mml:math id="mml-ieqn-74"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 99.66&#x0025;, <inline-formula id="ieqn-75"><mml:math id="mml-ieqn-75"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 100&#x0025;, <inline-formula id="ieqn-76"><mml:math id="mml-ieqn-76"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 99.29&#x0025;, <inline-formula id="ieqn-77"><mml:math id="mml-ieqn-77"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">score</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> of 99.67&#x0025;, and AUPR of 99.65&#x0025;. In addition, the ASDC-OSAML methodology has identified with average <inline-formula id="ieqn-78"><mml:math id="mml-ieqn-78"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 99.66&#x0025;, <inline-formula id="ieqn-79"><mml:math id="mml-ieqn-79"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 99.65&#x0025;, <inline-formula id="ieqn-80"><mml:math id="mml-ieqn-80"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 99.65&#x0025;, <inline-formula id="ieqn-81"><mml:math id="mml-ieqn-81"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">score</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> of 99.66&#x0025;, and AUPR of 99.65&#x0025;.</p>
<fig id="fig-5"><label>Figure 5</label><caption><title>Average analysis of ASDC-OSAML approach on ASD_children dataset</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_32729-fig-5.png"/></fig>
<p><xref ref-type="fig" rid="fig-6">Fig. 6</xref> demonstrates brief outcome scrutiny of the ASDC-OSAML technique on the test ASD_adolescent dataset. The ASDC-OSAML approach has identified Yes class with <inline-formula id="ieqn-82"><mml:math id="mml-ieqn-82"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 99.04&#x0025;, <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:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 98.41&#x0025;, <inline-formula id="ieqn-84"><mml:math id="mml-ieqn-84"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 100&#x0025;, <inline-formula id="ieqn-85"><mml:math id="mml-ieqn-85"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">score</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> of 99.20&#x0025;, and AUPR of 99.21&#x0025;. Besides, the ASDC-OSAML method has identified No class with <inline-formula id="ieqn-86"><mml:math id="mml-ieqn-86"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 99.04&#x0025;, <inline-formula id="ieqn-87"><mml:math id="mml-ieqn-87"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 100&#x0025;, <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:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 98.41&#x0025;, <inline-formula id="ieqn-89"><mml:math id="mml-ieqn-89"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">score</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> of 98.80&#x0025;, and AUPR of 99.21&#x0025;. Moreover, the ASDC-OSAML algorithm has identified with average <inline-formula id="ieqn-90"><mml:math id="mml-ieqn-90"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 99.04&#x0025;, <inline-formula id="ieqn-91"><mml:math id="mml-ieqn-91"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 99.21&#x0025;, <inline-formula id="ieqn-92"><mml:math id="mml-ieqn-92"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 99.21&#x0025;, <inline-formula id="ieqn-93"><mml:math id="mml-ieqn-93"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">score</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> of 99&#x0025;, and AUPR of 99.21&#x0025;.</p>
<fig id="fig-6"><label>Figure 6</label><caption><title>Average analysis of ASDC-OSAML approach on ASD_adolescent dataset</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_32729-fig-6.png"/></fig>
<p><xref ref-type="fig" rid="fig-7">Fig. 7</xref> signifies a brief result analysis of the ASDC-OSAML algorithm on the test ASD_adult dataset. The ASDC-OSAML method has identified Yes class with <inline-formula id="ieqn-94"><mml:math id="mml-ieqn-94"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 98.72&#x0025;, <inline-formula id="ieqn-95"><mml:math id="mml-ieqn-95"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 100&#x0025;, <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:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 98.25&#x0025;, <inline-formula id="ieqn-97"><mml:math id="mml-ieqn-97"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">score</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> of 97.67&#x0025;, and AUPR of 99.13&#x0025;. Additionally, the ASDC-OSAML approach has identified No class with <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:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 98.72&#x0025;, <inline-formula id="ieqn-99"><mml:math id="mml-ieqn-99"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 98.25&#x0025;, <inline-formula id="ieqn-100"><mml:math id="mml-ieqn-100"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 100&#x0025;, <inline-formula id="ieqn-101"><mml:math id="mml-ieqn-101"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">score</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> of 99.12&#x0025;, and AUPR of 99.13&#x0025;. Moreover, the ASDC-OSAML technique has identified with average <inline-formula id="ieqn-102"><mml:math id="mml-ieqn-102"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 98.72&#x0025;, <inline-formula id="ieqn-103"><mml:math id="mml-ieqn-103"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 99.13&#x0025;, <inline-formula id="ieqn-104"><mml:math id="mml-ieqn-104"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 99.13&#x0025;, <inline-formula id="ieqn-105"><mml:math id="mml-ieqn-105"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">score</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> of 98.40&#x0025;, and AUPR of 99.13&#x0025;.</p>
<fig id="fig-7"><label>Figure 7</label><caption><title>Average analysis of ASDC-OSAML approach on ASD_adult dataset</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_32729-fig-7.png"/></fig>
<p><xref ref-type="fig" rid="fig-8">Fig. 8</xref> presents the accuracy and loss graph analysis of the ASDC-OSAML method under different datasets. The results show the accuracy value tends to rise and loss value tends to reduction with an increase in epoch count. It can be observed that the training loss is low and validation accuracy is high on different datasets.</p>
<fig id="fig-8"><label>Figure 8</label><caption><title>(a and b) Graph of Accuracy and loss on ASD_children dataset (c and d) Graph of Accuracy and loss on ASD_adolescent dataset (e and f) Graph of Accuracy and loss on ASD_adult dataset</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_32729-fig-8.png"/></fig>
<p><xref ref-type="table" rid="table-3">Table 3</xref> illustrates a comparison study of ASDC-OSAML model with recent models such as quasi-oppositional dragonfly with deep stacked autoencoder network (QODF-DSAN), logistic regression (LOR), neural network (NN), k-nearest neighbour (KNN), and SVM-linear model [<xref ref-type="bibr" rid="ref-24">24</xref>,<xref ref-type="bibr" rid="ref-25">25</xref>].</p>
<table-wrap id="table-3"><label>Table 3</label><caption><title>Comparative analysis of ASDC-OSAML approach with existing methodologies</title></caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left">Methods</th>
<th align="left">Accuracy</th>
<th align="left">Sensitivity</th>
<th align="left">Specificity</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">ASDC-OSAML</td>
<td align="left">99.66</td>
<td align="left">99.65</td>
<td align="left">99.65</td>
</tr>
<tr>
<td align="left">QODF-DSAN</td>
<td align="left">97.81</td>
<td align="left">97.05</td>
<td align="left">96.77</td>
</tr>
<tr>
<td align="left">LOR model</td>
<td align="left">64.22</td>
<td align="left">63.06</td>
<td align="left">68.22</td>
</tr>
<tr>
<td align="left">NN model</td>
<td align="left">65.42</td>
<td align="left">58.94</td>
<td align="left">78.35</td>
</tr>
<tr>
<td align="left">KNN model</td>
<td align="left">68.14</td>
<td align="left">50.63</td>
<td align="left">76.65</td>
</tr>
<tr>
<td align="left">SVM-Linear model</td>
<td align="left">67.19</td>
<td align="left">58.69</td>
<td align="left">69.20</td>
</tr>
</tbody>
</table>
</table-wrap>
<p><xref ref-type="fig" rid="fig-9">Fig. 9</xref> renders a comparative review of the ASDC-OSAML system with other models interms of <inline-formula id="ieqn-106"><mml:math id="mml-ieqn-106"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-107"><mml:math id="mml-ieqn-107"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>. The figure depicted the LOR and NN methodologies have shown lower values of <inline-formula id="ieqn-108"><mml:math id="mml-ieqn-108"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-109"><mml:math id="mml-ieqn-109"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> At the same time, the KNN and SVM-linear techniques have reported moderately enhanced <inline-formula id="ieqn-110"><mml:math id="mml-ieqn-110"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-111"><mml:math id="mml-ieqn-111"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> values. Though the QODF-DSAN approach has accomplished reasonable <inline-formula id="ieqn-112"><mml:math id="mml-ieqn-112"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-113"><mml:math id="mml-ieqn-113"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 97.05&#x0025; and 96.77&#x0025;, the ASDC-OSAML method has reached higher <inline-formula id="ieqn-114"><mml:math id="mml-ieqn-114"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-115"><mml:math id="mml-ieqn-115"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 99.65&#x0025; and 99.65&#x0025;.</p>
<fig id="fig-9"><label>Figure 9</label><caption><title><inline-formula id="ieqn-121"><mml:math id="mml-ieqn-121"><mml:mi>S</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-122"><mml:math id="mml-ieqn-122"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> analysis of ASDC-OSAML approach with recent methodologies</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_32729-fig-9.png"/></fig>
<p><xref ref-type="fig" rid="fig-10">Fig. 10</xref> provides a comparative inspection of the ASDC-OSAML model with other models interms of <inline-formula id="ieqn-116"><mml:math id="mml-ieqn-116"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>. The figure indicated that the LOR and NN models have shown lower values of <inline-formula id="ieqn-117"><mml:math id="mml-ieqn-117"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>. At the same time, the KNN and SVM-linear models have reported moderately enhanced <inline-formula id="ieqn-118"><mml:math id="mml-ieqn-118"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> values. Though the QODF-DSAN model has accomplished reasonable <inline-formula id="ieqn-119"><mml:math id="mml-ieqn-119"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 97.81&#x0025;, the ASDC-OSAML model has gained higher <inline-formula id="ieqn-120"><mml:math id="mml-ieqn-120"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 99.66&#x0025;. From the detailed results and discussion, it is apparent that the ASDC-OSAML model has resulted in maximum classification performance over recent models.</p>
<fig id="fig-10"><label>Figure 10</label><caption><title><inline-formula id="ieqn-123"><mml:math id="mml-ieqn-123"><mml:mi>A</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> analysis of ASDC-OSAML approach with recent methodologies</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_32729-fig-10.png"/></fig>
</sec>
<sec id="s4"><label>4</label><title>Conclusion</title>
<p>In this paper, a new ASDC-OSAML approach was advanced for the classification and identification of ASD. The presented ASDC-OSAML model follows min-max normalization approach as a pre-processing stage. Next, the OSA-FS model is used to derive feature subsets. Then, BSAS algorithm with ID3 classification method was implemented for ASD detection and classification. The design of BSAS algorithm helps to determine the parameter values of the ID3 classifier. The performance analysis of the ASDC-OSAML model is performed using benchmark dataset. Extensive comparison study highlighted the supremacy of the ASDC-OSAML model over recent state of art approaches. Thus, the presented ASDC-OSAML technique was applied as an effectual tool for ASD classification. In future, an ensemble of three DL approaches has been applied to boost the classifier results.</p>
</sec>
</body>
<back>
<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 through Large Groups Project Under Grant Number (61/43). Princess Nourah bint Abdulrahman University Researchers Supporting Project Number (PNURSP2022R114), 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: (22UQU4310373DSR26).</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>
<ref-list content-type="authoryear">
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