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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">25280</article-id>
<article-id pub-id-type="doi">10.32604/cmc.2023.025280</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Sailfish Optimizer with EfficientNet Model for Apple Leaf Disease Detection</article-title>
<alt-title alt-title-type="left-running-head">Sailfish Optimizer with EfficientNet Model for Apple Leaf Disease Detection</alt-title>
<alt-title alt-title-type="right-running-head">Sailfish Optimizer with EfficientNet Model for Apple Leaf Disease Detection</alt-title>
</title-group>
<contrib-group content-type="authors">
<contrib id="author-1" contrib-type="author">
<name name-style="western"><surname>Alqahtani</surname><given-names>Mazen Mushabab</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>Dutta</surname><given-names>Ashit Kumar</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>Almotairi</surname><given-names>Sultan</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>Ilayaraja</surname><given-names>M.</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>Albraikan</surname><given-names>Amani Abdulrahman</given-names>
</name><xref ref-type="aff" rid="aff-5">5</xref></contrib>
<contrib id="author-6" contrib-type="author" corresp="yes">
<name name-style="western"><surname>Al-Wesabi</surname><given-names>Fahd N.</given-names>
</name><xref ref-type="aff" rid="aff-6">6</xref>
<xref ref-type="aff" rid="aff-7">7</xref><email>falwesabi@kku.edu.sa</email></contrib>
<contrib id="author-7" contrib-type="author">
<name name-style="western"><surname>Duhayyim</surname><given-names>Mesfer Al</given-names>
</name><xref ref-type="aff" rid="aff-8">8</xref></contrib>
<aff id="aff-1"><label>1</label><institution>Physical Therapy Department, Majmaah University</institution>, <addr-line>Majmaah, 11952</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-2"><label>2</label><institution>Department of Computer Science and Information Systems, College of Applied Sciences, AlMaarefa University</institution>, <addr-line>Ad Diriyah, 13713, Riyadh</addr-line>, <country></country><country>Saudi Arabia</country></aff>
<aff id="aff-3"><label>3</label><institution>Department of Natural and Applied Sciences, Faculty of Community College, Majmaah University</institution>, <addr-line>Majmaah, 11952</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-4"><label>4</label><institution>School of Computing, Kalasalingam Academy of Research and Education</institution>, <addr-line>Krishnankoil, 626128</addr-line>, <country>India</country></aff>
<aff id="aff-5"><label>5</label><institution>Department of Computer Sciences, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, P.O.Box 84428</institution>, <addr-line>Riyadh, 11671</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-6"><label>6</label><institution>Department of Computer Science, College of Science &#x0026; Art at Mahayil, King Khalid University</institution>, <addr-line>62529</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-7"><label>7</label><institution>Faculty of Computer and IT, Sana&#x2019;a University</institution>, <country>Sana&#x2019;a</country>, <addr-line>1247</addr-line>, <country>Yemen</country></aff>
<aff id="aff-8"><label>8</label><institution>Department of Natural and Applied Sciences, College of Community - Aflaj, Prince Sattam Bin Abdulaziz University</institution>, <country>Saudi Arabia</country></aff>
</contrib-group>
<author-notes>
<corresp id="cor1"><label>&#x002A;</label>Corresponding Author: Fahd N. Al-Wesabi. Email: <email>falwesabi@kku.edu.sa</email></corresp>
</author-notes>
<pub-date pub-type="epub" date-type="pub" iso-8601-date="2022-08-16"><day>16</day>
<month>08</month>
<year>2022</year></pub-date>
<volume>74</volume>
<issue>1</issue>
<fpage>217</fpage>
<lpage>233</lpage>
<history>
<date date-type="received">
<day>18</day>
<month>11</month>
<year>2021</year>
</date>
<date date-type="accepted">
<day>17</day>
<month>1</month>
<year>2022</year>
</date>
</history>
<permissions>
<copyright-statement>&#x00A9; 2023 Alqahtani et al.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Alqahtani 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_25280.pdf"></self-uri>
<abstract>
<p>Recent developments in digital cameras and electronic gadgets coupled with Machine Learning (ML) and Deep Learning (DL)-based automated apple leaf disease detection models are commonly employed as reasonable alternatives to traditional visual inspection models. In this background, the current paper devises an Effective Sailfish Optimizer with EfficientNet-based Apple Leaf disease detection (ESFO-EALD) model. The goal of the proposed ESFO-EALD technique is to identify the occurrence of plant leaf diseases automatically. In this scenario, Median Filtering (MF) approach is utilized to boost the quality of apple plant leaf images. Moreover, SFO with Kapur&#x0027;s entropy-based segmentation technique is also utilized for the identification of the affected plant region from test image. Furthermore, Adam optimizer with EfficientNet-based feature extraction and Spiking Neural Network (SNN)-based classification are employed to detect and classify the apple plant leaf images. A wide range of simulations was conducted to ensure the effective outcomes of ESFO-EALD technique on benchmark dataset. The results reported the supremacy of the proposed ESFO-EALD approach than the existing approaches.</p>
</abstract>
<kwd-group kwd-group-type="author">
<kwd>Agriculture</kwd>
<kwd>computer vision</kwd>
<kwd>image processing</kwd>
<kwd>deep learning</kwd>
<kwd>metaheuristics</kwd>
<kwd>image segmentation</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1">
<label>1</label>
<title>Introduction</title>
<p>Agriculture is one of the primary sectors that contribute to economic development of a country. Being a backbone of country&#x2019;s development, the sector faces a lot of challenges to survive. Plant disease is one such prominent challenge that causes disruption in agricultural crop production. However, this issue can be resolved through the adoption of advanced agricultural technologies [<xref ref-type="bibr" rid="ref-1">1</xref>]. Having said that, it is really hard to attain the goal, owing to lack of awareness, high cost, implementation challenges, etc. But, the costs incurred upon the technique can be decreased by employing image processing applications that make use of Deep Learning (DL) and Machine Learning (ML) methods. Identification of leaf disease using Artificial Intelligence (AI) technique [<xref ref-type="bibr" rid="ref-2">2</xref>] can result in high yield and uncompromised quality products compared to traditional disease detection techniques. Furthermore, leaf diseases tend to occur based on climate and survival conditions. At most of the times, leaf diseases are caused by fungi, viruses, and bacteria [<xref ref-type="bibr" rid="ref-3">3</xref>]. Apple is one of the most cultivated fruits around the globe and it possess high medicinal and nutritional values. But many diseases recurrently affect apple production on a massive scale which cause considerable economic loss. Hence, effective and timely recognition of apple leaf disease is a critical challenge to overcome for healthy growth of apples and increased production. Recently, it has become a hot research topic in agriculture [<xref ref-type="bibr" rid="ref-4">4</xref>]. There is a considerable increase observed in apple planting region and output in the recent years, thanks to its high nutritional content and economic value. But, apple plant leaf disease incur heavy loss in terms of production and economic activities. It reduces the quantity and quality of fruit industry outputs. Hence, it becomes necessary to have a precise detection method for apple leaf disease [<xref ref-type="bibr" rid="ref-5">5</xref>].</p>
<p>In general, visual inspection by professionals is the preferred method for diagnosing plant diseases for a long time. But it involves the risk for error, because of individual perceptions [<xref ref-type="bibr" rid="ref-6">6</xref>]. In such event, many imaging and spectroscopic methods have been investigated for plant disease detection. But there is a need exists for bulky sensors and precise instruments that produce high efficiency at low cost. With the popularity of digital cameras and electronic gadgets in recent years, automated plant disease detection using ML method is being extensively applied these days as an effective alternative [<xref ref-type="bibr" rid="ref-7">7</xref>]. Over the past few years, conventional ML techniques have made considerable progress in apple leaf diseases detection. DL techniques performed an extraordinary innovation in advanced Computer Vision (CV) systems, owing to the development of deep convolution network in AlexNet [<xref ref-type="bibr" rid="ref-8">8</xref>]. Further, it is also commonly employed in diagnosis and identification of plant disease, thanks to its excellent robustness and automated extraction of image features. Many authors have used DL method in the detection of apple leaf diseases.</p>
<p>In the study conducted by Zhong&#x00A0;et&#x00A0;al.&#x00A0;[<xref ref-type="bibr" rid="ref-9">9</xref>], apple leaf image dataset that consists of 2462 images, belonging to six apple leaf diseases, was employed for method evaluation and data modeling. In this study, DenseNet-121 deep convolutional network, three regression techniques, focus loss function and multilabel classification were presented for the identification of apple leaf disease. Michalak&#x00A0;et&#x00A0;al.&#x00A0;[<xref ref-type="bibr" rid="ref-10">10</xref>] introduced an apple leaf disease recognition technique based on pattern recognition methods and image and processing techniques. In this study, a colour conversion technique for the input Red, Green, and Blue (RGB) image was initially presented. Later RGB pattern was changed to grey, and Hue, Saturation, and Intensity (HSI) patterns. The background was detached according to certain threshold values. Later, the disease spot image was divided using Region Growing Algorithm (RGA). A total of 38 features, used for categorization, such as shape, colour, and texture was extracted from all the spot images. In order to enhance the precision of apple leaf disease diagnosis and decrease the dimensionality of feature space, only the effective features were chosen by integrating Correlation-based Feature Selection (CFS) and Genetic Algorithm (GA) methods. Lastly, the disease was detected using Support Vector Machine (SVM) classification method.</p>
<p>Jiang&#x00A0;et&#x00A0;al.&#x00A0;[<xref ref-type="bibr" rid="ref-11">11</xref>] presented a DL method based on enhanced Convolutional Neural Network (CNN) method for real-time recognition of apple leaf disease. In this study, Apple Leaf Disease Data set (ALDD) was used to validate the proposed model. According to the authors, a novel apple leaf disease recognition method that employs Deep Convolutional Neural Network (DCNN) was presented in this study using Rainbow concatenation and GoogLeNet Inception model. Liu&#x00A0;et&#x00A0;al.&#x00A0;[<xref ref-type="bibr" rid="ref-12">12</xref>] presented a precise detection methodology for apple leaf diseases based on DCNN model. It involves the designing of a new framework using DCNN-based AlexNet and generation of adequate pathological images to identify apple leaf disease. In Umamageswari&#x00A0;et&#x00A0;al.&#x00A0;[<xref ref-type="bibr" rid="ref-13">13</xref>], a novel framework was proposed for the detection of plant leaf diseases. Initially, image contrast level was improved as well as overfitting and unwanted noise were detached. Then, fuzzy c-means based Chameleon Swarm Algorithm (FCM-CSA) was employed for the segmentation of plant leaf disease parts. Next, feature extraction was executed using a fast Grey Level Co-occurrence Matrix (GLCM) feature extraction method. Lastly, Progressive Neural Architecture Search (PNAS) was applied for the identification of plant diseases. Tahir&#x00A0;et&#x00A0;al.&#x00A0;[<xref ref-type="bibr" rid="ref-14">14</xref>] presented a novel deep methodology for the classification of apple leaf diseases. Some of the most popular apple leaf diseases are apple cedar, Apple Scab (AS), and brown spot. After the feature was extracted using Transfer Learning (TL) method, the feature was down-sampled using a new variance-controlled method. Tiwari&#x00A0;et&#x00A0;al.&#x00A0;[<xref ref-type="bibr" rid="ref-15">15</xref>] presented a DL-based method for detection and classification of plant diseases identified from leaf images captured in multiple resolutions. The dense CNN framework was trained on a massive plant leaf image datasets from several nations. The six yields, under 27 distinct classes, were taken in the presented method for both laboratory and on-field conditions into account.</p>
<p>The current research paper devises an Effective Sailfish Optimizer with EfficientNet based Apple Leaf Disease detection (ESFO-EALD) model. The proposed ESFO-EALD technique applies Median Filtering (MF) approach to boost the quality of apple plant leaf images. Moreover, SFO with Kapur&#x0027;s entropy-based segmentation technique is utilized in this study for identification of the affected plant region from test image. Furthermore, Adam optimizer with EfficientNet based feature extraction and Spiking Neural Network (SNN)-based classification are employed for both detection and classification of apple plant leaf images. A wide range of simulations was conducted to validate the effective outcomes of ESFO-EALD technique on benchmark dataset. The results established the supremacy of the proposed ESFO-EALD technique than existing approaches.</p>
<p>Rest of the paper is organized as follows. Section 2 introduces the proposed model, Section 3 validates the proposed model, and Section 4 concludes the work.</p>
</sec>
<sec id="s2">
<label>2</label>
<title>Materials and Methods</title>
<p>In this study, an effective ESFO-EALD technique has been developed for identification and classification of apple plant leaf images. The proposed ESFO-EALD method involves MF-based pre-processing, SFO using Kapur&#x2019;s entropy-based segmentation, EfficientNet-based feature extraction, Adam optimizer-based hyperparameter tuning, and SNN-based classification. The utilization of ESFO-based threshold value selection and Adam optimizer-based hyperparameter selection help in accomplishing enhanced outcomes. <xref ref-type="fig" rid="fig-1">Fig. 1</xref> illustrates the overall process of ESFO-EALD technique.</p>
<fig id="fig-1">
<label>Figure 1</label>
<caption>
<title>Overall process of ESFO-EALD technique</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_25280-fig-1.png"/>
</fig>
<sec id="s2_1">
<label>2.1</label>
<title>Data Collection</title>
<p>In this study, the researchers used benchmark plant disease dataset from Kaggle repository. The dataset includes images under four classes namely AS, Black Rot (BR), Cedar Rust (CR), and healthy (HY). Among these, AS dataset includes 2,016 trained images and 504 tested images. In line with this, BR dataset contains 1,987 trained images and 497 tested images. Moreover, CR dataset comprises of 1,760 trained images and 440 tested images. Furthermore, HY dataset includes 2,008 trained images and 502 tested images.</p>
</sec>
<sec id="s2_2">
<label>2.2</label>
<title>MF Based Pre-Processing</title>
<p>Primarily, MF technique gets rid of the noise present in apple plant leaf images. Being a non-linear method, it is effective in decreasing salt-and-pepper or impulsive noises. Further, it also conserves the edges in image effectively, while decreasing random noises. Salt-and pepper or impulsive noise tend to occur due to arbitrary bit error in transmission network. In median filter, the median intensity value of the pixel within the window and a window that slides alongside the image become the output intensity of pixels. Median filtering smoothens the image and is effective in noise reduction. On the contrary to low-pass filter, median filter could retain discontinuity in a step-wise manner and could smoothen some pixels with value that differs considerably from their surroundings without impacting other pixels.</p>
</sec>
<sec id="s2_3">
<label>2.3</label>
<title>ESFO with Kapur&#x2019;s Entropy-Based Segmentation</title>
<p>During segmentation, SFO algorithm with Kapur&#x2019;s entropy technique is used to identify the regions affected with plant disease. Kapur&#x2019;s entropy approach is another thresholding method which is employed in the implementation of segmentation principle. Kapur&#x2019;s method selects the optimum threshold value-based maximization of entropy. The arithmetical expression is shown in the following equation:</p>
<p><disp-formula id="eqn-1"><label>(1)</label><mml:math id="mml-eqn-1" display="block"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">k</mml:mi><mml:mi mathvariant="italic">a</mml:mi><mml:mi mathvariant="italic">p</mml:mi><mml:mi mathvariant="italic">u</mml:mi><mml:mi mathvariant="italic">r</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mi>h</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math></disp-formula></p>
<p>Here, <inline-formula id="ieqn-1"><mml:math id="mml-ieqn-1"><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-2"><mml:math id="mml-ieqn-2"><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> entropies are calculated as follows.</p>
<p><disp-formula id="eqn-2"><label>(2)</label><mml:math id="mml-eqn-2" display="block"><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:munderover><mml:mo movablelimits="false">&#x2211;</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:munderover><mml:mfrac><mml:mrow><mml:mi>P</mml:mi><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:msub><mml:mi>&#x03C9;</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mfrac><mml:mi>l</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mfrac><mml:mrow><mml:mi>P</mml:mi><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:msub><mml:mi>&#x03C9;</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mfrac><mml:mo>)</mml:mo></mml:mrow><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mspace width="thickmathspace" /><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:munderover><mml:mo movablelimits="false">&#x2211;</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mi>t</mml:mi><mml:mi>h</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:munderover><mml:mfrac><mml:mrow><mml:mi>P</mml:mi><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:msub><mml:mi>&#x03C9;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mfrac><mml:mi>l</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mfrac><mml:mrow><mml:mi>P</mml:mi><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:msub><mml:mi>&#x03C9;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mfrac><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>Let <inline-formula id="ieqn-3"><mml:math id="mml-ieqn-3"><mml:mi>P</mml:mi><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> be the probability distribution of intensity levels, <inline-formula id="ieqn-4"><mml:math id="mml-ieqn-4"><mml:msub><mml:mi>&#x03C9;</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mi>h</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> and <inline-formula id="ieqn-5"><mml:math id="mml-ieqn-5"><mml:msub><mml:mi>&#x03C9;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mi>h</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> denote probability distribution-based classes such as <inline-formula id="ieqn-6"><mml:math id="mml-ieqn-6"><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-7"><mml:math id="mml-ieqn-7"><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>.</mml:mo></mml:math></inline-formula> <inline-formula id="ieqn-8"><mml:math id="mml-ieqn-8"><mml:mi>ln</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mo>&#x22C5;</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> indicates the natural logarithm [<xref ref-type="bibr" rid="ref-16">16</xref>]. Entropy-based model has transformed for multi-threshold values that are analogous to Otsu algorithm. It is significant to divide the image to <inline-formula id="ieqn-9"><mml:math id="mml-ieqn-9"><mml:mi>N</mml:mi></mml:math></inline-formula> classes with <inline-formula id="ieqn-10"><mml:math id="mml-ieqn-10"><mml:mi>N</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:math></inline-formula> threshold and is expressed through <xref ref-type="disp-formula" rid="eqn-3">Eq. (3)</xref>.</p>
<p><disp-formula id="eqn-3"><label>(3)</label><mml:math id="mml-eqn-3" display="block"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">k</mml:mi><mml:mi mathvariant="italic">a</mml:mi><mml:mi mathvariant="italic">p</mml:mi><mml:mi mathvariant="italic">u</mml:mi><mml:mi mathvariant="italic">r</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mi>H</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:munderover><mml:mo movablelimits="false">&#x2211;</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:munderover><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></disp-formula></p>
<p>Here, a vector that comprises of numerous thresholds is <inline-formula id="ieqn-11"><mml:math id="mml-ieqn-11"><mml:mi>T</mml:mi><mml:mi>H</mml:mi><mml:mo>=</mml:mo><mml:mo stretchy="false">[</mml:mo><mml:mi>t</mml:mi><mml:mi>h</mml:mi><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mi>h</mml:mi><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mi>h</mml:mi><mml:mi>N</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">]</mml:mo></mml:math></inline-formula>. All the entropies are individually calculated with respective values (<italic>th</italic>), hence <xref ref-type="disp-formula" rid="eqn-3">Eq. (3)</xref>. For <inline-formula id="ieqn-12"><mml:math id="mml-ieqn-12"><mml:mi>N</mml:mi></mml:math></inline-formula>, entropy is extended by <xref ref-type="disp-formula" rid="eqn-4">Eq. (4)</xref>:</p>
<p><disp-formula id="eqn-4"><label>(4)</label><mml:math id="mml-eqn-4" display="block"><mml:msubsup><mml:mi>H</mml:mi><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:munderover><mml:mo movablelimits="false">&#x2211;</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mi>t</mml:mi><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>N</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:munderover><mml:mfrac><mml:mrow><mml:mi>P</mml:mi><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:msub><mml:mi>&#x03C9;</mml:mi><mml:mrow><mml:mi>N</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mfrac><mml:mi>l</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mfrac><mml:mrow><mml:mi>P</mml:mi><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:msub><mml:mi>&#x03C9;</mml:mi><mml:mrow><mml:mi>N</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mfrac><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>The probability value occurrence <inline-formula id="ieqn-13"><mml:math id="mml-ieqn-13"><mml:mo stretchy="false">(</mml:mo><mml:msubsup><mml:mi>&#x03C9;</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:msub><mml:mi>&#x03C9;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>&#x03C9;</mml:mi><mml:mrow><mml:mi>N</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> of <inline-formula id="ieqn-14"><mml:math id="mml-ieqn-14"><mml:mi>N</mml:mi></mml:math></inline-formula> classes and <inline-formula id="ieqn-15"><mml:math id="mml-ieqn-15"><mml:mi>P</mml:mi><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> denotes the probability distribution. In order to the optimum threshold values of Kapur&#x2019;s entropy, SFO algorithm is utilized.</p>
<p>SFO is a new, nature-inspired meta-heuristic algorithm which is modelled after a group of hunting sailfish. It demonstrates a remarkable performance compared to commonly available meta-heuristic approaches. The location of <inline-formula id="ieqn-16"><mml:math id="mml-ieqn-16"><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> sailfish in <inline-formula id="ieqn-17"><mml:math id="mml-ieqn-17"><mml:mi>k</mml:mi><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> searching iteration is represented by <inline-formula id="ieqn-18"><mml:math id="mml-ieqn-18"><mml:mi>S</mml:mi><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:math></inline-formula>, and its respective fitness is calculated using <inline-formula id="ieqn-19"><mml:math id="mml-ieqn-19"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>S</mml:mi><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:mo stretchy="false">)</mml:mo></mml:math></inline-formula>. Sardine is the other important participant in SFO method. The location of <inline-formula id="ieqn-20"><mml:math id="mml-ieqn-20"><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> sardine is represented by <inline-formula id="ieqn-21"><mml:math id="mml-ieqn-21"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> while its respective fitness is evaluated using <inline-formula id="ieqn-22"><mml:math id="mml-ieqn-22"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>. In SFO model, the sailfish that occupies the optimal location is chosen as &#x2018;elite sailfish&#x2019; and it affects the acceleration and maneuverability of sardines during attacks. In addition, the location of an injured sardine, during all the iterations, is chosen as an optimal location for collective hunting by sailfishes. Elite sailfish and the injured sardine are represented as <inline-formula id="ieqn-23"><mml:math id="mml-ieqn-23"><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: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:mrow></mml:msubsup></mml:math></inline-formula> and <inline-formula id="ieqn-24"><mml:math id="mml-ieqn-24"><mml:msubsup><mml:mi>Y</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">j</mml:mi><mml:mi mathvariant="italic">u</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula>, correspondingly during <inline-formula id="ieqn-25"><mml:math id="mml-ieqn-25"><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> iteration. At the time of hunting, a sailfish attack alternative method is frequently employed for enhancing the hunting results [<xref ref-type="bibr" rid="ref-17">17</xref>]. The novel location of sailfish <inline-formula id="ieqn-26"><mml:math id="mml-ieqn-26"><mml:msubsup><mml:mi>Y</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>e</mml:mi><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:mrow></mml:msubsup></mml:math></inline-formula> is upgraded by <xref ref-type="disp-formula" rid="eqn-5">Eq. (5)</xref>.</p>
<p><disp-formula id="eqn-5"><label>(5)</label><mml:math id="mml-eqn-5" display="block"><mml:msubsup><mml:mi>Y</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>e</mml:mi><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:mrow></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: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:mrow></mml:msubsup><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>&#x03BB;</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:mrow><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">a</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">d</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">m</mml:mi></mml:mrow><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: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>t</mml:mi><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:mrow></mml:msubsup><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">j</mml:mi><mml:mi mathvariant="italic">u</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup></mml:mrow><mml:mn>2</mml:mn></mml:mfrac><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">u</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi><mml:mi mathvariant="italic">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:mrow></mml:msubsup><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:math></disp-formula></p>
<p>Here, <inline-formula id="ieqn-27"><mml:math id="mml-ieqn-27"><mml:msubsup><mml:mi>Y</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">u</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi><mml:mi mathvariant="italic">n</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mtext>t</mml:mtext></mml:mrow><mml:mrow><mml:mrow><mml:mtext>SF</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> denotes the present location of sailfish and is arbitrarily in the range of zero and one<inline-formula id="ieqn-28"><mml:math id="mml-ieqn-28"><mml:mo>.</mml:mo></mml:math></inline-formula></p>
<p>The parameter <inline-formula id="ieqn-29"><mml:math id="mml-ieqn-29"><mml:msub><mml:mi>&#x03BB;</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> denotes the coefficient in <inline-formula id="ieqn-30"><mml:math id="mml-ieqn-30"><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> iteration:</p>
<p><disp-formula id="eqn-6"><label>(6)</label><mml:math id="mml-eqn-6" display="block"><mml:msub><mml:mi>&#x03BB;</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><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: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: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:mo>,</mml:mo></mml:math></disp-formula></p>
<p>Here, <inline-formula id="ieqn-31"><mml:math id="mml-ieqn-31"><mml:mi>S</mml:mi><mml:mi>D</mml:mi></mml:math></inline-formula> indicates sardine density that represents the amount of sardines during all the iterations.</p>
<p>The parameter <inline-formula id="ieqn-32"><mml:math id="mml-ieqn-32"><mml:mi>S</mml:mi><mml:mi>D</mml:mi></mml:math></inline-formula> is acquired by <xref ref-type="disp-formula" rid="eqn-7">Eq. (7)</xref></p>
<p><disp-formula id="eqn-7"><label>(7)</label><mml:math id="mml-eqn-7" 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:mfrac><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:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>S</mml:mi><mml:mi>F</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:math></disp-formula></p>
<p>In this equation, <inline-formula id="ieqn-33"><mml:math id="mml-ieqn-33"><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>S</mml:mi><mml:mi>F</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-34"><mml:math id="mml-ieqn-34"><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> signify the amount of sailfish and sardines correspondingly.</p>
<p>During early stage of the hunt, sardines do not get injured/tired and sailfish remain energetic. Sardine can rapidly escape the hunting scene. But, with constant hunting, the strength of sailfish attacks gets reduced gradually. In the meantime, sardines get tired and their awareness about the position of sailfish also gets reduced. As a consequence, the sardine is hunted. According to the algorithmic procedure, the novel location of sardine <inline-formula id="ieqn-35"><mml:math id="mml-ieqn-35"><mml:msubsup><mml:mi>Y</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> gets upgraded by <xref ref-type="disp-formula" rid="eqn-8">Eq. (8)</xref>.</p>
<p><disp-formula id="eqn-8"><label>(8)</label><mml:math id="mml-eqn-8" display="block"><mml:msubsup><mml:mi>Y</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mrow><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">a</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">d</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">m</mml:mi></mml:mrow><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: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: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:mrow></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:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:mi>A</mml:mi><mml:mi>T</mml:mi><mml:mi>P</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:math></disp-formula></p>
<p>Now, <inline-formula id="ieqn-36"><mml:math id="mml-ieqn-36"><mml:msubsup><mml:mi>Y</mml:mi><mml:mrow><mml:mi>o</mml:mi><mml:mi>l</mml:mi><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> represents the older location of sardine which is in arbitrary range of zero and one<inline-formula id="ieqn-37"><mml:math id="mml-ieqn-37"><mml:mo>.</mml:mo></mml:math></inline-formula> <inline-formula id="ieqn-38"><mml:math id="mml-ieqn-38"><mml:mi>A</mml:mi><mml:mi>T</mml:mi><mml:mi>P</mml:mi></mml:math></inline-formula> signifies the power of sailfish attack.</p>
<p>The parameter <inline-formula id="ieqn-39"><mml:math id="mml-ieqn-39"><mml:mi>A</mml:mi><mml:mi>T</mml:mi><mml:mi>P</mml:mi></mml:math></inline-formula> is evaluated using <xref ref-type="disp-formula" rid="eqn-9">Eq. (9)</xref>:</p>
<p><disp-formula id="eqn-9"><label>(9)</label><mml:math id="mml-eqn-9" 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:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>&#x00D7;</mml:mo><mml:mi>I</mml:mi><mml:mi>t</mml:mi><mml:mi>r</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>&#x03B5;</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>While <inline-formula id="ieqn-40"><mml:math id="mml-ieqn-40"><mml:mi>B</mml:mi></mml:math></inline-formula> and <inline-formula id="ieqn-41"><mml:math id="mml-ieqn-41"><mml:mi>&#x03B5;</mml:mi></mml:math></inline-formula> represent the coefficients employed for linear reduction of attack power from <inline-formula id="ieqn-42"><mml:math id="mml-ieqn-42"><mml:mi>B</mml:mi></mml:math></inline-formula> to <inline-formula id="ieqn-43"><mml:math id="mml-ieqn-43"><mml:mn>0</mml:mn></mml:math></inline-formula> whereas <inline-formula id="ieqn-44"><mml:math id="mml-ieqn-44"><mml:mi>I</mml:mi><mml:mi>t</mml:mi><mml:mi>r</mml:mi></mml:math></inline-formula> indicates the number of iterations. Since the attack power of sailfish gets reduced over hunting time, this reduction promotes search convergence. Once the attack power (ATP) becomes higher, e.g., greater than 0.5, the location of each sardine also gets upgraded. However, <inline-formula id="ieqn-45"><mml:math id="mml-ieqn-45"><mml:mi>&#x03B1;</mml:mi></mml:math></inline-formula> sardine with <inline-formula id="ieqn-46"><mml:math id="mml-ieqn-46"><mml:mi>&#x03B2;</mml:mi></mml:math></inline-formula> parameter upgrades their locations. The number of sardines that upgrade their location, is measured by <xref ref-type="disp-formula" rid="eqn-10">Eq. (10)</xref>:</p>
<p><disp-formula id="eqn-10"><label>(10)</label><mml:math id="mml-eqn-10" display="block"><mml:mi>&#x03B1;</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:msub><mml:mo>&#x00D7;</mml:mo><mml:mi>A</mml:mi><mml:mi>T</mml:mi><mml:mi>P</mml:mi><mml:mo>,</mml:mo></mml:math></disp-formula></p>
<p>Let <inline-formula id="ieqn-47"><mml:math id="mml-ieqn-47"><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> be the number of sardines during all the iterations. The amount of parameters of the sardine that upgrades its locations is attained as follows.</p>
<p><disp-formula id="eqn-11"><label>(11)</label><mml:math id="mml-eqn-11" display="block"><mml:mi>&#x03B2;</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>&#x00D7;</mml:mo><mml:mi>A</mml:mi><mml:mi>T</mml:mi><mml:mi>P</mml:mi><mml:mo>,</mml:mo></mml:math></disp-formula>whereas <inline-formula id="ieqn-48"><mml:math id="mml-ieqn-48"><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> denotes the number of parameters during <inline-formula id="ieqn-49"><mml:math id="mml-ieqn-49"><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> iteration. Once the sardines are hunted, it is understood that its fitness values should be higher than sailfish. In this condition, the location of sailfish <inline-formula id="ieqn-50"><mml:math id="mml-ieqn-50"><mml:msubsup><mml:mi>Y</mml:mi><mml:mrow><mml:mi>S</mml:mi><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> gets upgraded with the newest location of the hunted sardine, <inline-formula id="ieqn-51"><mml:math id="mml-ieqn-51"><mml:msubsup><mml:mi>Y</mml:mi><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> to promote the hunting of novel sardines.</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>S</mml:mi><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup><mml:mi>i</mml:mi><mml:mi>f</mml:mi><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x003C;</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>S</mml:mi><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>.</mml:mo></mml:math></disp-formula></p>
</sec>
<sec id="s2_4">
<label>2.4</label>
<title>Optimal EfficientNet Based Feature Extraction</title>
<p>After segmentation process, the next stage is the generation of useful collection of feature vectors. EfficientNet is a kind of CNN which effectively scales up based on input resolution, layer depth, layer width, and the integration of each factor. It is an advanced DL method that heavily focuses on improving the accuracy and efficiency of the model. It has different versions in the range of B0 to B7. The basic component is MBConv in which the excitation and compression optimization are included. Such block creates shortcuts between the starting and ending points of convolution blocks. The input activation map is extended by 1 &#x00D7; 1 convolution to increase the depth of feature map. The shortcut connection is utilized in this method to link the narrow layer together, when a wider layer is situated between the jump links. <xref ref-type="fig" rid="fig-2">Fig. 2</xref> illustrates the Efficientnet structure layer [<xref ref-type="bibr" rid="ref-18">18</xref>]. This framework helps in reducing the size and overall amount of essential transactions. Adam optimizer is used to choose the hyperparameters of EfficientNet model proficiently.</p>
<fig id="fig-2">
<label>Figure 2</label>
<caption>
<title>Layer of efficientnet structure</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_25280-fig-2.png"/>
</fig>
<p>DL frequently consumes much time and computer resources to train. Thus, optimization techniques are extremely apprehensive. Adam&#x0027;s (adaptive momentum) technique consumes less resources and creates the method convergence earlier. This in turn accelerates the learning speed and enhance the effects. Adam optimizer is a 1<sup>st</sup>-order optimization approach which changes the conventional stochastic gradient descent procedure. It connects the 2<sup>nd</sup> moment evaluation on fundamental momentum of 1<sup>st</sup>-order moment evaluation and increases a moment to Adadelta. The rate of learning for all the parameters gets dynamically modified with the help of 1<sup>st</sup> and 2<sup>nd</sup> moment&#x2019;s evaluation of gradients [<xref ref-type="bibr" rid="ref-19">19</xref>]. The bias correction also occurs which further creates the parameters that are comparatively stable.</p>
<p>The iterative equations are as follows:</p>
<p><disp-formula id="ueqn-13"><mml:math id="mml-ueqn-13" display="block"><mml:mi>g</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>&#x03B8;</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msup><mml:mo>&#x2212;</mml:mo><mml:msup><mml:mi>y</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msup><mml:mo>,</mml:mo></mml:math></disp-formula></p>
<p><disp-formula id="ueqn-14"><mml:math id="mml-ueqn-14" display="block"><mml:msub><mml:mi>m</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi>m</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2217;</mml:mo><mml:mi>g</mml:mi><mml:mo>,</mml:mo></mml:math></disp-formula></p>
<p><disp-formula id="ueqn-15"><mml:math id="mml-ueqn-15" display="block"><mml:msub><mml:mi>&#x03BD;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi>&#x03BD;</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2217;</mml:mo><mml:msup><mml:mi>g</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>,</mml:mo></mml:math></disp-formula></p>
<p><disp-formula id="eqn-13"><label>(13)</label><mml:math id="mml-eqn-13" display="block"><mml:msubsup><mml:mi>m</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mo>&#x223C;</mml:mo></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mi>m</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mfrac><mml:mo>,</mml:mo></mml:math></disp-formula></p>
<p><disp-formula id="ueqn-17"><mml:math id="mml-ueqn-17" display="block"><mml:msubsup><mml:mi>&#x03BD;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mo>&#x223C;</mml:mo></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mi>&#x03BD;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mfrac><mml:mo>,</mml:mo></mml:math></disp-formula></p>
<p><disp-formula id="ueqn-18"><mml:math id="mml-ueqn-18" display="block"><mml:msub><mml:mi>&#x03B8;</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>&#x03B8;</mml:mi><mml:mrow><mml:mi>j</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mi>m</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mo>&#x223C;</mml:mo></mml:mrow></mml:msubsup><mml:mo>&#x2217;</mml:mo><mml:mfrac><mml:mi>&#x03B1;</mml:mi><mml:mrow><mml:msqrt><mml:msubsup><mml:mi>&#x03BD;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mo>&#x223C;</mml:mo></mml:mrow></mml:msubsup></mml:msqrt><mml:mo>+</mml:mo><mml:mi>e</mml:mi></mml:mrow></mml:mfrac><mml:mo>,</mml:mo></mml:math></disp-formula>where <inline-formula id="ieqn-52"><mml:math id="mml-ieqn-52"><mml:mi>g</mml:mi></mml:math></inline-formula> refers to the computed gradients, <inline-formula id="ieqn-53"><mml:math id="mml-ieqn-53"><mml:msub><mml:mi>m</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> stands for 1<sup>st</sup> moment of gradient <inline-formula id="ieqn-54"><mml:math id="mml-ieqn-54"><mml:mi>g</mml:mi></mml:math></inline-formula> which is also the expectation of gradient <inline-formula id="ieqn-55"><mml:math id="mml-ieqn-55"><mml:mi>g</mml:mi><mml:mo>,</mml:mo></mml:math></inline-formula> <inline-formula id="ieqn-56"><mml:math id="mml-ieqn-56"><mml:msub><mml:mi>&#x03BD;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> defines the 2<sup>nd</sup> moment of gradient <inline-formula id="ieqn-57"><mml:math id="mml-ieqn-57"><mml:mi>g</mml:mi><mml:mo>,</mml:mo></mml:math></inline-formula> <inline-formula id="ieqn-58"><mml:math id="mml-ieqn-58"><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> implies the 1<sup>st</sup>-order moment attenuation coefficients, <inline-formula id="ieqn-59"><mml:math id="mml-ieqn-59"><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> determines the 2<sup>nd</sup> moment attenuation coefficients, <inline-formula id="ieqn-60"><mml:math id="mml-ieqn-60"><mml:mi>&#x03B8;</mml:mi></mml:math></inline-formula> represents the parameter which requires that resolved (or upgraded), and <inline-formula id="ieqn-61"><mml:math id="mml-ieqn-61"><mml:msubsup><mml:mi>m</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mo>&#x223C;</mml:mo></mml:mrow></mml:msubsup></mml:math></inline-formula> and <inline-formula id="ieqn-62"><mml:math id="mml-ieqn-62"><mml:msubsup><mml:mi>&#x03BD;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mo>&#x223C;</mml:mo></mml:mrow></mml:msubsup></mml:math></inline-formula> denote the offset corrections of <inline-formula id="ieqn-63"><mml:math id="mml-ieqn-63"><mml:msub><mml:mi>m</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-64"><mml:math id="mml-ieqn-64"><mml:msub><mml:mi>&#x03BD;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, correspondingly.</p>
</sec>
<sec id="s2_5">
<label>2.5</label>
<title>SNN-Based Classification</title>
<p>In this last stage, SNN model is utilized as a classifier to allot proper class labels. SNN method is employed for analyzing the learning process and network dynamic features. Assume that <inline-formula id="ieqn-65"><mml:math id="mml-ieqn-65"><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> indicates the number of spikes in ith spike train and <inline-formula id="ieqn-66"><mml:math id="mml-ieqn-66"><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>I</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> represents the overall amount of synaptic inputs. <inline-formula id="ieqn-67"><mml:math id="mml-ieqn-67"><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>o</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> denotes the synapse weight from <inline-formula id="ieqn-68"><mml:math id="mml-ieqn-68"><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> input to output neurons. <inline-formula id="ieqn-69"><mml:math id="mml-ieqn-69"><mml:msubsup><mml:mi>t</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>f</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> signifies the <inline-formula id="ieqn-70"><mml:math id="mml-ieqn-70"><mml:mi>f</mml:mi></mml:math></inline-formula>th spike firing time of <inline-formula id="ieqn-71"><mml:math id="mml-ieqn-71"><mml:mi>i</mml:mi></mml:math></inline-formula> input neuron. The neuron possibility can be determined by the summation of potential postsynaptic, which is induced by each input spike from presynaptic neuron. Once the <inline-formula id="ieqn-72"><mml:math id="mml-ieqn-72"><mml:mi>u</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> internal state surpasses the neuron thresholding <inline-formula id="ieqn-73"><mml:math id="mml-ieqn-73"><mml:mi>&#x03B8;</mml:mi></mml:math></inline-formula>, the output neurons fire at a spike whereas the internal state immediately reduces to resting potentials. This stage is otherwise named as repolarization [<xref ref-type="bibr" rid="ref-20">20</xref>]. The postsynaptic potential neurons at time <inline-formula id="ieqn-74"><mml:math id="mml-ieqn-74"><mml:mi>t</mml:mi></mml:math></inline-formula> can be estimated using the following equation.</p>
<p><disp-formula id="eqn-14"><label>(14)</label><mml:math id="mml-eqn-14" display="block"><mml:mi>u</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:munderover><mml:mo movablelimits="false">&#x2211;</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>I</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:munderover><mml:mo movablelimits="false">&#x2211;</mml:mo><mml:mrow><mml:mi>f</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>o</mml:mi></mml:mrow></mml:msub><mml:mi>&#x03B5;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mi>t</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>f</mml:mi></mml:mrow></mml:msubsup><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>&#x03C1;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:msup><mml:mi>t</mml:mi><mml:mrow><mml:mi>f</mml:mi></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula>where <inline-formula id="ieqn-75"><mml:math id="mml-ieqn-75"><mml:mi>&#x03B5;</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>s</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mi>s</mml:mi><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>&#x03C4;</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mi>exp</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mi>s</mml:mi><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>&#x03C4;</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mi>H</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>s</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> denotes the spike response function, <inline-formula id="ieqn-76"><mml:math id="mml-ieqn-76"><mml:mi>&#x03C1;</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>s</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mi>&#x03B8;</mml:mi><mml:mi>exp</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mi>s</mml:mi><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:msub><mml:mi>&#x03C4;</mml:mi><mml:mrow><mml:mi>R</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mi>H</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>s</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> indicates the refractoriness function, in which <inline-formula id="ieqn-77"><mml:math id="mml-ieqn-77"><mml:mi>&#x03C4;</mml:mi></mml:math></inline-formula> and <inline-formula id="ieqn-78"><mml:math id="mml-ieqn-78"><mml:msub><mml:mi>&#x03C4;</mml:mi><mml:mrow><mml:mi>R</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> denote time constant and <inline-formula id="ieqn-79"><mml:math id="mml-ieqn-79"><mml:mi>H</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>s</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> signifies the Heaviside function. Like conventional Artificial Neural Network (ANN), SNNs have recurrent, feedforward, and other network frameworks too. In this work, FFNN framework is adopted with output and input layers separated into learning and encoding stages for image classification and recognition.</p>
<p>The presented method is employed for image classification and recognition issues. In coding phase, the latency-phase encoding technique is utilized for transforming the pixels of respective image fields into accurately-timed spike train. Here, the spike train is employed to represent the outside image stimuli data. At the time of learning phase, all the spike trains correspond to input neurons and become the input to SNN. The synaptic weight can be learned using supervised multiple spike learning model. The SNN provides the output for the targeted spike patterns of the provided image.</p>
</sec>
</sec>
<sec id="s3">
<label>3</label>
<title>Experimental Validation</title>
<p>The performance validation of the proposed ESFO-EALD technique was conducted using benchmark plant disease dataset [<xref ref-type="bibr" rid="ref-21">21</xref>] and the current section details the same with results. The results were investigated under three test runs. A few sample images are demonstrated in <xref ref-type="fig" rid="fig-3	">Fig. 3</xref>.</p>
<fig id="fig-3">
<label>Figure 3</label>
<caption>
<title>Sample images</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_25280-fig-3.png"/>
</fig>
<p>The confusion matrix generated by ESFO-EALD technique on test dataset under run-2 is shown in <xref ref-type="fig" rid="fig-4">Fig. 4</xref>. It is noticed that ESFO-EALD technique categorized 497 images under AS, 488 images under BR, 438 images under CR, and 496 images under HY.</p>
<fig id="fig-4">
<label>Figure 4</label>
<caption>
<title>Confusion matrix of ESFO-EALD method on run-1</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_25280-fig-4.png"/>
</fig>
<p><xref ref-type="table" rid="table-1">Tab. 1</xref> offers a detailed overview of the results of classification analysis accomplished by ESFO-EALD technique on test run-1. The results demonstrate that ESFO-EALD technique identified the instances under AS class with <inline-formula id="ieqn-85"><mml:math id="mml-ieqn-85"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-86"><mml:math id="mml-ieqn-86"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-87"><mml:math id="mml-ieqn-87"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:math></inline-formula> and <inline-formula id="ieqn-88"><mml:math id="mml-ieqn-88"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> scores such as 0.9923, 0.9842, 0.9861, 0.9944, and 0.9851 respectively. Besides, the outcomes exhibit that the proposed ESFO-EALD method identified the instances under BR class with <inline-formula id="ieqn-89"><mml:math id="mml-ieqn-89"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-90"><mml:math id="mml-ieqn-90"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-91"><mml:math id="mml-ieqn-91"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:math></inline-formula> and <inline-formula id="ieqn-92"><mml:math id="mml-ieqn-92"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> values being 0.9913, 0.9839, 0.9819, 0.9945, and 0.9829 correspondingly. Moreover, ESFO-EALD algorithm recognized the instances under CR class with <inline-formula id="ieqn-93"><mml:math id="mml-ieqn-93"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-94"><mml:math id="mml-ieqn-94"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-95"><mml:math id="mml-ieqn-95"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:math></inline-formula> and <inline-formula id="ieqn-96"><mml:math id="mml-ieqn-96"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> values such as 0.9949, 0.9821, 0.9955, 0.9947, and 0.9887 respectively. Furthermore, the proposed ESFO-EALD approach classified the instances under HY class with <inline-formula id="ieqn-97"><mml:math id="mml-ieqn-97"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-98"><mml:math id="mml-ieqn-98"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-99"><mml:math id="mml-ieqn-99"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:math></inline-formula> and <inline-formula id="ieqn-100"><mml:math id="mml-ieqn-100"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> values being 0.9969, 1.0, 0.988, 1.0, and 0.994.</p>
<table-wrap id="table-1">
<label>Table 1</label>
<caption>
<title>Classification analysis results of ESFO-EALD technique on run-1</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>Class</th>
<th><inline-formula id="ieqn-80"><mml:math id="mml-ieqn-80"><mml:mrow><mml:mi mathvariant="bold-italic">a</mml:mi><mml:mi mathvariant="bold-italic">c</mml:mi></mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">c</mml:mi><mml:mrow><mml:mi mathvariant="bold-italic">y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
<th><inline-formula id="ieqn-81"><mml:math id="mml-ieqn-81"><mml:mrow><mml:mi mathvariant="bold-italic">p</mml:mi><mml:mi mathvariant="bold-italic">r</mml:mi><mml:mi mathvariant="bold-italic">e</mml:mi></mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">c</mml:mi><mml:mrow><mml:mi mathvariant="bold-italic">n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
<th><inline-formula id="ieqn-82"><mml:math id="mml-ieqn-82"><mml:mrow><mml:mi mathvariant="bold-italic">r</mml:mi><mml:mi mathvariant="bold-italic">e</mml:mi></mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">c</mml:mi><mml:mrow><mml:mi mathvariant="bold-italic">l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
<th><inline-formula id="ieqn-83"><mml:math id="mml-ieqn-83"><mml:mrow><mml:mi mathvariant="bold-italic">s</mml:mi><mml:mi mathvariant="bold-italic">p</mml:mi></mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">e</mml:mi><mml:mrow><mml:mi mathvariant="bold-italic">y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
<th><inline-formula id="ieqn-84"><mml:math id="mml-ieqn-84"><mml:msub><mml:mi mathvariant="bold-italic">F</mml:mi><mml:mrow><mml:mi mathvariant="bold-italic">s</mml:mi><mml:mi mathvariant="bold-italic">c</mml:mi><mml:mi mathvariant="bold-italic">o</mml:mi><mml:mi mathvariant="bold-italic">r</mml:mi><mml:mi mathvariant="bold-italic">e</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
</tr>
</thead>
<tbody>
<tr>
<td>AS</td>
<td>0.9923</td>
<td>0.9842</td>
<td>0.9861</td>
<td>0.9944</td>
<td>0.9851</td>
</tr>
<tr>
<td>BR</td>
<td>0.9913</td>
<td>0.9839</td>
<td>0.9819</td>
<td>0.9945</td>
<td>0.9829</td>
</tr>
<tr>
<td>CR</td>
<td>0.9949</td>
<td>0.9821</td>
<td>0.9955</td>
<td>0.9947</td>
<td>0.9887</td>
</tr>
<tr>
<td>HY</td>
<td>0.9969</td>
<td>1.0</td>
<td>0.988</td>
<td>1.0</td>
<td>0.994</td>
</tr>
<tr>
<td>Average</td>
<td>0.9938</td>
<td>0.9875</td>
<td>0.9879</td>
<td>0.9959</td>
<td>0.9877</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The confusion matrix generated by ESFO-EALD system on test dataset under run-2 is depicted in <xref ref-type="fig" rid="fig-5">Fig. 5</xref>. It is clear that the proposed ESFO-EALD approach categorized 494 images under AS, 490 images under BR, 437 images under CR, and 496 images under HY.</p>
<fig id="fig-5">
<label>Figure 5</label>
<caption>
<title>Confusion matrix of ESFO-EALD method on run-3</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_25280-fig-5.png"/>
</fig>
<p><xref ref-type="table" rid="table-2">Tab. 2</xref> portrays the results of classification analysis attained by ESFO-EALD method on test run-2. The outcomes portray that ESFO-EALD method categorized the instances under AS class with <inline-formula id="ieqn-106"><mml:math id="mml-ieqn-106"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-107"><mml:math id="mml-ieqn-107"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-108"><mml:math id="mml-ieqn-108"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:math></inline-formula> and <inline-formula id="ieqn-109"><mml:math id="mml-ieqn-109"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> values being 0.9918, 0.988, 0.9802, 0.9958, and 0.9841 respectively. Followed by, the outcomes display that the proposed ESFO-EALD algorithm classified the instances under BR class with <inline-formula id="ieqn-110"><mml:math id="mml-ieqn-110"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-111"><mml:math id="mml-ieqn-111"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-112"><mml:math id="mml-ieqn-112"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:math></inline-formula> and <inline-formula id="ieqn-113"><mml:math id="mml-ieqn-113"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> values such as 0.9918, 0.982, 0.9859, 0.9938, and 0.9839 correspondingly. Additionally, the results demonstrate that the proposed ESFO-EALD system categorized the instances under CR class by achieving <inline-formula id="ieqn-114"><mml:math id="mml-ieqn-114"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-115"><mml:math id="mml-ieqn-115"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-116"><mml:math id="mml-ieqn-116"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:math></inline-formula> and <inline-formula id="ieqn-117"><mml:math id="mml-ieqn-117"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> values such as 0.9928, 0.9754, 0.9932, 0.9927, and 0.9842 respectively. Also, the results showcase that the proposed ESFO-EALD method classified the instances under HY class with <inline-formula id="ieqn-118"><mml:math id="mml-ieqn-118"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-119"><mml:math id="mml-ieqn-119"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-120"><mml:math id="mml-ieqn-120"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:math></inline-formula> and <inline-formula id="ieqn-121"><mml:math id="mml-ieqn-121"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> values being 0.9969, 1.0, 0.988, 1.0, and 0.994 correspondingly.</p>
<table-wrap id="table-2">
<label>Table 2</label>
<caption>
<title>Classification analysis results of ESFO-EALD technique on run-2</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>Class</th>
<th><inline-formula id="ieqn-101"><mml:math id="mml-ieqn-101"><mml:mrow><mml:mi mathvariant="bold-italic">a</mml:mi><mml:mi mathvariant="bold-italic">c</mml:mi></mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">c</mml:mi><mml:mrow><mml:mi mathvariant="bold-italic">y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
<th><inline-formula id="ieqn-102"><mml:math id="mml-ieqn-102"><mml:mrow><mml:mi mathvariant="bold-italic">p</mml:mi><mml:mi mathvariant="bold-italic">r</mml:mi><mml:mi mathvariant="bold-italic">e</mml:mi></mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">c</mml:mi><mml:mrow><mml:mi mathvariant="bold-italic">n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
<th><inline-formula id="ieqn-103"><mml:math id="mml-ieqn-103"><mml:mrow><mml:mi mathvariant="bold-italic">r</mml:mi><mml:mi mathvariant="bold-italic">e</mml:mi></mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">c</mml:mi><mml:mrow><mml:mi mathvariant="bold-italic">l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
<th><inline-formula id="ieqn-104"><mml:math id="mml-ieqn-104"><mml:mrow><mml:mi mathvariant="bold-italic">s</mml:mi><mml:mi mathvariant="bold-italic">p</mml:mi></mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">e</mml:mi><mml:mrow><mml:mi mathvariant="bold-italic">y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
<th><inline-formula id="ieqn-105"><mml:math id="mml-ieqn-105"><mml:msub><mml:mi mathvariant="bold-italic">F</mml:mi><mml:mrow><mml:mi mathvariant="bold-italic">s</mml:mi><mml:mi mathvariant="bold-italic">c</mml:mi><mml:mi mathvariant="bold-italic">o</mml:mi><mml:mi mathvariant="bold-italic">r</mml:mi><mml:mi mathvariant="bold-italic">e</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
</tr>
</thead>
<tbody>
<tr>
<td>AS</td>
<td>0.9918</td>
<td>0.988</td>
<td>0.9802</td>
<td>0.9958</td>
<td>0.9841</td>
</tr>
<tr>
<td>BR</td>
<td>0.9918</td>
<td>0.982</td>
<td>0.9859</td>
<td>0.9938</td>
<td>0.9839</td>
</tr>
<tr>
<td>CR</td>
<td>0.9928</td>
<td>0.9754</td>
<td>0.9932</td>
<td>0.9927</td>
<td>0.9842</td>
</tr>
<tr>
<td>HY</td>
<td>0.9969</td>
<td>1.0</td>
<td>0.988</td>
<td>1.0000</td>
<td>0.994</td>
</tr>
<tr>
<td>Average</td>
<td>0.9933</td>
<td>0.9864</td>
<td>0.9868</td>
<td>0.9956</td>
<td>0.9866</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The confusion matrix generated by the proposed ESFO-EALD approach on test dataset under run-3 is depicted in <xref ref-type="fig" rid="fig-6">Fig. 6</xref>. It is observed that ESFO-EALD system categorized 497 images under AS, 490 images under BR, 437 images under CR, and 498 images under HY.</p>
<fig id="fig-6">
<label>Figure 6</label>
<caption>
<title>Confusion matrix of ESFO-EALD method on run-3</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_25280-fig-6.png"/>
</fig>
<p><xref ref-type="table" rid="table-3">Tab. 3</xref> provides a brief overview of results from classification analysis accomplished by ESFO-EALD method on test run-3. The outcomes show that ESFO-EALD algorithm categorized the instances under AS class with <inline-formula id="ieqn-127"><mml:math id="mml-ieqn-127"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-128"><mml:math id="mml-ieqn-128"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-129"><mml:math id="mml-ieqn-129"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:math></inline-formula> and <inline-formula id="ieqn-130"><mml:math id="mml-ieqn-130"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> scores such as 0.9933, 0.9881, 0.9861, 0.9958, and 0.9871 respectively. At the same time, the results demonstrate that ESFO-EALD manner classified the instances under BR class with <inline-formula id="ieqn-131"><mml:math id="mml-ieqn-131"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-132"><mml:math id="mml-ieqn-132"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-133"><mml:math id="mml-ieqn-133"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:math></inline-formula> and <inline-formula id="ieqn-134"><mml:math id="mml-ieqn-134"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> values such as 0.9928, 0.9859, 0.9859, 0.9952, and 0.9859 correspondingly. Likewise, the results demonstrate that ESFO-EALD approach placed the instances under CR class with <inline-formula id="ieqn-135"><mml:math id="mml-ieqn-135"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-136"><mml:math id="mml-ieqn-136"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-137"><mml:math id="mml-ieqn-137"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:math></inline-formula> and <inline-formula id="ieqn-138"><mml:math id="mml-ieqn-138"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> values such as 0.9943, 0.982, 0.9932, 0.9947, and 0.9876 correspondingly. Eventually, the results demonstrate that ESFO-EALD method identified the instances under HY class with <inline-formula id="ieqn-139"><mml:math id="mml-ieqn-139"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-140"><mml:math id="mml-ieqn-140"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-141"><mml:math id="mml-ieqn-141"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:math></inline-formula> and <inline-formula id="ieqn-142"><mml:math id="mml-ieqn-142"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> values such as 0.9979, 1.0, 0.992, 1.0, and 0.996 respectively.</p>
<table-wrap id="table-3">
<label>Table 3</label>
<caption>
<title>Classification analysis results of ESFO-EALD technique on run-3</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>Class</th>
<th><inline-formula id="ieqn-122"><mml:math id="mml-ieqn-122"><mml:mrow><mml:mi mathvariant="bold-italic">a</mml:mi><mml:mi mathvariant="bold-italic">c</mml:mi></mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">c</mml:mi><mml:mrow><mml:mi mathvariant="bold-italic">y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
<th><inline-formula id="ieqn-123"><mml:math id="mml-ieqn-123"><mml:mrow><mml:mi mathvariant="bold-italic">p</mml:mi><mml:mi mathvariant="bold-italic">r</mml:mi><mml:mi mathvariant="bold-italic">e</mml:mi></mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">c</mml:mi><mml:mrow><mml:mi mathvariant="bold-italic">n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
<th><inline-formula id="ieqn-124"><mml:math id="mml-ieqn-124"><mml:mrow><mml:mi mathvariant="bold-italic">r</mml:mi><mml:mi mathvariant="bold-italic">e</mml:mi></mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">c</mml:mi><mml:mrow><mml:mi mathvariant="bold-italic">l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
<th><inline-formula id="ieqn-125"><mml:math id="mml-ieqn-125"><mml:mrow><mml:mi mathvariant="bold-italic">s</mml:mi><mml:mi mathvariant="bold-italic">p</mml:mi></mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">e</mml:mi><mml:mrow><mml:mi mathvariant="bold-italic">y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
<th><inline-formula id="ieqn-126"><mml:math id="mml-ieqn-126"><mml:msub><mml:mi mathvariant="bold-italic">F</mml:mi><mml:mrow><mml:mi mathvariant="bold-italic">s</mml:mi><mml:mi mathvariant="bold-italic">c</mml:mi><mml:mi mathvariant="bold-italic">o</mml:mi><mml:mi mathvariant="bold-italic">r</mml:mi><mml:mi mathvariant="bold-italic">e</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
</tr>
</thead>
<tbody>
<tr>
<td>AS</td>
<td>0.9933</td>
<td>0.9881</td>
<td>0.9861</td>
<td>0.9958</td>
<td>0.9871</td>
</tr>
<tr>
<td>BR</td>
<td>0.9928</td>
<td>0.9859</td>
<td>0.9859</td>
<td>0.9952</td>
<td>0.9859</td>
</tr>
<tr>
<td>CR</td>
<td>0.9943</td>
<td>0.982</td>
<td>0.9932</td>
<td>0.9947</td>
<td>0.9876</td>
</tr>
<tr>
<td>HY</td>
<td>0.9979</td>
<td>1.0</td>
<td>0.992</td>
<td>1.0000</td>
<td>0.996</td>
</tr>
<tr>
<td>Average</td>
<td>0.9946</td>
<td>0.989</td>
<td>0.9893</td>
<td>0.9964</td>
<td>0.9891</td>
</tr>
</tbody>
</table>
</table-wrap>
<p><xref ref-type="fig" rid="fig-7">Fig. 7</xref> shows the results of accuracy analysis achieved by ESFO-EALD technique under different number of epochs. The figure exposes that the proposed ESFO-EALD system improved both training and validation accuracies with increase in the number of epochs.</p>
<fig id="fig-7">
<label>Figure 7</label>
<caption>
<title>Accuracy graph analysis results of ESFO-EALD technique</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_25280-fig-7.png"/>
</fig>
<p><xref ref-type="fig" rid="fig-8">Fig. 8</xref> portrays the loss analysis results accomplished by ESFO-EALD manner under distinct number of epochs. The figure reveals that ESFO-EALD method gained low training and validation accuracies with increasing number of epochs. <xref ref-type="table" rid="table-4">Tab. 4</xref> demonstrates the results accomplished by ESFO-EALD algorithm in memory space and training time analysis.</p>
<fig id="fig-8">
<label>Figure 8</label>
<caption>
<title>Loss graph analysis of ESFO-EALD technique</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_25280-fig-8.png"/>
</fig>
<table-wrap id="table-4">
<label>Table 4</label>
<caption>
<title>Comparative analysis results of ESFO-EALD approach in terms of memory space and training time</title>
</caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th>Methods</th>
<th>Space (MB)</th>
<th>Time (min)</th>
</tr>
</thead>
<tbody>
<tr>
<td>AlexNet</td>
<td>3368.96</td>
<td>33.06</td>
</tr>
<tr>
<td>GoogLeNet</td>
<td>4433.92</td>
<td>34.80</td>
</tr>
<tr>
<td>VGGNet-16</td>
<td>8908.80</td>
<td>145.98</td>
</tr>
<tr>
<td>ResNet-20</td>
<td>12288.00</td>
<td>163.02</td>
</tr>
<tr>
<td>DCNN</td>
<td>2897.92</td>
<td>34.74</td>
</tr>
<tr>
<td>AIE-ALDC</td>
<td>2621.44</td>
<td>31.08</td>
</tr>
<tr>
<td>ESFO-EALD</td>
<td>2138.21</td>
<td>28.65</td>
</tr>
</tbody>
</table>
</table-wrap>
<p><xref ref-type="fig" rid="fig-9">Fig. 9</xref> demonstrates the results achieved by ESFO-EALD system against other methods in terms of memory space analysis. The results show that visual geometry group (VGGNet)-16 and ResNet-16 models accomplished heavy memory spaces such as 8908.80 and 12288.00 MB respectively. In line with these, both AlexNet and GoogleNet approaches obtained somewhat reduced memory space of 3368.96 and 4433.92 MB respectively. Moreover, DCNN and AI-enabled Apple Leaf Disease Classification (AIE-ALDC) techniques gained considerable memory spaces such as 2897.92 and 2621.44 MB respectively. However, the presented ESFO-EALD technique gained the least memory space of 2138.21 MB.</p>
<fig id="fig-9">
<label>Figure 9</label>
<caption>
<title>Memory space analysis results of ESFO-EALD approach</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_25280-fig-9.png"/>
</fig>
<p><xref ref-type="fig" rid="fig-10">Fig. 10</xref> shows the results of training time analysis accomplished by ESFO-EALD method against other systems. The outcomes depict that both VGGNet-16 and ResNet-16 approaches took lengthy training times such as 145.98 and 163.02 min correspondingly. Also, GoogleNet and DCNN systems obtained somewhat reduced training times such as 34.80 and 34.74 min correspondingly. Afterward, AlexNet and AIE-ALDC methods took considerable training times such as 33.06 and 31.08 min correspondingly. However, the presented ESFO-EALD technique consumed a minimum training time of 28.65 min.</p>
<fig id="fig-10">
<label>Figure 10</label>
<caption>
<title>Training time analysis results of ESFO-EALD method</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_25280-fig-10.png"/>
</fig>
<p>Finally, a detailed comparative <inline-formula id="ieqn-143"><mml:math id="mml-ieqn-143"><mml:mrow><mml:mi mathvariant="bold-italic">a</mml:mi><mml:mi mathvariant="bold-italic">c</mml:mi></mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">c</mml:mi><mml:mrow><mml:mi mathvariant="bold-italic">y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> analysis was conducted between ESFO-EALD technique and other recent techniques and the results are shown in <xref ref-type="table" rid="table-5">Tab. 5</xref> and <xref ref-type="fig" rid="fig-11">Fig. 11</xref> [<xref ref-type="bibr" rid="ref-22">22</xref>]. The results show that both RNet-101 and RNet-50 models obtained the least <inline-formula id="ieqn-144"><mml:math id="mml-ieqn-144"><mml:mrow><mml:mi mathvariant="bold-italic">a</mml:mi><mml:mi mathvariant="bold-italic">c</mml:mi></mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">c</mml:mi><mml:mrow><mml:mi mathvariant="bold-italic">y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> values namely, 91.16% and 92.43%. At the same time, slightly improved <inline-formula id="ieqn-145"><mml:math id="mml-ieqn-145"><mml:mrow><mml:mi mathvariant="bold-italic">a</mml:mi><mml:mi mathvariant="bold-italic">c</mml:mi></mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">c</mml:mi><mml:mrow><mml:mi mathvariant="bold-italic">y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> values such as 93.17% and 93.64% were obtained by RNet-34 and RNet-18 models. Moreover, the improved CNN (ICNN) and AIE-ALDC techniques accomplished reasonable <inline-formula id="ieqn-146"><mml:math id="mml-ieqn-146"><mml:mrow><mml:mi mathvariant="bold-italic">a</mml:mi><mml:mi mathvariant="bold-italic">c</mml:mi></mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">c</mml:mi><mml:mrow><mml:mi mathvariant="bold-italic">y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> values such as 97.14% and 99.20% respectively. However, the proposed ESFO-EALD technique surpassed all other techniques and achieved a maximum <inline-formula id="ieqn-147"><mml:math id="mml-ieqn-147"><mml:mrow><mml:mi mathvariant="bold-italic">a</mml:mi><mml:mi mathvariant="bold-italic">c</mml:mi></mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">c</mml:mi><mml:mrow><mml:mi mathvariant="bold-italic">y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 99.39%. The above mentioned tables and figures establish that ESFO-EALD technique is an excellent performer in both detection and classification of apple plant leaf images.</p>
<table-wrap id="table-5">
<label>Table 5</label>
<caption>
<title>Comparative analysis results of ESFO-EALD method in terms of accuracy</title>
</caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th>Methods</th>
<th><inline-formula id="ieqn-148"><mml:math id="mml-ieqn-148"><mml:mrow><mml:mi mathvariant="bold-italic">A</mml:mi><mml:mi mathvariant="bold-italic">c</mml:mi></mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">c</mml:mi><mml:mrow><mml:mi mathvariant="bold-italic">y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> (%)</th>
</tr>
</thead>
<tbody>
<tr>
<td>RNet-101 model</td>
<td>91.16</td>
</tr>
<tr>
<td>RNet-50 model</td>
<td>92.43</td>
</tr>
<tr>
<td>RNet-34 model</td>
<td>93.17</td>
</tr>
<tr>
<td>RNet-18 model</td>
<td>93.64</td>
</tr>
<tr>
<td>ICNN</td>
<td>97.14</td>
</tr>
<tr>
<td>AIE-ALDC</td>
<td>99.20</td>
</tr>
<tr>
<td>ESFO-EALD</td>
<td>99.39</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="fig-11">
<label>Figure 11</label>
<caption>
<title>Comparative analysis results of ESFO-EALD method in terms of accuracy</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_25280-fig-11.png"/>
</fig>
</sec>
<sec id="s4">
<label>4</label>
<title>Conclusion</title>
<p>In this study, an effective ESFO-EALD technique is developed for identification and classification of apple plant leaf images. The proposed ESFO-EALD approach includes MF-based preprocessing, ESFO with Kapur&#x2019;s entropy-based segmentation, EfficientNet-based Feature extraction, Adam optimizer-based hyperparameter tuning, and SNN-based classification. The utilization of SFO-based threshold value selection and Adam optimizer-based hyperparameter selection helps in accomplishing enhanced outcomes. A wide range of simulations was conducted to validate the effective outcomes of ESFO-EALD technique on benchmark dataset. The results showcased the betterment of ESFO-EALD technique over recent state-of-the-art approaches. So, it can be concluded that ESFO-EALD technique can be utilized as a proficient tool in detection of plant diseases. In future, the detection performance can be boosted using advanced DL approaches.</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 under grant number (RGP 2/209/42).</p>
</fn>
<fn fn-type="other"><p>Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2022R191), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.</p>
</fn>
<fn fn-type="conflict"><p><bold>Conflicts of Interest:</bold> The authors declare that they have no conflicts of interest to report regarding the present study.</p>
</fn>
</fn-group>
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