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<front>
<journal-meta>
<journal-id journal-id-type="pmc">CSSE</journal-id>
<journal-id journal-id-type="nlm-ta">CSSE</journal-id>
<journal-id journal-id-type="publisher-id">CSSE</journal-id>
<journal-title-group>
<journal-title>Computer Systems Science &#x0026; Engineering</journal-title>
</journal-title-group>
<issn pub-type="ppub">0267-6192</issn>
<publisher>
<publisher-name>Tech Science Press</publisher-name>
<publisher-loc>USA</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">36296</article-id>
<article-id pub-id-type="doi">10.32604/csse.2023.036296</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Harris Hawks Optimizer with Graph Convolutional Network Based Weed Detection in Precision Agriculture</article-title><alt-title alt-title-type="left-running-head">Harris Hawks Optimizer with Graph Convolutional Network Based Weed Detection in Precision Agriculture</alt-title><alt-title alt-title-type="right-running-head">Harris Hawks Optimizer with Graph Convolutional Network Based Weed Detection in Precision Agriculture</alt-title>
</title-group>
<contrib-group>
<contrib id="author-1" contrib-type="author">
<name name-style="western"><surname>Yonbawi</surname><given-names>Saud</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>Alahmari</surname><given-names>Sultan</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>Satyanarayana Murthy</surname><given-names>T.</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>Maddala</surname><given-names>Padmakar</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>Laxmi Lydia</surname><given-names>E.</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>Kadry</surname><given-names>Seifedine</given-names></name>
<xref ref-type="aff" rid="aff-6">6</xref>
<xref ref-type="aff" rid="aff-7">7</xref>
<xref ref-type="aff" rid="aff-8">8</xref><email>skadry@gmail.com</email>
</contrib>
<contrib id="author-7" contrib-type="author">
<name name-style="western"><surname>Kim</surname><given-names>Jungeun</given-names></name>
<xref ref-type="aff" rid="aff-9">9</xref>
</contrib>
<aff id="aff-1"><label>1</label><institution>Department of Software Engineering, College of Computer Science and Engineering, University of Jeddah</institution>, <addr-line>Jeddah</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-2"><label>2</label><institution>King Abdul Aziz City for Science and Technology</institution>, <addr-line>Riyadh</addr-line>, <country>Kingdom of Saudi Arabia</country></aff>
<aff id="aff-3"><label>3</label><institution>Chaitanya Bharathi Institute of Technology</institution>, <addr-line>Hyderabad, Telangana</addr-line>, <country>India</country></aff>
<aff id="aff-4"><label>4</label><institution>Department of Civil Engineering, Vignan&#x2019;s Institute of Information and Technology (A)</institution>, <addr-line>Duvvada, Visakhapatnam, AP, 530049</addr-line>, <country>India</country></aff>
<aff id="aff-5"><label>5</label><institution>Department of Computer Science and Engineering, Vignan&#x2019;s Institute of Information Technology</institution>, <addr-line>Visakhapatnam, 530049</addr-line>, <country>India</country></aff>
<aff id="aff-6"><label>6</label><institution>Department of Applied Data Science, Noroff University College</institution>, <addr-line>Kristiansand</addr-line>, <country>Norway</country></aff>
<aff id="aff-7"><label>7</label><institution>Artificial Intelligence Research Center (AIRC), College of Engineering and Information Technology, Ajman University</institution>, <addr-line>Ajman</addr-line>, <country>United Arab Emirates</country></aff>
<aff id="aff-8"><label>8</label><institution>Department of Electrical and Computer Engineering, Lebanese American University</institution>, <addr-line>Byblos</addr-line>, <country>Lebanon</country></aff>
<aff id="aff-9"><label>9</label><institution>Department of Software, Kongju National University</institution>, <addr-line>Cheonan, 31080</addr-line>, <country>Korea</country></aff>
</contrib-group><author-notes><corresp id="cor1"><label>&#x002A;</label>Corresponding Author: Seifedine Kadry. Email: <email>skadry@gmail.com</email></corresp></author-notes>
<pub-date date-type="collection" publication-format="electronic">
<year>2023</year></pub-date>
<pub-date date-type="pub" publication-format="electronic"><day>6</day>
<month>2</month>
<year>2023</year></pub-date>
<volume>46</volume>
<issue>2</issue>
<fpage>1533</fpage>
<lpage>1547</lpage>
<history>
<date date-type="received"><day>24</day><month>9</month><year>2022</year></date>
<date date-type="accepted"><day>21</day><month>11</month><year>2022</year></date>
</history>
<permissions>
<copyright-statement>&#x00A9; 2023 Yonbawi et al.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Yonbawi et al.</copyright-holder>
<license xlink:href="https://creativecommons.org/licenses/by/4.0/">
<license-p>This work is licensed under a <ext-link ext-link-type="uri" xlink:type="simple" xlink:href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International License</ext-link>, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</license-p>
</license>
</permissions>
<self-uri content-type="pdf" xlink:href="TSP_CSSE_36296.pdf"></self-uri>
<abstract>
<p>Precision agriculture includes the optimum and adequate use of resources depending on several variables that govern crop yield. Precision agriculture offers a novel solution utilizing a systematic technique for current agricultural problems like balancing production and environmental concerns. Weed control has become one of the significant problems in the agricultural sector. In traditional weed control, the entire field is treated uniformly by spraying the soil, a single herbicide dose, weed, and crops in the same way. For more precise farming, robots could accomplish targeted weed treatment if they could specifically find the location of the dispensable plant and identify the weed type. This may lessen by large margin utilization of agrochemicals on agricultural fields and favour sustainable agriculture. This study presents a Harris Hawks Optimizer with Graph Convolutional Network based Weed Detection (HHOGCN-WD) technique for Precision Agriculture. The HHOGCN-WD technique mainly focuses on identifying and classifying weeds for precision agriculture. For image pre-processing, the HHOGCN-WD model utilizes a bilateral normal filter (BNF) for noise removal. In addition, coupled convolutional neural network (CCNet) model is utilized to derive a set of feature vectors. To detect and classify weed, the GCN model is utilized with the HHO algorithm as a hyperparameter optimizer to improve the detection performance. The experimental results of the HHOGCN-WD technique are investigated under the benchmark dataset. The results indicate the promising performance of the presented HHOGCN-WD model over other recent approaches, with increased accuracy of 99.13&#x0025;.</p>
</abstract>
<kwd-group kwd-group-type="author">
<kwd>Weed detection</kwd>
<kwd>precision agriculture</kwd>
<kwd>graph convolutional network</kwd>
<kwd>harris hawks optimizer</kwd>
<kwd>hyperparameter tuning</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1">
<label>1</label>
<title>Introduction</title>
<p>Weeds are unwanted plants that grow in fields and compete with crops for light, water, space, and nutrients. If uncontrollable, they might have many adverse impacts like loss of crop yields, contamination of grain during harvesting, and production of a considerable amount of seeds, thus forming a weed seed bank in the fields [<xref ref-type="bibr" rid="ref-1">1</xref>]. Conventionally, weed management program involves the control of weeds via mechanical or chemical resources, namely the uniform application of herbicides all over the fields [<xref ref-type="bibr" rid="ref-2">2</xref>]. But, the spatial density of weeds isn&#x2019;t uniform throughout the fields, thus resulting in the overuse of chemicals that lead to the evolution of herbicide-resistant weeds and environmental concerns. A site-specific weed management (SSWM) concept that represents detecting weed patches and removal or spot spraying by mechanical resources was introduced to resolve these shortcomings in the early 90s [<xref ref-type="bibr" rid="ref-3">3</xref>]. Earlier control of Weeds in the season is crucial because the weed will compete with the crop yields for the resource in the development phase of the crops, which leads to potential yield loss [<xref ref-type="bibr" rid="ref-4">4</xref>&#x2013;<xref ref-type="bibr" rid="ref-6">6</xref>]. A considerable study has developed specific variable spraying methods to prevent waste and herbicide residual difficulties caused by conventional full-coverage spraying [<xref ref-type="bibr" rid="ref-7">7</xref>]. To accomplish accurate variable spraying, a major problem must be resolved in real-time accurate identification and detection of weeds and crops. Approaches to realizing the weed detection field through the computer vision (CV) technique primarily involve deep learning (DL) and conventional image processing [<xref ref-type="bibr" rid="ref-8">8</xref>]. While the detection of weeds is carried out with conventional image-processing techniques, extracting features, like shape, color, and texture, of the image and combining with conventional machine learning (ML) approaches like Support Vector Machine (SVM) or random forest (RF) approach, for the detection of weeds are needed [<xref ref-type="bibr" rid="ref-9">9</xref>]. Such techniques should have high dependence and design features manually on the quality of feature extraction, pre-processing methods, and image acquisition methods. With the increase in data volume and the advancement in computing power, the DL algorithm could extract multi-dimensional and multi-scale spatial semantic features of weed via Convolution Neural Network (CNN) because of their improved data expression abilities for images, which avoids the disadvantage of conventional extraction method [<xref ref-type="bibr" rid="ref-10">10</xref>]. Consequently, they have gained considerable interest among the researcher workers.</p>
<p>Ukaegbu et al. [<xref ref-type="bibr" rid="ref-11">11</xref>] define the advancement of a modular unmanned aerial vehicle (UAV) to eradicate and detect weeds on farmland. Precision agriculture involves resolving the issue of poor agricultural yield because of competition for nutrients by weeds and offers a rapid method to eliminate the difficult weeds utilizing developing technologies. This work has solved the mentioned problem. A quadcopter has been built, and lightweight resources accumulate elements. The system has a lithium polymer (li-po) battery, electric motor, propellers, receiver, flight controller, electronic speed controller, GPS, and frame. In [<xref ref-type="bibr" rid="ref-12">12</xref>], a DL mechanism can be advanced to find crops and weeds in croplands. The advanced system has been enforced and assessed by high-resolution UAV images captured on 2 different target fields: strawberry and pea; the advanced system can find weeds. In [<xref ref-type="bibr" rid="ref-13">13</xref>], a method can be advanced for accelerating the manual labelling of pixels utilizing a 2-step process. Firstly, the foreground and background were divided by maximum likelihood classification; secondly, the weed pixels were labelled manually. These labelled data were utilized for training semantic segmentation techniques that classify crop and background pixels into one class and other vegetation into the second class.</p>
<p>Osorio et al. [<xref ref-type="bibr" rid="ref-14">14</xref>] devise 3 techniques for weed estimation related to DL image processing in lettuce crops and a comparison made to visual assessments by professionals. One technique depended on SVM utilizing histograms of oriented gradients (HOG) as feature descriptors. The second one depends on YOLOV3 (you only look once at V3), using its robust structure for object detection. The last method relies upon Mask R-CNN (region-oriented CNN) to receive an instance segmentation for every individual. Such techniques are supplemented with a normalized difference vegetation index (NDVI) index (normal difference vegetation indexes) as a background sub-tractor to remove non-photosynthetic objects. In [<xref ref-type="bibr" rid="ref-15">15</xref>], a novel technique that integrates high-resolution RGB and low-resolution MS imageries is presented for detecting Gramineae weed in rice fields with plants 50 days afterwards emergence. The images were taken from a UAV. The presented technique will combine the texture data offered by high-resolution RGB imagery and the reflectance data presented by low-resolution MS imagery to obtain an integrated RGB-MS image with superior weed-discriminating features. After scrutinizing the normalized green-red difference index (NGRDI) and NDVI for detecting weeds, it is noted that NGRDI provides superior features.</p>
<p>This study presents a Harris Hawks Optimizer with Graph Convolutional Network based Weed Detection (HHOGCN-WD) technique for Precision Agriculture. The presented HHOGCN-WD technique mainly focuses on identifying and classifying weeds for precision agriculture. For image pre-processing, the HHOGCN-WD model utilizes a normal bilateral filter (BNF) for noise removal. In addition, coupled convolutional neural network (CCNet) model is utilized to derive a set of feature vectors. To detect and classify weed, the GCN model is utilized with the HHO algorithm as a hyperparameter optimizer to improve the detection performance. The experimental results of the HHOGCN-WD technique are investigated under the benchmark dataset.</p>
</sec>
<sec id="s2">
<label>2</label>
<title>The Proposed Model</title>
<p>This study developed a new HHOGCN-WD technique for weed detection and classification for Precision Agriculture. The presented HHOGCN-WD technique mainly focuses on identifying and classifying weeds for precision agriculture. <xref ref-type="fig" rid="fig-1">Fig. 1</xref> depicts the overall block diagram of the HHOGCN-WD approach.</p>
<fig id="fig-1">
<label>Figure 1</label>
<caption>
<title>Overall block diagram of HHOGCN-WD approach</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_36296-fig-1.tif"/>
</fig>
<sec id="s2_1">
<label>2.1</label>
<title>Image Pre-Processing</title>
<p>For image pre-processing, the HHOGCN-WD model utilizes BNF for noise removal. The BNF technique is a two-stage process that upgrades normal Niter time and later upgrades vertices Viter times [<xref ref-type="bibr" rid="ref-16">16</xref>]. The procedure of denoising process with the BNF is denoted by (update normal)<inline-formula id="ieqn-1">
<mml:math id="mml-ieqn-1"><mml:msup><mml:mtext>&#x00A0;</mml:mtext><mml:mrow><mml:mi>N</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi></mml:mrow></mml:msup><mml:mtext>&#xA0;</mml:mtext><mml:mo>+</mml:mo></mml:math>
</inline-formula> (update vertices)<inline-formula id="ieqn-2">
<mml:math id="mml-ieqn-2"><mml:msup><mml:mtext>&#x00A0;</mml:mtext><mml:mrow><mml:mi>V</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi></mml:mrow></mml:msup></mml:math>
</inline-formula>. The BNF upgrades the normal vector through the weighted average of the noisy neighbourhood normal vector in the following [<xref ref-type="bibr" rid="ref-16">16</xref>]:
<disp-formula id="eqn-1"><label>(1)</label>
<mml:math id="mml-eqn-1" display="block"><mml:msub><mml:mrow><mml:mover><mml:mi>n</mml:mi><mml:mo stretchy="false">&#x007E;</mml:mo></mml:mover></mml:mrow><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:msubsup><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mi>j</mml:mi><mml:mi>&#x03F5;</mml:mi><mml:msub><mml:mi>&#x03D5;</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow><mml:mtext>&#x00A0;</mml:mtext></mml:msubsup><mml:mo>&#x2061;</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:msub><mml:mi>W</mml:mi><mml:mi>C</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo></mml:mrow><mml:mi>c</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mtext>&#x00A0;</mml:mtext></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>c</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mrow><mml:mtext>&#x00A0;</mml:mtext></mml:mrow><mml:msub><mml:mi>&#x03C3;</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi>S</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo></mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mrow><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mrow><mml:mtext>&#x00A0;</mml:mtext></mml:mrow><mml:msub><mml:mi>&#x03C3;</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mstyle></mml:math>
</disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-1">Eq. (1)</xref>, <inline-formula id="ieqn-3">
<mml:math id="mml-ieqn-3"><mml:msub><mml:mi>K</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:math>
</inline-formula> denotes the normalization factor. <inline-formula id="ieqn-4">
<mml:math id="mml-ieqn-4"><mml:msub><mml:mi>&#x03C3;</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math>
</inline-formula> and <inline-formula id="ieqn-5">
<mml:math id="mml-ieqn-5"><mml:msub><mml:mi>&#x03C3;</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:math>
</inline-formula> control the kernel width of Gaussian function <inline-formula id="ieqn-6">
<mml:math id="mml-ieqn-6"><mml:msub><mml:mi>W</mml:mi><mml:mi>C</mml:mi></mml:msub></mml:math>
</inline-formula> and <inline-formula id="ieqn-7">
<mml:math id="mml-ieqn-7"><mml:msub><mml:mi>W</mml:mi><mml:mi>S</mml:mi></mml:msub></mml:math>
</inline-formula>, correspondingly [<xref ref-type="bibr" rid="ref-16">16</xref>],
<disp-formula id="eqn-2"><label>(2)</label>
<mml:math id="mml-eqn-2" display="block"><mml:msub><mml:mi>W</mml:mi><mml:mi>C</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo></mml:mrow><mml:mi>c</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>c</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mrow><mml:mtext>&#x00A0;</mml:mtext></mml:mrow><mml:msub><mml:mi>&#x03C3;</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mtext>&#x00A0;</mml:mtext><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">x</mml:mi><mml:mi mathvariant="normal">p</mml:mi><mml:mtext>&#x00A0;</mml:mtext></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo></mml:mrow><mml:mi>c</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>c</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mrow><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:msubsup><mml:mi>&#x03C3;</mml:mi><mml:mi>c</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext></mml:math>
</disp-formula>
<disp-formula id="eqn-3"><label>(3)</label>
<mml:math id="mml-eqn-3" display="block"><mml:msub><mml:mi>W</mml:mi><mml:mi>S</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo></mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mrow><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mrow><mml:mtext>&#x00A0;</mml:mtext></mml:mrow><mml:msub><mml:mi>&#x03C3;</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mtext>&#x00A0;</mml:mtext><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">x</mml:mi><mml:mi mathvariant="normal">p</mml:mi><mml:mtext>&#x00A0;</mml:mtext></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo></mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:msup><mml:mrow><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:msubsup><mml:mi>&#x03C3;</mml:mi><mml:mi>s</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>.</mml:mo></mml:math>
</disp-formula></p>
<p>Function <inline-formula id="ieqn-8">
<mml:math id="mml-ieqn-8"><mml:msub><mml:mi>W</mml:mi><mml:mi>C</mml:mi></mml:msub></mml:math>
</inline-formula> provides a smaller weight while the distance between the geometric center (the centroids) of <inline-formula id="ieqn-9">
<mml:math id="mml-ieqn-9"><mml:mtext>&#x00A0;</mml:mtext><mml:msub><mml:mi>f</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:math>
</inline-formula> and the adjacent face is larger. Function <inline-formula id="ieqn-10">
<mml:math id="mml-ieqn-10"><mml:msub><mml:mi>W</mml:mi><mml:mi>S</mml:mi></mml:msub></mml:math>
</inline-formula> provides additional weight as a similarity between neighbouring normal and <inline-formula id="ieqn-11">
<mml:math id="mml-ieqn-11"><mml:msub><mml:mi>n</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:math>
</inline-formula> rises.</p>
</sec>
<sec id="s2_2">
<label>2.2</label>
<title>Feature Extraction: CCNet Model</title>
<p>The CCNet model is utilized at this stage to derive a set of feature vectors. It is well-known that CNN has established impressive abilities in image processing. Likewise, numerous CNN and derivative has been proposed for capturing the neighbourhood spatial feature from the image in weed classification [<xref ref-type="bibr" rid="ref-17">17</xref>]. The discriminatory feature allows discrimination against targeted regions in complicated scenes.</p>
<p>It is noted that the input dataset <inline-formula id="ieqn-12">
<mml:math id="mml-ieqn-12"><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mtext>&#x00A0;</mml:mtext></mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi>H</mml:mi></mml:msub><mml:mrow><mml:mtext>&#x00A0;</mml:mtext></mml:mrow><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mrow><mml:mtext>&#x00A0;</mml:mtext></mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi>L</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> is initially transported to the adjacency patch sampler that samples and produces a sequence of adjacency patches (3D spectral cubes <inline-formula id="ieqn-13">
<mml:math id="mml-ieqn-13"><mml:msub><mml:mi>P</mml:mi><mml:mi>H</mml:mi></mml:msub><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mi>p</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>p</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>D</mml:mi></mml:mrow></mml:msup></mml:math>
</inline-formula> or 2D elevation path <inline-formula id="ieqn-14">
<mml:math id="mml-ieqn-14"><mml:msub><mml:mi>P</mml:mi><mml:mi>L</mml:mi></mml:msub><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mi>p</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>p</mml:mi></mml:mrow></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:math>
</inline-formula> from the novel dataset based on the provided neighborhood size <inline-formula id="ieqn-15">
<mml:math id="mml-ieqn-15"><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>p</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>p</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula>. Then, they are fed into the respective CNN module for representation learning or feature extraction. Especially the model primarily comprises two nearly similar CNN architectures for LiDAR and HS datasets, correspondingly. The input to the CNN at the top of the figure is <inline-formula id="ieqn-16">
<mml:math id="mml-ieqn-16"><mml:msub><mml:mi>P</mml:mi><mml:mi>H</mml:mi></mml:msub></mml:math>
</inline-formula> extracted from the hyperspectral images, whereas the input to the CNN at the bottom is <inline-formula id="ieqn-17">
<mml:math id="mml-ieqn-17"><mml:msub><mml:mi>P</mml:mi><mml:mi>L</mml:mi></mml:msub></mml:math>
</inline-formula> extracted from the LiDAR images. It should be noticeable that the two used CNN network contains 4 convolution blocks. Those blocks have the same architecture comprising nonlinear activation, convolution, batch normalization (BN), and MaxPooling layers. For all the CNN networks, the amount of convolution kernels in four convolution layers is 32, 64, 128, and 128, correspondingly. The initial 3 convolution layer uses a size of <inline-formula id="ieqn-18">
<mml:math id="mml-ieqn-18"><mml:mn>3</mml:mn><mml:mspace width="thinmathspace" /><mml:mo>&#x00D7;</mml:mo><mml:mspace width="thinmathspace" /><mml:mn>3</mml:mn><mml:mrow><mml:mtext>&#x00A0;</mml:mtext></mml:mrow></mml:math>
</inline-formula> convolution kernel, and the final layer is <inline-formula id="ieqn-19">
<mml:math id="mml-ieqn-19"><mml:mn>1</mml:mn><mml:mspace width="thinmathspace" /><mml:mo>&#x00D7;</mml:mo><mml:mspace width="thinmathspace" /><mml:mn>1</mml:mn></mml:math>
</inline-formula>. <inline-formula id="ieqn-20">
<mml:math id="mml-ieqn-20"><mml:msub><mml:mi>C</mml:mi><mml:mi>H</mml:mi></mml:msub><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mi>N</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mn>128</mml:mn></mml:mrow></mml:msup></mml:math>
</inline-formula> and <inline-formula id="ieqn-21">
<mml:math id="mml-ieqn-21"><mml:msub><mml:mi>C</mml:mi><mml:mi>L</mml:mi></mml:msub><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mi>N</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mn>128</mml:mn></mml:mrow></mml:msup></mml:math>
</inline-formula> represent the short-range spatial feature extracted from the CNN on LiDAR and HS dataset, correspondingly.</p>
<p>Because of the weight-sharing module, the two CNN networks share the parameter and setting of the additional 3 convolution layers, excluding the initial convolution layer. It has the apparent advantage of a larger reduction in several major variables. Then, the convolutional operation rule of the two CNN models is shown below:<disp-formula id="eqn-4"><label>(4)</label>
<mml:math id="mml-eqn-4" display="block"><mml:msubsup><mml:mi>H</mml:mi><mml:mi>j</mml:mi><mml:mrow><mml:mi>l</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msubsup><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mi>m</mml:mi><mml:mtext>&#x00A0;</mml:mtext></mml:msubsup><mml:mo>&#x2061;</mml:mo><mml:msubsup><mml:mi>H</mml:mi><mml:mi>m</mml:mi><mml:mi>l</mml:mi></mml:msubsup><mml:msubsup><mml:mi>W</mml:mi><mml:mrow><mml:mi>j</mml:mi><mml:mo>,</mml:mo><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>l</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mi>b</mml:mi><mml:mrow><mml:mi>j</mml:mi><mml:mo>,</mml:mo><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>l</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>.</mml:mo></mml:math>
</disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-4">Eq. (4)</xref>, <inline-formula id="ieqn-22">
<mml:math id="mml-ieqn-22"><mml:msubsup><mml:mi>H</mml:mi><mml:mi>m</mml:mi><mml:mi>l</mml:mi></mml:msubsup></mml:math>
</inline-formula> indicates the <inline-formula id="ieqn-23">
<mml:math id="mml-ieqn-23"><mml:mi>m</mml:mi><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math>
</inline-formula> feature maps at the <inline-formula id="ieqn-24">
<mml:math id="mml-ieqn-24"><mml:mi>l</mml:mi><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math>
</inline-formula> layers. <inline-formula id="ieqn-25">
<mml:math id="mml-ieqn-25"><mml:msubsup><mml:mi>W</mml:mi><mml:mrow><mml:mi>j</mml:mi><mml:mo>,</mml:mo><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>l</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:math>
</inline-formula> signifies the <inline-formula id="ieqn-26">
<mml:math id="mml-ieqn-26"><mml:mi>j</mml:mi><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math>
</inline-formula> convolutional kernel interconnected with the <inline-formula id="ieqn-27">
<mml:math id="mml-ieqn-27"><mml:mi>m</mml:mi><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math>
</inline-formula> feature map at <inline-formula id="ieqn-28">
<mml:math id="mml-ieqn-28"><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>l</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math>
</inline-formula> layers, and <inline-formula id="ieqn-29">
<mml:math id="mml-ieqn-29"><mml:msubsup><mml:mi>b</mml:mi><mml:mrow><mml:mi>j</mml:mi><mml:mo>,</mml:mo><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>l</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:math>
</inline-formula> indicates the corresponding bias. Now, <inline-formula id="ieqn-30">
<mml:math id="mml-ieqn-30"><mml:msup><mml:mi>H</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mi>H</mml:mi></mml:msub></mml:math>
</inline-formula> or <inline-formula id="ieqn-31">
<mml:math id="mml-ieqn-31"><mml:msub><mml:mi>P</mml:mi><mml:mi>L</mml:mi></mml:msub><mml:mo>.</mml:mo><mml:mspace width="thinmathspace" /><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mo>.</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> represents the nonlinear activation functions such as ReLU. The size of the sampled neighborhood could considerably affect the concluding classifier outcome.</p>
</sec>
<sec id="s2_3">
<label>2.3</label>
<title>Weed Detection Using GCN Model</title>
<p>This study utilises the GCN model to detect and classify weeds. Assume an input image <italic>I</italic>, the objective of multilabel image classifier is to evaluate a <italic>f</italic> function which forecasts the occurrence or not of label belonging to a set <inline-formula id="ieqn-32">
<mml:math id="mml-ieqn-32"><mml:mrow><mml:mi>&#x02112;</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mtext>&#x00A0;&#x00A0;</mml:mtext><mml:mi>N</mml:mi></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:math>
</inline-formula>, and it is formulated in the following [<xref ref-type="bibr" rid="ref-18">18</xref>],</p>
<p><disp-formula id="ueqn-1">
<mml:math id="mml-ueqn-1" display="block"><mml:mi>f</mml:mi><mml:mo>&#x003A;</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mi>w</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>h</mml:mi></mml:mrow></mml:msup><mml:mo stretchy="false">&#x2192;</mml:mo><mml:mo stretchy="false">[</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mn>1</mml:mn><mml:msup><mml:mo stretchy="false">]</mml:mo><mml:mi>N</mml:mi></mml:msup></mml:math>
</disp-formula></p>
<p><disp-formula id="ueqn-2">
<mml:math id="mml-ueqn-2" display="block"><mml:mi>I</mml:mi><mml:mo stretchy="false">&#x21A6;</mml:mo><mml:mi>y</mml:mi><mml:mo>=</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>&#x2208;</mml:mo><mml:mrow><mml:mi>&#x02112;</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext></mml:math>
</disp-formula></p>
<p>where <italic>w</italic> and <italic>h</italic> correspondingly represent the pixel-wise width and height of the image. Noted that <inline-formula id="ieqn-33">
<mml:math id="mml-ieqn-33"><mml:msub><mml:mi>y</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math>
</inline-formula> when the label <italic>i</italic> exists in <italic>I</italic> or <inline-formula id="ieqn-34">
<mml:math id="mml-ieqn-34"><mml:msub><mml:mi>y</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:math>
</inline-formula>. As deliberated in Section 1, graph-based multi-label models, namely IML-GCN and ML-GCN, comprise two subdivisions. The initial one depends on the out-off-shelf CNN models, which allow the extraction of discriminatory image representation. Especially, IML-GCN and ML-GCN integrate a TResNet-M and ResNet-101. The latter comprises an effective form of ResNet-50. The next branch depends on a specific GCN aim is to generate N inter-dependent binary classifications. Consider the input graph &#x003D; <inline-formula id="ieqn-35">
<mml:math id="mml-ieqn-35"><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mi>V</mml:mi><mml:mo>,</mml:mo><mml:mtext>&#x00A0;&#x00A0;</mml:mtext><mml:mi>E</mml:mi><mml:mo>,</mml:mo><mml:mtext>&#x00A0;&#x00A0;</mml:mtext><mml:mi>F</mml:mi></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:math>
</inline-formula>, with V &#x003D; <inline-formula id="ieqn-36">
<mml:math id="mml-ieqn-36"><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mtext>&#x00A0;&#x00A0;</mml:mtext><mml:msub><mml:mi>v</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mtext>&#x00A0;&#x00A0;</mml:mtext><mml:msub><mml:mi>v</mml:mi><mml:mi>N</mml:mi></mml:msub></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:math>
</inline-formula> the subset of vertices so that <inline-formula id="ieqn-37">
<mml:math id="mml-ieqn-37"><mml:msub><mml:mi>v</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:math>
</inline-formula> corresponding to the vertex related to the label, <inline-formula id="ieqn-38">
<mml:math id="mml-ieqn-38"><mml:mrow><mml:mi mathvariant="normal">E</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mtext>&#x00A0;&#x00A0;</mml:mtext><mml:msub><mml:mi>e</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mtext>&#x00A0;&#x00A0;</mml:mtext><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mtext>&#x00A0;&#x00A0;</mml:mtext><mml:msub><mml:mi>e</mml:mi><mml:mi>M</mml:mi></mml:msub></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:math>
</inline-formula> the subset generated using M edges interconnecting the vertices and <inline-formula id="ieqn-39">
<mml:math id="mml-ieqn-39"><mml:mrow><mml:mi mathvariant="normal">F</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mtext>&#x00A0;&#x00A0;</mml:mtext><mml:msub><mml:mi>f</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mtext>&#x00A0;&#x00A0;</mml:mtext><mml:msub><mml:mi>f</mml:mi><mml:mi>N</mml:mi></mml:msub></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:math>
</inline-formula> the vertex features so that <inline-formula id="ieqn-40">
<mml:math id="mml-ieqn-40"><mml:msub><mml:mi>f</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow></mml:mrow></mml:mrow><mml:mi>d</mml:mi></mml:msup></mml:math>
</inline-formula> characterizes the feature of vertex <italic>i</italic>. Consider <inline-formula id="ieqn-41">
<mml:math id="mml-ieqn-41"><mml:mi>A</mml:mi><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mi>N</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>N</mml:mi></mml:mrow></mml:msup></mml:math>
</inline-formula> as the neighborhood matrix defining the topology of the graph. A is evaluated by assuming the <inline-formula id="ieqn-42">
<mml:math id="mml-ieqn-42"><mml:mi>c</mml:mi><mml:mi>o</mml:mi></mml:math>
</inline-formula>-occurrence possibility of the label. Additionally, a threshold <inline-formula id="ieqn-43">
<mml:math id="mml-ieqn-43"><mml:mi>&#x03C4;</mml:mi></mml:math>
</inline-formula> is fixed and is utilized for ignoring rare <inline-formula id="ieqn-44">
<mml:math id="mml-ieqn-44"><mml:mi>c</mml:mi><mml:mi>o</mml:mi></mml:math>
</inline-formula>-occurrence that is regarded as noisy. For <inline-formula id="ieqn-45">
<mml:math id="mml-ieqn-45"><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mspace width="thinmathspace" /><mml:mi>j</mml:mi><mml:mo>&#x2208;</mml:mo><mml:mrow><mml:mi>&#x02112;</mml:mi></mml:mrow><mml:mo>,</mml:mo></mml:math>
</inline-formula><disp-formula id="eqn-5"><label>(5)</label>
<mml:math id="mml-eqn-5" display="block"><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mtable rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mtext>&#x00A0;&#x00A0;</mml:mtext><mml:mi>i</mml:mi><mml:mi>f</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x003C;</mml:mo><mml:mi>T</mml:mi><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mtext>&#x00A0;&#x00A0;</mml:mtext><mml:mi>i</mml:mi><mml:mi>f</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2265;</mml:mo><mml:mi>T</mml:mi><mml:msup><mml:mtext>&#x00A0;</mml:mtext><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo></mml:mrow></mml:math>
</disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-5">Eq. (5)</xref>, <inline-formula id="ieqn-46">
<mml:math id="mml-ieqn-46"><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>j</mml:mi><mml:mo fence="false" stretchy="false">|</mml:mo><mml:mi>i</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>
</inline-formula> indicates the <inline-formula id="ieqn-47">
<mml:math id="mml-ieqn-47"><mml:mi>c</mml:mi><mml:mi>o</mml:mi></mml:math>
</inline-formula>-occurrence probability that the label <italic>j</italic> seems provided that <italic>i</italic> is previously presented.</p>
<p>Next, assume that <inline-formula id="ieqn-48">
<mml:math id="mml-ieqn-48"><mml:msup><mml:mi>F</mml:mi><mml:mi>l</mml:mi></mml:msup><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:msup><mml:mi>d</mml:mi><mml:mi>l</mml:mi></mml:msup></mml:mrow></mml:msup></mml:math>
</inline-formula> encoded the input vertex feature of <inline-formula id="ieqn-49">
<mml:math id="mml-ieqn-49"><mml:msup><mml:mi>l</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msup></mml:math>
</inline-formula> layer, the GCN calculates the node feature of <inline-formula id="ieqn-50">
<mml:math id="mml-ieqn-50"><mml:mo stretchy="false">(</mml:mo><mml:mi>l</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msup></mml:math>
</inline-formula> layer <inline-formula id="ieqn-51">
<mml:math id="mml-ieqn-51"><mml:msup><mml:mi>F</mml:mi><mml:mrow><mml:mi>l</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:msup><mml:mi>d</mml:mi><mml:mrow><mml:mi>l</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:msup></mml:math>
</inline-formula>,<disp-formula id="eqn-6"><label>(6)</label>
<mml:math id="mml-eqn-6" display="block"><mml:msup><mml:mi>F</mml:mi><mml:mrow><mml:mi>l</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mi>h</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>A</mml:mi><mml:msup><mml:mi>F</mml:mi><mml:mi>l</mml:mi></mml:msup><mml:msup><mml:mi>W</mml:mi><mml:mi>l</mml:mi></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>.</mml:mo></mml:math>
</disp-formula>where <italic>h</italic> refers to the nonlinear activation function frequently selected as a Leaky Rectified Linear Unit (Leaky ReLU), <inline-formula id="ieqn-52">
<mml:math id="mml-ieqn-52"><mml:msup><mml:mi>W</mml:mi><mml:mi>l</mml:mi></mml:msup><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:msup><mml:mi>d</mml:mi><mml:mi>l</mml:mi></mml:msup><mml:mo>&#x00D7;</mml:mo><mml:msup><mml:mi>d</mml:mi><mml:mrow><mml:mi>l</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:msup></mml:math>
</inline-formula> the learned weight matrixes of layer l. Noted that A is standardized beforehand employing the above equation. Lastly, the vertex feature is generated using the final layer from the N inter-dependent classifier.</p>
</sec>
<sec id="s2_4">
<label>2.4</label>
<title>Hyperparameter Tuning</title>
<p>This study applies the HHO algorithm as a hyperparameter optimizer to improve detection performance. The HHO technique utilized 2 distinct approaches to searching functions from the exploration stage [<xref ref-type="bibr" rid="ref-19">19</xref>]. Each of the approaches is chosen dependent upon <italic>q</italic>; If <inline-formula id="ieqn-53">
<mml:math id="mml-ieqn-53"><mml:mi>q</mml:mi><mml:mo>&#x2265;</mml:mo><mml:mn>0.5</mml:mn></mml:math>
</inline-formula>, a direct approach has been utilized for searching nearby most other hawks arbitrarily. However, if <inline-formula id="ieqn-54">
<mml:math id="mml-ieqn-54"><mml:mi>q</mml:mi><mml:mo>&#x003C;</mml:mo><mml:mn>0.5</mml:mn></mml:math>
</inline-formula>, the second approach has been utilized for the searching function formulated in <xref ref-type="disp-formula" rid="eqn-7">Eq. (7)</xref> [<xref ref-type="bibr" rid="ref-19">19</xref>].<disp-formula id="eqn-7"><label>(7)</label>
<mml:math id="mml-eqn-7" display="block"><mml:mi>X</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mtable rowspacing="4pt" columnspacing="1em" columnalign="left"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:mo>|</mml:mo><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mn>2</mml:mn><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>|</mml:mo></mml:mrow><mml:mi>q</mml:mi><mml:mo>&#x2265;</mml:mo><mml:mn>0.5</mml:mn></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>b</mml:mi><mml:mi>b</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mi>m</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>L</mml:mi><mml:mi>B</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>U</mml:mi><mml:mi>B</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>L</mml:mi><mml:mi>B</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>q</mml:mi><mml:mo>&#x003C;</mml:mo><mml:mn>0.5</mml:mn></mml:mrow></mml:mtd></mml:mtr></mml:mtable><mml:mo>.</mml:mo></mml:mrow><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo></mml:mrow><mml:mtext>&#x00A0;</mml:mtext></mml:math>
</disp-formula></p>
<p>whereas <inline-formula id="ieqn-55">
<mml:math id="mml-ieqn-55"><mml:msub><mml:mi>X</mml:mi><mml:mi>m</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> is computed dependent upon <xref ref-type="disp-formula" rid="eqn-8">Eq. (8)</xref>.<disp-formula id="eqn-8"><label>(8)</label>
<mml:math id="mml-eqn-8" display="block"><mml:msub><mml:mi>X</mml:mi><mml:mi>m</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mi>N</mml:mi></mml:mfrac></mml:mrow><mml:msubsup><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>N</mml:mi></mml:msubsup><mml:mo>&#x2061;</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>.</mml:mo><mml:mtext>&#x00A0;</mml:mtext></mml:mstyle></mml:math>
</disp-formula></p>
<p>A distinct process was utilized for moving from the exploration to the exploitation stages. In optimized functions, the exploration function was carried out first, then the exploitation function, by improving the iterations, defining an optimum solution, and creating a promising solution. <xref ref-type="disp-formula" rid="eqn-9">Eq. (9)</xref> has been utilized for mathematical modeling.<disp-formula id="eqn-9"><label>(9)</label>
<mml:math id="mml-eqn-9" display="block"><mml:mi>E</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:msub><mml:mi>E</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mi>t</mml:mi><mml:mi>T</mml:mi></mml:mfrac></mml:mrow></mml:mstyle></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>.</mml:mo><mml:mtext>&#x00A0;</mml:mtext></mml:math>
</disp-formula></p>
<p>If <inline-formula id="ieqn-56">
<mml:math id="mml-ieqn-56"><mml:mrow><mml:mo>|</mml:mo><mml:mi>E</mml:mi><mml:mo>|</mml:mo></mml:mrow><mml:mo>&#x2265;</mml:mo><mml:mn>1</mml:mn></mml:math>
</inline-formula>, this technique enters the exploration stage. However, if <inline-formula id="ieqn-57">
<mml:math id="mml-ieqn-57"><mml:mrow><mml:mo>|</mml:mo><mml:mi>E</mml:mi><mml:mo>|</mml:mo></mml:mrow><mml:mo>&#x003C;</mml:mo><mml:mn>1</mml:mn></mml:math>
</inline-formula>, it enters the exploitation stage. The value of <italic>E</italic> is a reducing movement in the maximum of iterations. The HHO technique utilizes 4 distinct approaches for carrying out optimized functions from the exploitation stage. If <inline-formula id="ieqn-58">
<mml:math id="mml-ieqn-58"><mml:mi>E</mml:mi><mml:mo>&#x2265;</mml:mo><mml:mrow><mml:mtext>&#x00A0;</mml:mtext></mml:mrow><mml:mn>0.5</mml:mn></mml:math>
</inline-formula>, 2 approaches were employed, such as besiege and soft besiege with advanced rapid dives. On the contrary, if <inline-formula id="ieqn-59">
<mml:math id="mml-ieqn-59"><mml:mi>E</mml:mi><mml:mo>&#x003C;</mml:mo><mml:mn>0.5</mml:mn></mml:math>
</inline-formula>, 2 approaches like besiege and hard besiege with advanced rapid dives were utilized. All of these approaches are described under.</p>
<p><bold>Soft besiege</bold></p>
<p>If <inline-formula id="ieqn-60">
<mml:math id="mml-ieqn-60"><mml:mi>r</mml:mi><mml:mo>&#x2265;</mml:mo><mml:mn>0.5</mml:mn><mml:mtext>&#x00A0;</mml:mtext><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mrow><mml:mo>|</mml:mo><mml:mi>E</mml:mi><mml:mo>|</mml:mo></mml:mrow><mml:mo>&#x2265;</mml:mo><mml:mn>0.5</mml:mn></mml:math>
</inline-formula>, the HHO technique employs a soft besiege technique to optimize functions. During this case, hawks could not simply hunt rabbits as has a lot of energy for escaping, as determined in <xref ref-type="disp-formula" rid="eqn-10">Eqs. (10)</xref> and <xref ref-type="disp-formula" rid="eqn-11">(11)</xref>.</p>
<p><disp-formula id="eqn-10"><label>(10)</label>
<mml:math id="mml-eqn-10" display="block"><mml:mi>X</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi mathvariant="normal">&#x0394;</mml:mi><mml:mi>X</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>E</mml:mi><mml:mrow><mml:mo>|</mml:mo><mml:mrow><mml:mi>J</mml:mi><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>b</mml:mi><mml:mi>b</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>X</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>|</mml:mo></mml:mrow><mml:mo>.</mml:mo><mml:mtext>&#x00A0;</mml:mtext></mml:math>
</disp-formula></p>
<p><disp-formula id="eqn-11"><label>(11)</label>
<mml:math id="mml-eqn-11" display="block"><mml:mi mathvariant="normal">&#x0394;</mml:mi><mml:mi>X</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>b</mml:mi><mml:mi>b</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>X</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>.</mml:mo><mml:mtext>&#x00A0;</mml:mtext></mml:math>
</disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-10">Eq. (10)</xref>, <inline-formula id="ieqn-61">
<mml:math id="mml-ieqn-61"><mml:mi mathvariant="normal">&#x0394;</mml:mi><mml:mi>X</mml:mi></mml:math>
</inline-formula>, achieved utilizing in <xref ref-type="disp-formula" rid="eqn-11">Eq. (11)</xref>, signifies the distance of chosen hawk to a rabbit, and <italic>E</italic> has been attained utilizing in <xref ref-type="disp-formula" rid="eqn-14">Eq. (14)</xref>. <italic>J</italic> is also escaping the energy of rabbits, which is achieved by utilizing Eq. <inline-formula id="ieqn-62">
<mml:math id="mml-ieqn-62"><mml:mi>J</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mn>5</mml:mn></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula>.</p>
<p><bold>Hard besiege</bold></p>
<p>If <inline-formula id="ieqn-63">
<mml:math id="mml-ieqn-63"><mml:mi>r</mml:mi><mml:mo>&#x2265;</mml:mo><mml:mn>0.5</mml:mn><mml:mtext>&#x00A0;</mml:mtext><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mrow><mml:mo>|</mml:mo><mml:mi>E</mml:mi><mml:mo>|</mml:mo></mml:mrow><mml:mo>&#x003C;</mml:mo><mml:mn>0.5</mml:mn></mml:math>
</inline-formula>, the HHO approach utilizes a hard besiege method to optimize functions. During this work, the hawks hunt rabbits with a rapid attack as it no longer has sufficient energy to escape. The mathematical process of this motion was formulated utilizing <xref ref-type="disp-formula" rid="eqn-12">Eq. (12)</xref>.<disp-formula id="eqn-12"><label>(12)</label>
<mml:math id="mml-eqn-12" display="block"><mml:mi>X</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>b</mml:mi><mml:mi>b</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>E</mml:mi><mml:mrow><mml:mo>|</mml:mo><mml:mrow><mml:mi mathvariant="normal">&#x0394;</mml:mi><mml:mi>X</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>|</mml:mo></mml:mrow><mml:mo>.</mml:mo><mml:mtext>&#x00A0;</mml:mtext></mml:math>
</disp-formula></p>
<p>If <inline-formula id="ieqn-64">
<mml:math id="mml-ieqn-64"><mml:mrow><mml:mo>|</mml:mo><mml:mi>E</mml:mi><mml:mo>|</mml:mo></mml:mrow><mml:mo>&#x2265;</mml:mo><mml:mn>0.5</mml:mn></mml:math>
</inline-formula> but r <inline-formula id="ieqn-65">
<mml:math id="mml-ieqn-65"><mml:mo>&#x003C;</mml:mo><mml:mn>0.5</mml:mn></mml:math>
</inline-formula>, the soft besiege technique with progressive rapid dives has been utilized. Then, the rabbit is sufficient energy to escape, and there is until a soft besiege. This process was comparatively more advanced than the earlier process.<disp-formula id="eqn-13"><label>(13)</label>
<mml:math id="mml-eqn-13" display="block"><mml:mi>Y</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>b</mml:mi><mml:mi>b</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>E</mml:mi><mml:mrow><mml:mo>|</mml:mo><mml:mrow><mml:mi>J</mml:mi><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>b</mml:mi><mml:mi>b</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>X</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>|</mml:mo></mml:mrow><mml:mo>.</mml:mo><mml:mtext>&#x00A0;</mml:mtext></mml:math>
</disp-formula></p>
<p>This method utilizes a L&#x00E9;vy flight (LF) to improve efficiency. In addition, the 2 states of <xref ref-type="disp-formula" rid="eqn-18">Eq. (18)</xref> were related to the present solution. The LF could not be utilized as an outcome of <italic>Y</italic> but is employed in <italic>Z</italic>, provided in <xref ref-type="disp-formula" rid="eqn-8">Eq. (8)</xref>.<disp-formula id="eqn-14"><label>(14)</label>
<mml:math id="mml-eqn-14" display="block"><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mi>Y</mml:mi><mml:mo>+</mml:mo><mml:mi>S</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>L</mml:mi><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>D</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>.</mml:mo><mml:mtext>&#x00A0;</mml:mtext></mml:math>
</disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-14">Eq. (14)</xref>, <italic>S</italic> refers to the arbitrary number from the dimension of problems from the range of zero and one, and <inline-formula id="ieqn-66">
<mml:math id="mml-ieqn-66"><mml:mi>L</mml:mi><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> refers to the LF from the dimensional of problems demonstrated in <xref ref-type="disp-formula" rid="eqn-15">Eq. (15)</xref>.</p>
<p><disp-formula id="eqn-15"><label>(15)</label>
<mml:math id="mml-eqn-15" display="block"><mml:mi>L</mml:mi><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>0.01</mml:mn><mml:mo>&#x00D7;</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>u</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>&#x03C3;</mml:mi></mml:mrow><mml:mrow><mml:mo fence="false" stretchy="false">|</mml:mo><mml:mi>v</mml:mi><mml:msup><mml:mo fence="false" stretchy="false">|</mml:mo><mml:mrow><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mi>&#x03B2;</mml:mi></mml:mfrac></mml:mrow></mml:mrow></mml:msup></mml:mrow></mml:mfrac></mml:mrow><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mi>&#x03C3;</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mi></mml:mi><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mi>r</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mi>&#x03B2;</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:mfrac></mml:mrow></mml:mstyle></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mi>&#x03B2;</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mn>2</mml:mn><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>&#x03B2;</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:mfrac></mml:mrow></mml:mstyle></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mstyle></mml:mrow><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mi mathvariant="normal">&#x0393;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mi>&#x03B2;</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mi>sin</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>&#x03C0;</mml:mi><mml:mi>&#x03B2;</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:mfrac></mml:mrow></mml:mstyle></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mstyle></mml:mrow></mml:msubsup><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mi>&#x03B2;</mml:mi></mml:mfrac></mml:mrow></mml:mrow></mml:msup><mml:mo>.</mml:mo><mml:mtext>&#x00A0;</mml:mtext></mml:mstyle></mml:math>
</disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-15">Eq. (15)</xref>, <italic>u</italic> and <italic>v</italic> represent the 2 arbitrary numbers between <inline-formula id="ieqn-67">
<mml:math id="mml-ieqn-67"><mml:mi>z</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>o</mml:mi></mml:math>
</inline-formula> and one, and <inline-formula id="ieqn-68">
<mml:math id="mml-ieqn-68"><mml:mi>&#x03B2;</mml:mi></mml:math>
</inline-formula> has a set and default number, that is, 1.5.<disp-formula id="eqn-16"><label>(16)</label>
<mml:math id="mml-eqn-16" display="block"><mml:mi>X</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mtable rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mrow><mml:mi>Y</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>i</mml:mi><mml:mi>f</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>Y</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x003C;</mml:mo><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>X</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mi>Z</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>i</mml:mi><mml:mi>f</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>Z</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x003C;</mml:mo><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>X</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo></mml:mrow><mml:mo>.</mml:mo><mml:mtext>&#x00A0;</mml:mtext></mml:math>
</disp-formula></p>
<p>Based on <xref ref-type="disp-formula" rid="eqn-16">Eq. (16)</xref>, the outcome of <xref ref-type="disp-formula" rid="eqn-13">Eq. (13)</xref> is superior to the present solutions and, therefore, changes it; else, the solution achieved in <xref ref-type="disp-formula" rid="eqn-14">Eq. (14)</xref> is related to the present solutions. Assume that <inline-formula id="ieqn-69">
<mml:math id="mml-ieqn-69"><mml:mrow><mml:mo>|</mml:mo><mml:mi>E</mml:mi><mml:mo>|</mml:mo></mml:mrow><mml:mo>&#x003C;</mml:mo><mml:mn>0.5</mml:mn><mml:mtext>&#x00A0;</mml:mtext><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>r</mml:mi><mml:mo>&#x003C;</mml:mo><mml:mn>0.5</mml:mn></mml:math>
</inline-formula>, the hard besiege approach with advanced rapid dives has been utilized to optimize functions. Then, the rabbit could not have sufficient energy to escape and was besieged hard before the surprise pounced to catch the rabbit. <xref ref-type="disp-formula" rid="eqn-18">Eqs. (18)</xref> and <xref ref-type="disp-formula" rid="eqn-19">(19)</xref> execute dependent upon <xref ref-type="disp-formula" rid="eqn-17">Eq. (17)</xref>.<disp-formula id="eqn-17"><label>(17)</label>
<mml:math id="mml-eqn-17" display="block"><mml:mi>X</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mtable rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mrow><mml:mi>Y</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>i</mml:mi><mml:mi>f</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>Y</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x003C;</mml:mo><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>X</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mi>Z</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>i</mml:mi><mml:mi>f</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>Z</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x003C;</mml:mo><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>X</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo></mml:mrow><mml:mo>.</mml:mo><mml:mtext>&#x00A0;</mml:mtext></mml:math>
</disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-17">Eq. (17)</xref>, <italic>Y</italic> and <italic>Z</italic> are attained utilizing <xref ref-type="disp-formula" rid="eqn-18">Eqs. (18)</xref> and <xref ref-type="disp-formula" rid="eqn-19">(19)</xref>.<disp-formula id="eqn-18"><label>(18)</label>
<mml:math id="mml-eqn-18" display="block"><mml:mi>Y</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>b</mml:mi><mml:mi>b</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>E</mml:mi><mml:mrow><mml:mo>|</mml:mo><mml:mrow><mml:mi>J</mml:mi><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>b</mml:mi><mml:mi>b</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mi>m</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>|</mml:mo></mml:mrow><mml:mo>.</mml:mo><mml:mtext>&#x00A0;</mml:mtext></mml:math>
</disp-formula><disp-formula id="eqn-19"><label>(19)</label>
<mml:math id="mml-eqn-19" display="block"><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mi>Y</mml:mi><mml:mo>+</mml:mo><mml:mi>S</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>L</mml:mi><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>D</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>.</mml:mo><mml:mtext>&#x00A0;</mml:mtext></mml:math>
</disp-formula></p>
<p>During this approach, the solution achieved in <xref ref-type="disp-formula" rid="eqn-18">Eq. (18)</xref> changes the present solution when it can be more effective than others; else, the solution achieved in <xref ref-type="disp-formula" rid="eqn-19">Eq. (19)</xref> is exchanged when it can be more effective than the present solution. <xref ref-type="fig" rid="fig-2">Fig. 2</xref> showcases the flowchart of the HHO technique.</p>
<fig id="fig-2">
<label>Figure 2</label>
<caption>
<title>Flowchart of HHO technique</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_36296-fig-2.tif"/>
</fig>
</sec>
</sec>
<sec id="s3">
<label>3</label>
<title>Results and Discussion</title>
<p>The weed detection performance of the HHOGCN-WD model is tested using a benchmark weed dataset [<xref ref-type="bibr" rid="ref-20">20</xref>]. The dataset holds 3000 samples with two classes, as in <xref ref-type="table" rid="table-1">Table 1</xref>. A few sample images are demonstrated in <xref ref-type="fig" rid="fig-3">Fig. 3</xref>.</p>
<table-wrap id="table-1"><label>Table 1</label>
<caption>
<title>Dataset details</title></caption>
<table><colgroup><col align="left"/><col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left">Class</th>
<th align="left">No. of samples</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">Crop</td>
<td align="left">287</td>
</tr>
<tr>
<td align="left">Weed</td>
<td align="left">2713</td>
</tr>
<tr>
<td align="left"><bold>Total No. of samples</bold></td>
<td align="left"><bold>3000</bold></td>
</tr>
</tbody>
</table>
</table-wrap><fig id="fig-3">
<label>Figure 3</label>
<caption>
<title>Sample images</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_36296-fig-3.tif"/>
</fig>
<p><xref ref-type="fig" rid="fig-4">Fig. 4</xref> depicts the confusion matrices offered by the HHOGCN-WD model under five distinct runs. The figure implied that the HHOGCN-WD model had identified the weeds proficiently under each class. For instance, on run-1, the HHOGCN-WD model detected 274 samples under crop and 2693 samples under weed class. Moreover, on run-2, the HHOGCN-WD technique detected 278 samples under crop and 2692 samples under weed class. Further, on run-3, the HHOGCN-WD approach detected 274 samples under crop and 2693 samples under weed class. Then, on run-4, the HHOGCN-WD technique detected 270 samples under crop and 2695 samples under weed class. Next, on run-5, the HHOGCN-WD method detected 282 samples under crop and 2692 samples under weed class.</p>
<fig id="fig-4">
<label>Figure 4</label>
<caption>
<title>Confusion matrices of HHOGCN-WD approach (a) Run1, (b) Run2, (c) Run3, (d) Run4, and (e) Run5</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_36296-fig-4.tif"/>
</fig>
<p><xref ref-type="table" rid="table-2">Table 2</xref> and <xref ref-type="fig" rid="fig-5">Fig. 5</xref> demonstrate the overall weed detection outcomes of the HHOGCN-WD model under five distinct runs. The results indicated that the HHOGCN-WD model had shown enhanced weed detection outcomes. For instance, on run-1, the HHOGCN-WD model has offered average <inline-formula id="ieqn-70">
<mml:math id="mml-ieqn-70"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:math>
</inline-formula>, <inline-formula id="ieqn-71">
<mml:math id="mml-ieqn-71"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:math>
</inline-formula>, <inline-formula id="ieqn-72">
<mml:math id="mml-ieqn-72"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:math>
</inline-formula>, <inline-formula id="ieqn-73">
<mml:math id="mml-ieqn-73"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:math>
</inline-formula>, and MCC of 98.90&#x0025;, 96.36&#x0025;, 97.37&#x0025;, <inline-formula id="ieqn-74">
<mml:math id="mml-ieqn-74"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:math>
</inline-formula> of 96.86&#x0025;, and MCC of 93.72&#x0025;. In the meantime, on run-2, the HHOGCN-WD technique has rendered average <inline-formula id="ieqn-75">
<mml:math id="mml-ieqn-75"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:math>
</inline-formula>, <inline-formula id="ieqn-76">
<mml:math id="mml-ieqn-76"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:math>
</inline-formula>, <inline-formula id="ieqn-77">
<mml:math id="mml-ieqn-77"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:math>
</inline-formula>, <inline-formula id="ieqn-78">
<mml:math id="mml-ieqn-78"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:math>
</inline-formula>, and MCC of 99&#x0025;, 96.32&#x0025;, 98.05&#x0025;, <inline-formula id="ieqn-79">
<mml:math id="mml-ieqn-79"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:math>
</inline-formula> of 97.16&#x0025;, and MCC of 94.35&#x0025;. Similarly, on run-3, the HHOGCN-WD method has presented average <inline-formula id="ieqn-80">
<mml:math id="mml-ieqn-80"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:math>
</inline-formula>, <inline-formula id="ieqn-81">
<mml:math id="mml-ieqn-81"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:math>
</inline-formula>, <inline-formula id="ieqn-82">
<mml:math id="mml-ieqn-82"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:math>
</inline-formula>, <inline-formula id="ieqn-83">
<mml:math id="mml-ieqn-83"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:math>
</inline-formula>, and MCC of 98.90&#x0025;, 96.36&#x0025;, 97.37&#x0025;, <inline-formula id="ieqn-84">
<mml:math id="mml-ieqn-84"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:math>
</inline-formula> of 96.86&#x0025;, and MCC of 93.72&#x0025;. Additionally, on run-4, the HHOGCN-WD methodology has rendered average <inline-formula id="ieqn-85">
<mml:math id="mml-ieqn-85"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:math>
</inline-formula>, <inline-formula id="ieqn-86">
<mml:math id="mml-ieqn-86"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:math>
</inline-formula>, <inline-formula id="ieqn-87">
<mml:math id="mml-ieqn-87"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:math>
</inline-formula>, <inline-formula id="ieqn-88">
<mml:math id="mml-ieqn-88"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:math>
</inline-formula>, and MCC of 98.90&#x0025;, 96.56&#x0025;, 96.71&#x0025;, <inline-formula id="ieqn-89">
<mml:math id="mml-ieqn-89"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:math>
</inline-formula> of 96.63&#x0025;, and MCC of 93.27&#x0025;. Finally, on run-5, the HHOGCN-WD algorithm has provided average <inline-formula id="ieqn-90">
<mml:math id="mml-ieqn-90"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:math>
</inline-formula>, <inline-formula id="ieqn-91">
<mml:math id="mml-ieqn-91"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:math>
</inline-formula>, <inline-formula id="ieqn-92">
<mml:math id="mml-ieqn-92"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:math>
</inline-formula>, <inline-formula id="ieqn-93">
<mml:math id="mml-ieqn-93"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:math>
</inline-formula>, and MCC of 99.13&#x0025;, 96.44&#x0025;, 98.74&#x0025;, <inline-formula id="ieqn-94">
<mml:math id="mml-ieqn-94"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:math>
</inline-formula> of 97.56&#x0025;, and MCC of 95.16&#x0025;.</p>
<table-wrap id="table-2"><label>Table 2</label>
<caption>
<title>Result analysis of HHOGCN-WD approach with distinct measures and runs</title></caption>
<table><colgroup><col align="left"/><col align="left"/><col align="left"/><col align="left"/><col align="left"/><col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left">Class</th>
<th align="left">Accuracy</th>
<th align="left">Precision</th>
<th align="left">Recall</th>
<th align="left">F-Score</th>
<th align="left">MCC</th>
</tr>
</thead>
<tbody><tr>
<td align="left" colspan="6">Run-1</td>
</tr>
<tr>
<td align="left">Crop</td>
<td align="left">98.90</td>
<td align="left">93.20</td>
<td align="left">95.47</td>
<td align="left">94.32</td>
<td align="left">93.72</td>
</tr>
<tr>
<td align="left">Weed</td>
<td align="left">98.90</td>
<td align="left">99.52</td>
<td align="left">99.26</td>
<td align="left">99.39</td>
<td align="left">93.72</td>
</tr><tr>
<td align="left"><bold>Average</bold></td>
<td align="left"><bold>98.90</bold></td>
<td align="left"><bold>96.36</bold></td>
<td align="left"><bold>97.37</bold></td>
<td align="left"><bold>96.86</bold></td>
<td align="left"><bold>93.72</bold></td>
</tr><tr>
<td align="left" colspan="6">Run-2</td>
</tr>
<tr>
<td align="left">Crop</td>
<td align="left">99.00</td>
<td align="left">92.98</td>
<td align="left">96.86</td>
<td align="left">94.88</td>
<td align="left">94.35</td>
</tr>
<tr>
<td align="left">Weed</td>
<td align="left">99.00</td>
<td align="left">99.67</td>
<td align="left">99.23</td>
<td align="left">99.45</td>
<td align="left">94.35</td>
</tr><tr>
<td align="left"><bold>Average</bold></td>
<td align="left"><bold>99.00</bold></td>
<td align="left"><bold>96.32</bold></td>
<td align="left"><bold>98.05</bold></td>
<td align="left"><bold>97.16</bold></td>
<td align="left"><bold>94.35</bold></td>
</tr><tr>
<td align="left" colspan="6">Run-3</td>
</tr>
<tr>
<td align="left">Crop</td>
<td align="left">98.90</td>
<td align="left">93.20</td>
<td align="left">95.47</td>
<td align="left">94.32</td>
<td align="left">93.72</td>
</tr>
<tr>
<td align="left">Weed</td>
<td align="left">98.90</td>
<td align="left">99.52</td>
<td align="left">99.26</td>
<td align="left">99.39</td>
<td align="left">93.72</td>
</tr>
<tr>
<td align="left"><bold>Average</bold></td>
<td align="left"><bold>98.90</bold></td>
<td align="left"><bold>96.36</bold></td>
<td align="left"><bold>97.37</bold></td>
<td align="left"><bold>96.86</bold></td>
<td align="left"><bold>93.72</bold></td>
</tr><tr>
<td align="left" colspan="6">Run-4</td>
</tr>
<tr>
<td align="left">Crop</td>
<td align="left">98.83</td>
<td align="left">93.75</td>
<td align="left">94.08</td>
<td align="left">93.91</td>
<td align="left">93.27</td>
</tr>
<tr>
<td align="left">Weed</td>
<td align="left">98.83</td>
<td align="left">99.37</td>
<td align="left">99.34</td>
<td align="left">99.35</td>
<td align="left">93.27</td>
</tr><tr>
<td align="left"><bold>Average</bold></td>
<td align="left"><bold>98.83</bold></td>
<td align="left"><bold>96.56</bold></td>
<td align="left"><bold>96.71</bold></td>
<td align="left"><bold>96.63</bold></td>
<td align="left"><bold>93.27</bold></td>
</tr><tr>
<td align="left" colspan="6">Run-5</td>
</tr>
<tr>
<td align="left">Crop</td>
<td align="left">99.13</td>
<td align="left">93.07</td>
<td align="left">98.26</td>
<td align="left">95.59</td>
<td align="left">95.16</td>
</tr>
<tr>
<td align="left">Weed</td>
<td align="left">99.13</td>
<td align="left">99.81</td>
<td align="left">99.23</td>
<td align="left">99.52</td>
<td align="left">95.16</td>
</tr>
<tr>
<td align="left"><bold>Average</bold></td>
<td align="left"><bold>99.13</bold></td>
<td align="left"><bold>96.44</bold></td>
<td align="left"><bold>98.74</bold></td>
<td align="left"><bold>97.56</bold></td>
<td align="left"><bold>95.16</bold></td>
</tr>
</tbody>
</table>
</table-wrap><fig id="fig-5">
<label>Figure 5</label>
<caption>
<title>Average analysis of HHOGCN-WD approach (a) Run1, (b) Run2, (c) Run3, (d) Run4, and (e) Run5</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_36296-fig-5.tif"/>
</fig>
<p>The training accuracy (TRA) and validation accuracy (VLA) acquired by the HHOGCN-WD approach in the test dataset is shown in <xref ref-type="fig" rid="fig-6">Fig. 6</xref>. The experimental outcome implicit in the HHOGCN-WD method has attained maximal values of TRA and VLA. Seemingly the VLA is greater than TRA.</p>
<fig id="fig-6">
<label>Figure 6</label>
<caption>
<title>TRA and VLA analysis of HHOGCN-WD approach</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_36296-fig-6.tif"/>
</fig>
<p>The training loss (TRL) and validation loss (VLL) obtained by the HHOGCN-WD method in the test dataset are accomplished in <xref ref-type="fig" rid="fig-7">Fig. 7</xref>. The experimental outcome denotes the HHOGCN-WD approach has exhibited the least values of TRL and VLL. Particularly, the VLL is lesser than TRL.</p>
<fig id="fig-7">
<label>Figure 7</label>
<caption>
<title>TRL and VLL analysis of the HHOGCN-WD approach</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_36296-fig-7.tif"/>
</fig>
<p>A clear precision-recall inspection of the HHOGCN-WD algorithm in the test dataset is given in <xref ref-type="fig" rid="fig-8">Fig. 8</xref>. The figure representing the HHOGCN-WD approach has resulted in enhanced precision-recall values in all classes.</p>
<fig id="fig-8">
<label>Figure 8</label>
<caption>
<title>Precision-recall analysis of the HHOGCN-WD approach</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_36296-fig-8.tif"/>
</fig>
<p>A brief ROC investigation of the HHOGCN-WD technique under the test dataset is portrayed in <xref ref-type="fig" rid="fig-9">Fig. 9</xref>. The results implicit the HHOGCN-WD method has displayed its ability in classifying distinct class labels in the test dataset.</p>
<fig id="fig-9">
<label>Figure 9</label>
<caption>
<title>ROC analysis of HHOGCN-WD approach</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_36296-fig-9.tif"/>
</fig>
<p><xref ref-type="table" rid="table-3">Table 3</xref> and <xref ref-type="fig" rid="fig-10">Fig. 10</xref> depict the comparison weed detection results of the HHOGCN-WD model with other existing models [<xref ref-type="bibr" rid="ref-21">21</xref>,<xref ref-type="bibr" rid="ref-22">22</xref>]. The results implied that the HHOGCN-WD model has obtained enhanced results in terms of different measures. For instance, concerning <inline-formula id="ieqn-95">
<mml:math id="mml-ieqn-95"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:math>
</inline-formula>, the HHOGCN-WD model has offered an increased <inline-formula id="ieqn-96">
<mml:math id="mml-ieqn-96"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:math>
</inline-formula> of 99.13&#x0025;, whereas the AlexNet, GoogleNet, Inception v3, Mask RCNN, and CNN-WIS model have reached a reduced <inline-formula id="ieqn-97">
<mml:math id="mml-ieqn-97"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:math>
</inline-formula> of 96.33&#x0025;, 95.38&#x0025;, 97.57&#x0025;, 97.49&#x0025;, and 97.38&#x0025; respectively. Temporarily, concerning <inline-formula id="ieqn-98">
<mml:math id="mml-ieqn-98"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>n</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math>
</inline-formula>, the HHOGCN-WD algorithm has presented an increased <inline-formula id="ieqn-99">
<mml:math id="mml-ieqn-99"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>n</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math>
</inline-formula> of 96.44&#x0025; whereas the AlexNet, GoogleNet, Inception v3, Mask RCNN, and CNN-WIS technique have attained a reduced <inline-formula id="ieqn-100">
<mml:math id="mml-ieqn-100"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>n</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math>
</inline-formula> of 95.60&#x0025;, 94.50&#x0025;, 95.56&#x0025;, 95.86&#x0025;, and 95.69&#x0025; correspondingly.</p>
<table-wrap id="table-3"><label>Table 3</label>
<caption>
<title>Comparative analysis of HHOGCN-WD approach with existing methodologies</title></caption>
<table><colgroup><col align="left"/><col align="left"/><col align="left"/><col align="left"/><col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left">Methods</th>
<th align="left">Accuracy</th>
<th align="left">Precision</th>
<th align="left">Recall</th>
<th align="left">F-score</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">HHOGCN-WD</td>
<td align="left">99.13</td>
<td align="left">96.44</td>
<td align="left">98.74</td>
<td align="left">97.56</td>
</tr>
<tr>
<td align="left">AlexNet</td>
<td align="left">96.33</td>
<td align="left">95.60</td>
<td align="left">98.35</td>
<td align="left">97.47</td>
</tr>
<tr>
<td align="left">GoogleNet</td>
<td align="left">95.38</td>
<td align="left">94.50</td>
<td align="left">98.27</td>
<td align="left">97.23</td>
</tr>
<tr>
<td align="left">InceptionV3</td>
<td align="left">97.57</td>
<td align="left">95.56</td>
<td align="left">98.09</td>
<td align="left">96.55</td>
</tr>
<tr>
<td align="left">Mask R-CNN</td>
<td align="left">97.49</td>
<td align="left">95.86</td>
<td align="left">98.09</td>
<td align="left">97.15</td>
</tr>
<tr>
<td align="left">CNN-WIS</td>
<td align="left">97.38</td>
<td align="left">95.69</td>
<td align="left">97.46</td>
<td align="left">96.46</td>
</tr>
</tbody>
</table>
</table-wrap><fig id="fig-10">
<label>Figure 10</label>
<caption>
<title>Comparative analysis of HHOGCN-WD approach with existing methodologies</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_36296-fig-10.tif"/>
</fig>
<p>Finally, for <inline-formula id="ieqn-101">
<mml:math id="mml-ieqn-101"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:math>
</inline-formula>, the HHOGCN-WD method has rendered an increased <inline-formula id="ieqn-102">
<mml:math id="mml-ieqn-102"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:math>
</inline-formula> of 98.74&#x0025; whereas the AlexNet, GoogleNet, Inception v3, Mask RCNN, and CNN-WIS approach has reached reduced <inline-formula id="ieqn-103">
<mml:math id="mml-ieqn-103"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:math>
</inline-formula> of 98.35&#x0025;, 98.27&#x0025;, 98.09&#x0025;, 98.09&#x0025;, and 97.46&#x0025; correspondingly. At last, for <inline-formula id="ieqn-104">
<mml:math id="mml-ieqn-104"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:math>
</inline-formula>, the HHOGCN-WD method has presented an increased <inline-formula id="ieqn-105">
<mml:math id="mml-ieqn-105"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:math>
</inline-formula> of 97.56&#x0025; whereas the AlexNet, GoogleNet, Inception v3, Mask RCNN, and CNN-WIS techniques have reached a reduced <inline-formula id="ieqn-106">
<mml:math id="mml-ieqn-106"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:math>
</inline-formula> of 97.47&#x0025;, 97.23&#x0025;, 96.55&#x0025;, 97.15&#x0025;, and 96.46&#x0025; correspondingly.</p>
</sec>
<sec id="s4">
<label>4</label>
<title>Conclusion</title>
<p>In this study, a new HHOGCN-WD technique has been developed for weed detection and classification for Precision Agriculture. The presented HHOGCN-WD technique mainly focuses on the identification and classification of weeds for precision agriculture. For image pre-processing, the HHOGCN-WD model utilizes BNF for noise removal. In addition, the CCNet model is utilized to derive a set of feature vectors. To detect and classify weed, the GCN model is utilized with the HHO algorithm as a hyperparameter optimizer to improve the detection performance. The experimental results of the HHOGCN-WD technique are investigated under the benchmark dataset. The results indicate the promising performance of the presented HHOGCN-WD model over other recent approaches.</p>
</sec>
</body>
<back>
<sec>
<title>Funding Statement</title>
<p>This research was partly supported by the <funding-source>Technology Development Program of MSS</funding-source> [No. <award-id>S3033853</award-id>] and by Basic Science Research Program through the <funding-source>National Research Foundation of Korea (NRF)</funding-source> funded by the Ministry of Education (No. <award-id>2020R1I1A3069700</award-id>).</p>
</sec>
<sec sec-type="COI-statement">
<title>Conflicts of Interest</title>
<p>The authors declare that they have no conflicts of interest to report regarding the present study.</p>
</sec>
<ref-list content-type="authoryear">
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