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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">27050</article-id>
<article-id pub-id-type="doi">10.32604/cmc.2023.027050</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Deep Consensus Network for Recycling Waste Detection in Smart Cities</article-title>
<alt-title alt-title-type="left-running-head">Deep Consensus Network for Recycling Waste Detection in Smart Cities</alt-title>
<alt-title alt-title-type="right-running-head">Deep Consensus Network for Recycling Waste Detection in Smart Cities</alt-title>
</title-group>
<contrib-group>
<contrib id="author-1" contrib-type="author" corresp="yes">
<name name-style="western"><surname>Hamza</surname><given-names>Manar Ahmed</given-names></name><xref ref-type="aff" rid="aff-1">1</xref><email>ma.hamza@psau.edu.sa</email></contrib>
<contrib id="author-2" contrib-type="author">
<name name-style="western"><surname>Mengash</surname><given-names>Hanan Abdullah</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>Negm</surname><given-names>Noha</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>Marzouk</surname><given-names>Radwa</given-names></name><xref ref-type="aff" rid="aff-2">2</xref></contrib>
<contrib id="author-5" contrib-type="author">
<name name-style="western"><surname>Motwakel</surname><given-names>Abdelwahed</given-names></name><xref ref-type="aff" rid="aff-1">1</xref></contrib>
<contrib id="author-6" contrib-type="author">
<name name-style="western"><surname>Zamani</surname><given-names>Abu Sarwar</given-names></name><xref ref-type="aff" rid="aff-1">1</xref></contrib>
<aff id="aff-1"><label>1</label><institution>Department of Computer and Self Development, Preparatory Year Deanship, Prince Sattam bin Abdulaziz University</institution>, <addr-line>16278, AlKharj</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-2"><label>2</label><institution>Department of Information Systems, 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-3"><label>3</label><institution>Department of Computer Science, College of Science and Arts, King Khalid University</institution>, <addr-line>Mahayil Asir, 62529</addr-line>,<country>Saudi Arabia</country></aff>
</contrib-group>
<author-notes>
<corresp id="cor1"><label>&#x002A;</label>Corresponding Author: Manar Ahmed Hamza. Email: <email>ma.hamza@psau.edu.sa</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>27</day><month>3</month><year>2023</year></pub-date>
<volume>75</volume>
<issue>2</issue>
<fpage>4191</fpage>
<lpage>4205</lpage>
<history>
<date date-type="received">
<day>10</day><month>1</month><year>2022</year>
</date>
<date date-type="accepted">
<day>04</day><month>3</month><year>2022</year>
</date>
</history>
<permissions>
<copyright-statement>&#x00A9; 2023 Hamza et al.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Hamza 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_27050.pdf"></self-uri>
<abstract><p>Recently, urbanization becomes a major concern for developing as well as developed countries. Owing to the increased urbanization, one of the important challenging issues in smart cities is waste management. So, automated waste detection and classification model becomes necessary for the smart city and to accomplish better recyclable waste management. Effective recycling of waste offers the chance of reducing the quantity of waste disposed to the land fill by minimizing the requirement of collecting raw materials. This study develops a novel Deep Consensus Network with Whale Optimization Algorithm for Recycling Waste Object Detection (DCNWO-RWOD) in Smart Cities. The goal of the DCNWO-RWOD technique intends to properly identify and classify the objects into recyclable and non-recyclable ones. The proposed DCNWO-RWOD technique involves the design of deep consensus network (DCN) to detect waste objects in the input image. For improving the overall object detection performance of the DCN model, the whale optimization algorithm (WOA) is exploited. Finally, Na&#x00EF;ve Bayes (NB) classifier is used for the classification of detected waste objects into recyclable and non-recyclable ones. The performance validation of the DCNWO-RWOD technique takes place using the open access dataset. The extensive comparative study reported the enhanced performance of the DCNWO-RWOD technique interms of several measures.</p>
</abstract>
<kwd-group kwd-group-type="author">
<kwd>Smart city</kwd>
<kwd>waste management</kwd>
<kwd>object detection</kwd>
<kwd>recycling</kwd>
<kwd>deep consensus network</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1">
<label>1</label>
<title>Introduction</title>
<p>Waste management is most serious problem that the world in 21st century is about to face. A recent study reported that the amount of waste annually reaches up to 2.2 billion tons in the next 3&#x2013;4 years that might cost around $375 billion to the management of waste [<xref ref-type="bibr" rid="ref-1">1</xref>]. Other studies of the Food and Agriculture Organization (FAO) of the United Nations has shown that almost 33% of the overall food is produced worldwide for everyday utilization which is almost 1.3 billion tons in weight, is wasted or lost [<xref ref-type="bibr" rid="ref-2">2</xref>]. This irregular waste management might cause a negative effect on the environments, public health, and economy [<xref ref-type="bibr" rid="ref-3">3</xref>]. The waste recycling method is extremely important interms of the environment and economy [<xref ref-type="bibr" rid="ref-4">4</xref>]. In many emerging nations, the local municipal corporation manually recycles the waste that is costly, time utilizing, and very inefficient since the corporation has to recruit a great number of laborer&#x2019;s to manually work [<xref ref-type="bibr" rid="ref-5">5</xref>]. <xref ref-type="fig" rid="fig-1">Fig. 1</xref> illustrates the application of smart city.</p>
<fig id="fig-1">
<label>Figure 1</label>
<caption>
<title>Smart city applications</title>
</caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CMC_27050-fig-1.tif"/>
</fig>
<p>Machine Learning (ML) method describes an important process of Artificial Intelligent (AI) technique which permits a system the capacity for automatically making the decision and learn with no being explicitly trained [<xref ref-type="bibr" rid="ref-6">6</xref>]. The ML method is scientific research of several statistical algorithms and models. Because of the exceptional feature in computing, the prevalence of ML was obtained the maximum peaks. These statistics obviously shows the prominence of ML based application. Likewise, deep learning (DL) methods are an important part of ML method [<xref ref-type="bibr" rid="ref-7">7</xref>]. The convolution neural networks (CNN) are momentous classes of deep neural network (DNN) systems, especially, DL method. The CNN presents considerable advances in image classification. Generally, it can be employed to estimate visual imagery and frequently functioned besides image recognition.</p>
<p>CNN was enjoyed a great achievement in image classification and recognition [<xref ref-type="bibr" rid="ref-8">8</xref>]. The accuracy and popularity of the CNN to an image classifier was improved because of the high-speed GPU, wide largescale integrated system, and accessibility of public data of image for the learning and image processing [<xref ref-type="bibr" rid="ref-9">9</xref>]. The hybrid model of utilizing a multi-layer perceptron with CNN is another effective method. The sensor technique fused in the scheme is capable of detecting metal waste object that is later categorized into certain groups [<xref ref-type="bibr" rid="ref-10">10</xref>]. Therefore, image processing using DL method has assisted municipalities to discard manual waste classification. The application of smart waste classification has been employed and provides better outcomes.</p>
<p>This study develops a novel Deep Consensus Network with Whale Optimization Algorithm for Recycling Waste Object Detection (DCNWO-RWOD) in Smart Cities. The proposed DCNWO-RWOD technique involves the design of deep consensus network (DCN) to detect waste objects in the input image. For improving the overall object detection efficiency of the DCN model, the whale optimization algorithm (WOA) is exploited. Finally, Na&#x00EF;ve Bayes (NB) classifier is used for the classification of detected waste objects into recyclable and non-recyclable ones. The performance validation of the DCNWO-RWOD technique takes place using the open access dataset.</p>
</sec>
<sec id="s2">
<label>2</label>
<title>Related Works</title>
<p>Ghanshala et al. [<xref ref-type="bibr" rid="ref-11">11</xref>] presented ML based structure for classifying the regions that are free in garbage and regions containing maximum density garbage. Baker et al. [<xref ref-type="bibr" rid="ref-12">12</xref>] examined the developing requirement for automatic e-waste recycling as a vital condition for coping with fast-developinge-waste streaming and it can be shed the light on effect of AI from supportive the recycling procedure with smart classifier of devices, in which the smartphone was analysis. This technique was executes transfer learning (TL) as a particular method of AI with fine-tune the resultant layer of AlexNet as pre-training method and implementing the execution on small-size data set which has 12 classes in 6 smartphone brands. Niu et al. [<xref ref-type="bibr" rid="ref-13">13</xref>] analyzed for implementing TL approaches for constructing a robust method dependent upon somewhat small set of trained data with transmitting data in present deep network namely AlexNet, Resnet, and DensNet. While the alteration, can be present a novel domain loss function, Dual Dynamic Domain Distance (4D) for producing further correct area distance measurements.</p>
<p>Alqahtani et al. [<xref ref-type="bibr" rid="ref-14">14</xref>] progress the IoT based Urban Waste Management system. An IoT device is utilized for monitoring human activity and for supporting waste management. The information on a city has gathering and processing from cuckoo search (CS)-optimizing long short-term recurrent neural network (RNN). The network enabled the study of waste sources, waste variety, and truck size. This data notified the waste management center for appropriating performances are obtained. Khoa et al. [<xref ref-type="bibr" rid="ref-15">15</xref>] propose the examination case executed at the real campus of Ton Duc Thang University (Vietnam) for evaluating the efficiency and feasibility of model execution. It can be examining data transfer on LoRa component and illustrate the benefits of presented method that is executed with easy circuit planned with minimum cost, usability, and replaceability. This method saved time by determining an optimum route from the management of waste collections.</p>
<p>In [<xref ref-type="bibr" rid="ref-16">16</xref>], an effective solution to smart and effective waste management utilizing ML and IoT was presented. During the presented solution, the researchers have utilized moisture sensor, Arduino UNO microcontroller, and ultrasonic sensor. The hardware prototype is also established to present structure. Therefore, the projected solution to effective waste management realizes the purpose of establishing clean and pollution-free city. In [<xref ref-type="bibr" rid="ref-17">17</xref>], the concept of realtime smart waste classifier technique was projected which utilizes a hybrid method for classifying waste as to different classes. There are 2 ML techniques as multilayer perceptron (MLP) and multilayer CNN (ML-CNN) are executed. The MLP was utilized for providing binary classifiers, for instance, metal or non-metal wastes, and CNN recognizes the class of non-metal wastes. The camera was located facing the waste conveyor belt that gets an image of wastes and classifies it.</p>
</sec>
<sec id="s3">
<label>3</label>
<title>The Proposed Model</title>
<p>In this study, an effective DCNWO-RWOD technique has been developed to properly identify and classify the objects into recyclable and non-recyclable ones. The proposed DCNWO-RWOD technique undergoes major subprocesses namely DCN based object detection, WOA based hyperparameter tuning, and NB based classification. For improving the overall object detection efficiency of the DCN model, the WOA is exploited.</p>
<sec id="s3_1">
<label>3.1</label>
<title>Object Detection Using DCN Model</title>
<p>Initially, the DCN model is employed for the detection of waste objects in smart cities [<xref ref-type="bibr" rid="ref-18">18</xref>]. The DCN is an identical structure as RetinaNet and utilizes a Feature Pyramid Network (FPN) for extracting features at several scales in ResNet-50 support with squeeze-and-excite process to residual. For enabling notice tiny objects, it can be utilized a maximum resolution different of FPN. In order to high-resolution DCN, it is comprised of a further upsampling layer for restoring the similar spatial resolution as input. The extracting feature map at all scales was forwarded to Centroid Proposal Network (CPN). Besides the RetinaNet, the CPNs at all the scales don&#x2019;t share weights for capturing distinct demonstrations at all scales as every image in the assumed that microscopy data sets are similar magnification. Conversely, an region proposal network (RPN) that forecasts the bounding boxes, the CPN forecasts the group of centroids <inline-formula id="ieqn-1"><mml:math id="mml-ieqn-1"><mml:msup><mml:mtext>v</mml:mtext><mml:mo>&#x2032;</mml:mo></mml:msup></mml:math></inline-formula> with equivalent confidence score <inline-formula id="ieqn-2"><mml:math id="mml-ieqn-2"><mml:mo>(</mml:mo><mml:msup><mml:mtext>v</mml:mtext><mml:mo>&#x2032;</mml:mo></mml:msup><mml:mo>)</mml:mo></mml:math></inline-formula>. Related to the RPN from RetinaNet, it can be utilized anchor as prior, however with distinct configurations.</p>
<p>To all spatial place from <inline-formula id="ieqn-3"><mml:math id="mml-ieqn-3"><mml:mn>2</mml:mn><mml:mi>D</mml:mi></mml:math></inline-formula> grid, it can be utilized <inline-formula id="ieqn-4"><mml:math id="mml-ieqn-4"><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>a</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>17</mml:mn></mml:math></inline-formula> anchors from entire containing one anchor with no offset, 8 anchors with length 0.5 pixels, and 8 anchors with length one pixel. The anchor vector is replaced that it well covers a unit disk. The <inline-formula id="ieqn-5"><mml:math id="mml-ieqn-5"><mml:msup><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> anchors <inline-formula id="ieqn-6"><mml:math id="mml-ieqn-6"><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> was implemented to <inline-formula id="ieqn-7"><mml:math id="mml-ieqn-7"><mml:msup><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> forecasted vector <inline-formula id="ieqn-8"><mml:math id="mml-ieqn-8"><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mo>&#x2032;</mml:mo></mml:msup></mml:mrow></mml:msubsup><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> obtaining:</p>
<p><disp-formula id="eqn-1"><label>(1)</label><mml:math id="mml-eqn-1" display="block"><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>s</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mo>&#x2032;</mml:mo></mml:msup></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>p</mml:mi><mml:mi>o</mml:mi><mml:mi>s</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mo>&#x2032;</mml:mo></mml:msup></mml:mrow></mml:msubsup><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula>where <inline-formula id="ieqn-9"><mml:math id="mml-ieqn-9"><mml:mi>p</mml:mi><mml:mi>o</mml:mi><mml:mi>s</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mo>&#x2032;</mml:mo></mml:msup></mml:mrow></mml:msubsup><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> refers the spatial place from the grids and <inline-formula id="ieqn-10"><mml:math id="mml-ieqn-10"><mml:mi>s</mml:mi></mml:math></inline-formula> represents the scaling factor for normalizing the distributions of <inline-formula id="ieqn-11"><mml:math id="mml-ieqn-11"><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mo>&#x2032;</mml:mo></mml:msup></mml:mrow></mml:msubsup></mml:math></inline-formula>. Therefore, every feasible anchor from the anchor outline is added to every place from the grid. The network regresses offset vector in these places. Relating the anchor with spatial places from the grid supports individual neuron for specializing, as it is concentrated on forecasting tiny offsets of the subset of centroid places. For encouraging the network to favour anchor that equal, the confidence score <inline-formula id="ieqn-12"><mml:math id="mml-ieqn-12"><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mo>&#x2032;</mml:mo></mml:msup></mml:mrow></mml:msubsup><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> of huge regression values to the magnitude of <inline-formula id="ieqn-13"><mml:math id="mml-ieqn-13"><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mo>&#x2032;</mml:mo></mml:msup></mml:mrow></mml:msubsup></mml:math></inline-formula> are penalization (regularization) for computing the confidence score of <inline-formula id="ieqn-14"><mml:math id="mml-ieqn-14"><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>:</p>
<p><disp-formula id="eqn-2"><label>(2)</label><mml:math id="mml-eqn-2" display="block"><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mo>&#x2032;</mml:mo></mml:msup></mml:mrow></mml:msubsup><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>ln</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo symmetric="true">&#x2016;</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mo>&#x2032;</mml:mo></mml:msup></mml:mrow></mml:msubsup><mml:mo symmetric="true">&#x2016;</mml:mo></mml:mrow></mml:mrow></mml:msup></mml:math></disp-formula></p>
<p>In order to numerical reason, the CPN forecasts the logit (logarithm of odds)<inline-formula id="ieqn-15"><mml:math id="mml-ieqn-15"><mml:mspace width="thinmathspace" /><mml:msubsup><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mo>&#x2032;</mml:mo></mml:msup></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mrow><mml:mi mathvariant="italic">L</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">g</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">t</mml:mi></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mo>&#x2032;</mml:mo></mml:msup></mml:mrow></mml:msubsup><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x2208;</mml:mo><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow></mml:math></inline-formula> Rather of directly forecasting the confidence score <inline-formula id="ieqn-16"><mml:math id="mml-ieqn-16"><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mo>&#x2032;</mml:mo></mml:msup></mml:mrow></mml:msubsup><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><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:mrow></mml:msup></mml:math></inline-formula>. Therefore, the regularized from (2) was executed from logit space obtained the regularization logit <inline-formula id="ieqn-17"><mml:math id="mml-ieqn-17"><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2208;</mml:mo><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow></mml:math></inline-formula>:</p>
<p><disp-formula id="ueqn-3"><mml:math id="mml-ueqn-3" display="block"><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mi mathvariant="italic">L</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">g</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">t</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mi mathvariant="italic">L</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">g</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">t</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mo>&#x2032;</mml:mo></mml:msup></mml:mrow></mml:msubsup><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>ln</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mo>&#x2032;</mml:mo></mml:msup></mml:mrow></mml:msubsup><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p><disp-formula id="eqn-3"><label>(3)</label><mml:math id="mml-eqn-3" display="block"><mml:mtext>&#x00A0;&#x00A0;&#x00A0;</mml:mtext><mml:mspace width="1em" /><mml:mo>=</mml:mo><mml:mrow><mml:mi mathvariant="italic">L</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">g</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">t</mml:mi></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mo>&#x2032;</mml:mo></mml:msup></mml:mrow></mml:msubsup><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo><mml:mrow><mml:mi mathvariant="italic">L</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">g</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">t</mml:mi></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>ln</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo symmetric="true">&#x2016;</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mo>&#x2032;</mml:mo></mml:msup></mml:mrow></mml:msubsup><mml:mo symmetric="true">&#x2016;</mml:mo></mml:mrow></mml:mrow></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:math></disp-formula></p>
<p><disp-formula id="ueqn-5"><mml:math id="mml-ueqn-5" display="block"><mml:mspace width="2em" /><mml:mo>=</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mo>&#x2032;</mml:mo></mml:msup></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:mi>ln</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>ln</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo symmetric="true">&#x2016;</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mo>&#x2032;</mml:mo></mml:msup></mml:mrow></mml:msubsup><mml:mo symmetric="true">&#x2016;</mml:mo></mml:mrow></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>ln</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>ln</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo symmetric="true">&#x2016;</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mo>&#x2032;</mml:mo></mml:msup></mml:mrow></mml:msubsup><mml:mo symmetric="true">&#x2016;</mml:mo></mml:mrow></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p><disp-formula id="ueqn-6"><mml:math id="mml-ueqn-6" display="block"><mml:mspace width="2em" /><mml:mo>=</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mo>&#x2032;</mml:mo></mml:msup></mml:mrow></mml:msubsup><mml:mo>&#x2212;</mml:mo><mml:mi>ln</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mo>&#x2032;</mml:mo></mml:msup></mml:mrow></mml:msubsup><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mi>ln</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>ln</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo symmetric="true">&#x2016;</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mo>&#x2032;</mml:mo></mml:msup></mml:mrow></mml:msubsup><mml:mo symmetric="true">&#x2016;</mml:mo></mml:mrow></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>The feature extracting of presented CPN was various in RPN from RetinaNet with concatenating the regressed <inline-formula id="ieqn-18"><mml:math id="mml-ieqn-18"><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> offset <inline-formula id="ieqn-19"><mml:math id="mml-ieqn-19"><mml:mrow><mml:mi>v</mml:mi><mml:mtext>&#x2032;</mml:mtext><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mi>&#x211D;</mml:mi><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>&#x00D7;</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> with features extracting in the FPN resultant <inline-formula id="ieqn-20"><mml:math id="mml-ieqn-20"><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mi>p</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula>, with <inline-formula id="ieqn-21"><mml:math id="mml-ieqn-21"><mml:mi>p</mml:mi></mml:math></inline-formula> feature map, previously forecasting the logit vector <inline-formula id="ieqn-22"><mml:math id="mml-ieqn-22"><mml:mrow><mml:mi>x</mml:mi><mml:mtext>&#x2032;</mml:mtext><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mi>&#x211D;</mml:mi><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> of confidence score <inline-formula id="ieqn-23"><mml:math id="mml-ieqn-23"><mml:mrow><mml:mi>P</mml:mi><mml:mo stretchy='false'>(</mml:mo><mml:mi>v</mml:mi><mml:mtext>'</mml:mtext><mml:mo stretchy='false'>)</mml:mo></mml:mrow></mml:math></inline-formula>.</p>
</sec>
<sec id="s3_2">
<label>3.2</label>
<title>Hyperparameter Tuning Using WOA</title>
<p>For optimally modifying the hyperparameters of the DCN model, the WOA [<xref ref-type="bibr" rid="ref-19">19</xref>] is applied to it to increase the classifier results. Mirjalili and Lewis developed a WOA which is Meta heuristic method where it stimulates the foraging behavior of humpback whales. As another optimization model, the WOA optimization method begins with random population initialization. The entire searching method is separated as, search the prey, encircle the target, and spiral bubble-net feeding maneuver. Since a system efficiency is based on the balance among local and global search models, WOA employs these 3 stages for balancing between exploitation and exploration phases, based on certain conditions. Finally, the algorithm ends according to predetermined conditions.</p>
<p>Based on its existing position, whales randomly search the target [<xref ref-type="bibr" rid="ref-20">20</xref>]. These characteristics of humpback whales are utilized for amplifying the exploration ability. It could be mathematically expressed by the subsequent formula:</p>
<p><disp-formula id="eqn-4"><label>(4)</label><mml:math id="mml-eqn-4" display="block"><mml:mover><mml:mi>D</mml:mi><mml:mo accent="false">&#x00AF;</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mi>C</mml:mi><mml:mo>.</mml:mo><mml:msubsup><mml:mi>P</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msubsup><mml:mo>&#x2212;</mml:mo><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></disp-formula></p>
<p><disp-formula id="eqn-5"><label>(5)</label><mml:math id="mml-eqn-5" display="block"><mml:msup><mml:mi>P</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:msubsup><mml:mi>P</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msubsup><mml:mo>&#x2212;</mml:mo><mml:mi>A</mml:mi><mml:mo>.</mml:mo><mml:mover><mml:mi>D</mml:mi><mml:mo accent="false">&#x00AF;</mml:mo></mml:mover></mml:math></disp-formula>where as <inline-formula id="ieqn-24"><mml:math id="mml-ieqn-24"><mml:mi>P</mml:mi></mml:math></inline-formula> denotes a location vector of population, <inline-formula id="ieqn-25"><mml:math id="mml-ieqn-25"><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> indicates a vector is arbitrarily selected in the existing populations, the existing iteration is signified as <inline-formula id="ieqn-26"><mml:math id="mml-ieqn-26"><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mover><mml:mi>D</mml:mi><mml:mo accent="false">&#x00AF;</mml:mo></mml:mover></mml:math></inline-formula> shows the distance amongst the current and random individual of populations, the dot operator specifies the element-wise multiplication procedure, and <inline-formula id="ieqn-27"><mml:math id="mml-ieqn-27"><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow></mml:math></inline-formula> is utilized for defining accurate values.</p>
<p>The two variables also called as <inline-formula id="ieqn-28"><mml:math id="mml-ieqn-28"><mml:mi>A</mml:mi></mml:math></inline-formula>, and <inline-formula id="ieqn-29"><mml:math id="mml-ieqn-29"><mml:mi>C</mml:mi></mml:math></inline-formula> coefficient vectors are estimated by:</p>
<p><disp-formula id="eqn-6"><label>(6)</label><mml:math id="mml-eqn-6" display="block"><mml:mi>A</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>&#x00D7;</mml:mo><mml:mi>r</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></disp-formula></p>
<p><disp-formula id="eqn-7"><label>(7)</label><mml:math id="mml-eqn-7" display="block"><mml:mi>C</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mo>&#x00D7;</mml:mo><mml:mi>r</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:math></disp-formula></p>
<p>In which the value of <inline-formula id="ieqn-30"><mml:math id="mml-ieqn-30"><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> represent a value linearly reduced from 2 to <inline-formula id="ieqn-31"><mml:math id="mml-ieqn-31"><mml:mn>0</mml:mn></mml:math></inline-formula> at the iteration time, and <inline-formula id="ieqn-32"><mml:math id="mml-ieqn-32"><mml:mi>r</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:math></inline-formula> indicates an arbitrary value. In the prey encircling process, the optimal solution established until now is considered as the solution which is closer to the optimum values. The residual individual in the population updates the position nearer the existing optimal solution. It could be mathematically expressed by the subsequent formula as:</p>
<p><disp-formula id="eqn-8"><label>(8)</label><mml:math id="mml-eqn-8" display="block"><mml:mi>D</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>|</mml:mo><mml:mi>C</mml:mi><mml:mo>.</mml:mo><mml:msubsup><mml:mi>P</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>e</mml:mi><mml:mi>s</mml:mi><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msubsup><mml:mo>&#x2212;</mml:mo><mml:msup><mml:mi>P</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msup><mml:mo>|</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p><disp-formula id="eqn-9"><label>(9)</label><mml:math id="mml-eqn-9" display="block"><mml:msup><mml:mi>P</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:msubsup><mml:mi>P</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>e</mml:mi><mml:mi>s</mml:mi><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msubsup><mml:mo>&#x2212;</mml:mo><mml:mi>A</mml:mi><mml:mo>.</mml:mo><mml:mover><mml:mi>D</mml:mi><mml:mo accent="false">&#x00AF;</mml:mo></mml:mover></mml:math></disp-formula></p>
<p>In which <inline-formula id="ieqn-33"><mml:math id="mml-ieqn-33"><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>e</mml:mi><mml:mi>s</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> denotes the present optimal solution. In WOA, during the search process, the bubble-net strategy is executed by:</p>
<p><disp-formula id="eqn-10"><label>(10)</label><mml:math id="mml-eqn-10" display="block"><mml:msup><mml:mi>D</mml:mi><mml:mrow><mml:mo>&#x22C6;</mml:mo></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:msubsup><mml:mi>P</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>e</mml:mi><mml:mi>s</mml:mi><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msubsup><mml:mo>&#x2212;</mml:mo><mml:msup><mml:mi>P</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msup></mml:math></disp-formula></p>
<p><disp-formula id="eqn-11"><label>(11)</label><mml:math id="mml-eqn-11" display="block"><mml:msup><mml:mi>P</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:msup><mml:mi>D</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup><mml:mo>&#x22C5;</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>l</mml:mi></mml:mrow></mml:msup><mml:mo>&#x22C5;</mml:mo><mml:mi>cos</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mi mathvariant="normal">&#x03A0;</mml:mi><mml:mi>l</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msubsup><mml:mi>P</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>e</mml:mi><mml:mi>s</mml:mi><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:math></disp-formula></p>
<p>In which b is utilized for determining the shape of logarithmic spiral, and the values of <inline-formula id="ieqn-34"><mml:math id="mml-ieqn-34"><mml:mi>b</mml:mi></mml:math></inline-formula> has a constant, <inline-formula id="ieqn-35"><mml:math id="mml-ieqn-35"><mml:mi>l</mml:mi></mml:math></inline-formula> denotes an arbitrary value estimated by the <xref ref-type="disp-formula" rid="eqn-12">Eq. (12)</xref>:</p>
<p><disp-formula id="eqn-12"><label>(12)</label><mml:math id="mml-eqn-12" display="block"><mml:mi>l</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mi>r</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math></disp-formula></p>
<p>In the equation, the values of <inline-formula id="ieqn-36"><mml:math id="mml-ieqn-36"><mml:mi>a</mml:mi><mml:mi>i</mml:mi><mml:mi>s</mml:mi></mml:math></inline-formula> linearly reduce with the values <inline-formula id="ieqn-37"><mml:math id="mml-ieqn-37"><mml:mo stretchy="false">(</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> to <inline-formula id="ieqn-38"><mml:math id="mml-ieqn-38"><mml:mo stretchy="false">(</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> in the iteration, and <inline-formula id="ieqn-39"><mml:math id="mml-ieqn-39"><mml:mi>r</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:math></inline-formula> is an arbitrary value within [0, 1]. In the searching phase, switching between the exploitation and exploration phase is selected on the basis of <inline-formula id="ieqn-40"><mml:math id="mml-ieqn-40"><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mi>A</mml:mi><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mo>.</mml:mo></mml:math></inline-formula> When <inline-formula id="ieqn-41"><mml:math id="mml-ieqn-41"><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mi>A</mml:mi><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mo>&#x2265;</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo></mml:math></inline-formula> the exploration phase takes place that allows global search through <xref ref-type="disp-formula" rid="eqn-4">Eqs. (4)</xref> and <xref ref-type="disp-formula" rid="eqn-5">(5)</xref>. If <inline-formula id="ieqn-42"><mml:math id="mml-ieqn-42"><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mi>A</mml:mi><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mo>&#x003C;</mml:mo><mml:mn>1</mml:mn></mml:math></inline-formula>, upgrade the position of individual is implemented by <xref ref-type="disp-formula" rid="eqn-9">Eqs. (9)</xref> or <xref ref-type="disp-formula" rid="eqn-11">(11)</xref>. Based on a <inline-formula id="ieqn-43"><mml:math id="mml-ieqn-43"><mml:mi>&#x03B2;</mml:mi></mml:math></inline-formula> probabilities value that is 0.5 to all the WOA processes switch among encircling prey or bubble-net attack model. <xref ref-type="fig" rid="fig-2">Fig. 2</xref> demonstrates the flowchart of WOA.</p>
<fig id="fig-2">
<label>Figure 2</label>
<caption>
<title>Flowchart of WOA</title>
</caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CMC_27050-fig-2.tif"/>
</fig>
<p><disp-formula id="eqn-13"><label>(13)</label><mml:math id="mml-eqn-13" display="block"><mml:mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mml:mtr><mml:mtd><mml:msup><mml:mi>P</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msup></mml:mtd><mml:mtd><mml:mi></mml:mi><mml:mo>=</mml:mo><mml:msubsup><mml:mi>P</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>e</mml:mi><mml:mi>s</mml:mi><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msubsup><mml:mo>&#x2212;</mml:mo><mml:mi>A</mml:mi><mml:mo>.</mml:mo><mml:mover><mml:mi>D</mml:mi><mml:mo accent="false">&#x00AF;</mml:mo></mml:mover><mml:mspace width="2em" /><mml:mspace width="2em" /><mml:mspace width="1em" /><mml:mtext>&#x00A0;&#x00A0;&#x00A0;</mml:mtext><mml:mi>i</mml:mi><mml:mi>f</mml:mi><mml:mspace width="thinmathspace" /><mml:mi>&#x03B2;</mml:mi><mml:mo>&#x003C;</mml:mo><mml:mn>0.5</mml:mn></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msup><mml:mi>P</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msup></mml:mtd><mml:mtd><mml:mi></mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mi>D</mml:mi><mml:mrow><mml:mo>&#x22C6;</mml:mo></mml:mrow></mml:msup><mml:mo>&#x22C5;</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>l</mml:mi></mml:mrow></mml:msup><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>s</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mi>&#x03C0;</mml:mi><mml:mi>l</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo><mml:msubsup><mml:mi>P</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>e</mml:mi><mml:mi>s</mml:mi><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msubsup><mml:mspace width="1em" /><mml:mi>i</mml:mi><mml:mi>f</mml:mi><mml:mspace width="thinmathspace" /><mml:mi>&#x03B2;</mml:mi><mml:mo>&#x2265;</mml:mo><mml:mn>0.5</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula></p>
</sec>
<sec id="s3_3">
<label>3.3</label>
<title>Object Classification Using NB Model</title>
<p>At the last stage, the NB classifier [<xref ref-type="bibr" rid="ref-21">21</xref>] is utilized for the classification of detected waste objects into recyclable and non-recyclable ones. The NB classifier method was dependent upon Bayes rule that considers that every feature <inline-formula id="ieqn-44"><mml:math id="mml-ieqn-44"><mml:msub><mml:mi>X</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>X</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> are conditional independent of everyone. So, if <inline-formula id="ieqn-45"><mml:math id="mml-ieqn-45"><mml:mi>X</mml:mi></mml:math></inline-formula> has of <inline-formula id="ieqn-46"><mml:math id="mml-ieqn-46"><mml:mi>n</mml:mi></mml:math></inline-formula> features conditional independent of one another provided <inline-formula id="ieqn-47"><mml:math id="mml-ieqn-47"><mml:mi>Y</mml:mi></mml:math></inline-formula>, it can be determined as <xref ref-type="disp-formula" rid="eqn-14">Eq. (14)</xref></p>
<p><disp-formula id="eqn-14"><label>(14)</label><mml:math id="mml-eqn-14" display="block"><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>X</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>X</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>Y</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:munderover><mml:mo>&#x220F;</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:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>Y</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></disp-formula></p>
<p>Usually, <inline-formula id="ieqn-48"><mml:math id="mml-ieqn-48"><mml:mi>Y</mml:mi></mml:math></inline-formula> has some discrete value variable and features <inline-formula id="ieqn-49"><mml:math id="mml-ieqn-49"><mml:msub><mml:mi>X</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>X</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> are some separate or real valued feature. The purpose is for training a classifier which resultants the probability on feasible values of <inline-formula id="ieqn-50"><mml:math id="mml-ieqn-50"><mml:mi>Y</mml:mi></mml:math></inline-formula>, to all novel instances <inline-formula id="ieqn-51"><mml:math id="mml-ieqn-51"><mml:mi>X</mml:mi></mml:math></inline-formula> is that forecasted. Based on the Bayes rule, the probabilities that <inline-formula id="ieqn-52"><mml:math id="mml-ieqn-52"><mml:mi>Y</mml:mi></mml:math></inline-formula> is undertaking their <inline-formula id="ieqn-53"><mml:math id="mml-ieqn-53"><mml:msup><mml:mi>k</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> feasible value was provided 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>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>Y</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mfrac><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>Y</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>X</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:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mi>Y</mml:mi></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:munder><mml:mo>&#x2211;</mml:mo><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:munder><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>Y</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>X</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:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mi>Y</mml:mi></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:math></disp-formula>where the sum over entire feasible values <inline-formula id="ieqn-54"><mml:math id="mml-ieqn-54"><mml:mi>o</mml:mi><mml:mi>f</mml:mi><mml:mspace width="thinmathspace" /><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of <inline-formula id="ieqn-55"><mml:math id="mml-ieqn-55"><mml:mi>Y</mml:mi></mml:math></inline-formula> was attained. According to the assumption that feature <inline-formula id="ieqn-56"><mml:math id="mml-ieqn-56"><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> are conditional independent offered <inline-formula id="ieqn-57"><mml:math id="mml-ieqn-57"><mml:mi>Y</mml:mi></mml:math></inline-formula>, <xref ref-type="disp-formula" rid="eqn-15">Eq. (15)</xref> is altered as <xref ref-type="disp-formula" rid="eqn-16">Eq. (16)</xref> that is the elementary formula to NB technique.</p>
<p><disp-formula id="eqn-16"><label>(16)</label><mml:math id="mml-eqn-16" display="block"><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>Y</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:msub><mml:mi>X</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>X</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>Y</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:munder><mml:mo>&#x220F;</mml:mo><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:munder><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>Y</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:munder><mml:mo>&#x2211;</mml:mo><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:munder><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>Y</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:munder><mml:mo>&#x220F;</mml:mo><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:munder><mml:mrow><mml:mtext>P</mml:mtext></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>Y</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mfrac></mml:math></disp-formula></p>
<p>In order to a novel test instance, <inline-formula id="ieqn-58"><mml:math id="mml-ieqn-58"><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mi>w</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>X</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>X</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>, the above in <xref ref-type="disp-formula" rid="eqn-16">Eq. (16)</xref> computes the probabilities that <inline-formula id="ieqn-59"><mml:math id="mml-ieqn-59"><mml:mi>Y</mml:mi></mml:math></inline-formula> is affect a certain class, provided the observed feature values of <inline-formula id="ieqn-60"><mml:math id="mml-ieqn-60"><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mi>w</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, distribution <inline-formula id="ieqn-61"><mml:math id="mml-ieqn-61"><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>Y</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> and <inline-formula id="ieqn-62"><mml:math id="mml-ieqn-62"><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>Y</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> as evaluated in the trained data. For determining the high probable value of <inline-formula id="ieqn-63"><mml:math id="mml-ieqn-63"><mml:mi>Y</mml:mi></mml:math></inline-formula>, the last decision rule to NB classifying is provided in <xref ref-type="disp-formula" rid="eqn-17">Eq. (17)</xref></p>
<p><disp-formula id="eqn-17"><label>(17)</label><mml:math id="mml-eqn-17" display="block"><mml:mi>y</mml:mi><mml:mo stretchy="false">&#x2190;</mml:mo><mml:munder><mml:mrow><mml:mtext>argmax</mml:mtext></mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:munder><mml:mspace width="thinmathspace" /><mml:mfrac><mml:mrow><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>Y</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:munder><mml:mo>&#x220F;</mml:mo><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:munder><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>Y</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:munder><mml:mo>&#x2211;</mml:mo><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:munder><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>Y</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:munder><mml:mo>&#x220F;</mml:mo><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:munder><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>Y</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mfrac></mml:math></disp-formula></p>
<p>As the denominator was independent <inline-formula id="ieqn-64"><mml:math id="mml-ieqn-64"><mml:mi>o</mml:mi><mml:mi>f</mml:mi><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, to decreases to the subsequent in <xref ref-type="disp-formula" rid="eqn-18">Eq. (18)</xref></p>
<p><disp-formula id="eqn-18"><label>(18)</label><mml:math id="mml-eqn-18" display="block"><mml:mi>y</mml:mi><mml:mo stretchy="false">&#x2190;</mml:mo><mml:msub><mml:mrow><mml:mrow><mml:mtext>argmax</mml:mtext></mml:mrow></mml:mrow><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>Y</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:munder><mml:mo>&#x220F;</mml:mo><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:munder><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mfrac><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mi>Y</mml:mi></mml:mfrac><mml:mo>=</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
</sec>
</sec>
<sec id="s4">
<label>4</label>
<title>Experimental Validation</title>
<p>The performance validation of the proposed model takes place using the benchmark dataset from Kaggle repository (available at <ext-link ext-link-type="uri" xlink:href="https://www.kaggle.com/asdasdasasdas/garbage-classification">https://www.kaggle.com/asdasdasasdas/garbage-classification</ext-link>). The dataset comprises images under six class labels namely cardboard, glass, metal, paper, plastic, and trash. The results are examined in two ways namely training/testing of 80:20 and 70:30. The amount of samples under each class is depicted in <xref ref-type="table" rid="table-1">Table 1</xref>. <xref ref-type="fig" rid="fig-3">Figs. 3</xref>&#x2013;<xref ref-type="fig" rid="fig-4">4</xref> illustrates the sample images of waste classification.</p>
<table-wrap id="table-1">
<label>Table 1</label>
<caption>
<title>Training and testing dataset analysis under different classes</title>
</caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th>Classes</th>
<th>Total images</th>
<th>Train/Test (80:20)</th>
<th>Train/Test (70:30)</th>
</tr>
</thead>
<tbody>
<tr>
<td>Cardboard (0)</td>
<td>393</td>
<td>314:79</td>
<td>275:118</td>
</tr>
<tr>
<td>Glass (1)</td>
<td>491</td>
<td>393:98</td>
<td>344:147</td>
</tr>
<tr>
<td>Metal (2)</td>
<td>400</td>
<td>320:80</td>
<td>280:120</td>
</tr>
<tr>
<td>Paper (3)</td>
<td>584</td>
<td>467:117</td>
<td>409:175</td>
</tr>
<tr>
<td>Plastic (4)</td>
<td>472</td>
<td>378:94</td>
<td>330:142</td>
</tr>
<tr>
<td>Trash (5)</td>
<td>127</td>
<td>102:25</td>
<td>89:38</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="CMC_27050-fig-3.tif"/>
</fig><fig id="fig-4">
<label>Figure 4</label>
<caption>
<title>Sample waste classification</title>
</caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CMC_27050-fig-4.tif"/>
</fig>
<p><xref ref-type="fig" rid="fig-5">Fig. 5</xref> depicts the confusion matrix derived by the DCNWO-RWOD technique on the train/test data of 80:20. The figure reported that the DCNWO-RWOD technique has proficiently classified 75 images into class 0, 95 images into class 1, 80 images into class 2, 115 images into class 3, 93 images into class 4, and 22 images into class 5.</p>
<fig id="fig-5">
<label>Figure 5</label>
<caption>
<title>Confusion matrix of DCNWO-RWOD technique under train/test data of 80:20</title>
</caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CMC_27050-fig-5.tif"/>
</fig>
<p><xref ref-type="table" rid="table-2">Table 2</xref> and <xref ref-type="fig" rid="fig-6">Fig. 6</xref> demonstrate the overall classifier result analysis of the DCNWO-RWOD technique under train/test data of 80:20. The results have shown the effectual outcome of the DCNWO-RWOD technique under all class labels. For instance, with class 0, the DCNWO-RWOD technique has attained <inline-formula id="ieqn-65"><mml:math id="mml-ieqn-65"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 0.9747, <inline-formula id="ieqn-66"><mml:math id="mml-ieqn-66"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 0.9747, <inline-formula id="ieqn-67"><mml:math id="mml-ieqn-67"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 0.9919, <inline-formula id="ieqn-68"><mml:math id="mml-ieqn-68"><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> of 0.9747, and MCC of 0.9699. Simultaneously, with class 3, the DCNWO-RWOD methodology has gained <inline-formula id="ieqn-69"><mml:math id="mml-ieqn-69"><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> of 0.9831, <inline-formula id="ieqn-70"><mml:math id="mml-ieqn-70"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 0.9915, <inline-formula id="ieqn-71"><mml:math id="mml-ieqn-71"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 0.9939, <inline-formula id="ieqn-72"><mml:math id="mml-ieqn-72"><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> of 0.9872, and MCC of 0.9833. Concurrently, with class 5, the DCNWO-RWOD approach has obtained <inline-formula id="ieqn-73"><mml:math id="mml-ieqn-73"><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> of 0.9600, <inline-formula id="ieqn-74"><mml:math id="mml-ieqn-74"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 0.9600, <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:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 0.9959, <inline-formula id="ieqn-76"><mml:math id="mml-ieqn-76"><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> of 0.9600, and MCC of 0.9579.</p>
<table-wrap id="table-2">
<label>Table 2</label>
<caption>
<title>Result analysis of DCNWO-RWOD technique with different measures under train/test data of 80:20</title>
</caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th align="center" colspan="6">Training/Testing (80:20)</th>
</tr>
</thead>
<tbody>
<tr>
<td>Classes</td>
<td>Precision</td>
<td>Recall</td>
<td>Accuracy</td>
<td>F-Score</td>
<td>MCC</td>
</tr>
<tr>
<td>0</td>
<td>0.9747</td>
<td>0.9747</td>
<td>0.9919</td>
<td>0.9747</td>
<td>0.9699</td>
</tr>
<tr>
<td>1</td>
<td>0.9897</td>
<td>0.9796</td>
<td>0.9939</td>
<td>0.9846</td>
<td>0.9808</td>
</tr>
<tr>
<td>2</td>
<td>0.9875</td>
<td>0.9875</td>
<td>0.9959</td>
<td>0.9875</td>
<td>0.9851</td>
</tr>
<tr>
<td>3</td>
<td>0.9831</td>
<td>0.9915</td>
<td>0.9939</td>
<td>0.9872</td>
<td>0.9833</td>
</tr>
<tr>
<td>4</td>
<td>0.9894</td>
<td>0.9894</td>
<td>0.9959</td>
<td>0.9894</td>
<td>0.9869</td>
</tr>
<tr>
<td>5</td>
<td>0.9600</td>
<td>0.9600</td>
<td>0.9959</td>
<td>0.9600</td>
<td>0.9579</td>
</tr>
<tr>
<td>Average</td>
<td>0.9807</td>
<td>0.9804</td>
<td>0.9946</td>
<td>0.9806</td>
<td>0.9773</td>
</tr>
</tbody>
</table>
</table-wrap><fig id="fig-6">
<label>Figure 6</label>
<caption>
<title>Result analysis of DCNWO-RWOD technique under train/test data of 80:20</title>
</caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CMC_27050-fig-6.tif"/>
</fig>
<p><xref ref-type="fig" rid="fig-7">Fig. 7</xref> showcases the confusion matrix derived by the DCNWO-RWOD approach on the train/test data of 70:30. The figure portrayed that the DCNWO-RWOD system has proficiently classified 115 images into class 0, 144 images into class 1, 117 images into class 2, 173 images into class 3, 138 images into class 4, and 32 images into class 5.</p>
<fig id="fig-7">
<label>Figure 7</label>
<caption>
<title>Confusion matrix of DCNWO-RWOD technique under train/test data of 70:30</title>
</caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CMC_27050-fig-7.tif"/>
</fig>
<p><xref ref-type="table" rid="table-3">Table 3</xref> and <xref ref-type="fig" rid="fig-8">Fig. 8</xref> illustrate the overall classifier result analysis of the DCNWO-RWOD approach under train/test data of 70:30. The outcomes exhibited the effectual outcome of the DCNWO-RWOD approach under all class labels. For instance, with class 0, the DCNWO-RWOD method has obtained <inline-formula id="ieqn-77"><mml:math id="mml-ieqn-77"><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> of 0.9664, <inline-formula id="ieqn-78"><mml:math id="mml-ieqn-78"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 0.9746, <inline-formula id="ieqn-79"><mml:math id="mml-ieqn-79"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 0.9905, <inline-formula id="ieqn-80"><mml:math id="mml-ieqn-80"><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> of 0.9705, and MCC of 0.9648. Besides, with class 3, the DCNWO-RWOD method has attained <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:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 0.9886, <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:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 0.9886, <inline-formula id="ieqn-83"><mml:math id="mml-ieqn-83"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 0.9946, <inline-formula id="ieqn-84"><mml:math id="mml-ieqn-84"><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> of 0.9886, and MCC of 0.9850. Finally, with class 5, the DCNWO-RWOD methodology has gained <inline-formula id="ieqn-85"><mml:math id="mml-ieqn-85"><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> of 0.8889, <inline-formula id="ieqn-86"><mml:math id="mml-ieqn-86"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 0.8421, <inline-formula id="ieqn-87"><mml:math id="mml-ieqn-87"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 0.9865, <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> of 0.8649, and MCC of 0.8581.</p>
<table-wrap id="table-3">
<label>Table 3</label>
<caption>
<title>Result analysis of DCNWO-RWOD technique with different measures under train/test data of 70:30</title>
</caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th align="center" colspan="6">Training/Testing (70:30)</th>
</tr>
</thead>
<tbody>
<tr>
<td>Classes</td>
<td>Precision</td>
<td>Recall</td>
<td>Accuracy</td>
<td>F-score</td>
<td>MCC</td>
</tr>
<tr>
<td>0</td>
<td>0.9664</td>
<td>0.9746</td>
<td>0.9905</td>
<td>0.9705</td>
<td>0.9648</td>
</tr>
<tr>
<td>1</td>
<td>0.9796</td>
<td>0.9796</td>
<td>0.9919</td>
<td>0.9796</td>
<td>0.9745</td>
</tr>
<tr>
<td>2</td>
<td>0.9669</td>
<td>0.9750</td>
<td>0.9905</td>
<td>0.9710</td>
<td>0.9653</td>
</tr>
<tr>
<td>3</td>
<td>0.9886</td>
<td>0.9886</td>
<td>0.9946</td>
<td>0.9886</td>
<td>0.9850</td>
</tr>
<tr>
<td>4</td>
<td>0.9718</td>
<td>0.9718</td>
<td>0.9892</td>
<td>0.9718</td>
<td>0.9651</td>
</tr>
<tr>
<td>5</td>
<td>0.8889</td>
<td>0.8421</td>
<td>0.9865</td>
<td>0.8649</td>
<td>0.8581</td>
</tr>
<tr>
<td>Average</td>
<td>0.9604</td>
<td>0.9553</td>
<td>0.9905</td>
<td>0.9577</td>
<td>0.9522</td>
</tr>
</tbody>
</table>
</table-wrap><fig id="fig-8">
<label>Figure 8</label>
<caption>
<title>Result analysis of DCNWO-RWOD technique under train/test data of 70:30</title>
</caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CMC_27050-fig-8.tif"/>
</fig>
<p><xref ref-type="fig" rid="fig-10">Fig. 10</xref> portrays the receiver operating characteristic (ROC) analysis of the DCNWO-RWOD method train/test data of 70:30. The figure depicted that the DCNWO-RWOD approach has reached improved outcomes with a maximum ROC of 99.9469.</p>
<fig id="fig-9">
<label>Figure 9</label>
<caption>
<title>Sample waste classification results of DCNWO-RWOD technique</title>
</caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CMC_27050-fig-9.tif"/>
</fig>
<fig id="fig-10">
<label>Figure 10</label>
<caption>
<title><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>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> analysis of DCNWO-RWOD technique with existing methods</title>
</caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CMC_27050-fig-10.tif"/>
</fig>
<p><xref ref-type="fig" rid="fig-9">Fig. 9</xref> demonstrates the sample waste classification results obtained by the DCNWO-RWOD technique. The figure reported that the DCNWO-RWOD technique has effectually identified and classified different classes of waste objects.</p>
<p>A comparison study of the garbage waste classification model with recent approaches is shown in <xref ref-type="table" rid="table-4">Table 4</xref>. <xref ref-type="fig" rid="fig-10">Fig. 10</xref> illustrates the comparative <inline-formula id="ieqn-89"><mml:math id="mml-ieqn-89"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> analysis of the DCNWO-RWOD approach with recent methods. The figure reported that the CNN model has accomplished ineffectual outcome with the lower <inline-formula id="ieqn-90"><mml:math id="mml-ieqn-90"><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> value of 0.8860. In line with, the MHS technique has resulted in slightly increased <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:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> value of 0.9710. Followed by, the MLP and ML-CNN techniques have accomplished moderately closer <inline-formula id="ieqn-92"><mml:math id="mml-ieqn-92"><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>values of 0.9800 and 0.9800 respectively. But the DCNWO-RWOD technique has surpassed the other methods with <inline-formula id="ieqn-93"><mml:math id="mml-ieqn-93"><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> of 0.9807.</p>
<table-wrap id="table-4">
<label>Table 4</label>
<caption>
<title>Comparative analysis of DCNWO-RWOD technique with existing approaches</title>
</caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th>Methods</th>
<th>Precision</th>
<th>Recall</th>
<th>Accuracy</th>
</tr>
</thead>
<tbody>
<tr>
<td>CNN model</td>
<td>0.8860</td>
<td>0.0680</td>
<td>0.8770</td>
</tr>
<tr>
<td>MHS model</td>
<td>0.9710</td>
<td>0.9230</td>
<td>0.9160</td>
</tr>
<tr>
<td>MLP model</td>
<td>0.9800</td>
<td>0.0840</td>
<td>0.9900</td>
</tr>
<tr>
<td>ML-CNN model</td>
<td>0.9800</td>
<td>0.9800</td>
<td>0.9900</td>
</tr>
<tr>
<td>DCNWO-RWOD</td>
<td>0.9807</td>
<td>0.9804</td>
<td>0.9946</td>
</tr>
</tbody>
</table>
</table-wrap>
<p><xref ref-type="fig" rid="fig-11">Fig. 11</xref> depicts the comparison <inline-formula id="ieqn-94"><mml:math id="mml-ieqn-94"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> analysis of the DCNWO-RWOD approach with recent techniques. The figure revealed that the CNN approach has accomplished ineffectual outcome with the lower <inline-formula id="ieqn-95"><mml:math id="mml-ieqn-95"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> value of 0.0680. Likewise, the MHS approach has resulted in somewhat superior <inline-formula id="ieqn-96"><mml:math id="mml-ieqn-96"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> value of 0.9230. Also, the MLP and ML-CNN systems have accomplished moderately closer <inline-formula id="ieqn-97"><mml:math id="mml-ieqn-97"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> values of 0.0840 and 0.9800 respectively. But the DCNWO-RWOD method has surpassed the other techniques with <inline-formula id="ieqn-98"><mml:math id="mml-ieqn-98"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 0.9804.</p>
<fig id="fig-11">
<label>Figure 11</label>
<caption>
<title><inline-formula id="ieqn-100"><mml:math id="mml-ieqn-100"><mml:mi>R</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> analysis of DCNWO-RWOD technique with existing methods</title>
</caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CMC_27050-fig-11.tif"/>
</fig>
<p><xref ref-type="fig" rid="fig-12">Fig. 12</xref> demonstrates the comparative <inline-formula id="ieqn-101"><mml:math id="mml-ieqn-101"><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:math></inline-formula> analysis of the DCNWO-RWOD system with recent methods. The figure portrayed that the CNN method has accomplished ineffectual outcomes with the lesser <inline-formula id="ieqn-102"><mml:math id="mml-ieqn-102"><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:math></inline-formula> value of 0.8770. Also, the MHS approach has resulted in slightly higher <inline-formula id="ieqn-103"><mml:math id="mml-ieqn-103"><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:math></inline-formula> value of 0.9160. Afterward, the MLP and ML-CNN systems have accomplished moderately similar <inline-formula id="ieqn-104"><mml:math id="mml-ieqn-104"><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:math></inline-formula> values of 0.9900. But the DCNWO-RWOD methodology has surpassed the other approaches with <inline-formula id="ieqn-105"><mml:math id="mml-ieqn-105"><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:math></inline-formula> of 0.9946.</p>
<fig id="fig-12">
<label>Figure 12</label>
<caption>
<title><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:math></inline-formula> analysis of DCNWO-RWOD technique with existing methods</title>
</caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CMC_27050-fig-12.tif"/>
</fig>
</sec>
<sec id="s5">
<label>5</label>
<title>Conclusion</title>
<p>In this study, an effective DCNWO-RWOD technique has been developed to properly identify and classify the objects into recyclable and non-recyclable ones. The proposed DCNWO-RWOD technique undergoes major subprocesses namely DCN based object detection, WOA based hyperparameter tuning, and NB based classification. For improving the overall object detection efficiency of the DCN model, the WOA is exploited. Finally, the NB classifier is used for the classification of detected waste objects into recyclable and non-recyclable ones. The performance validation of the DCNWO-RWOD technique takes place using the open access dataset. The extensive comparative study reported the enhanced performance of the DCNWO-RWOD technique interms of several measures. Therefore, the DCNWO-RWOD technique has been employed as an effective tool for waste object detection and classification. In future, the detection performance of the DCNWO-RWOD technique can be boosted by the design of ensemble of DL models.</p>
</sec>
</body>
<back>
<sec><title>Funding Statement</title>
<p>The authors extend their appreciation to the <funding-source>Deanship of Scientific Research at King Khalid University</funding-source> for funding this work under grant number (<award-id>RGP2/42/43</award-id>). <funding-source>Princess Nourah bint Abdulrahman University Researchers</funding-source> Supporting Project number (<award-id>PNURSP2022R114</award-id>), <funding-source>Princess Nourah bint Abdulrahman University</funding-source>, Riyadh, Saudi Arabia.</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>
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