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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">31625</article-id>
<article-id pub-id-type="doi">10.32604/cmc.2022.031625</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Hunger Search Optimization with Hybrid Deep Learning Enabled Phishing Detection and Classification Model</article-title>
<alt-title alt-title-type="left-running-head">Hunger Search Optimization with Hybrid Deep Learning Enabled Phishing Detection and Classification Model</alt-title>
<alt-title alt-title-type="right-running-head">Hunger Search Optimization with Hybrid Deep Learning Enabled Phishing Detection and Classification Model</alt-title>
</title-group>
<contrib-group content-type="authors">
<contrib id="author-1" contrib-type="author">
<name name-style="western"><surname>Shaiba</surname><given-names>Hadil</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>Alzahrani</surname><given-names>Jaber S.</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>Eltahir</surname><given-names>Majdy M.</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-4">4</xref></contrib>
<contrib id="author-5" contrib-type="author">
<name name-style="western"><surname>Mohsen</surname><given-names>Heba</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>Hamza</surname><given-names>Manar Ahmed</given-names>
</name><xref ref-type="aff" rid="aff-6">6</xref><email>ma.hamza@psau.edu.sa</email></contrib>
<aff id="aff-1"><label>1</label><institution>Department of Computer Sciences, College of Computer and Information Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428</institution>, <addr-line>Riyadh, 11671</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-2"><label>2</label><institution>Department of Industrial Engineering, College of Engineering at Alqunfudah, Umm Al-Qura University</institution>, <country>Saudi Arabia</country></aff>
<aff id="aff-3"><label>3</label><institution>Department of Information Systems, College of Science &#x0026; Art at Mahayil, King Khalid University</institution>, <country>Saudi Arabia</country></aff>
<aff id="aff-4"><label>4</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-5"><label>5</label><institution>Department of Computer Science, Faculty of Computers and Information Technology, Future University in Egypt</institution>, <addr-line>New Cairo, 11835</addr-line>, <country>Egypt</country></aff>
<aff id="aff-6"><label>6</label><institution>Department of Computer and Self Development, Preparatory Year Deanship, Prince Sattam bin Abdulaziz University</institution>, <addr-line>AlKharj</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 pub-type="epub" date-type="pub" iso-8601-date="2022-07-25"><day>25</day>
<month>07</month>
<year>2022</year></pub-date>
<volume>73</volume>
<issue>3</issue>
<fpage>6425</fpage>
<lpage>6441</lpage>
<history>
<date date-type="received">
<day>22</day>
<month>4</month>
<year>2022</year>
</date>
<date date-type="accepted">
<day>07</day>
<month>6</month>
<year>2022</year>
</date>
</history>
<permissions>
<copyright-statement>&#x00A9; 2022 Shaiba et al.</copyright-statement>
<copyright-year>2022</copyright-year>
<copyright-holder>Shaiba 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_31625.pdf"></self-uri>
<abstract>
<p>Phishing is one of the simplest ways in cybercrime to hack the reliable data of users such as passwords, account identifiers, bank details, etc. In general, these kinds of cyberattacks are made at users through phone calls, emails, or instant messages. The anti-phishing techniques, currently under use, are mainly based on source code features that need to scrape the webpage content. In third party services, these techniques check the classification procedure of phishing Uniform Resource Locators (URLs). Even though Machine Learning (ML) techniques have been lately utilized in the identification of phishing, they still need to undergo feature engineering since the techniques are not well-versed in identifying phishing offenses. The tremendous growth and evolution of Deep Learning (DL) techniques paved the way for increasing the accuracy of classification process. In this background, the current research article presents a Hunger Search Optimization with Hybrid Deep Learning enabled Phishing Detection and Classification (HSOHDL-PDC) model. The presented HSOHDL-PDC model focuses on effective recognition and classification of phishing based on website URLs. In addition, SOHDL-PDC model uses character-level embedding instead of word-level embedding since the URLs generally utilize words with no importance. Moreover, a hybrid Convolutional Neural Network-Long Short Term Memory (HCNN-LSTM) technique is also applied for identification and classification of phishing. The hyperparameters involved in HCNN-LSTM model are optimized with the help of HSO algorithm which in turn produced improved outcomes. The performance of the proposed HSOHDL-PDC model was validated using different datasets and the outcomes confirmed the supremacy of the proposed model over other recent approaches.</p>
</abstract>
<kwd-group kwd-group-type="author">
<kwd>Uniform resource locators</kwd>
<kwd>phishing</kwd>
<kwd>cyberattacks</kwd>
<kwd>machine learning</kwd>
<kwd>deep learning</kwd>
<kwd>hyperparameter optimization</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1">
<label>1</label>
<title>Introduction</title>
<p>The rapid developments in information communication technologies and worldwide networks induced a paradigm shift from traditional working space to cyberspace, in terms of day-to-day activities such as e-commerce, electronic banking, social networking, and many more [<xref ref-type="bibr" rid="ref-1">1</xref>]. Anonymous, open, and uncontrolled structure of the internet is a splendid medium to make cyberattacks. It translates into the fact that not only the networks are prone to attacks, but the individual and experienced users too face such issues [<xref ref-type="bibr" rid="ref-2">2</xref>]. Though the users are experienced and cautious about cyberattacks, it has become impossible to prevent them from falling into phishing scam to the fullest. In order to increase the success rate of phishing attacks, cyber-attackers consider the personality features of the users too, in particular terms, to deceive the experienced users [<xref ref-type="bibr" rid="ref-3">3</xref>].</p>
<p>The analogy of the phishing attacks can be extracted from &#x2018;fishing&#x2019; the victims. In recent times, these kinds of attacks grab high attention from the researchers. Attackers or phishers consider opening a few deceptive websites as an attractive and promising method. In these methods, exact famous model and legal sites over internet are reciprocated [<xref ref-type="bibr" rid="ref-4">4</xref>]. Even though such webpages consist of similar Graphical User Interfaces (GUI), it tend to have distinct Uniform Resource Locators (URLs) than the original page. Predominantly, a prudent and well-experienced user can identify such malignant web pages by just watching the URLs [<xref ref-type="bibr" rid="ref-5">5</xref>]. However, users tend to miss or not examine the complete address of their web page properly, due to hurried life style. These malicious webpages remain active and is usually sent through social networking tools, other web pages, or just by email messages.</p>
<p>Several anti-phishing methods have evolved in recent years to reduce the effect of phishing sites. Such methods are classified under four categories such as hybrid, lists, information flow method, and heuristics [<xref ref-type="bibr" rid="ref-6">6</xref>]. Among these, lists-related method includes two orders of lists such as blacklist and whitelist. While the former lists the phishing URLs and the latter lists legitimate URLs [<xref ref-type="bibr" rid="ref-7">7</xref>]. Heuristics-based method derives the characteristics of a page&#x2019;s URL and its content. It identifies the phishing sites through complete analysis of such features [<xref ref-type="bibr" rid="ref-8">8</xref>,<xref ref-type="bibr" rid="ref-9">9</xref>]. Hybrid method blends both heuristic-based and lists-based methods. Information flow technique adds bogus credentials to the original credential back and forth to a phishing website randomly [<xref ref-type="bibr" rid="ref-10">10</xref>]. Even though the researchers have enhanced feasible approaches to block phishing sites, attackers also evolved in the meantime to bypass recent tools and are able to deceive the victims.</p>
<p>The researchers in the study conducted earlier [<xref ref-type="bibr" rid="ref-11">11</xref>] projected a Machine Learning (ML) approach-based anti-phishing technique named as PHISH-SAFE based on URL feature. In order to estimate the efficacy of the suggested model, the study considered 14 features from URLs to differentiate whether a web page is phishing or not. The projected technique was trained upon 33,000 phishing and legitimate URLs using Na&#x00EF;ve Bayes (NB) and Support Vector Machine (SVM) classifiers. Wang&#x00A0;et&#x00A0;al.&#x00A0;[<xref ref-type="bibr" rid="ref-12">12</xref>] developed a rapid phishing website recognition method named PDRCNN based on URL of the website. It retrieves the content from target website or uses third-party service as a prior approach.</p>
<p>Barraclough&#x00A0;et&#x00A0;al.&#x00A0;[<xref ref-type="bibr" rid="ref-13">13</xref>,<xref ref-type="bibr" rid="ref-14">14</xref>] proposed modern techniques combining web content-based, heuristic-based, and blacklist-based methodologies along with ML algorithms using comprehensive features to assist in proper recognition of phishing attacks. In the study conducted earlier [<xref ref-type="bibr" rid="ref-15">15</xref>&#x2013;<xref ref-type="bibr" rid="ref-17">17</xref>], a technique based on Non-Inverse matrix Online Sequence Extreme Learning Machine (NIOSELM) was proposed to detect phishing attacks. This method considers three kinds of features to systematically describe a webpage. With the NIOSELM approach, Sherman Morriso Woodbury formula was used to prevent the matrix inversion function and presented the concept of Online Sequence Extreme Learning Machine (OSELM) to update the training module.</p>
<p>Ramana&#x00A0;et&#x00A0;al.&#x00A0;[<xref ref-type="bibr" rid="ref-18">18</xref>] presented a smart technology using an ensemble of feature selection techniques to detect the phishing sites and achieve considerable results. The study employed different ML methods to find out the optimal classification method and proposed an ensemble technique using Extreme Gradient Boosting (XGBoost), Random forest, (RF), and Decision tree (DT) algorithms. In literature [<xref ref-type="bibr" rid="ref-19">19</xref>], an ML-based phishing recognition technique was presented to protect the webpage and users from cyber-attacks. In order to optimize the outcomes in an effective manner, Term Frequency-Inverse Document Frequency (TF-IDF) value of the website was applied with the technique. ML methodologies namely, Stochastic Gradient Descent (SGD), Logistic Regression (LR), RF, SVM, and NB were employed to train and test the attained data.</p>
<p>In this background, the current research article presents a Hunger Search Optimization with Hybrid Deep Learning enabled Phishing Detection and Classification (HSOHDL-PDC) model. The presented HSOHDL-PDC model focuses on effective recognition and classification of phishing based on website URLs. In addition, SOHDL-PDC model uses character-level embedding instead of word-level embedding since URLs generally use words of no importance. Moreover, a hybrid Convolutional Neural Network-Long Short Term Memory (HCNN-LSTM) technique is applied for identification and classification of phishing. Furthermore, the hyperparameters of HCNN-LSTM model are optimized with the help of HSO algorithm which in turn results in improved outcomes. The performance of the proposed HSOHDL-PDC model was validated using different datasets.</p>
</sec>
<sec id="s2">
<label>2</label>
<title>The Proposed Model</title>
<p>In this study, a novel HSOHDL-PDC model has been proposed for effective recognition and classification of phishing based on website URLs. The proposed HSOHDL-PDC model mainly utilizes character-level embedding rather than word-level embedding since URLs generally utilize words of no importance. Followed by, HSO is applied with HCNN-LSTM model for identification and classification of phishing. <xref ref-type="fig" rid="fig-1">Fig. 1</xref> illustrates the overall process of the proposed HSOHDL-PDC technique.</p>
<sec id="s2_1">
<label>2.1</label>
<title>Character Level Embedding Process</title>
<p>In this work, HSOHDL-PDC model mainly utilizes character-level embedding instead of word-level embedding since URLs generally utilize words of no importance. URLs are processed at Character Level (CL) which remains a solution for difficult vocabulary. Data has been found to be comprised at CL level. The attacker simulates the URLs of original website by altering many unnoticeable characters. For sample, <uri xlink:href="http://google.com">google.com</uri> can be altered to <uri xlink:href="http://google.com">google.com</uri> by replacing &#x2018;oo&#x2019; with &#x2018;00&#x2019;. CL embedding is utilized here to determine this derivative data which in turn enhances the efficiency of malicious URLs identification process. URLs are embedded by defining the m-sized alphabet to input language. Then, all the characters are embedded using one-hot encode. Next, the order of characters is changed to sequence these m-sized vectors at a fixed length, L.
<list list-type="bullet">
<list-item>
<p>Tokenizer: Here, the tokenizer is utilized to proceed the URL from &#x2018;char level&#x2019; and a token is added to the vocabulary. Afterwards, appropriate data is trained while the tokenizer comprises of all the essential info of the data.</p></list-item>
<list-item>
<p>The vocabulary: The alphabets, utilized in general, contain 95 characters such as 10 numbers, 26 upper-case English letters, 26 lower-case English letters, and 33 other characters (e.g.,;.!?: &#x2019; /_@#$&#x2026;etc.)</p></list-item>
<list-item>
<p>Character to index: Next the right vocabulary is received while every URL is demonstrated with the help of character index</p></list-item>
<list-item>
<p>Padding: URL has to be at a distinct length and NN handles only the fixed-length vector. Thus, every URL is supposed to be equivalent length so that CNN procedure can be applied upon the batch data.</p></list-item>
</list></p>
<fig id="fig-1">
<label>Figure 1</label>
<caption>
<title>Overall process of HSOHDL-PDC technique</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31625-fig-1.png"/>
</fig>
</sec>
<sec id="s2_2">
<label>2.2</label>
<title>Hybrid CNN-LSTM Based Classification Model</title>
<p>During data classification process, HCNN-LSTM model is utilized to recognize proper classes. Usually, Recurrent Neural Network (RNN) examines the input data for hidden consecutive designs. This is performed by concatenating the preceding data with present data in both spatial and temporal dimensions and forecasting the future sequence. While RNN extracts the hidden time-series pattern from consecutive data (for instance, video, sensor, or audio data), it is ineffective to remember or hold long data for a long period of time. Eventually, it fails in dealing the issues which involve long-term sequences. A similar kind of problem is signified by gradient exploding or vanishing gradient which is overcome using different types of RNNs, for instance Long Short Term Memory (LSTM). It has the ability to remember the data for a long period [<xref ref-type="bibr" rid="ref-20">20</xref>]. The internal structure of LSTM comprises of many gates (like output, input, and forget gates), whereas, during every iteration, the input in the preceding gate is forwarded to the next gate so as to control the flow of data near the last output. Every gate is generally measured by sigmoid or tanh activation function, i.e., the input gate <inline-formula id="ieqn-1"><mml:math id="mml-ieqn-1"><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> which is responsible for updating the data. But the value of <inline-formula id="ieqn-2"><mml:math id="mml-ieqn-2"><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> is calculated by scalar product of <inline-formula id="ieqn-3"><mml:math id="mml-ieqn-3"><mml:msub><mml:mn>0</mml:mn><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and tanh of <inline-formula id="ieqn-4"><mml:math id="mml-ieqn-4"><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>. Conversely, recurrent unit <inline-formula id="ieqn-5"><mml:math id="mml-ieqn-5"><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> evaluates the state of previous cell <inline-formula id="ieqn-6"><mml:math id="mml-ieqn-6"><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> and present input value <inline-formula id="ieqn-7"><mml:math id="mml-ieqn-7"><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> with the help of tanh activation functions. <xref ref-type="fig" rid="fig-2">Fig. 2</xref> depicts the framework of CNN-LSTM method.</p>
<fig id="fig-2">
<label>Figure 2</label>
<caption>
<title>Structure of CNN-LSTM</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31625-fig-2.png"/>
</fig>
<p>At last, the ultimate result is achieved by passing <inline-formula id="ieqn-8"><mml:math id="mml-ieqn-8"><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> to softmax classification. Mathematically, the functions of the aforementioned gates are formulated herewith.</p>
<p><disp-formula id="eqn-1"><label>(1)</label><mml:math id="mml-eqn-1" display="block"><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant="normal">&#x03A6;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mrow><mml:mover><mml:mi>W</mml:mi><mml:mo stretchy="false">&#x005E;</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>f</mml:mi></mml:mrow></mml:msub><mml:mo>&#x22C5;</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:msup><mml:mn>1</mml:mn><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:msub><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>]</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mi>f</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p><disp-formula id="eqn-2"><label>(2)</label><mml:math id="mml-eqn-2" display="block"><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant="normal">&#x03A6;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mrow><mml:mover><mml:mi>W</mml:mi><mml:mo stretchy="false">&#x005E;</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>&#x22C5;</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:msup><mml:mn>1</mml:mn><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:msub><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>]</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><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:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>t</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>h</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mrow><mml:mover><mml:mi>W</mml:mi><mml:mo stretchy="false">&#x005E;</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:msub><mml:mo>&#x22C5;</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>]</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p><disp-formula id="eqn-4"><label>(4)</label><mml:math id="mml-eqn-4" display="block"><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mi>x</mml:mi><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mi>x</mml:mi><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></disp-formula></p>
<p><disp-formula id="eqn-5"><label>(5)</label><mml:math id="mml-eqn-5" display="block"><mml:msub><mml:mn>0</mml:mn><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant="normal">&#x03A6;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>&#x22C5;</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:msup><mml:mn>1</mml:mn><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:msub><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>]</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p><disp-formula id="eqn-6"><label>(6)</label><mml:math id="mml-eqn-6" display="block"><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>o</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mi mathvariant="italic">x</mml:mi><mml:mi mathvariant="italic">t</mml:mi><mml:mi mathvariant="italic">a</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">h</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="normal">&#x03A6;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p><disp-formula id="eqn-7"><label>(7)</label><mml:math id="mml-eqn-7" display="block"><mml:mrow><mml:mi mathvariant="italic">O</mml:mi><mml:mi mathvariant="italic">u</mml:mi><mml:mi mathvariant="italic">t</mml:mi><mml:mi mathvariant="italic">p</mml:mi><mml:mi mathvariant="italic">u</mml:mi><mml:mi mathvariant="italic">t</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">f</mml:mi><mml:mi mathvariant="italic">t</mml:mi><mml:mi mathvariant="italic">m</mml:mi><mml:mi mathvariant="italic">a</mml:mi><mml:mi mathvariant="italic">x</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>It can be presented in the name of HCNN-LSTM method, whereas the features are extracted in the layer of primary method and then forwarded to other methods for learning and modelling purposes. <inline-formula id="ieqn-9"><mml:math id="mml-ieqn-9"><mml:mn>1</mml:mn></mml:math></inline-formula>-CNN has been developed by the researchers to achieve excellent performance in terms of removing spatial and discriminative features from the data. But, LSTM is utilized by several researchers since it demonstrated its efficacy from sequential and time-series data. By searching these two models, the features with <inline-formula id="ieqn-10"><mml:math id="mml-ieqn-10"><mml:mn>1</mml:mn><mml:mi>D</mml:mi></mml:math></inline-formula>-CNN can be extracted and then these features are forwarded for LSTM to learn and model. These features, found in CNN procedure, are then passed onto two LSTM layers of similar cell size i.e., 64 from all the layers. Adam optimization is utilized in this method with a learning rate of 0.0001.</p>
</sec>
<sec id="s2_3">
<label>2.3</label>
<title>Hyperparameter Optimization</title>
<p>Finally, the hyperparameter of HCNN-LSTM model are optimized with the help of HSO algorithm which in turn results in improved outcomes [<xref ref-type="bibr" rid="ref-21">21</xref>&#x2013;<xref ref-type="bibr" rid="ref-24">24</xref>]. HSO algorithm is stimulated based on foraging and hunger behaviour of animals [<xref ref-type="bibr" rid="ref-25">25</xref>]. In case of (t) individual, its place is decided based on foraging performance and is demonstrated as a mathematical model below.</p>
<p><disp-formula id="eqn-8"><label>(8)</label><mml:math id="mml-eqn-8" display="block"><mml:mover><mml:mrow><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mml:mtr><mml:mtd><mml:mi>G</mml:mi><mml:mi>a</mml:mi><mml:mi>m</mml:mi><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>&#x003A;</mml:mo><mml:mover><mml:mrow><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>&#x00D7;</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mrow><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">a</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">d</mml:mi><mml:mi mathvariant="italic">n</mml:mi></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">)</mml:mo><mml:mo>.</mml:mo></mml:mtd><mml:mtd><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>&#x003C;</mml:mo><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mi>H</mml:mi><mml:mi>G</mml:mi><mml:mi>S</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mi>G</mml:mi><mml:mi>a</mml:mi><mml:mi>m</mml:mi><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>&#x003A;</mml:mo><mml:mover><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>&#x00D7;</mml:mo><mml:mover><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>+</mml:mo><mml:mover><mml:mi>R</mml:mi><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>&#x00D7;</mml:mo><mml:mover><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>&#x00D7;</mml:mo><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mover><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>&#x2212;</mml:mo><mml:mover><mml:mrow><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mo>.</mml:mo></mml:mtd><mml:mtd><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>&#x003E;</mml:mo><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mi>H</mml:mi><mml:mi>G</mml:mi><mml:mi>S</mml:mi></mml:mrow></mml:msub><mml:mo>.</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>&#x003E;</mml:mo><mml:mi>E</mml:mi></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mi>G</mml:mi><mml:mi>a</mml:mi><mml:mi>m</mml:mi><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo>&#x003A;</mml:mo><mml:mover><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>&#x00D7;</mml:mo><mml:mover><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>&#x2212;</mml:mo><mml:mover><mml:mi>R</mml:mi><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>&#x00D7;</mml:mo><mml:mover><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>&#x00D7;</mml:mo><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mover><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>&#x2212;</mml:mo><mml:mover><mml:mrow><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>&#x003E;</mml:mo><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mi>H</mml:mi><mml:mi>G</mml:mi><mml:mi>S</mml:mi></mml:mrow></mml:msub><mml:mo>.</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>&#x003C;</mml:mo><mml:mi>E</mml:mi></mml:mtd></mml:mtr></mml:mtable><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>The factor <inline-formula id="ieqn-11"><mml:math id="mml-ieqn-11"><mml:mover><mml:mrow><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>&#x00D7;</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mrow><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">a</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">d</mml:mi><mml:mi mathvariant="italic">n</mml:mi></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> processes the individual searching for food, at the existing place itself, with an arbitrary hunger performance. In the meantime, the factor <inline-formula id="ieqn-12"><mml:math id="mml-ieqn-12"><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mover><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>&#x2212;</mml:mo><mml:mover><mml:mrow><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow></mml:math></inline-formula> demonstrates the <inline-formula id="ieqn-13"><mml:math id="mml-ieqn-13"><mml:msup><mml:mi>t</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> individual&#x2019;s activity range and the multiplication by factor <inline-formula id="ieqn-14"><mml:math id="mml-ieqn-14"><mml:mover><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2192;</mml:mo></mml:mover></mml:math></inline-formula> put on the effect of hunger on individual&#x2019;s activity. In order to control the activity of the individual, the term <inline-formula id="ieqn-15"><mml:math id="mml-ieqn-15"><mml:mover><mml:mi>R</mml:mi><mml:mo>&#x2192;</mml:mo></mml:mover></mml:math></inline-formula> is established. If <inline-formula id="ieqn-16"><mml:math id="mml-ieqn-16"><mml:mi>R</mml:mi></mml:math></inline-formula> is slow and equal to <inline-formula id="ieqn-17"><mml:math id="mml-ieqn-17"><mml:mn>0</mml:mn></mml:math></inline-formula>, then it denotes that the individual is no longer hungry and its activities are halted. Then, the term <inline-formula id="ieqn-18"><mml:math id="mml-ieqn-18"><mml:mover><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>&#x00D7;</mml:mo><mml:mover><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2192;</mml:mo></mml:mover></mml:math></inline-formula> is added or subtracted to simulate the individual that their peer has reached the place of food. This simulation motivates the individual to search for food in their existing place. Here, the term <inline-formula id="ieqn-19"><mml:math id="mml-ieqn-19"><mml:mover><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2192;</mml:mo></mml:mover></mml:math></inline-formula> implies the error experienced by the individual in obtaining the actual place of the food. In order to calculate the difference in terms of controlling from every position, the subsequent formula is utilized.</p>
<p><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:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:mi>h</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>B</mml:mi><mml:mi>F</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula>whereas <inline-formula id="ieqn-20"><mml:math id="mml-ieqn-20"><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mo>&#x22EF;</mml:mo><mml:mo>,</mml:mo><mml:mi>n</mml:mi></mml:math></inline-formula>. Also, sech <inline-formula id="ieqn-21"><mml:math id="mml-ieqn-21"><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mn>2</mml:mn><mml:mrow><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mfrac><mml:mo>.</mml:mo><mml:mover><mml:mi>R</mml:mi><mml:mo>&#x2192;</mml:mo></mml:mover></mml:math></inline-formula> is computed utilizing the subsequent equation,.</p>
<p><disp-formula id="eqn-10"><label>(10)</label><mml:math id="mml-eqn-10" display="block"><mml:mover><mml:mi>R</mml:mi><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mo>&#x00D7;</mml:mo><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">h</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">k</mml:mi></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">h</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">k</mml:mi></mml:mrow></mml:math></disp-formula></p>
<p><disp-formula id="eqn-11"><label>(11)</label><mml:math id="mml-eqn-11" display="block"><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">h</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">k</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mo>&#x00D7;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mfrac><mml:mi>t</mml:mi><mml:mi>T</mml:mi></mml:mfrac><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>In problem space, HGS functions on the basis of logic of search as given herewith.
<list list-type="bullet">
<list-item>
<p>Searching based on <inline-formula id="ieqn-22"><mml:math id="mml-ieqn-22"><mml:mover><mml:mi>X</mml:mi><mml:mo>&#x2192;</mml:mo></mml:mover></mml:math></inline-formula>: The 1<sup>st</sup> game processes the individual&#x2019;s independent effort to search for the food, out of hunger. This is an approach that is non-cooperative with another individual.</p></list-item>
<list-item>
<p>Searching based on <inline-formula id="ieqn-23"><mml:math id="mml-ieqn-23"><mml:mover><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2192;</mml:mo></mml:mover></mml:math></inline-formula>: Both 2<sup>nd</sup> and 3<sup>rd</sup> games process the cooperation amongst the individuals by means of shared data, assuming the place of food. By tuning the variables <inline-formula id="ieqn-24"><mml:math id="mml-ieqn-24"><mml:mover><mml:mi>R</mml:mi><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>,</mml:mo></mml:math></inline-formula> <inline-formula id="ieqn-25"><mml:math id="mml-ieqn-25"><mml:mover><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>,</mml:mo></mml:math></inline-formula> and <inline-formula id="ieqn-26"><mml:math id="mml-ieqn-26"><mml:mover><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2192;</mml:mo></mml:mover></mml:math></inline-formula>, the places of the individuals are upgraded based on the fundamental determination of other individuals.</p></list-item>
</list></p>
<p>At this point, the individual hunger <inline-formula id="ieqn-27"><mml:math id="mml-ieqn-27"><mml:mover><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2192;</mml:mo></mml:mover></mml:math></inline-formula>, in <xref ref-type="disp-formula" rid="eqn-8">Eq. (8)</xref> is modeled utilizing the following method.</p>
<p><disp-formula id="eqn-12"><label>(12)</label><mml:math id="mml-eqn-12" display="block"><mml:mover><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mml:mtr><mml:mtd><mml:mrow><mml:mi mathvariant="italic">h</mml:mi><mml:mi mathvariant="italic">u</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">g</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">y</mml:mi></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>i</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x00D7;</mml:mo><mml:mfrac><mml:mi>N</mml:mi><mml:mrow><mml:mi mathvariant="italic">S</mml:mi><mml:mi mathvariant="italic">H</mml:mi><mml:mi mathvariant="italic">u</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">g</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">y</mml:mi></mml:mrow></mml:mfrac><mml:mo>&#x00D7;</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub><mml:mo>.</mml:mo></mml:mtd><mml:mtd><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo>&#x003C;</mml:mo><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mi>H</mml:mi><mml:mi>G</mml:mi><mml:mi>S</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mn>1.</mml:mn></mml:mtd><mml:mtd><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo>&#x003E;</mml:mo><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mi>H</mml:mi><mml:mi>G</mml:mi><mml:mi>S</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>In the meantime, the other hunger <inline-formula id="ieqn-28"><mml:math id="mml-ieqn-28"><mml:mover><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2192;</mml:mo></mml:mover></mml:math></inline-formula> as in <xref ref-type="disp-formula" rid="eqn-11">Eq. (11)</xref> is denoted by the equation given below.</p>
<p><disp-formula id="eqn-13"><label>(13)</label><mml:math id="mml-eqn-13" display="block"><mml:mover><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>=</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:mrow><mml:mo>(</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mo>|</mml:mo><mml:mrow><mml:mi mathvariant="italic">h</mml:mi><mml:mi mathvariant="italic">u</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">g</mml:mi><mml:mi mathvariant="italic">e</mml:mi><mml:mi mathvariant="italic">y</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mi mathvariant="italic">S</mml:mi><mml:mi mathvariant="italic">H</mml:mi><mml:mi mathvariant="italic">u</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">g</mml:mi><mml:mi mathvariant="italic">e</mml:mi><mml:mi mathvariant="italic">y</mml:mi></mml:mrow><mml:mo>|</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mn>5</mml:mn></mml:mrow></mml:msub><mml:mo>&#x00D7;</mml:mo><mml:mn>2</mml:mn></mml:math></disp-formula></p>
<p>Here, &#x2018;hungry&#x2019; signifies the <inline-formula id="ieqn-29"><mml:math id="mml-ieqn-29"><mml:mrow><mml:mi mathvariant="italic">h</mml:mi><mml:mi mathvariant="italic">u</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">g</mml:mi><mml:mi mathvariant="italic">e</mml:mi><mml:mi mathvariant="italic">r</mml:mi></mml:mrow></mml:math></inline-formula> of all the individuals.</p>
<p>For calculating the term <inline-formula id="ieqn-30"><mml:math id="mml-ieqn-30"><mml:mrow><mml:mi mathvariant="italic">h</mml:mi><mml:mi mathvariant="italic">u</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">g</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">y</mml:mi></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>i</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> was utilized:</p>
<p><disp-formula id="eqn-14"><label>(14)</label><mml:math id="mml-eqn-14" display="block"><mml:mrow><mml:mi mathvariant="italic">h</mml:mi><mml:mi mathvariant="italic">u</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">g</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">y</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mml:mtr><mml:mtd><mml:mn>0.</mml:mn></mml:mtd><mml:mtd><mml:mrow><mml:mi mathvariant="italic">A</mml:mi><mml:mi mathvariant="italic">l</mml:mi><mml:mi mathvariant="italic">l</mml:mi><mml:mi mathvariant="italic">F</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">t</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">e</mml:mi><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">s</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>==</mml:mo><mml:mi>B</mml:mi><mml:mi>F</mml:mi></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mi mathvariant="italic">h</mml:mi><mml:mi mathvariant="italic">u</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">g</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">y</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>H</mml:mi><mml:mo>.</mml:mo></mml:mtd><mml:mtd><mml:mrow><mml:mi mathvariant="italic">A</mml:mi><mml:mi mathvariant="italic">l</mml:mi><mml:mi mathvariant="italic">l</mml:mi><mml:mi mathvariant="italic">P</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">t</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">e</mml:mi><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">s</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>!</mml:mo><mml:mo>==</mml:mo><mml:mi>B</mml:mi><mml:mi>P</mml:mi></mml:mtd></mml:mtr></mml:mtable><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo></mml:mrow></mml:math></disp-formula>whereas <inline-formula id="ieqn-31"><mml:math id="mml-ieqn-31"><mml:mrow><mml:mi mathvariant="italic">A</mml:mi><mml:mi mathvariant="italic">l</mml:mi><mml:mi mathvariant="italic">l</mml:mi><mml:mi mathvariant="italic">F</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">t</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">e</mml:mi><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">s</mml:mi></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>i</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> signifies the fitness value of every individual from this iteration. In order to process some more iterations, the hunger value of the optimum individual is fixed at <inline-formula id="ieqn-32"><mml:math id="mml-ieqn-32"><mml:mn>0</mml:mn></mml:math></inline-formula>. The equation of (H) is projected in <xref ref-type="disp-formula" rid="eqn-15">Eqs. (15)</xref> and <xref ref-type="disp-formula" rid="eqn-16">(16)</xref>.</p>
<p><disp-formula id="eqn-15"><label>(15)</label><mml:math id="mml-eqn-15" display="block"><mml:mi>T</mml:mi><mml:mi>H</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>F</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>i</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mi>B</mml:mi><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>W</mml:mi><mml:mi>P</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>B</mml:mi><mml:mi>F</mml:mi></mml:mrow></mml:mfrac><mml:mo>&#x00D7;</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mn>6</mml:mn></mml:mrow></mml:msub><mml:mo>&#x00D7;</mml:mo><mml:mn>2</mml:mn><mml:mo>&#x00D7;</mml:mo><mml:mrow><mml:mo>(</mml:mo><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:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p><disp-formula id="eqn-16"><label>(16)</label><mml:math id="mml-eqn-16" display="block"><mml:mi>H</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mml:mtr><mml:mtd><mml:mi>L</mml:mi><mml:mi>H</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mi>r</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>.</mml:mo></mml:mtd><mml:mtd><mml:mi>T</mml:mi><mml:mi>H</mml:mi><mml:mo>&#x003C;</mml:mo><mml:mi>L</mml:mi><mml:mi>H</mml:mi></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mi>T</mml:mi><mml:mi>H</mml:mi><mml:mo>.</mml:mo></mml:mtd><mml:mtd><mml:mi>T</mml:mi><mml:mi>H</mml:mi><mml:mo>&#x2265;</mml:mo><mml:mi>L</mml:mi><mml:mi>H</mml:mi></mml:mtd></mml:mtr></mml:mtable><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>The factor <inline-formula id="ieqn-33"><mml:math id="mml-ieqn-33"><mml:mi>F</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>i</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mi>B</mml:mi><mml:mi>P</mml:mi></mml:math></inline-formula> implies the count of food required by the <inline-formula id="ieqn-34"><mml:math id="mml-ieqn-34"><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> individual to satisfy their hunger. It can be value variations with all the iterations. In the meantime, the factor <inline-formula id="ieqn-35"><mml:math id="mml-ieqn-35"><mml:mi>W</mml:mi><mml:mi>P</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>B</mml:mi><mml:mi>P</mml:mi></mml:math></inline-formula> defines the capacity of the individual to search for food. Hunger ratio is calculated through <inline-formula id="ieqn-36"><mml:math id="mml-ieqn-36"><mml:mfrac><mml:mrow><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mtext>BF</mml:mtext></mml:mrow></mml:mrow><mml:mrow><mml:mi>W</mml:mi><mml:mi>F</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mtext>BF</mml:mtext></mml:mrow></mml:mrow></mml:mfrac></mml:math></inline-formula>. At last, the factor <inline-formula id="ieqn-37"><mml:math id="mml-ieqn-37"><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mn>6</mml:mn></mml:mrow></mml:msub><mml:mo>&#x00D7;</mml:mo><mml:mn>2</mml:mn></mml:math></inline-formula> establishes the positive or negative effect of factors from the neighboring environment on the individual&#x2019;s hunger.</p>
<p>HSO system develops a Fitness Function (FF) to obtain enhanced classification performance. Optimum solution translates into lesser error rate whereas the worst solution means enhanced error rate. FF is provided herewith.</p>
<p><disp-formula id="eqn-17"><label>(17)</label><mml:math id="mml-eqn-17" display="block"><mml:mrow><mml:mi mathvariant="italic">f</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">t</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">e</mml:mi><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">s</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><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:mo>=</mml:mo><mml:mrow><mml:mi mathvariant="italic">C</mml:mi><mml:mi mathvariant="italic">l</mml:mi><mml:mi mathvariant="italic">a</mml:mi><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">f</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">e</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">E</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">R</mml:mi><mml:mi mathvariant="italic">a</mml:mi><mml:mi mathvariant="italic">t</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><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:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:mrow><mml:mrow><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">u</mml:mi><mml:mi mathvariant="italic">m</mml:mi><mml:mi mathvariant="italic">b</mml:mi><mml:mi mathvariant="italic">e</mml:mi><mml:mi mathvariant="italic">r</mml:mi></mml:mrow><mml:mspace width="thickmathspace" /><mml:mi>o</mml:mi><mml:mi>f</mml:mi><mml:mspace width="thickmathspace" /><mml:mrow><mml:mi mathvariant="italic">m</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">l</mml:mi><mml:mi mathvariant="italic">a</mml:mi><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">f</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">e</mml:mi><mml:mi mathvariant="italic">d</mml:mi></mml:mrow><mml:mspace width="thickmathspace" /><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">a</mml:mi><mml:mi mathvariant="italic">m</mml:mi><mml:mi mathvariant="italic">p</mml:mi><mml:mi mathvariant="italic">l</mml:mi><mml:mi mathvariant="italic">e</mml:mi><mml:mi mathvariant="italic">s</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="italic">T</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">t</mml:mi><mml:mi mathvariant="italic">a</mml:mi><mml:mi mathvariant="italic">l</mml:mi></mml:mrow><mml:mspace width="thickmathspace" /><mml:mrow><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">u</mml:mi><mml:mi mathvariant="italic">m</mml:mi><mml:mi mathvariant="italic">b</mml:mi><mml:mi mathvariant="italic">e</mml:mi><mml:mi mathvariant="italic">r</mml:mi></mml:mrow><mml:mspace width="thickmathspace" /><mml:mi>o</mml:mi><mml:mi>f</mml:mi><mml:mspace width="thickmathspace" /><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">a</mml:mi><mml:mi mathvariant="italic">m</mml:mi><mml:mi mathvariant="italic">p</mml:mi><mml:mi mathvariant="italic">l</mml:mi><mml:mi mathvariant="italic">e</mml:mi><mml:mi mathvariant="italic">s</mml:mi></mml:mrow></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>&#x2217;</mml:mo><mml:mn>100</mml:mn></mml:math></disp-formula></p>
</sec>
</sec>
<sec id="s3">
<label>3</label>
<title>Experimental Validation</title>
<p>The proposed HSOHDL-PDC model was experimentally validated using two datasets [<xref ref-type="bibr" rid="ref-26">26</xref>]. The details of the dataset are provided in <xref ref-type="table" rid="table-1">Tab. 1</xref>.</p>
<table-wrap id="table-1">
<label>Table 1</label>
<caption>
<title>Dataset description</title>
</caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th>Dataset</th>
<th>Benign URLs</th>
<th>Phishing URLs</th>
<th>Total No. of URLs</th>
</tr>
</thead>
<tbody>
<tr>
<td>Dataset-1</td>
<td>36400</td>
<td>37175</td>
<td>73575</td>
</tr>
<tr>
<td>Dataset-2</td>
<td>43189</td>
<td>40668</td>
<td>83857</td>
</tr>
</tbody>
</table>
</table-wrap>
<p><xref ref-type="fig" rid="fig-3">Fig. 3</xref> illustrates a set of confusion matrices generated by the proposed HSOHDL-PDC model on dataset-1. With entire dataset, the proposed HSOHDL-PDC model categorized 35,820 samples under benign class and 36,935 samples under phishing class. Along with that, with 70% of training (TR) dataset, HSOHDL-PDC approach categorized 25,008 samples under benign class and 25,898 samples under phishing class. Further, with 30% of testing (TS) dataset, the presented HSOHDL-PDC technique categorized 10,817 samples under benign class and 11,037 samples under phishing class.</p>
<fig id="fig-3">
<label>Figure 3</label>
<caption>
<title>Confusion matrices generated by HSOHDL-PDC technique on dataset-1 (a) Entire dataset, (b) 70% of TR, and (c) 30% of TS</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31625-fig-3.png"/>
</fig>
<p><xref ref-type="table" rid="table-2">Tab. 2</xref> and <xref ref-type="fig" rid="fig-4">Fig. 4</xref> report the overall classification analysis results achieved by the proposed HSOHDL-PDC model on test dataset-1. The table values imply that the proposed HSOHDL-PDC model produced improved outcomes under all the cases. For instance, with entire dataset, HSOHDL-PDC model provided average <inline-formula id="ieqn-38"><mml:math id="mml-ieqn-38"><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>, <inline-formula id="ieqn-39"><mml:math id="mml-ieqn-39"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-40"><mml:math id="mml-ieqn-40"><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>, <inline-formula id="ieqn-41"><mml:math id="mml-ieqn-41"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-42"><mml:math id="mml-ieqn-42"><mml:mi>F</mml:mi><mml:msub><mml:mn>1</mml:mn><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>, and Area Under the Curve (AUC) values such as 98.89%, 98.89%, 98.88%, 98.88%, 98.89%, and 98.88% respectively. Moreover, with 70% of TR dataset, HSOHDL-PDC approach obtained average <inline-formula id="ieqn-43"><mml:math id="mml-ieqn-43"><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>, <inline-formula id="ieqn-44"><mml:math id="mml-ieqn-44"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-45"><mml:math id="mml-ieqn-45"><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>, <inline-formula id="ieqn-46"><mml:math id="mml-ieqn-46"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-47"><mml:math id="mml-ieqn-47"><mml:mi>F</mml:mi><mml:msub><mml:mn>1</mml:mn><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>, and AUC values such as 98.83%, 98.84%, 98.83%, 98.83%, 98.83%, and 98.83% correspondingly. Furthermore, with 30% of TS dataset, HSOHDL-PDC technique offered average <inline-formula id="ieqn-48"><mml:math id="mml-ieqn-48"><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>, <inline-formula id="ieqn-49"><mml:math id="mml-ieqn-49"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-50"><mml:math id="mml-ieqn-50"><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>, <inline-formula id="ieqn-51"><mml:math id="mml-ieqn-51"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-52"><mml:math id="mml-ieqn-52"><mml:mi>F</mml:mi><mml:msub><mml:mn>1</mml:mn><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>, and AUC values such as 99.01%, 99.01%, 99.01%, 99.01%, 99.01%, and 99.01% correspondingly.</p>
<table-wrap id="table-2">
<label>Table 2</label>
<caption>
<title>Results of the analysis of HSOHDL-PDC technique under different measures on dataset-1</title>
</caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th colspan="7">Dataset-1</th>
</tr>
<tr>
<td>Classes</td>
<td>Accuracy</td>
<td>Precision</td>
<td>Recall</td>
<td>Specificity</td>
<td>F-score</td>
<td>AUC score</td>
</tr>
</thead>
<tbody>
<tr>
<td colspan="7">Entire dataset</td>
</tr>
<tr>
<td>Benign</td>
<td>98.89</td>
<td>99.33</td>
<td>98.41</td>
<td>99.35</td>
<td>98.87</td>
<td>98.88</td>
</tr>
<tr>
<td>Phishing</td>
<td>98.89</td>
<td>98.45</td>
<td>99.35</td>
<td>98.41</td>
<td>98.90</td>
<td>98.88</td>
</tr>
<tr>
<td>Average</td>
<td>98.89</td>
<td>98.89</td>
<td>98.88</td>
<td>98.88</td>
<td>98.89</td>
<td>98.88</td>
</tr>
<tr>
<td colspan="7">Training phase (70%)</td>
</tr>
<tr>
<td>Benign</td>
<td>98.83</td>
<td>99.30</td>
<td>98.33</td>
<td>99.32</td>
<td>98.81</td>
<td>98.83</td>
</tr>
<tr>
<td>Phishing</td>
<td>98.83</td>
<td>98.39</td>
<td>99.32</td>
<td>98.33</td>
<td>98.85</td>
<td>98.83</td>
</tr>
<tr>
<td>Average</td>
<td>98.83</td>
<td>98.84</td>
<td>98.83</td>
<td>98.83</td>
<td>98.83</td>
<td>98.83</td>
</tr>
<tr>
<td colspan="7">Testing phase (30%)</td>
</tr>
<tr>
<td>Benign</td>
<td>99.01</td>
<td>99.42</td>
<td>98.58</td>
<td>99.43</td>
<td>99.00</td>
<td>99.01</td>
</tr>
<tr>
<td>Phishing</td>
<td>99.01</td>
<td>98.61</td>
<td>99.43</td>
<td>98.58</td>
<td>99.02</td>
<td>99.01</td>
</tr>
<tr>
<td>Average</td>
<td>99.01</td>
<td>99.01</td>
<td>99.01</td>
<td>99.01</td>
<td>99.01</td>
<td>99.01</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="fig-4">
<label>Figure 4</label>
<caption>
<title>Results of the analysis of HSOHDL-PDC technique under different measures on dataset-1</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31625-fig-4.png"/>
</fig>
<p>A brief precision-recall examination was conducted upon HSOHDL-PDC technique on test dataset-1 and the results are portrayed in <xref ref-type="fig" rid="fig-5">Fig. 5</xref>. By observing the figure, it can be inferred that the proposed HSOHDL-PDC model accomplished the maximum precision-recall performance under all the classes.</p>
<fig id="fig-5">
<label>Figure 5</label>
<caption>
<title>Precision-recall curve analysis results of HSOHDL-PDC technique on dataset-1</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31625-fig-5.png"/>
</fig>
<p>A detailed ROC investigation was conducted upon HSOHDL-PDC method on test dataset-1 and the results are portrayed in <xref ref-type="fig" rid="fig-6">Fig. 6</xref>. The results imply that the proposed HSOHDL-PDC model exhibited its ability to differentiate two distinct classes such as &#x2018;benign&#x2019; and &#x2018;phishing&#x2019; on test dataset.</p>
<fig id="fig-6">
<label>Figure 6</label>
<caption>
<title>ROC curve analysis results of HSOHDL-PDC technique on dataset-1</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31625-fig-6.png"/>
</fig>
<p><xref ref-type="fig" rid="fig-7">Figs. 7</xref> and <xref ref-type="fig" rid="fig-8">8</xref> provide an overview on comprehensive comparative analysis results accomplished by HSOHDL-PDC and other recent models [<xref ref-type="bibr" rid="ref-27">27</xref>]. The results indicate that Gaussian NB model achieved the least performance over other methods. Followed by, multinomial NB, LR, RF, and XGBoost models showcased moderately closer classification performance. Moreover, Deep Neural Network (DNN) and CNN models demonstrated reasonable outcomes with <inline-formula id="ieqn-53"><mml:math id="mml-ieqn-53"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> values being 95.24% and 95.41% respectively. However, the proposed HSOHDL-PDC model accomplished maximum <inline-formula id="ieqn-54"><mml:math id="mml-ieqn-54"><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>, <inline-formula id="ieqn-55"><mml:math id="mml-ieqn-55"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-56"><mml:math id="mml-ieqn-56"><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>, <inline-formula id="ieqn-57"><mml:math id="mml-ieqn-57"><mml:mi>F</mml:mi><mml:msub><mml:mn>1</mml:mn><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>, and AUC values such as 99.01%, 99.01%, 99.01%, 99.01%, and 99.01% respectively.</p>
<fig id="fig-7">
<label>Figure 7</label>
<caption>
<title>Comparative analysis results of HSOHDL-PDC technique on dataset-1</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31625-fig-7.png"/>
</fig>
<fig id="fig-8">
<label>Figure 8</label>
<caption>
<title>AUC and F1-score analyses results of HSOHDL-PDC technique on dataset-1</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31625-fig-8.png"/>
</fig>
<p><xref ref-type="fig" rid="fig-9">Fig. 9</xref> shows a set of confusion matrices generated by HSOHDL-PDC technique on dataset-2. With entire dataset, the proposed HSOHDL-PDC model categorized 42,348 samples under benign class and 39,973 samples under phishing class. In addition, with 70% of TR dataset, the proposed HSOHDL-PDC model categorized 29,675 samples under benign class and 27,973 samples under phishing class. Eventually, with 30% of TS dataset, HSOHDL-PDC algorithm categorized 12,673 samples under benign class and 12,000 samples under phishing class.</p>
<fig id="fig-9">
<label>Figure 9</label>
<caption>
<title>Confusion matrices generated by HSOHDL-PDC technique on Dataset-2 (a) Entire dataset, (b) 70% of TR, and (c) 30% of TS</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31625-fig-9.png"/>
</fig>
<p><xref ref-type="table" rid="table-3">Tab. 3</xref> and <xref ref-type="fig" rid="fig-10">Fig. 10</xref> demonstrate the overall classification output accomplished by HSOHDL-PDC system on test dataset-2. The table values infer that the proposed HSOHDL-PDC model resulted in improved outcomes under all the cases. For instance, with entire dataset, HSOHDL-PDC model offered average <inline-formula id="ieqn-58"><mml:math id="mml-ieqn-58"><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>, <inline-formula id="ieqn-59"><mml:math id="mml-ieqn-59"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-60"><mml:math id="mml-ieqn-60"><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>, <inline-formula id="ieqn-61"><mml:math id="mml-ieqn-61"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-62"><mml:math id="mml-ieqn-62"><mml:mi>F</mml:mi><mml:msub><mml:mn>1</mml:mn><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>, and AUC values such as 98.17%, 98.16%, 98.17%, 98.17%, 98.17%, and 98.17% respectively. Followed by, with 70% of TR dataset, HSOHDL-PDC method attained average <inline-formula id="ieqn-63"><mml:math id="mml-ieqn-63"><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>, <inline-formula id="ieqn-64"><mml:math id="mml-ieqn-64"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-65"><mml:math id="mml-ieqn-65"><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>, <inline-formula id="ieqn-66"><mml:math id="mml-ieqn-66"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-67"><mml:math id="mml-ieqn-67"><mml:mi>F</mml:mi><mml:msub><mml:mn>1</mml:mn><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>, and AUC values such as 98.21%, 98.20%, 98.21%, 98.21%, 98.21%, and 98.21% correspondingly. Moreover, with 30% of TS dataset, the proposed HSOHDL-PDC technique provided average <inline-formula id="ieqn-68"><mml:math id="mml-ieqn-68"><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>, <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>, <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>, <inline-formula id="ieqn-71"><mml:math id="mml-ieqn-71"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-72"><mml:math id="mml-ieqn-72"><mml:mi>F</mml:mi><mml:msub><mml:mn>1</mml:mn><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>, and AUC values such as 98.07%, 98.07%, 98.07%, 98.07%, 98.07%, and 98.07% correspondingly.</p>
<table-wrap id="table-3">
<label>Table 3</label>
<caption>
<title>Results of the analysis of HSOHDL-PDC technique under different measures on Dataset-2</title>
</caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th colspan="7">Dataset-2</th>
</tr>
<tr>
<td>Classes</td>
<td>Accuracy</td>
<td>Precision</td>
<td>Recall</td>
<td>Specificity</td>
<td>F-score</td>
<td>AUC score</td>
</tr>
</thead>
<tbody>
<tr>
<td colspan="7">Entire dataset</td>
</tr>
<tr>
<td>Benign</td>
<td>98.17</td>
<td>98.39</td>
<td>98.05</td>
<td>98.29</td>
<td>98.22</td>
<td>98.17</td>
</tr>
<tr>
<td>Phishing</td>
<td>98.17</td>
<td>97.94</td>
<td>98.29</td>
<td>98.05</td>
<td>98.11</td>
<td>98.17</td>
</tr>
<tr>
<td>Average</td>
<td>98.17</td>
<td>98.16</td>
<td>98.17</td>
<td>98.17</td>
<td>98.17</td>
<td>98.17</td>
</tr>
<tr>
<td colspan="7">Training phase (70%)</td>
</tr>
<tr>
<td>Benign</td>
<td>98.21</td>
<td>98.44</td>
<td>98.08</td>
<td>98.34</td>
<td>98.26</td>
<td>98.21</td>
</tr>
<tr>
<td>Phishing</td>
<td>98.21</td>
<td>97.97</td>
<td>98.34</td>
<td>98.08</td>
<td>98.16</td>
<td>98.21</td>
</tr>
<tr>
<td>Average</td>
<td>98.21</td>
<td>98.20</td>
<td>98.21</td>
<td>98.21</td>
<td>98.21</td>
<td>98.21</td>
</tr>
<tr>
<td colspan="7">Testing phase (30%)</td>
</tr>
<tr>
<td>Benign</td>
<td>98.07</td>
<td>98.26</td>
<td>97.98</td>
<td>98.17</td>
<td>98.12</td>
<td>98.07</td>
</tr>
<tr>
<td>Phishing</td>
<td>98.07</td>
<td>97.87</td>
<td>98.17</td>
<td>97.98</td>
<td>98.02</td>
<td>98.07</td>
</tr>
<tr>
<td>Average</td>
<td>98.07</td>
<td>98.07</td>
<td>98.07</td>
<td>98.07</td>
<td>98.07</td>
<td>98.07</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="fig-10">
<label>Figure 10</label>
<caption>
<title>Results of the analysis of HSOHDL-PDC technique under different measures on Dataset-2</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31625-fig-10.png"/>
</fig>
<p>A detailed precision-recall examination was conducted upon HSOHDL-PDC model on test Dataset-2 and the results are shown in <xref ref-type="fig" rid="fig-11">Fig. 11</xref>. By observing the figure, it can be understood that the proposed HSOHDL-PDC technique accomplished the maximum precision-recall performance under all the classes.</p>
<fig id="fig-11">
<label>Figure 11</label>
<caption>
<title>Precision-recall curve analysis results of HSOHDL-PDC technique on dataset-2</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31625-fig-11.png"/>
</fig>
<p>A brief Receiver Operating Characteristic (ROC) analysis was conducted upon HSOHDL-PDC method on test dataset-2 and the results are shown in <xref ref-type="fig" rid="fig-12">Fig. 12</xref>. The outcomes imply that the proposed HSOHDL-PDC approach exhibited its ability to differentiate two different classes such as &#x2018;benign&#x2019; and &#x2018;phishing&#x2019; on the test dataset.</p>

<fig id="fig-12">
<label>Figure 12</label>
<caption>
<title>ROC curve analysis results of HSOHDL-PDC technique on dataset-2</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_31625-fig-12.png"/>
</fig>
<p><xref ref-type="table" rid="table-4">Tab. 4</xref> shows the comprehensive comparative analysis results accomplished by the proposed HSOHDL-PDC technique and other recent techniques. The outcomes imply that Gaussian NB approach produced the least performance over other methodologies. Next, multinomial NB, LR, RF, and XGBoost models showcased moderately closer classification performance. Besides, DNN and CNN algorithms exhibited reasonable outcomes with <inline-formula id="ieqn-73"><mml:math id="mml-ieqn-73"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> values being 95.23% and 95.34% respectively. At last, the proposed HSOHDL-PDC model accomplished reasonable outcomes with maximal <inline-formula id="ieqn-74"><mml:math id="mml-ieqn-74"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-75"><mml:math id="mml-ieqn-75"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-76"><mml:math id="mml-ieqn-76"><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>, <inline-formula id="ieqn-77"><mml:math id="mml-ieqn-77"><mml:mi>F</mml:mi><mml:msub><mml:mn>1</mml:mn><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>, and AUC values such as 98.07%, 98.07%, 98.07%, 98.07%, and 98.07% correspondingly.</p>
<table-wrap id="table-4">
<label>Table 4</label>
<caption>
<title>Comparative analysis results of HSOHDL-PDC technique and other existing approaches on Dataset-2</title>
</caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th>Methods</th>
<th>Accuracy</th>
<th>Precision</th>
<th>Recall</th>
<th>F1-score</th>
<th>AUC score</th>
</tr>
</thead>
<tbody>
<tr>
<td>Multinomial NB</td>
<td>96.54</td>
<td>95.04</td>
<td>94.25</td>
<td>94.83</td>
<td>95.83</td>
</tr>
<tr>
<td>LR Model</td>
<td>94.93</td>
<td>96.23</td>
<td>94.88</td>
<td>95.37</td>
<td>94.20</td>
</tr>
<tr>
<td>Gaussian NB</td>
<td>95.29</td>
<td>94.11</td>
<td>96.96</td>
<td>95.77</td>
<td>96.30</td>
</tr>
<tr>
<td>RF Model</td>
<td>96.92</td>
<td>94.42</td>
<td>96.15</td>
<td>95.96</td>
<td>96.11</td>
</tr>
<tr>
<td>eXtreme GB</td>
<td>95.49</td>
<td>94.79</td>
<td>94.05</td>
<td>96.12</td>
<td>94.07</td>
</tr>
<tr>
<td>DNN Model</td>
<td>95.23</td>
<td>94.89</td>
<td>96.78</td>
<td>95.87</td>
<td>94.35</td>
</tr>
<tr>
<td>CNN Model</td>
<td>95.34</td>
<td>95.30</td>
<td>94.57</td>
<td>94.51</td>
<td>94.78</td>
</tr>
<tr>
<td>HSOHDL-PDC</td>
<td>98.07</td>
<td>98.07</td>
<td>98.07</td>
<td>98.07</td>
<td>98.07</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s4">
<label>4</label>
<title>Conclusion</title>
<p>In this study, a novel HSOHDL-PDC model has been developed for effective recognition and classification of phishing based on website URLs. The proposed HSOHDL-PDC model mainly utilizes character-level embedding instead of word-level embedding since URLs generally utilize words of no importance. Followed by, HSO is applied with HCNN-LSTM model for identification and classification of phishing. Furthermore, the hyperparameters of HCNN-LSTM model are optimized with the help of HSO algorithm which in turn results in improved outcomes. The performance of the proposed HSOHDL-PDC model was validated using different datasets and the outcomes confirmed the supremacy of the proposed model over recent approaches. In future, hybrid HSO algorithm can be applied to enhance the performance of he HSOHDL-PDC model.</p>
</sec>
</body>
<back>
<fn-group>
<fn fn-type="other"><p><bold>Funding Statement:</bold> The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through Large Groups Project under grant number (158/43). Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2022R135), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia. The authors would like to thank the Deanship of Scientific Research at Umm Al-Qura University for supporting this work by Grant Code: 22UQU4340237DSR22.</p>
</fn>
<fn fn-type="conflict"><p><bold>Conflicts of Interest:</bold> The authors declare that they have no conflicts of interest to report regarding the present study.</p>
</fn>
</fn-group>
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