<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.1 20151215//EN" "http://jats.nlm.nih.gov/publishing/1.1/JATS-journalpublishing1.dtd">
<article xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xml:lang="en" article-type="research-article" dtd-version="1.1">
<front>
<journal-meta>
<journal-id journal-id-type="pmc">IASC</journal-id>
<journal-id journal-id-type="nlm-ta">IASC</journal-id>
<journal-id journal-id-type="publisher-id">IASC</journal-id>
<journal-title-group>
<journal-title>Intelligent Automation &#x0026; Soft Computing</journal-title>
</journal-title-group>
<issn pub-type="epub">2326-005X</issn>
<issn pub-type="ppub">1079-8587</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">39718</article-id>
<article-id pub-id-type="doi">10.32604/iasc.2023.039718</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Enhanced Metaheuristics with Machine Learning Enabled Cyberattack Detection Model</article-title>
<alt-title alt-title-type="left-running-head">Enhanced Metaheuristics with Machine Learning Enabled Cyberattack Detection Model</alt-title>
<alt-title alt-title-type="right-running-head">Enhanced Metaheuristics with Machine Learning Enabled Cyberattack Detection Model</alt-title>
</title-group>
<contrib-group>
<contrib id="author-1" contrib-type="author" corresp="yes">
<name name-style="western"><surname>Almasoud</surname><given-names>Ahmed S.</given-names></name><email>almasoud@psu.edu.sa</email></contrib>
<aff id="aff-1"><institution>Department of Information Systems, College of Computer and Information Sciences, Prince Sultan University</institution>, <addr-line>Riyadh, 12435</addr-line>, <country>Saudi Arabia</country></aff>
</contrib-group>
<author-notes>
<corresp id="cor1"><label>&#x002A;</label>Corresponding Author: Ahmed S. Almasoud. Email: <email>almasoud@psu.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>11</day><month>9</month><year>2023</year></pub-date>
<volume>37</volume>
<issue>3</issue>
<fpage>2849</fpage>
<lpage>2863</lpage>
<history>
<date date-type="received"><day>13</day><month>2</month><year>2023</year></date>
<date date-type="accepted"><day>14</day><month>4</month><year>2023</year></date>
</history>
<permissions>
<copyright-statement>&#x00A9; 2023 Almasoud</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Almasoud</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_IASC_39718.pdf"></self-uri>
<abstract>
<p>The Internet of Things (IoT) is considered the next-gen connection network and is ubiquitous since it is based on the Internet. Intrusion Detection System (IDS) determines the intrusion performance of terminal equipment and IoT communication procedures from IoT environments after taking equivalent defence measures based on the identified behaviour. In this background, the current study develops an Enhanced Metaheuristics with Machine Learning enabled Cyberattack Detection and Classification (EMML-CADC) model in an IoT environment. The aim of the presented EMML-CADC model is to detect cyberattacks in IoT environments with enhanced efficiency. To attain this, the EMML-CADC model primarily employs a data preprocessing stage to normalize the data into a uniform format. In addition, Enhanced Cat Swarm Optimization based Feature Selection (ECSO-FS) approach is followed to choose the optimal feature subsets. Besides, Mayfly Optimization (MFO) with Twin Support Vector Machine (TSVM), called the MFO-TSVM model, is utilized for the detection and classification of cyberattacks. Here, the MFO model has been exploited to fine-tune the TSVM variables for enhanced results. The performance of the proposed EMML-CADC model was validated using a benchmark dataset, and the results were inspected under several measures. The comparative study concluded that the EMML-CADC model is superior to other models under different measures.</p>
</abstract>
<kwd-group kwd-group-type="author">
<kwd>Metaheuristics</kwd>
<kwd>cyberattack detection</kwd>
<kwd>machine learning</kwd>
<kwd>cat swarm optimization</kwd>
<kwd>security</kwd>
</kwd-group>
<funding-group>
<award-group id="awg1">
<funding-source>Prince Sultan University</funding-source>
</award-group>
</funding-group>
</article-meta>
</front>
<body>
<sec id="s1"><label>1</label><title>Introduction</title>
<p>The Internet of Things (IoT) has developed significantly and is performing an important role in the day-to-day lives of human beings [<xref ref-type="bibr" rid="ref-1">1</xref>]. IoT nodes make use of internet protocol addresses and connect to the internet. Such self-configured smart nodes are directed over most cutting-edge application areas, namely, smart education, home automation, decision analytics, smart grids, smart cars, process automation, industrial development, health care system, and many more [<xref ref-type="bibr" rid="ref-2">2</xref>,<xref ref-type="bibr" rid="ref-3">3</xref>]. As per experts, the future is here in which the community exists with as many connected gadgets alike the individuals surviving on this globe. If the volume of applications for IoT increases, the risks also increase in terms of misusing the IoT gadgets for malignant activities such as spying on others, disruption of power networks, remote control of building control systems and even potentially operating traffic signals [<xref ref-type="bibr" rid="ref-4">4</xref>,<xref ref-type="bibr" rid="ref-5">5</xref>].</p>
<p>Conventional firewalls were used for packet filtering earlier, which had many disadvantages, such as rigid pre-defined rules for effective external network assaults. These assaults are very familiar to security specialists. So, there exists a demand for the incorporation of an extra Intrusion Detection System (IDS) with a firewall which alarms the system administrator in case of doubtful signs of anomalies [<xref ref-type="bibr" rid="ref-6">6</xref>]. This method allows the security of adaptable networks by which the anomaly-related IDS can provide a few valuable reviews to network administrators in terms of new and original attack forms as they appear. In general, a firewall necessitates an up-gradation together with an example of the attack types encountered earlier so that it can identify it in future encounters [<xref ref-type="bibr" rid="ref-7">7</xref>,<xref ref-type="bibr" rid="ref-8">8</xref>].</p>
<p>Based on the detection technologies utilized by the system, IDS may be split into Misused-related IDS (MIDS) and Anomaly-related IDS (AIDS). AIDS has the merit of identifying new forms of intrusions [<xref ref-type="bibr" rid="ref-9">9</xref>,<xref ref-type="bibr" rid="ref-10">10</xref>]. It accomplishes a profile of usual operations via Machine Learning (ML) technique. Whenever the activities of a recent subject diverge from its ordinary profile, it is classified as an &#x2018;intrusion&#x2019; conduct created by distinct algorithms [<xref ref-type="bibr" rid="ref-11">11</xref>]. Based on well-known system defects and intrusion designs, MIDS has the potential to identify a few distinctive attacks in a precise manner. However, it heavily depends on pre-defined security plans to identify strange attacks on the system, which results in a lack of identification altogether [<xref ref-type="bibr" rid="ref-12">12</xref>]. With the arrival of big data in recent times, conventional IDSs that depend upon signature-oriented recognition methodologies can be enhanced using ML and Artificial Intelligence (AI) techniques to achieve high-precision design based on previous attack data [<xref ref-type="bibr" rid="ref-13">13</xref>]. Such ML methods might depend on a single classifier using one classification method or multi-classifiers that employ different classification models simultaneously.</p>
<p>In the literature [<xref ref-type="bibr" rid="ref-14">14</xref>], the researchers developed an IDS and implemented and evaluated the precision of the technique. This novel IDS applies a hybrid placement approach related to a multi-agent scheme. This novel scheme contains data management modules, data collection modules, response modules, and analysis modules. To validate the proposed model, this study employed Deep Neural Network (DNN) architecture to detect intrusions. The researchers in the study conducted earlier [<xref ref-type="bibr" rid="ref-15">15</xref>] demonstrated an IDS-based ML method for implementation into an IoT platform as a Service. In this study, Random Forest was employed as a classifier to detect the intrusions while Neural Network (NN) classification was deployed for identifying the intrusion.</p>
<p>In the study conducted earlier [<xref ref-type="bibr" rid="ref-16">16</xref>], the researchers presented feature clusters in terms of Flow, Transmission Control Protocol (TCP), and Message Queuing Telemetry Transport (MQTT) through the UNSW-NB15 data feature. Then, the researchers overcome the challenges such as the curse of dimensionality, imbalanced dataset, and overfitting. Next, the study employed supervised ML techniques such as Artificial Neural Networks (ANNs), Random Forest (RF), and Support Vector Machine (SVM) on the cluster. Hawawreh et al. [<xref ref-type="bibr" rid="ref-17">17</xref>&#x2013;<xref ref-type="bibr" rid="ref-21">21</xref>] presented advanced anomaly detection methodologies that could validate and learn through data gathered from TCP/IP packets. It embraces a successive training procedure, implemented by Deep-FeedForward Neural Network (DNN-FFNN) and Autoencoder (AE) structure, estimated by two popular network datasets.</p>
<p>The current study develops an Enhanced Metaheuristics with Machine Learning enabled Cyberattack Detection and Classification (EMML-CADC) model in an IoT environment. The proposed EMML-CADC model primarily employs data pre-processing to normalize the data into a uniform format. In addition, the Enhanced Cat Swarm Optimization-based Feature Selection (ECSO-FS) approach is applied to choose the optimal feature subsets. Besides, Mayfly Optimization with Twin Support Vector Machine (MFO-TSVM) model is also utilized for the detection and classification of cyberattacks. The MFO model has been exploited to fine-tune the TSVM variables to achieve enhanced results. The proposed EMML-CADC model was experimentally validated for its performance using a benchmark dataset, and the results were inspected under several measures.</p>
</sec>
<sec id="s2"><label>2</label><title>Materials and Methods</title>
<p>In this study, a novel EMML-CADC model is developed to enhance the efficiency of cyberattack detection in an IoT environment. To attain this, the proposed EMML-CADC model primarily employs data pre-processing to normalize the data into a uniform format. In addition, the ECSO-FS approach is applied to choose the optimal feature subsets. Besides, the MFO-TSVM model is also utilized for the detection and classification of cyberattacks. The details related to each module are elaborated on in the succeeding sections.</p>
<sec id="s2_1"><label>2.1</label><title>Design of ECSO-FS Model</title>
<p>At the initial stage, the ECSO-FS model is developed to select an optimal subset of features. CSO approach is inspired by two features of cats Seeking Model (SM) and Tracking Mode (TM). In the CSO approach, the cat possesses the location, including the D-dimensional vector, the velocity of dimension and the fitness value, which denote the flag for detecting the incidence of SM or TM and the addition of the cat into the fitness function (FF) value. The &#x2018;finish&#x2019; solution would be the optimum position of the cat and sustain the optimum one until the process is over [<xref ref-type="bibr" rid="ref-22">22</xref>].</p>
<p>To model the features of cats in resting period and alert, SM is employed. It consists of seeking a memory pool (SMP), seeking a range of the selected dimension (SRD), counts of dimension to change (CDC), and self-position considering (SPC). The process included in SM is shown below:</p>
<p><bold>Step l:</bold> Generate <italic>j</italic> copies of the present position of <inline-formula id="ieqn-1"><mml:math id="mml-ieqn-1"><mml:mi>c</mml:mi><mml:mi>a</mml:mi><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, where <inline-formula id="ieqn-2"><mml:math id="mml-ieqn-2"><mml:mi>j</mml:mi><mml:mo>=</mml:mo></mml:math></inline-formula> SMP. After the SPC value becomes real, consider <inline-formula id="ieqn-3"><mml:math id="mml-ieqn-3"><mml:mi>j</mml:mi><mml:mo>=</mml:mo></mml:math></inline-formula> (SMP <inline-formula id="ieqn-4"><mml:math id="mml-ieqn-4"><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:math></inline-formula>). Then, retain the existing position of the candidate.</p>
<p><bold>Step 2:</bold> For every copy based on CDC, subtract the existing values of SRD per cent and substitute them with prior values.</p>
<p><bold>Step 3:</bold> Describe Fitness Value (FS) for all the candidate points.</p>
<p><bold>Step 4:</bold> If each FS is unequal, define the selection possibility of the candidate point, after which assume the selection possibility of the candidate point as 1.</p>
<p><bold>Step 5:</bold> Define the Fitness Function (FF) for each cat. Once the FF value for each cat is equal, then the selection probability of the cat becomes 1, or else the <inline-formula id="ieqn-5"><mml:math id="mml-ieqn-5"><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> probability is defined as given below:
<disp-formula id="eqn-1"><label>(1)</label><mml:math id="mml-eqn-1" display="block"><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mo>|</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo>|</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext>max</mml:mtext></mml:mrow></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext>min</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:math></disp-formula></p>
<p>Now Fi denotes the fitness value, <inline-formula id="ieqn-6"><mml:math id="mml-ieqn-6"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext>max</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> indicates the maximal fitness value, <inline-formula id="ieqn-7"><mml:math id="mml-ieqn-7"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext>min</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> represents the minimum fitness value, <inline-formula id="ieqn-8"><mml:math id="mml-ieqn-8"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> is provided for the minimization problem. Finally, <inline-formula id="ieqn-9"><mml:math id="mml-ieqn-9"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mtext>&#x00A0;</mml:mtext></mml:math></inline-formula> is given for the maximization problem.</p>
<p>TM signifies the following mode of CSO in which the case aims at tracing the target and food. The process is shown below.</p>
<p><bold>Step 1:</bold> Upgrade the velocity of each dimension using <xref ref-type="disp-formula" rid="eqn-2">Eq. (2)</xref>.</p>
<p><bold>Step 2:</bold> Ensure the velocity is at a high range. Once the new velocity is over-ranged, it is regarded as &#x2018;equal to limit&#x2019;.
<disp-formula id="eqn-2"><label>(2)</label><mml:math id="mml-eqn-2" display="block"><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>X</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:mo>,</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p><bold>Step 3:</bold> Upgrade the location of <inline-formula id="ieqn-10"><mml:math id="mml-ieqn-10"><mml:mi>t</mml:mi><mml:mi>h</mml:mi><mml:mi>e</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>c</mml:mi><mml:mi>a</mml:mi><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> using <xref ref-type="disp-formula" rid="eqn-3">(3)</xref>.
<disp-formula id="eqn-3"><label>(3)</label><mml:math id="mml-eqn-3" display="block"><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:msub></mml:math></disp-formula></p>
<p><inline-formula id="ieqn-11"><mml:math id="mml-ieqn-11"><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">bestd</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> indicates the position of the cat with optimum fitness, <inline-formula id="ieqn-12"><mml:math id="mml-ieqn-12"><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> denotes the position of <inline-formula id="ieqn-13"><mml:math id="mml-ieqn-13"><mml:mi>c</mml:mi><mml:mi>a</mml:mi><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, and <inline-formula id="ieqn-14"><mml:math id="mml-ieqn-14"><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> indicates the acceleration coefficient used for the expansion of velocity of the cat in moving towards the solution space. ECSO algorithm is derived with the help of chaotic concepts in the CSO algorithm rather than using rand, i.e., random value. A chaotic local search technique is introduced based on search strategies to improve the efficiency of CSO in accomplishing the optimum solution [<xref ref-type="bibr" rid="ref-23">23</xref>]. The suggested method aggravates the search method and drives them for progression to a position where the optimum solution is highly possible to be reached. This increases the capability of the exploitation process. Chaos is a popular event in natural non-linear systems. Its ergodic quality, especially traversing each state within a certain range without repetition, is extensively used as a supplementary process to escape from local optimum. In this study, the sinusoidal chaotic map is used to generate the applicable chaotic set. The map was generated using <xref ref-type="disp-formula" rid="eqn-4">Eq. (4)</xref>.
<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>k</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>2.3</mml:mn><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mspace width="thinmathspace" /><mml:mi>s</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mspace width="thinmathspace" /><mml:mi>p</mml:mi><mml:mi>i</mml:mi><mml:mo>&#x2217;</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>In this case, the initial value of the chaotic map is set to 0.8.</p>
<p>The purpose of the CSO technique is to identify the optimum feature subset for the offered dataset with superior classification accuracy and lesser features. At this point, it can be combined with a single weight indicator, and the same FF can be utilized as follows:
<disp-formula id="eqn-5"><label>(5)</label><mml:math id="mml-eqn-5" display="block"><mml:mrow><mml:mtext mathvariant="italic">fitness</mml:mtext></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>&#x03C9;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>&#x00D7;</mml:mo><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mtext mathvariant="italic">classifier</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x03C9;</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><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>s</mml:mi><mml:mi>p</mml:mi></mml:mfrac><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:math></disp-formula></p>
<p>Here, <italic>p</italic> typifies the total amount of features, and <italic>s</italic> refers to the quantity of the chosen features. At this point, the values of <inline-formula id="ieqn-15"><mml:math id="mml-ieqn-15"><mml:msub><mml:mi>&#x03C9;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-16"><mml:math id="mml-ieqn-16"><mml:msub><mml:mi>&#x03C9;</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> are 1 and 0.001, correspondingly. <inline-formula id="ieqn-17"><mml:math id="mml-ieqn-17"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mtext mathvariant="italic">classifer</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> implies the classifier accuracy achieved in the TSVM classifier, provided as follows.
<disp-formula id="eqn-6"><label>(6)</label><mml:math id="mml-eqn-6" display="block"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mtext mathvariant="italic">classifier</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>&#x00D7;</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mn>100</mml:mn><mml:mi mathvariant="normal">&#x0025;</mml:mi><mml:mo>.</mml:mo></mml:math></disp-formula></p>
<p>At this point, <inline-formula id="ieqn-18"><mml:math id="mml-ieqn-18"><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-19"><mml:math id="mml-ieqn-19"><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> stand for the number of inaccurate and accurate classification samples correspondingly.</p>
</sec>
<sec id="s2_2"><label>2.2</label><title>Process Involved in TSVM-Based Classification</title>
<p>In this process, the chosen features are passed onto the TSVM model for the classification process [<xref ref-type="bibr" rid="ref-24">24</xref>]. TSVM model finds two kernel-generated non-parallel functions called <inline-formula id="ieqn-20"><mml:math id="mml-ieqn-20"><mml:mi>&#x03B5;</mml:mi></mml:math></inline-formula>-insensitive downbound function <inline-formula id="ieqn-21"><mml:math id="mml-ieqn-21"><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>K</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mi>x</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:msup><mml:mi>U</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> and an up-bound function <inline-formula id="ieqn-22"><mml:math id="mml-ieqn-22"><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>K</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mi>x</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:msup><mml:mi>U</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula>, correspondingly. The formula for TSVM is given below:
<disp-formula id="ueqn-1">
<mml:math id="mml-ueqn-1" display="block"><mml:mrow><mml:mtext>min</mml:mtext></mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo><mml:mi>y</mml:mi><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>&#x03B5;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mi>e</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mi>K</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>U</mml:mi><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:msup><mml:mi>U</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mi>e</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mspace width="negativethinmathspace" /><mml:msup><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:msub><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></disp-formula></p>
<p>Subjected to,
<disp-formula id="eqn-7"><label>(7)</label><mml:math id="mml-eqn-7" display="block"><mml:mi>y</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mi>K</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>U</mml:mi><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:msup><mml:mi>U</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mi>e</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2265;</mml:mo><mml:msub><mml:mi>&#x03B5;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mi>e</mml:mi><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2265;</mml:mo><mml:mn>0</mml:mn></mml:math></disp-formula>and
<disp-formula id="ueqn-2">
<mml:math id="mml-ueqn-2" display="block"><mml:mrow><mml:mtext>min</mml:mtext></mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo><mml:mi>y</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x03B5;</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mi>e</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mi>K</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>U</mml:mi><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:msup><mml:mi>U</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mi>e</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mspace width="negativethinmathspace" /><mml:msup><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:msub><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math></disp-formula></p>
<p>Subjected to,
<disp-formula id="eqn-8"><label>(8)</label><mml:math id="mml-eqn-8" display="block"><mml:mrow><mml:mo>(</mml:mo><mml:mi>K</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>U</mml:mi><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:msup><mml:mi>U</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mi>e</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>y</mml:mi><mml:mo>&#x2265;</mml:mo><mml:msub><mml:mi>&#x03B5;</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mi>e</mml:mi><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2265;</mml:mo><mml:mn>0</mml:mn></mml:math></disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-8">Eq. (8)</xref>, the regularization parameter is <inline-formula id="ieqn-23"><mml:math id="mml-ieqn-23"><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>&#x003E;</mml:mo><mml:mn>0</mml:mn></mml:math></inline-formula>, and the input parameter is <inline-formula id="ieqn-24"><mml:math id="mml-ieqn-24"><mml:msub><mml:mi>&#x03B5;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>&#x03B5;</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>&#x003E;</mml:mo><mml:mn>0</mml:mn></mml:math></inline-formula>; the vector of the slack variable is <inline-formula id="ieqn-25"><mml:math id="mml-ieqn-25"><mml:msub><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-26"><mml:math id="mml-ieqn-26"><mml:msub><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula>. The dual problems are expressed as follows:</p>
<p><inline-formula id="ieqn-27"><mml:math id="mml-ieqn-27"><mml:mrow><mml:mtext>max</mml:mtext></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:mstyle><mml:mspace width="thinmathspace" /><mml:msubsup><mml:mrow><mml:mi>&#x03B2;</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:msubsup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msup><mml:mi>R</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:msubsup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msup><mml:mi>R</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula></p>
<p>Subjected to
<disp-formula id="eqn-9"><label>(9)</label><mml:math id="mml-eqn-9" display="block"><mml:mn>0</mml:mn><mml:mo>&#x2264;</mml:mo><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2264;</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mi>e</mml:mi></mml:math></disp-formula>and</p>
<p><inline-formula id="ieqn-28"><mml:math id="mml-ieqn-28"><mml:mrow><mml:mtext>max</mml:mtext></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:mstyle><mml:mspace width="thinmathspace" /><mml:msubsup><mml:mrow><mml:mi>&#x03B2;</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:msubsup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msup><mml:mi>S</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:msubsup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msup><mml:mi>S</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula></p>
<p>Subjected to
<disp-formula id="eqn-10"><label>(10)</label><mml:math id="mml-eqn-10" display="block"><mml:mn>0</mml:mn><mml:mo>&#x2264;</mml:mo><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2264;</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mi>e</mml:mi></mml:math></disp-formula>where <inline-formula id="ieqn-29"><mml:math id="mml-ieqn-29"><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x03B5;</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mi>e</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, and <inline-formula id="ieqn-30"><mml:math id="mml-ieqn-30"><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mi>K</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>U</mml:mi><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:msup><mml:mi>U</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow><mml:mtext>&#x00A0;</mml:mtext><mml:mi>e</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:math></inline-formula>. Furthermore, the <inline-formula id="ieqn-31"><mml:math id="mml-ieqn-31"><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mspace width="thinmathspace" /><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mspace width="thinmathspace" /><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mspace width="thinmathspace" /><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> values are defined by:
<disp-formula id="ueqn-3">
<mml:math id="mml-ueqn-3" display="block"><mml:mrow><mml:mo>[</mml:mo><mml:mtable rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable><mml:mo>]</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi mathvariant="normal">&#x2207;</mml:mi><mml:mi>I</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:msubsup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mi>R</mml:mi><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula>and
<disp-formula id="ueqn-4">
<mml:math id="mml-ueqn-4" display="block"><mml:mrow><mml:mo>[</mml:mo><mml:mtable rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable><mml:mo>]</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi mathvariant="normal">&#x2207;</mml:mi><mml:mi>I</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:msubsup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mi>S</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:math></disp-formula></p>
<p>Here, <inline-formula id="ieqn-32"><mml:math id="mml-ieqn-32"><mml:mi mathvariant="normal">&#x2207;</mml:mi><mml:mo>&#x003E;</mml:mo><mml:mn>0</mml:mn></mml:math></inline-formula> and <italic>I</italic> indicate the identity matrix. The term <inline-formula id="ieqn-33"><mml:math id="mml-ieqn-33"><mml:mi mathvariant="normal">&#x2207;</mml:mi><mml:mi>I</mml:mi></mml:math></inline-formula> is added by the matrix <inline-formula id="ieqn-34"><mml:math id="mml-ieqn-34"><mml:msubsup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> to make a positive definite matrix. <xref ref-type="fig" rid="fig-1">Fig. 1</xref> illustrates the structure of the support vector machine (SVM). The kernel estimation function is evaluated for a sample, x <inline-formula id="ieqn-35"><mml:math id="mml-ieqn-35"><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mi>R</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula>, by taking the average of the kernel-generated process.</p>
<fig id="fig-1"><label>Figure 1</label><caption><title>Structure of SVM</title></caption><graphic mimetype="image" mime-subtype="tif" xlink:href="IASC_39718-fig-1.tif"/></fig>
</sec>
<sec id="s2_3"><label>2.3</label><title>Design of MFO-Based Parameter Tuning</title>
<p>In this study, the MFO model is exploited to fine tune [<xref ref-type="bibr" rid="ref-25">25</xref>&#x2013;<xref ref-type="bibr" rid="ref-27">27</xref>] the TSVM variables for enhanced results. MFO algorithm is a robust hybrid algorithm which is designed as per the male mayfly&#x2019;s reproductive behaviour in terms of attracting females through dance. This process merges the advantage of the Firefly Algorithm (FA) and Genetic Algorithm (GA), according to particle swarm optimization (PSO). The MFO algorithm locally searches two populations and updates the speed and position based on particular rules. Individual male adjusts their position by comparing themselves with others [<xref ref-type="bibr" rid="ref-28">28</xref>]. The speed and position of individual males are defined as follows:
<disp-formula id="eqn-11"><label>(11)</label><mml:math id="mml-eqn-11" display="block"><mml:msubsup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mrow><mml:mi>v</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:math></disp-formula>
<disp-formula id="eqn-12"><label>(12)</label><mml:math id="mml-eqn-12" display="block"><mml:msubsup><mml:mrow><mml:mi>v</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mrow><mml:mi>v</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>&#x03B2;</mml:mi><mml:msubsup><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>p</mml:mi><mml:mi>b</mml:mi><mml:mi>e</mml:mi><mml:mi>s</mml:mi><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msubsup><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:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>&#x03B2;</mml:mi><mml:msubsup><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mtext mathvariant="italic">gbest</mml:mtext></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msubsup><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p><inline-formula id="ieqn-36"><mml:math id="mml-ieqn-36"><mml:msubsup><mml:mrow><mml:mi>X</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> indicates the location of <inline-formula id="ieqn-37"><mml:math id="mml-ieqn-37"><mml:mi>i</mml:mi></mml:math></inline-formula>-<inline-formula id="ieqn-38"><mml:math id="mml-ieqn-38"><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> mayfly in <inline-formula id="ieqn-39"><mml:math id="mml-ieqn-39"><mml:mi>k</mml:mi></mml:math></inline-formula>-<inline-formula id="ieqn-40"><mml:math id="mml-ieqn-40"><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> iteration; <inline-formula id="ieqn-41"><mml:math id="mml-ieqn-41"><mml:msubsup><mml:mrow><mml:mi>v</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> represents the speed of <inline-formula id="ieqn-42"><mml:math id="mml-ieqn-42"><mml:mi>i</mml:mi></mml:math></inline-formula>-<inline-formula id="ieqn-43"><mml:math id="mml-ieqn-43"><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> mayfly at <inline-formula id="ieqn-44"><mml:math id="mml-ieqn-44"><mml:mi>k</mml:mi></mml:math></inline-formula>-<inline-formula id="ieqn-45"><mml:math id="mml-ieqn-45"><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> iteration; <inline-formula id="ieqn-46"><mml:math id="mml-ieqn-46"><mml:mi>p</mml:mi><mml:mi>b</mml:mi><mml:mi>e</mml:mi><mml:mi>s</mml:mi><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> signifies the optimal location that <inline-formula id="ieqn-47"><mml:math id="mml-ieqn-47"><mml:mi>i</mml:mi></mml:math></inline-formula>-<inline-formula id="ieqn-48"><mml:math id="mml-ieqn-48"><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> mayfly has accomplished; <inline-formula id="ieqn-49"><mml:math id="mml-ieqn-49"><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-50"><mml:math id="mml-ieqn-50"><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> denote the positive attraction coefficients; <inline-formula id="ieqn-51"><mml:math id="mml-ieqn-51"><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> characterizes the Cartesian distance between mayfly location and the optimum location of an individual. Females fly towards males for breeding, and this also clarifies the mating process. The optimal female is allotted to the optimal male, and thus the location and speed of females are decided, which are shown below:
<disp-formula id="eqn-13"><label>(13)</label><mml:math id="mml-eqn-13" display="block"><mml:msubsup><mml:mrow><mml:mi>v</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mrow><mml:mi>v</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>&#x03B2;</mml:mi><mml:msubsup><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msubsup><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msubsup><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x003E;</mml:mo><mml:mi>f</mml:mi><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:math></disp-formula>
<disp-formula id="eqn-14"><label>(14)</label><mml:math id="mml-eqn-14" display="block"><mml:msubsup><mml:mrow><mml:mi>v</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mrow><mml:mi>v</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mi>f</mml:mi><mml:mi>l</mml:mi><mml:mo>&#x2217;</mml:mo><mml:mi>r</mml:mi><mml:mo>,</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2264;</mml:mo><mml:mi>f</mml:mi><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:math></disp-formula>
<disp-formula id="eqn-15"><label>(15)</label><mml:math id="mml-eqn-15" display="block"><mml:msubsup><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mrow><mml:mi>v</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:math></disp-formula></p>
<p>Amongst others, <inline-formula id="ieqn-52"><mml:math id="mml-ieqn-52"><mml:msubsup><mml:mrow><mml:mi>v</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> denotes the speed of female <inline-formula id="ieqn-53"><mml:math id="mml-ieqn-53"><mml:mi>i</mml:mi></mml:math></inline-formula>-<inline-formula id="ieqn-54"><mml:math id="mml-ieqn-54"><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> mayfly in the <inline-formula id="ieqn-55"><mml:math id="mml-ieqn-55"><mml:mi>k</mml:mi></mml:math></inline-formula>-<inline-formula id="ieqn-56"><mml:math id="mml-ieqn-56"><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> step, <inline-formula id="ieqn-57"><mml:math id="mml-ieqn-57"><mml:msubsup><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> indicates the location of female <inline-formula id="ieqn-58"><mml:math id="mml-ieqn-58"><mml:mi>i</mml:mi></mml:math></inline-formula>-<inline-formula id="ieqn-59"><mml:math id="mml-ieqn-59"><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> mayfly in <inline-formula id="ieqn-60"><mml:math id="mml-ieqn-60"><mml:mi>t</mml:mi><mml:mi>h</mml:mi><mml:mi>e</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>k</mml:mi></mml:math></inline-formula>-<inline-formula id="ieqn-61"><mml:math id="mml-ieqn-61"><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> step, <inline-formula id="ieqn-62"><mml:math id="mml-ieqn-62"><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>f</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> represents the speed of female mayfly from male, and <inline-formula id="ieqn-63"><mml:math id="mml-ieqn-63"><mml:mi>f</mml:mi><mml:mi>l</mml:mi></mml:math></inline-formula> implies the arbitrary movement coefficient. The basic MFO algorithm is a mating procedure between male and female populations. Based on the abovementioned principles of male-attracting-the-female, the crossover function is implemented using the location quantity of two populations. In the following equations, the crossover operation is demonstrated.
<disp-formula id="eqn-16"><label>(16)</label><mml:math id="mml-eqn-16" display="block"><mml:mrow><mml:mtext mathvariant="italic">offspring</mml:mtext></mml:mrow><mml:mn>1</mml:mn><mml:mo>=</mml:mo><mml:mi>L</mml:mi><mml:mo>&#x2217;</mml:mo><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>l</mml:mi><mml:mi>e</mml:mi><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mi>L</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2217;</mml:mo><mml:mrow><mml:mtext mathvariant="italic">female</mml:mtext></mml:mrow></mml:math></disp-formula>
<disp-formula id="eqn-17"><label>(17)</label><mml:math id="mml-eqn-17" display="block"><mml:mrow><mml:mtext mathvariant="italic">offspring</mml:mtext></mml:mrow><mml:mn>2</mml:mn><mml:mo>=</mml:mo><mml:mi>L</mml:mi><mml:mo>&#x2217;</mml:mo><mml:mrow><mml:mtext mathvariant="italic">female</mml:mtext></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mi>L</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2217;</mml:mo><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>l</mml:mi><mml:mi>e</mml:mi></mml:math></disp-formula></p>
<p>Here, <italic>L</italic> indicates an arbitrary number within a specific interval; male corresponds to an individual male mayfly; female implies an individual female mayfly; and offspring denotes the individual mayfly. In the principle of observance of population size constant and late generation population, once it accomplishes the best fitness value, the respective parameter of the preceding generation population is replaced. In other terms, the preceding generation&#x2019;s population would remain constant. Now, <inline-formula id="ieqn-64"><mml:math id="mml-ieqn-64"><mml:mi>f</mml:mi><mml:mspace width="negativethinmathspace" /><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>, i.e., the objective function, must be utilized for the selection and evaluation of the targeted population. <xref ref-type="fig" rid="fig-2">Fig. 2</xref> depicts the flowchart of the MFO technique.</p>
<fig id="fig-2"><label>Figure 2</label><caption><title>Flowchart of MFO</title></caption><graphic mimetype="image" mime-subtype="tif" xlink:href="IASC_39718-fig-2.tif"/></fig>
</sec>
</sec>
<sec id="s3"><label>3</label><title>Results and Discussion</title>
<p>In this section, the proposed model was experimentally validated using the UNSW-NB15 dataset (<ext-link ext-link-type="uri" xlink:href="https://research.unsw.edu.au/projects/unsw-nb15-dataset">https://research.unsw.edu.au/projects/unsw-nb15-dataset</ext-link>). The dataset contains a total of 2,540,044 records or network connections, and there are 10 different classes of attacks that can be detected, along with a class representing normal network traffic. Here are the details of the number of records for each class of attacks: Backdoor: 1746 DoS: 12264 Exploits: 44525 Fuzzers: 24246 Generic: 215481 Reconnaissance: 55604 Shellcode: 1511 Worms: 130 Analysis: 200 Normal: 93000. For experimental validation, ten-fold cross-validation is used.</p>
<p>The results were investigated under several measures. The proposed model is simulated using Python 3.6.5 tool on PC i5-8600k, GeForce 1050Ti 4GB, 16GB RAM, 250GB SSD, and 1TB HDD. The parameter settings are given as follows: learning rate: 0.01, dropout: 0.5, batch size: 5, epoch count: 50, and activation: ReLU. <xref ref-type="table" rid="table-1">Table 1</xref> reports the overall classification results achieved by the EMML-CADC model on distinct class labels. <xref ref-type="fig" rid="fig-3">Fig. 3</xref> illustrates a brief overview of <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>, <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>, and detection rate (DR) outcomes accomplished by the proposed EMML-CADC model under different classes. The figure indicates that the EMML-CADC model accomplished enhanced outcomes in every class. For instance, with normal class, the EMML-CADC model achieved <inline-formula id="ieqn-67"><mml:math id="mml-ieqn-67"><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-68"><mml:math id="mml-ieqn-68"><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>, and DR values such as 82.36&#x0025;, 86.60&#x0025;, and 86.35&#x0025;, respectively. At the same time, with the exploits class, the EMML-CADC system attained <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>, and DR values such as 82.68&#x0025;, 82.15&#x0025;, and 80.75&#x0025;, correspondingly. Moreover, with the Generic class, the proposed EMML-CADC method yielded <inline-formula id="ieqn-71"><mml:math id="mml-ieqn-71"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-72"><mml:math id="mml-ieqn-72"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, and DR values such as 80.89&#x0025;, 84.98&#x0025;, and 97.23&#x0025;, respectively. Also, with the worms class, EMML-CADC methodology accomplished <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>, <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>, and DR values such as 86.29&#x0025;, 83.39&#x0025;, and 83.78&#x0025;.</p>
<table-wrap id="table-1"><label>Table 1</label><caption><title>Results of the analysis of the EMML-CADC technique under various measures and class labels</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 align="left">Labels</th>
<th align="left">Precision</th>
<th align="left">Recall</th>
<th align="left">Detection rate</th>
<th align="left">Accuracy</th>
<th align="left">F-score</th>
<th align="left">MCC</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">Normal</td>
<td align="left">82.36</td>
<td align="left">86.60</td>
<td align="left">86.35</td>
<td align="left">92.16</td>
<td align="left">90.85</td>
<td align="left">81.53</td>
</tr>
<tr>
<td align="left">Analysis</td>
<td align="left">87.25</td>
<td align="left">81.04</td>
<td align="left">72.09</td>
<td align="left">88.29</td>
<td align="left">90.84</td>
<td align="left">81.53</td>
</tr>
<tr>
<td align="left">Backdoor</td>
<td align="left">82.61</td>
<td align="left">81.30</td>
<td align="left">66.39</td>
<td align="left">92.64</td>
<td align="left">89.81</td>
<td align="left">80.85</td>
</tr>
<tr>
<td align="left">DoS</td>
<td align="left">81.20</td>
<td align="left">79.24</td>
<td align="left">95.94</td>
<td align="left">90.96</td>
<td align="left">88.69</td>
<td align="left">80.15</td>
</tr>
<tr>
<td align="left">Exploits</td>
<td align="left">82.68</td>
<td align="left">83.15</td>
<td align="left">80.75</td>
<td align="left">88.10</td>
<td align="left">88.21</td>
<td align="left">79.67</td>
</tr>
<tr>
<td align="left">Fuzzers</td>
<td align="left">85.43</td>
<td align="left">81.54</td>
<td align="left">77.28</td>
<td align="left">92.38</td>
<td align="left">94.27</td>
<td align="left">87.16</td>
</tr>
<tr>
<td align="left">Generic</td>
<td align="left">80.89</td>
<td align="left">84.98</td>
<td align="left">97.23</td>
<td align="left">90.34</td>
<td align="left">88.75</td>
<td align="left">82.72</td>
</tr>
<tr>
<td align="left">Reconnaissance</td>
<td align="left">87.35</td>
<td align="left">78.50</td>
<td align="left">70.76</td>
<td align="left">91.95</td>
<td align="left">93.33</td>
<td align="left">81.69</td>
</tr>
<tr>
<td align="left">Shellcode</td>
<td align="left">85.24</td>
<td align="left">85.13</td>
<td align="left">72.61</td>
<td align="left">91.43</td>
<td align="left">91.61</td>
<td align="left">84.77</td>
</tr>
<tr>
<td align="left">Worms</td>
<td align="left">86.29</td>
<td align="left">83.39</td>
<td align="left">83.78</td>
<td align="left">90.54</td>
<td align="left">91.27</td>
<td align="left">85.29</td>
</tr>
<tr>
<td align="left">Average</td>
<td align="left">84.13</td>
<td align="left">82.49</td>
<td align="left">80.32</td>
<td align="left">90.88</td>
<td align="left">90.76</td>
<td align="left">82.54</td>
</tr>
</tbody>
</table>
</table-wrap><fig id="fig-3"><label>Figure 3</label><caption><title><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>, and DR analysis results of EMML-CADC technique under distinct class labels</title></caption><graphic mimetype="image" mime-subtype="tif" xlink:href="IASC_39718-fig-3.tif"/></fig>
<p><xref ref-type="fig" rid="fig-4">Fig. 4</xref> demonstrates a brief overview of <inline-formula id="ieqn-77"><mml:math id="mml-ieqn-77"><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-78"><mml:math id="mml-ieqn-78"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">score</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula>, and Mathew Correlation Coefficient (MCC) values accomplished by EMML-CADC methodology under different classes. MCC provides a balanced measure of classification performance. The MCC value ranges from &#x2212;100 to 100, where a score of 100 represents a perfect prediction, 0 represents a random prediction, and &#x2212;100 represents a total disagreement between the prediction and the true labels. The figure infers that the proposed EMML-CADC system accomplished enhanced outcomes under every class. For example, with typical class, the EMML-CADC model achieved an <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 92.16&#x0025;, <inline-formula id="ieqn-80"><mml:math id="mml-ieqn-80"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">score</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> of 90.85&#x0025; and MCC of 81.35&#x0025; correspondingly. Meanwhile, with the exploits class, the presented EMML-CADC method accomplished <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>, <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>, and DR values such as 88.10&#x0025;, 88.21&#x0025;, and 79.67&#x0025;, respectively. Additionally, with the Generic class, the proposed EMML-CADC algorithm attained <inline-formula id="ieqn-83"><mml:math id="mml-ieqn-83"><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-84"><mml:math id="mml-ieqn-84"><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>, and DR values such as 90.34&#x0025;, 88.75&#x0025;, and 82.72&#x0025; correspondingly. Likewise, with worms class, the proposed EMML-CADC model yielded <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>, <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>, and DR values such as 90.54&#x0025;, 91.27&#x0025;, and 85.29&#x0025;, respectively.</p>
<fig id="fig-4"><label>Figure 4</label><caption><title><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>, <inline-formula id="ieqn-88"><mml:math id="mml-ieqn-88"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">score</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula>, and MCC analysis results of EMML-CADC technique under distinct class labels</title></caption><graphic mimetype="image" mime-subtype="tif" xlink:href="IASC_39718-fig-4.tif"/></fig>
<p><xref ref-type="table" rid="table-2">Table 2</xref> and <xref ref-type="fig" rid="fig-5">Fig. 5</xref> demonstrate a brief overview of Elapsed Time (ET) analysis results achieved by the proposed EMML-CADC model on training (TR) and testing (TS) data. The experimental results demonstrate that the EMML-CADC model required the least ET values under both TR and TS data. For instance, under normal class, the proposed EMML-CADC model obtained an ET of 4.0500 and 2.0280&#x2005;s on TR and TS data, respectively. Meanwhile, with the DoS class, the EMML-CADC method attained an ET of 0.0110 and 0.0260&#x2005;s on TR and TS data correspondingly. Eventually, with a generic class, the presented EMML-CADC methodology obtained an ET of 1.9220 and 0.0510&#x2005;s on TR and TS data, respectively. Along with that, with the worms class, the EMML-CADC system reached an ET of 0.0030 and 0.0320&#x2005;s on TR and TS data correspondingly.</p>
<table-wrap id="table-2"><label>Table 2</label><caption><title>Elapsed time analysis results of EMML-CADC technique with TR and TS datasets</title></caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th align="center" colspan="3">Elapsed time (sec)</th>
</tr>
<tr>
<th align="left">Labels</th>
<th align="left">Training phase</th>
<th align="left">Testing phase</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">Normal</td>
<td align="left">4.0500</td>
<td align="left">2.0280</td>
</tr>
<tr>
<td align="left">Analysis</td>
<td align="left">0.0230</td>
<td align="left">0.0490</td>
</tr>
<tr>
<td align="left">Backdoor</td>
<td align="left">0.0600</td>
<td align="left">0.0420</td>
</tr>
<tr>
<td align="left">DoS</td>
<td align="left">0.0110</td>
<td align="left">0.0260</td>
</tr>
<tr>
<td align="left">Exploits</td>
<td align="left">1.0650</td>
<td align="left">0.0770</td>
</tr>
<tr>
<td align="left">Fuzzers</td>
<td align="left">1.0660</td>
<td align="left">0.0240</td>
</tr>
<tr>
<td align="left">Generic</td>
<td align="left">1.9220</td>
<td align="left">0.0510</td>
</tr>
<tr>
<td align="left">Reconnaissance</td>
<td align="left">0.1530</td>
<td align="left">0.0410</td>
</tr>
<tr>
<td align="left">Shellcode</td>
<td align="left">0.0090</td>
<td align="left">0.0580</td>
</tr>
<tr>
<td align="left">Worms</td>
<td align="left">0.0030</td>
<td align="left">0.0320</td>
</tr>
<tr>
<td align="left">Average</td>
<td align="left">0.8362</td>
<td align="left">0.2428</td>
</tr>
</tbody>
</table>
</table-wrap><fig id="fig-5"><label>Figure 5</label><caption><title>ET analysis results of EMML-CADC technique with TR and TS datasets</title></caption><graphic mimetype="image" mime-subtype="tif" xlink:href="IASC_39718-fig-5.tif"/></fig>
<p><xref ref-type="table" rid="table-3">Table 3</xref> and <xref ref-type="fig" rid="fig-6">Fig. 6</xref> provide a brief illustration of Computational Time (CT) analysis results achieved by the EMML-CADC model on TR and TS datasets. The experimental results demonstrate that the EMML-CADC system required the least CT values under both TR and TS datasets. For example, with normal class, the EMML-CADC model achieved a CT of 0.9200 and 0.0381&#x2005;s on TR and TS datasets, respectively. In the meantime, with the DoS class, the EMML-CADC model obtained a CT of 0.0110 and 0.0034&#x2005;s on TR and TS datasets correspondingly. Finally, with generic class, the proposed EMML-CADC model obtained a CT of 0.0940 and 0.0140&#x2005;s on TR and TS datasets, respectively. In addition to these, with worms class, the proposed EMML-CADC model obtained a CT of 0.0010 and 0.030&#x2005;s on TR and TS datasets correspondingly.</p>
<table-wrap id="table-3"><label>Table 3</label><caption><title>Computational time analysis results of EMML-CADC technique with TR and TS datasets</title></caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th align="center" colspan="3">Computational time (sec)</th>
</tr>
<tr>
<th align="left">Labels</th>
<th align="left">Training phase</th>
<th align="left">Testing phase</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">Normal</td>
<td align="left">0.9200</td>
<td align="left">0.0381</td>
</tr>
<tr>
<td align="left">Analysis</td>
<td align="left">0.0120</td>
<td align="left">0.0056</td>
</tr>
<tr>
<td align="left">Backdoor</td>
<td align="left">0.0050</td>
<td align="left">0.0031</td>
</tr>
<tr>
<td align="left">DoS</td>
<td align="left">0.0110</td>
<td align="left">0.0034</td>
</tr>
<tr>
<td align="left">Exploits</td>
<td align="left">0.0980</td>
<td align="left">0.0110</td>
</tr>
<tr>
<td align="left">Fuzzers</td>
<td align="left">0.0250</td>
<td align="left">0.0240</td>
</tr>
<tr>
<td align="left">Generic</td>
<td align="left">0.0940</td>
<td align="left">0.0140</td>
</tr>
<tr>
<td align="left">Reconnaissance</td>
<td align="left">0.0150</td>
<td align="left">0.0100</td>
</tr>
<tr>
<td align="left">Shellcode</td>
<td align="left">0.0010</td>
<td align="left">0.0030</td>
</tr>
<tr>
<td align="left">Worms</td>
<td align="left">0.0010</td>
<td align="left">0.0030</td>
</tr>
<tr>
<td align="left">Average</td>
<td align="left">0.1182</td>
<td align="left">0.0115</td>
</tr>
</tbody>
</table>
</table-wrap><fig id="fig-6"><label>Figure 6</label><caption><title>CT analysis results of EMML-CADC technique with TR and TS datasets</title></caption><graphic mimetype="image" mime-subtype="tif" xlink:href="IASC_39718-fig-6.tif"/></fig>
<p><xref ref-type="table" rid="table-4">Table 4</xref> and <xref ref-type="fig" rid="fig-7">Fig. 7</xref> portray the results of comparative DR analysis between the EMML-CADC model and other existing models. The results indicate that the proposed EMML-CADC model achieved better performance than other models. For instance, with standard class, the EMML-CADC model achieved a higher DR of 86.35&#x0025;, whereas Particle Swarm Optimization (PSO)-light Gradient Boosting Machine (GBM), CMLW, Opt. Convolution Neural Network (CNN), Na&#x00EF;ve Bayes (NB), and K-Nearest Neighbor (KNN) models achieved the least DR values such as 80.85&#x0025;, 57.68&#x0025;, 78.08&#x0025;, 52.70&#x0025;, and 83.60&#x0025;, respectively. In addition, with the Denial of Service (DoS) class, the EMML-CADC system attained a high DR of 95.94&#x0025;, while PSO-Light GBM, CMLW, Opt. CNN, NB, and KNN techniques achieved the least DR values, such as 15.40&#x0025;, 15.60&#x0025;, 36.22&#x0025;, 33.50&#x0025;, and 97.70&#x0025;. In line with these, with generic class, EMML-CADC methodology presented a high DR of 97.23&#x0025;, whereas PSO-Light GBM, CMLW, Opt. CNN, NB, and KNN approaches exhibited the least DR values, such as 84.34&#x0025;, 96.20&#x0025;, 96.19&#x0025;, 42.80&#x0025;, and 44.80&#x0025;, correspondingly. At last, with worms class, the EMML-CADC method offered a high DR of 83.78&#x0025;, whereas PSO-Light GBM, CMLW, Opt. CNN, NB, and KNN techniques accomplished the least DR values, such as 77.78&#x0025;, 33.67&#x0025;, 54.55&#x0025;, 40&#x0025;, and 51.15&#x0025;, correspondingly.</p>
<table-wrap id="table-4"><label>Table 4</label><caption><title>Detection rate analysis results of EMML-CADC and other existing techniques under distinct class labels</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 align="center" colspan="7">Detection rate (&#x0025;)</th>
</tr>
<tr>
<th align="left">Labels</th>
<th align="left">PSO-Light GBM</th>
<th align="left">CMLW</th>
<th align="left">Opt.-CNN</th>
<th align="left">NB</th>
<th align="left">KNN</th>
<th align="left">EMML-CADC</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">Normal</td>
<td align="left">80.85</td>
<td align="left">57.68</td>
<td align="left">78.08</td>
<td align="left">52.70</td>
<td align="left">83.60</td>
<td align="left">86.35</td>
</tr>
<tr>
<td align="left">Analysis</td>
<td align="left">26.67</td>
<td align="left">46.09</td>
<td align="left">36.19</td>
<td align="left">1.80</td>
<td align="left">63.50</td>
<td align="left">72.09</td>
</tr>
<tr>
<td align="left">Backdoor</td>
<td align="left">51.28</td>
<td align="left">1.54</td>
<td align="left">8.92</td>
<td align="left">46.50</td>
<td align="left">34.90</td>
<td align="left">66.39</td>
</tr>
<tr>
<td align="left">DoS</td>
<td align="left">15.40</td>
<td align="left">15.60</td>
<td align="left">36.22</td>
<td align="left">33.50</td>
<td align="left">97.70</td>
<td align="left">95.94</td>
</tr>
<tr>
<td align="left">Exploits</td>
<td align="left">48.56</td>
<td align="left">37.68</td>
<td align="left">43.17</td>
<td align="left">61.30</td>
<td align="left">58.80</td>
<td align="left">80.75</td>
</tr>
<tr>
<td align="left">Fuzzers</td>
<td align="left">45.63</td>
<td align="left">33.67</td>
<td align="left">40.88</td>
<td align="left">58.60</td>
<td align="left">20.00</td>
<td align="left">77.28</td>
</tr>
<tr>
<td align="left">Generic</td>
<td align="left">84.34</td>
<td align="left">96.20</td>
<td align="left">96.19</td>
<td align="left">42.80</td>
<td align="left">44.80</td>
<td align="left">97.23</td>
</tr>
<tr>
<td align="left">Reconnaissance</td>
<td align="left">31.33</td>
<td align="left">89.76</td>
<td align="left">23.80</td>
<td align="left">40.00</td>
<td align="left">33.80</td>
<td align="left">70.76</td>
</tr>
<tr>
<td align="left">Shellcode</td>
<td align="left">64.47</td>
<td align="left">3.70</td>
<td align="left">47.35</td>
<td align="left">50.00</td>
<td align="left">30.00</td>
<td align="left">72.61</td>
</tr>
<tr>
<td align="left">Worms</td>
<td align="left">77.78</td>
<td align="left">33.67</td>
<td align="left">54.55</td>
<td align="left">40.00</td>
<td align="left">51.15</td>
<td align="left">83.78</td>
</tr>
<tr>
<td align="left">Average</td>
<td align="left">52.63</td>
<td align="left">41.56</td>
<td align="left">46.54</td>
<td align="left">42.72</td>
<td align="left">51.83</td>
<td align="left">80.32</td>
</tr>
</tbody>
</table>
</table-wrap><fig id="fig-7"><label>Figure 7</label><caption><title>Detection rate analysis results of EMML-CADC and other existing techniques under distinct class labels</title></caption><graphic mimetype="image" mime-subtype="tif" xlink:href="IASC_39718-fig-7.tif"/></fig>
<p>A comparison study was conducted between the EMML-CADC model and other techniques in terms of accuracy, and the results are shown in <xref ref-type="table" rid="table-5">Table 5</xref> [<xref ref-type="bibr" rid="ref-29">29</xref>]. <xref ref-type="fig" rid="fig-8">Fig. 8</xref> depicts the comparative <inline-formula id="ieqn-89"><mml:math id="mml-ieqn-89"><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> examination results achieved by the EMML-CADC model against recent techniques. The improved Extreme Learning Machine (I-ELM) model achieved a slightly low <inline-formula id="ieqn-90"><mml:math id="mml-ieqn-90"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 67.01&#x0025;, whereas the Expectation-maximization model reported a moderately improved <inline-formula id="ieqn-91"><mml:math id="mml-ieqn-91"><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 78.47&#x0025;. Followed by Logistic Regression (LR) and NB models demonstrated slightly enhanced <inline-formula id="ieqn-92"><mml:math id="mml-ieqn-92"><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 such as 83.15&#x0025; and 82.07&#x0025;, respectively. In line with this, PSO-Light GBM, TSDL_DT, and Decision Tree (DT) models demonstrated considerably higher <inline-formula id="ieqn-93"><mml:math id="mml-ieqn-93"><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, such as 86.68&#x0025;, 85.56&#x0025;, and 85.56&#x0025;, respectively. However, the presented EMML-CADC model outperformed all other methods and achieved the highest <inline-formula id="ieqn-94"><mml:math id="mml-ieqn-94"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 90.88&#x0025;.</p>
<table-wrap id="table-5"><label>Table 5</label><caption><title>Comparative analysis results of EMML-CADC and other existing techniques [<xref ref-type="bibr" rid="ref-29">29</xref>]</title></caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left">Methods</th>
<th align="left">Accuracy</th>
<th align="left">FAR</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">PSO-Light GBM</td>
<td align="left">86.68</td>
<td align="left">10.62</td>
</tr>
<tr>
<td align="left">Expectation-maximization</td>
<td align="left">78.47</td>
<td align="left">23.79</td>
</tr>
<tr>
<td align="left">TSDL_DT</td>
<td align="left">85.56</td>
<td align="left">15.78</td>
</tr>
<tr>
<td align="left">Decision tree model</td>
<td align="left">85.56</td>
<td align="left">15.78</td>
</tr>
<tr>
<td align="left">LR model</td>
<td align="left">83.15</td>
<td align="left">18.48</td>
</tr>
<tr>
<td align="left">Naive Bayes</td>
<td align="left">82.07</td>
<td align="left">18.56</td>
</tr>
<tr>
<td align="left">I-ELM</td>
<td align="left">67.01</td>
<td align="left">31.96</td>
</tr>
<tr>
<td align="left">EMML-CADC</td>
<td align="left">90.88</td>
<td align="left">9.12</td>
</tr>
</tbody>
</table>
</table-wrap><fig id="fig-8"><label>Figure 8</label><caption><title><inline-formula id="ieqn-95"><mml:math id="mml-ieqn-95"><mml:mi>A</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> analysis results of EMML-CADC and other existing techniques</title></caption><graphic mimetype="image" mime-subtype="tif" xlink:href="IASC_39718-fig-8.tif"/></fig>
<p><xref ref-type="fig" rid="fig-9">Fig. 9</xref> shows the comparative False Acceptance Rate (FAR) analysis results accomplished by the EMML-CADC method and existing methods. The I-ELM model presented the highest FAR of 31.96&#x0025;, whereas the Expectation-maximization model achieved a moderately lesser FAR of 23.79&#x0025;. Next, LR and NB models accomplished slightly lesser FAR values, such as 18.48&#x0025; and 18.56&#x0025;, correspondingly. In line with this, PSO-Light GBM, TSDL_DT, and DT methodology illustrated significantly lesser FAR values, such as 10.62&#x0025;, 15.78&#x0025;, and 15.78&#x0025;, correspondingly. However, the proposed EMML-CADC model achieved the least FAR of 9.12&#x0025; and outperformed all other methods.</p>
<fig id="fig-9"><label>Figure 9</label><caption><title>FAR analysis of EMML-CADC technique with recent algorithms</title></caption><graphic mimetype="image" mime-subtype="tif" xlink:href="IASC_39718-fig-9.tif"/></fig>
<p>By looking into the above-mentioned tables and figures, it is apparent that the EMML-CADC model accomplished superior results over other methods.</p>
</sec>
<sec id="s4"><label>4</label><title>Conclusion</title>
<p>In this study, a novel EMML-CADC model has been developed to enhance the efficiency of cyberattack detection in an IoT environment. To attain this, the proposed EMML-CADC model primarily employs data pre-processing to normalize the data into a uniform format. In addition, the ECSO-FS approach is applied to choose the optimal feature subsets. Besides, the MFO-TSVM model is utilized for the detection and classification of cyberattacks. Here, the MFO model has been exploited to fine-tune the TSVM variables for enhanced results. The performance of the proposed EMML-CADC technique was validated using a benchmark dataset, and the results were inspected under several measures. The comparative study results conclude that the EMML-CADC method is superior to other existing approaches under distinct measures. In future, advanced deep learning classifiers can be involved in the proposed method to improve intrusion detection efficacy in IoT platforms.</p>
</sec>
</body>
<back>
<sec><title>Funding Statement</title>
<p>The author would like to thank Prince Sultan University for its support in paying the Article Processing Charges.</p></sec>
<sec sec-type="COI-statement"><title>Conflicts of Interest</title>
<p>The author declares that they have no conflicts of interest to report regarding the present study.</p></sec>
<ref-list content-type="authoryear">
<title>References</title>
<ref id="ref-1"><label>[1]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>A.</given-names> <surname>Verma</surname></string-name> and <string-name><given-names>V.</given-names> <surname>Ranga</surname></string-name></person-group>, &#x201C;<article-title>Machine learning based intrusion detection systems for IOT applications</article-title>,&#x201D; <source>Wireless Personal Communications</source>, vol. <volume>111</volume>, no. <issue>4</issue>, pp. <fpage>2287</fpage>&#x2013;<lpage>2310</lpage>, <year>2020</year>.</mixed-citation></ref>
<ref id="ref-2"><label>[2]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>K. A. P.</given-names> <surname>da Costa</surname></string-name>, <string-name><given-names>J. P.</given-names> <surname>Papa</surname></string-name>, <string-name><given-names>C. O.</given-names> <surname>Lisboa</surname></string-name>, <string-name><given-names>R.</given-names> <surname>Munoz</surname></string-name> and <string-name><given-names>V. H. C.</given-names> <surname>de Albuquerque</surname></string-name></person-group>, &#x201C;<article-title>Internet of Things: A survey on machine learning-based intrusion detection approaches</article-title>,&#x201D; <source>Computer Networks</source>, vol. <volume>151</volume>, pp. <fpage>147</fpage>&#x2013;<lpage>157</lpage>, <year>2019</year>.</mixed-citation></ref>
<ref id="ref-3"><label>[3]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>B.</given-names> <surname>Yin</surname></string-name> and <string-name><given-names>X. T.</given-names> <surname>Wei</surname></string-name></person-group>, &#x201C;<article-title>Communication-efficient data aggregation tree construction for complex queries in IoT applications</article-title>,&#x201D; <source>IEEE Internet of Things Journal</source>, vol. <volume>6</volume>, no. <issue>2</issue>, pp. <fpage>3352</fpage>&#x2013;<lpage>3363</lpage>, <year>2018</year>.</mixed-citation></ref>
<ref id="ref-4"><label>[4]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>M.</given-names> <surname>Driss</surname></string-name>, <string-name><given-names>I.</given-names> <surname>Almomani</surname></string-name>, <string-name><given-names>Z. E.</given-names> <surname>Huma</surname></string-name> and <string-name><given-names>J.</given-names> <surname>Ahmad</surname></string-name></person-group>, &#x201C;<article-title>A federated learning framework for cyberattack detection in vehicular sensor networks</article-title>,&#x201D; <source>Complex &#x0026; Intelligent Systems</source>, vol. <volume>8</volume>, pp. <fpage>4221</fpage>&#x2013;<lpage>4235</lpage>, <year>2022</year>. <pub-id pub-id-type="doi">10.1007/s40747-022-00705-w</pub-id></mixed-citation></ref>
<ref id="ref-5"><label>[5]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>S.</given-names> <surname>Alshathri</surname></string-name>, <string-name><given-names>A.</given-names> <surname>El-sayed</surname></string-name>, <string-name><given-names>W.</given-names> <surname>El-shafai</surname></string-name> and <string-name><given-names>E.</given-names> <surname>El-din Hemdan</surname></string-name></person-group>, &#x201C;<article-title>An efficient intrusion detection framework for industrial internet of things security</article-title>,&#x201D; <source>Computer Systems Science and Engineering</source>, vol. <volume>46</volume>, no. <issue>1</issue>, pp. <fpage>819</fpage>&#x2013;<lpage>834</lpage>, <year>2023</year>. <pub-id pub-id-type="doi">10.32604/csse.2023.034095</pub-id></mixed-citation></ref>
<ref id="ref-6"><label>[6]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>S. M.</given-names> <surname>He</surname></string-name>, <string-name><given-names>K.</given-names> <surname>Xie</surname></string-name>, <string-name><given-names>K. X.</given-names> <surname>Xie</surname></string-name>, <string-name><given-names>C.</given-names> <surname>Xu</surname></string-name> and <string-name><given-names>J.</given-names> <surname>Wang</surname></string-name></person-group>, &#x201C;<article-title>Interference-aware multisource transmission in multiradio and multichannel wireless network</article-title>,&#x201D; <source>IEEE Systems Journal</source>, vol. <volume>13</volume>, no. <issue>3</issue>, pp. <fpage>2507</fpage>&#x2013;<lpage>2518</lpage>, <year>2019</year>.</mixed-citation></ref>
<ref id="ref-7"><label>[7]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>Y. S.</given-names> <surname>Luo</surname></string-name>, <string-name><given-names>K.</given-names> <surname>Yang</surname></string-name>, <string-name><given-names>Q.</given-names> <surname>Tang</surname></string-name>, <string-name><given-names>J.</given-names> <surname>Zhang</surname></string-name> and <string-name><given-names>B.</given-names> <surname>Xiong</surname></string-name></person-group>, &#x201C;<article-title>A multi-criteria network-aware service composition algorithm in wireless environments</article-title>,&#x201D; <source>Computer Communications</source>, vol. <volume>35</volume>, no. <issue>15</issue>, pp. <fpage>1882</fpage>&#x2013;<lpage>1892</lpage>, <year>2012</year>.</mixed-citation></ref>
<ref id="ref-8"><label>[8]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>A.</given-names> <surname>Derhab</surname></string-name>, <string-name><given-names>O.</given-names> <surname>Cheikhrouhou</surname></string-name>, <string-name><given-names>A.</given-names> <surname>Allouch</surname></string-name>, <string-name><given-names>A.</given-names> <surname>Koubaa</surname></string-name>, <string-name><given-names>B.</given-names> <surname>Qureshi</surname></string-name> <etal>et al.,</etal></person-group> &#x201C;<article-title>Internet of drones security: Taxonomies, open issues, and future directions</article-title>,&#x201D; <source>Vehicular Communications</source>, vol. <volume>39</volume>, <fpage>100552</fpage>, <year>2022</year>. <pub-id pub-id-type="doi">10.1016/j.vehcom.2022.100552</pub-id></mixed-citation></ref>
<ref id="ref-9"><label>[9]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>Z. F.</given-names> <surname>Liao</surname></string-name>, <string-name><given-names>J. B.</given-names> <surname>Liang</surname></string-name> and <string-name><given-names>C. C.</given-names> <surname>Feng</surname></string-name></person-group>, &#x201C;<article-title>Mobile relay deployment in multihop relay networks</article-title>,&#x201D; <source>Computer Communications</source>, vol. <volume>112</volume>, no. <issue>1</issue>, pp. <fpage>14</fpage>&#x2013;<lpage>21</lpage>, <year>2017</year>.</mixed-citation></ref>
<ref id="ref-10"><label>[10]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>B.</given-names> <surname>Yin</surname></string-name> and <string-name><given-names>J.</given-names> <surname>Lu</surname></string-name></person-group>, &#x201C;<article-title>A cost-efficient framework for crowdsourced data collection in vehicular networks</article-title>,&#x201D; <source>IEEE Internet of Things Journal</source>, vol. <volume>8</volume>, no. <issue>17</issue>, pp. <fpage>13567</fpage>&#x2013;<lpage>13581</lpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-11"><label>[11]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>D.</given-names> <surname>Cao</surname></string-name>, <string-name><given-names>B.</given-names> <surname>Zheng</surname></string-name>, <string-name><given-names>B.</given-names> <surname>Ji</surname></string-name>, <string-name><given-names>Z.</given-names> <surname>Lei</surname></string-name> and <string-name><given-names>C.</given-names> <surname>Feng</surname></string-name></person-group>, &#x201C;<article-title>A robust distance-based relay selection for message dissemination in vehicular network</article-title>,&#x201D; <source>Wireless Networks</source>, vol. <volume>26</volume>, no. <issue>3</issue>, pp. <fpage>1755</fpage>&#x2013;<lpage>1771</lpage>, <year>2020</year>.</mixed-citation></ref>
<ref id="ref-12"><label>[12]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>W.</given-names> <surname>Sun</surname></string-name>, <string-name><given-names>G. C.</given-names> <surname>Zhang</surname></string-name>, <string-name><given-names>X. R.</given-names> <surname>Zhang</surname></string-name>, <string-name><given-names>X.</given-names> <surname>Zhang</surname></string-name> and <string-name><given-names>N. N.</given-names> <surname>Ge</surname></string-name></person-group>, &#x201C;<article-title>Fine-grained vehicle type classification using lightweight convolutional neural network with feature optimization and joint learning strategy</article-title>,&#x201D; <source>Multimedia Tools and Applications</source>, vol. <volume>80</volume>, no. <issue>20</issue>, pp. <fpage>30803</fpage>&#x2013;<lpage>30816</lpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-13"><label>[13]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>W.</given-names> <surname>Sun</surname></string-name>, <string-name><given-names>X.</given-names> <surname>Chen</surname></string-name>, <string-name><given-names>X. R.</given-names> <surname>Zhang</surname></string-name>, <string-name><given-names>G. Z.</given-names> <surname>Dai</surname></string-name>, <string-name><given-names>P. S.</given-names> <surname>Chang</surname></string-name> <etal>et al.,</etal></person-group> &#x201C;<article-title>A multi-feature learning model with enhanced local attention for vehicle re-identification</article-title>,&#x201D; <source>Computers, Materials &#x0026; Continua</source>, vol. <volume>69</volume>, no. <issue>3</issue>, pp. <fpage>3549</fpage>&#x2013;<lpage>3561</lpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-14"><label>[14]</label><mixed-citation publication-type="conf-proc"><person-group person-group-type="author"><string-name><given-names>C.</given-names> <surname>Liang</surname></string-name>, <string-name><given-names>B.</given-names> <surname>Shanmugam</surname></string-name>, <string-name><given-names>S.</given-names> <surname>Azam</surname></string-name>, <string-name><given-names>M.</given-names> <surname>Jonkman</surname></string-name>, <string-name><given-names>F. D.</given-names> <surname>Boer</surname></string-name> <etal>et al.,</etal></person-group> &#x201C;<article-title>Intrusion detection system for internet of things based on a machine learning approach</article-title>,&#x201D; in <conf-name>2019 Int. Conf. on Vision Towards Emerging Trends in Communication and Networking (ViTECoN)</conf-name>, <conf-loc>Vellore, India</conf-loc>, pp. <fpage>1</fpage>&#x2013;<lpage>6</lpage>, <year>2019</year>.</mixed-citation></ref>
<ref id="ref-15"><label>[15]</label><mixed-citation publication-type="conf-proc"><person-group person-group-type="author"><string-name><given-names>T.</given-names> <surname>Mohamed</surname></string-name>, <string-name><given-names>T.</given-names> <surname>Otsuka</surname></string-name> and <string-name><given-names>T.</given-names> <surname>Ito</surname></string-name></person-group>, &#x201C;<article-title>Towards machine learning based IoT intrusion detection service</article-title>,&#x201D; in <conf-name>Int. Conf. on Industrial, Engineering and other Applications of Applied Intelligent Systems, Lecture Notes in Computer Science Book Series</conf-name>, <publisher-loc>Montreal, CA</publisher-loc>, vol. <volume>10868</volume>, pp. <fpage>580</fpage>&#x2013;<lpage>585</lpage>, <year>2018</year>.</mixed-citation></ref>
<ref id="ref-16"><label>[16]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>M.</given-names> <surname>Ahmad</surname></string-name>, <string-name><given-names>Q.</given-names> <surname>Riaz</surname></string-name>, <string-name><given-names>M.</given-names> <surname>Zeeshan</surname></string-name>, <string-name><given-names>H.</given-names> <surname>Tahir</surname></string-name>, <string-name><given-names>S. A.</given-names> <surname>Haider</surname></string-name> <etal>et al.,</etal></person-group> &#x201C;<article-title>Intrusion detection in internet of things using supervised machine learning based on application and transport layer features using UNSW-NB15 data-set</article-title>,&#x201D; <source>EURASIP Journal on Wireless Communications and Networking</source>, vol. <volume>2021</volume>, no. <issue>1</issue>, pp. <fpage>10</fpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-17"><label>[17]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>M. A.</given-names> <surname>Hawawreh</surname></string-name>, <string-name><given-names>N.</given-names> <surname>Moustafa</surname></string-name> and <string-name><given-names>E.</given-names> <surname>Sitnikova</surname></string-name></person-group>, &#x201C;<article-title>Identification of malicious activities in industrial internet of things based on deep learning models</article-title>,&#x201D; <source>Journal of Information Security and Applications</source>, vol. <volume>41</volume>, pp. <fpage>1</fpage>&#x2013;<lpage>11</lpage>, <year>2018</year>.</mixed-citation></ref>
<ref id="ref-18"><label>[18]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>F.</given-names> <surname>Alrowais</surname></string-name>, <string-name><given-names>A. S.</given-names> <surname>Almasoud</surname></string-name>, <string-name><given-names>R.</given-names> <surname>Marzouk</surname></string-name>, <string-name><given-names>F. N.</given-names> <surname>Al-Wesabi</surname></string-name>, <string-name><given-names>A. M.</given-names> <surname>Hilal</surname></string-name> <etal>et al.,</etal></person-group> &#x201C;<article-title>Artificial intelligence based data offloading technique for secure mec systems</article-title>,&#x201D; <source>Computers, Materials &#x0026; Continua</source>, vol. <volume>72</volume>, no. <issue>2</issue>, pp. <fpage>2783</fpage>&#x2013;<lpage>2795</lpage>, <year>2022</year>.</mixed-citation></ref>
<ref id="ref-19"><label>[19]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>M. A.</given-names> <surname>Hamza</surname></string-name>, <string-name><given-names>S. B.</given-names> <surname>Haj Hassine</surname></string-name>, <string-name><given-names>I.</given-names> <surname>Abunadi</surname></string-name>, <string-name><given-names>F. N.</given-names> <surname>Al-Wesabi</surname></string-name>, <string-name><given-names>H.</given-names> <surname>Alsolai</surname></string-name> <etal>et al.,</etal></person-group> &#x201C;<article-title>Feature selection with optimal stacked sparse autoencoder for data mining</article-title>,&#x201D; <source>Computers, Materials &#x0026; Continua</source>, vol. <volume>72</volume>, no. <issue>2</issue>, pp. <fpage>2581</fpage>&#x2013;<lpage>2596</lpage>, <year>2022</year>.</mixed-citation></ref>
<ref id="ref-20"><label>[20]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>A. A.</given-names> <surname>Albraikan</surname></string-name>, <string-name><given-names>S. B.</given-names> <surname>Haj Hassine</surname></string-name>, <string-name><given-names>S. M.</given-names> <surname>Fati</surname></string-name>, <string-name><given-names>F. N.</given-names> <surname>Al-Wesabi</surname></string-name>, <string-name><given-names>A. M.</given-names> <surname>Hilal</surname></string-name> <etal>et al.,</etal></person-group> &#x201C;<article-title>Optimal deep learning-based cyberattack detection and classification technique on social networks</article-title>,&#x201D; <source>Computers, Materials &#x0026; Continua</source>, vol. <volume>72</volume>, no. <issue>1</issue>, pp. <fpage>907</fpage>&#x2013;<lpage>923</lpage>, <year>2022</year>.</mixed-citation></ref>
<ref id="ref-21"><label>[21]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>A. M.</given-names> <surname>Hilal</surname></string-name>, <string-name><given-names>J. S.</given-names> <surname>Alzahrani</surname></string-name>, <string-name><given-names>I.</given-names> <surname>Abunadi</surname></string-name>, <string-name><given-names>N.</given-names> <surname>Nemri</surname></string-name>, <string-name><given-names>F. N.</given-names> <surname>Al-Wesabi</surname></string-name> <etal>et al.,</etal></person-group> &#x201C;<article-title>Intelligent deep learning model for privacy preserving IIOT on 6G environment</article-title>,&#x201D; <source>Computers, Materials &#x0026; Continua</source>, vol. <volume>72</volume>, no. <issue>1</issue>, pp. <fpage>333</fpage>&#x2013;<lpage>348</lpage>, <year>2022</year>.</mixed-citation></ref>
<ref id="ref-22"><label>[22]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>A. M.</given-names> <surname>Ahmed</surname></string-name>, <string-name><given-names>T. A.</given-names> <surname>Rashid</surname></string-name> and <string-name><given-names>S. A. M.</given-names> <surname>Saeed</surname></string-name></person-group>, &#x201C;<article-title>Cat swarm optimization algorithm: A survey and performance evaluation</article-title>,&#x201D; <source>Computational Intelligence and Neuroscience</source>, vol. <volume>2020</volume>, pp. <fpage>1</fpage>&#x2013;<lpage>20</lpage>, <year>2020</year>.</mixed-citation></ref>
<ref id="ref-23"><label>[23]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>X.</given-names> <surname>Nie</surname></string-name>, <string-name><given-names>W.</given-names> <surname>Wang</surname></string-name> and <string-name><given-names>H.</given-names> <surname>Nie</surname></string-name></person-group>, &#x201C;<article-title>Chaos quantum-behaved cat swarm optimization algorithm and its application in the PV MPPT</article-title>,&#x201D; <source>Computational Intelligence and Neuroscience</source>, vol. <volume>2017</volume>, pp. <fpage>1</fpage>&#x2013;<lpage>11</lpage>, <year>2017</year>.</mixed-citation></ref>
<ref id="ref-24"><label>[24]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>D.</given-names> <surname>Tomar</surname></string-name> and <string-name><given-names>S.</given-names> <surname>Agarwal</surname></string-name></person-group>, &#x201C;<article-title>Twin support vector machine: A review from 2007 to 2014</article-title>,&#x201D; <source>Egyptian Informatics Journal</source>, vol. <volume>16</volume>, no. <issue>1</issue>, pp. <fpage>55</fpage>&#x2013;<lpage>69</lpage>, <year>2015</year>.</mixed-citation></ref>
<ref id="ref-25"><label>[25]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>K.</given-names> <surname>Shankar</surname></string-name>, <string-name><given-names>E.</given-names> <surname>Perumal</surname></string-name>, <string-name><given-names>M.</given-names> <surname>Elhoseny</surname></string-name>, <string-name><given-names>F.</given-names> <surname>Taher</surname></string-name>, <string-name><given-names>B. B.</given-names> <surname>Gupta</surname></string-name> <etal>et al.,</etal></person-group> &#x201C;<article-title>Synergic deep learning for smart health diagnosis of COVID-19 for connected living and smart cities</article-title>,&#x201D; <source>ACM Transactions on Internet Technology</source>, vol. <volume>22</volume>, no. <issue>3</issue>, 16, pp. <fpage>1</fpage>&#x2013;<lpage>14</lpage>, <year>2022</year>.</mixed-citation></ref>
<ref id="ref-26"><label>[26]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>D. N.</given-names> <surname>Le</surname></string-name>, <string-name><given-names>V. S.</given-names> <surname>Parvathy</surname></string-name>, <string-name><given-names>D.</given-names> <surname>Gupta</surname></string-name>, <string-name><given-names>A.</given-names> <surname>Khanna</surname></string-name>, <string-name><given-names>J. J. P. C.</given-names> <surname>Rodrigues</surname></string-name> <etal>et al.,</etal></person-group> &#x201C;<article-title>IoT enabled depthwise separable convolution neural network with deep support vector machine for COVID-19 diagnosis and classification</article-title>,&#x201D; <source>International Journal of Machine Learning and Cybernetics</source>, vol. <volume>12</volume>, pp. <fpage>3235</fpage>&#x2013;<lpage>3248</lpage>, <year>2021</year>; <pub-id pub-id-type="pmid">33727984</pub-id></mixed-citation></ref>
<ref id="ref-27"><label>[27]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>D.</given-names> <surname>Venugopal</surname></string-name>, <string-name><given-names>T.</given-names> <surname>Jayasankar</surname></string-name>, <string-name><given-names>M. Y.</given-names> <surname>Sikkandar</surname></string-name>, <string-name><given-names>M. I.</given-names> <surname>Waly</surname></string-name>, <string-name><given-names>I. V.</given-names> <surname>Pustokhina</surname></string-name> <etal>et al.,</etal></person-group> &#x201C;<article-title>A novel deep neural network for intracranial haemorrhage detection and classification</article-title>,&#x201D; <source>Computers, Materials &#x0026; Continua</source>, vol. <volume>68</volume>, no. <issue>3</issue>, pp. <fpage>2877</fpage>&#x2013;<lpage>2893</lpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-28"><label>[28]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>K.</given-names> <surname>Zervoudakis</surname></string-name> and <string-name><given-names>S.</given-names> <surname>Tsafarakis</surname></string-name></person-group>, &#x201C;<article-title>A mayfly optimization algorithm</article-title>,&#x201D; <source>Computers &#x0026; Industrial Engineering</source>, vol. <volume>145</volume>, pp. <fpage>106559</fpage>, <year>2020</year>.</mixed-citation></ref>
<ref id="ref-29"><label>[29]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>J.</given-names> <surname>Liu</surname></string-name>, <string-name><given-names>D.</given-names> <surname>Yang</surname></string-name>, <string-name><given-names>M.</given-names> <surname>Lian</surname></string-name> and <string-name><given-names>M.</given-names> <surname>Li</surname></string-name></person-group>, &#x201C;<article-title>Research on intrusion detection based on particle swarm optimization in IoT</article-title>,&#x201D; <source>IEEE Access</source>, vol. <volume>9</volume>, pp. <fpage>38254</fpage>&#x2013;<lpage>38268</lpage>, <year>2021</year>.</mixed-citation></ref>
</ref-list>
</back></article>