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<front>
<journal-meta>
<journal-id journal-id-type="pmc">CSSE</journal-id>
<journal-id journal-id-type="nlm-ta">CSSE</journal-id>
<journal-id journal-id-type="publisher-id">CSSE</journal-id>
<journal-title-group>
<journal-title>Computer Systems Science &#x0026; Engineering</journal-title>
</journal-title-group>
<issn pub-type="ppub">0267-6192</issn>
<publisher>
<publisher-name>Tech Science Press</publisher-name>
<publisher-loc>USA</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">27502</article-id>
<article-id pub-id-type="doi">10.32604/csse.2023.027502</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Optimal Weighted Extreme Learning Machine for Cybersecurity Fake News Classification</article-title><alt-title alt-title-type="left-running-head">Optimal Weighted Extreme Learning Machine for Cybersecurity Fake News Classification</alt-title><alt-title alt-title-type="right-running-head">Optimal Weighted Extreme Learning Machine for Cybersecurity Fake News Classification</alt-title>
</title-group>
<contrib-group content-type="authors">
<contrib id="author-1" contrib-type="author" corresp="yes">
<name name-style="western"><surname>Dutta</surname><given-names>Ashit Kumar</given-names></name>
<xref ref-type="aff" rid="aff-1">1</xref><email>adotta@mcst.edu.sa</email>
</contrib>
<contrib id="author-2" contrib-type="author">
<name name-style="western"><surname>Qureshi</surname><given-names>Basit</given-names></name>
<xref ref-type="aff" rid="aff-2">2</xref>
</contrib>
<contrib id="author-3" contrib-type="author">
<name name-style="western"><surname>Albagory</surname><given-names>Yasser</given-names></name>
<xref ref-type="aff" rid="aff-3">3</xref>
</contrib>
<contrib id="author-4" contrib-type="author">
<name name-style="western"><surname>Alsanea</surname><given-names>Majed</given-names></name>
<xref ref-type="aff" rid="aff-4">4</xref>
</contrib>
<contrib id="author-5" contrib-type="author">
<name name-style="western"><surname>Faraj</surname><given-names>Manal Al</given-names></name>
<xref ref-type="aff" rid="aff-1">1</xref>
</contrib>
<contrib id="author-6" contrib-type="author">
<name name-style="western"><surname>Sait</surname><given-names>Abdul Rahaman Wahab</given-names></name>
<xref ref-type="aff" rid="aff-5">5</xref>
</contrib>
<aff id="aff-1"><label>1</label><institution>Department of Computer Science and Information Systems, College of Applied Sciences, AlMaarefa University</institution>, <addr-line>Ad Diriyah, Riyadh, 13713</addr-line>, <country>Kingdom of Saudi Arabia</country></aff>
<aff id="aff-2"><label>2</label><institution>Department of Computer Science, Prince Sultan University</institution>, <addr-line>Riyadh, 11586</addr-line>, <country>Kingdom of Saudi Arabia</country></aff>
<aff id="aff-3"><label>3</label><institution>Department of Computer Engineering, College of Computers and Information Technology, Taif University</institution>, <addr-line>Taif, 21944</addr-line>, <country>Kingdom of Saudi Arabia</country></aff>
<aff id="aff-4"><label>4</label><institution>Department of Computing, Arabeast Colleges</institution>, <addr-line>Riyadh, 11583</addr-line>, <country>Kingdom of Saudi Arabia</country></aff>
<aff id="aff-5"><label>5</label><institution>Department of Archives and Communication, King Faisal University</institution>, <addr-line>Al Ahsa, Hofuf, 31982</addr-line>, <country>Kingdom of Saudi Arabia</country></aff>
</contrib-group><author-notes><corresp id="cor1"><label>&#x002A;</label>Corresponding Author: Ashit Kumar Dutta. Email: <email>adotta@mcst.edu.sa</email></corresp></author-notes>
<pub-date pub-type="epub" date-type="pub" iso-8601-date="2022-06-20"><day>20</day>
<month>06</month>
<year>2022</year></pub-date>
<volume>44</volume>
<issue>3</issue>
<fpage>2395</fpage>
<lpage>2409</lpage>
<history>
<date date-type="received"><day>19</day><month>1</month><year>2022</year></date>
<date date-type="accepted"><day>23</day><month>3</month><year>2022</year></date>
</history>
<permissions>
<copyright-statement>&#x00A9; 2023 Dutta et al.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Dutta et al.</copyright-holder>
<license xlink:href="https://creativecommons.org/licenses/by/4.0/">
<license-p>This work is licensed under a <ext-link ext-link-type="uri" xlink:type="simple" xlink:href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International License</ext-link>, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</license-p>
</license>
</permissions>
<self-uri content-type="pdf" xlink:href="TSP_CSSE_27502.pdf"></self-uri>
<abstract>
<p>Fake news and its significance carried the significance of affecting diverse aspects of diverse entities, ranging from a city lifestyle to a country global relativity, various methods are available to collect and determine fake news. The recently developed machine learning (ML) models can be employed for the detection and classification of fake news. This study designs a novel Chaotic Ant Swarm with Weighted Extreme Learning Machine (CAS-WELM) for Cybersecurity Fake News Detection and Classification. The goal of the CAS-WELM technique is to discriminate news into fake and real. The CAS-WELM technique initially pre-processes the input data and Glove technique is used for word embedding process. Then, N-gram based feature extraction technique is derived to generate feature vectors. Lastly, WELM model is applied for the detection and classification of fake news, in which the weight value of the WELM model can be optimally adjusted by the use of CAS algorithm. The performance validation of the CAS-WELM technique is carried out using the benchmark dataset and the results are inspected under several dimensions. The experimental results reported the enhanced outcomes of the CAS-WELM technique over the recent approaches.</p>
</abstract>
<kwd-group kwd-group-type="author">
<kwd>Cybersecurity</kwd>
<kwd>cybercrime</kwd>
<kwd>fake news</kwd>
<kwd>data classification</kwd>
<kwd>machine learning</kwd>
<kwd>metaheuristics</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1">
<label>1</label>
<title>Introduction</title>
<p>Online data is often accessible as a result of few clicks away. With the unique independence provided to users for sharing stories, the complexity to describe the root of false data increases gradually. The existence of dramatic headlines and clickbait titles is at its highest point that assists in the broadcast of inaccurate and unprofessional news in response to advertising revenues. User, wants to be part of this hot discussion or topic, adapt the innovative message with intention or by mistake that eventually results in the distribution of rumor on the internet. Fake news is inscribed for a hoax that leads to political or gains or financial spreading data disguised as propaganda [<xref ref-type="bibr" rid="ref-1">1</xref>], one might be utilized to influence public perception towards falseness. Even this encourages the beliefs and people ideology to some range that might create several damages [<xref ref-type="bibr" rid="ref-2">2</xref>]. This persuading is popular when a news story breaks out, whereby the supporter usually tends to share data in its complete originality, while the one opinion doesn&#x2019;t bring into line with the information mentioned resorting to share that similar data with few adjustments. Currently, media outlets are the only information resources. Specific contribution in news sharing has significantly developed over the last decade where it become ever more complex to discriminate news that originate from a reliable source from the one that is invented [<xref ref-type="bibr" rid="ref-3">3</xref>]. Consequently, fake news has gained several interests recently by organizations like Google, Twitter, Facebook, and by various authors, who are making continuous attempts in opposing the spread of fake stories. <xref ref-type="fig" rid="fig-1">Fig. 1</xref> illustrates the platform to detect fake news.</p>
<fig id="fig-1">
<label>Figure 1</label>
<caption>
<title>Platform to detect fake news</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CSSE_27502-fig-1.png"/>
</fig>
<p>Artificial intelligence (AI) technique is the evolving technology that has transformed the view at business problems [<xref ref-type="bibr" rid="ref-4">4</xref>]. An increasing amount of businesses are transforming to innovative analysis and machine learning to resolve problems. With this development, natural language processing (NLP) describes great potential for business that is concerned with understanding human sentiment via the current information. NLP functions with each kind of social and natural communication, involving text, audio, and video. In order to identify trends and many valuable patterns in the textual data set, text mining assisted to perform in this way [<xref ref-type="bibr" rid="ref-5">5</xref>]. In present market setting, strategic use of NLP assist business to obtain relative benefits. AI and NLP assist in combating the large unstructured data of various fields involving education, healthcare, business sectors, fake news, trust and security, opinion from the public in the government sector [<xref ref-type="bibr" rid="ref-6">6</xref>]. The NLP assists human-to-machine communication very efficiently that sequentially improves the overall efficiency and decision-making of the businesses. The NLP relates to how individual interacts, that consist of emotions, speech, and text. Fake news detection has gained much consideration in the NLP research field to mitigate the time-consuming human activity and burdensome data verification [<xref ref-type="bibr" rid="ref-7">7</xref>]. Despite that, the process of estimating the validity of news remains a challenge even for automatic systems.</p>
<p>Kumar et al. [<xref ref-type="bibr" rid="ref-8">8</xref>] gather 1356 news samples from different clients through media sources and Twitter including PolitiFact and construct various data sets for the fake and real news stories. We compared many advanced methods including attention mechanism, convolution neural network (CNN), long short term memory (LSTM), and ensemble approaches. Roy et al. [<xref ref-type="bibr" rid="ref-9">9</xref>] developed deep learning (DL) algorithms to identify fake news and classify them to the pre-determined fine-grained classes. Firstly, we designed CNN and bidirectional LSTM (Bi-LSTM) based systems. The representation attained from these two methods is given to a multilayer perceptron (MLP) for the last classification.</p>
<p>Aslam et al. [<xref ref-type="bibr" rid="ref-10">10</xref>] presented an ensemble-based DL method for classifying news as real or fake. Because of the nature of dataset traits, two DL methods have been employed. For the textual attributes &#x201C;statement,&#x201D; Bi-LSTM-gated recurrent unit (GRU)-dense DL method has been utilized, for the residual characteristics, dense DL algorithm has been employed.</p>
<p>In Agarwal et al. [<xref ref-type="bibr" rid="ref-11">11</xref>], researchers have experimented and discussed word embedding (GloVe) for text pre-processing to establish lingual relationships and create a vector space of words. The presented method is the combination of CNN and recurrent neural network (RNN) frameworks that have accomplished standard outcomes in predicting fake news, with the effectiveness of word embedding complementing the overall method. Furthermore, to guarantee the prediction quality, several model parameters were recorded and tuned for the optimal result.</p>
<p>Khanam et al. [<xref ref-type="bibr" rid="ref-12">12</xref>] make research analytics based fake news detection and examine the conventional machine learning (ML) methods for choosing the best, to construct a method of a product using supervised ML method, which could categorize fake news as false or true, by utilizing python scikit-learn, NLP for text analysis. Bangyal et al. [<xref ref-type="bibr" rid="ref-13">13</xref>] developed a precise model for SA of fake news. The fake news datasets contain fake news; the study initiates by data pre-processing (replaces the stemming, tokenization, noise removal, and missing value). The study employed a semantic method with inverse document frequency and term frequency weighting for representing information. In the evaluation and measuring stage, we employed 8 ML approaches.</p>
<p>This study designs a novel Chaotic Ant Swarm with Weighted Extreme Learning Machine (CAS-WELM) for Cybersecurity Fake News Detection and Classification. The goal of the CAS-WELM system is to discriminate news into fake and real. The CAS-WELM technique initially pre-processes the input data and Glove technique is used for word embedding process. Then, N-gram based feature extraction technique is derived to generate feature vectors. Lastly, WELM model is applied for the detection and classification of fake news, in which the weight value of the WELM model can be optimally adjusted by the use of CAS algorithm. The performance validation of the CAS-WELM technique is carried out using the benchmark dataset and the results are inspected under several dimensions.</p>
</sec>
<sec id="s2">
<label>2</label>
<title>The Proposed Model</title>
<p>In this study, a novel CAS-WELM technique has been developed for Cybersecurity Fake News Detection and Classification. The CAS-WELM technique mainly intends to discriminate news into fake and real. The CAS-WELM technique undergoes different stages of operations namely pre-processing, Glove based word embedding, N-gram based feature extraction, WELM based classification, and CAS based parameter optimization. Besides, the weight value of the WELM model can be optimally adjusted by the use of CAS algorithm.</p>
<sec id="s2_1">
<label>2.1</label>
<title>Pre-processing</title>
<p>The data set is considered into two groups, true category, and false category. Data visualization assists in comprehending comparative data mean by demonstrating information in visual contexts, namely graphs or maps. This makes it easy to spot outliers, trends, and patterns in massive datasets by creating the data to analyze for the human mind. The data set is categorized into two classes, original and fake news. The fake news class is denoted as &#x2018;0&#x2019; and true news class is denoted as &#x2018;1&#x2019;. When certain words exist in the group of a <italic>corpus</italic>, then the word is removed [<xref ref-type="bibr" rid="ref-14">14</xref>]. Data pre-processing is a major phase that includes data manipulation beforehand it is implemented, to improve efficacy. It includes data transformation and cleansing. To remove the stop word from the sentence, the text can be separated into words, and then it is verified to understand whether the word exist in the Natural Language Toolkit (NLTK) list of stop words. Stemming represents the extraction of word root or stems form that may or may not completely reflects semantic intellectual. The procedure of lemmatization is the decrease of inflectional format generally useful word-to common form. Glove embedding and Keras embedding layer, utilized to train NN system on textual information. This is a flexible layer, utilized for loading pre-trained GloVe embedding of hundred dimensions.</p>
</sec>
<sec id="s2_2">
<label>2.2</label>
<title>N-gram Based Feature Extraction</title>
<p>Consider <inline-formula id="ieqn-1">
<mml:math id="mml-ieqn-1"><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>&#x2208;</mml:mo><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mi>d</mml:mi></mml:msup></mml:mrow></mml:math>
</inline-formula> represent the word vector for <inline-formula id="ieqn-2">
<mml:math id="mml-ieqn-2"><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math>
</inline-formula> word in a sentence of <inline-formula id="ieqn-3">
<mml:math id="mml-ieqn-3"><mml:mi>d</mml:mi></mml:math>
</inline-formula> dimension. Where <inline-formula id="ieqn-4">
<mml:math id="mml-ieqn-4"><mml:mi>x</mml:mi><mml:mo>&#x2208;</mml:mo><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mrow><mml:mi>L</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>
</inline-formula> signify the input sentence using length <inline-formula id="ieqn-5">
<mml:math id="mml-ieqn-5"><mml:mi>L</mml:mi></mml:math>
</inline-formula>. Take <inline-formula id="ieqn-6">
<mml:math id="mml-ieqn-6"><mml:mi>k</mml:mi></mml:math>
</inline-formula> as the filter length, also <inline-formula id="ieqn-7">
<mml:math id="mml-ieqn-7"><mml:mi>m</mml:mi><mml:mo>&#x2208;</mml:mo><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>
</inline-formula> represent a filter for the convolutional process. For all the location, <inline-formula id="ieqn-8">
<mml:math id="mml-ieqn-8"><mml:mi>j</mml:mi></mml:math>
</inline-formula> in the sentence, a window vector <inline-formula id="ieqn-9">
<mml:math id="mml-ieqn-9"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> consist of <inline-formula id="ieqn-10">
<mml:math id="mml-ieqn-10"><mml:mi>k</mml:mi></mml:math>
</inline-formula> successive word vectors are evaluated,</p>
<p><disp-formula id="eqn-1"><label>(1)</label>
<mml:math id="mml-eqn-1" display="block"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mrow><mml:mover><mml:mi>j</mml:mi><mml:mo>&#x02D9;</mml:mo></mml:mover></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mover><mml:mrow><mml:mi>j</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>.</mml:mo></mml:mover></mml:mrow></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>j</mml:mi><mml:mo>+</mml:mo><mml:mi>k</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:math>
</disp-formula></p>
<p>Now, the comma represents row vector concatenation. A filter <inline-formula id="ieqn-11">
<mml:math id="mml-ieqn-11"><mml:mi>m</mml:mi></mml:math>
</inline-formula> integrates to the window vector (<inline-formula id="ieqn-12">
<mml:math id="mml-ieqn-12"><mml:mi>k</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>g</mml:mi><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>m</mml:mi><mml:mi>s</mml:mi></mml:math>
</inline-formula>) and all the locations in an approach to construct a feature map <inline-formula id="ieqn-13">
<mml:math id="mml-ieqn-13"><mml:mi>c</mml:mi><mml:mo>&#x2208;</mml:mo><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mrow><mml:mi>L</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>
</inline-formula>; all the elements <inline-formula id="ieqn-14">
<mml:math id="mml-ieqn-14"><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> of feature maps for window vector <inline-formula id="ieqn-15">
<mml:math id="mml-ieqn-15"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> is generated by:</p>
<p><disp-formula id="eqn-2"><label>(2)</label>
<mml:math id="mml-eqn-2" display="block"><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mo>&#x2218;</mml:mo><mml:mi>m</mml:mi><mml:mo>+</mml:mo><mml:mi>b</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</disp-formula></p>
<p>whereas <inline-formula id="ieqn-16">
<mml:math id="mml-ieqn-16"><mml:mo>&#x2218;</mml:mo></mml:math>
</inline-formula> indicates element-by-element multiplication, <inline-formula id="ieqn-17">
<mml:math id="mml-ieqn-17"><mml:mi>b</mml:mi><mml:mo>&#x2208;</mml:mo><mml:mi>R</mml:mi></mml:math>
</inline-formula> show a bias term and <inline-formula id="ieqn-18">
<mml:math id="mml-ieqn-18"><mml:mi>f</mml:mi></mml:math>
</inline-formula> denotes a non-linear conversion with probable kinds such as sigmoid, hyperbolic tangent, linear, rectified linear unit (ReLU), softmax, and so on. In this case, ReLU is employed. A filter amount is utilized for producing feature map [<xref ref-type="bibr" rid="ref-15">15</xref>]. For <inline-formula id="ieqn-19">
<mml:math id="mml-ieqn-19"><mml:mi>n</mml:mi></mml:math>
</inline-formula> filters of equivalent size, the generated <inline-formula id="ieqn-20">
<mml:math id="mml-ieqn-20"><mml:mi>n</mml:mi></mml:math>
</inline-formula> feature map is rearranged as feature representation for all the window <inline-formula id="ieqn-21">
<mml:math id="mml-ieqn-21"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mo>,</mml:mo></mml:math>
</inline-formula></p>
<p><disp-formula id="eqn-3"><label>(3)</label>
<mml:math id="mml-eqn-3" display="block"><mml:mi>W</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:mo>;</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>;</mml:mo><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:math>
</disp-formula></p>
<p>Here, <inline-formula id="ieqn-22">
<mml:math id="mml-ieqn-22"><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> denotes the feature map generated using the <inline-formula id="ieqn-23">
<mml:math id="mml-ieqn-23"><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math>
</inline-formula> filter and Semicolon signifies column vector concatenation. All the rows <inline-formula id="ieqn-24">
<mml:math id="mml-ieqn-24"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> of <inline-formula id="ieqn-25">
<mml:math id="mml-ieqn-25"><mml:mi>W</mml:mi><mml:mo>&#x2208;</mml:mo><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>L</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x00D7;</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>
</inline-formula> represent the feature depiction generated from <inline-formula id="ieqn-26">
<mml:math id="mml-ieqn-26"><mml:mi>n</mml:mi></mml:math>
</inline-formula> feature for window vector at location provided by <inline-formula id="ieqn-27">
<mml:math id="mml-ieqn-27"><mml:mi>j</mml:mi></mml:math>
</inline-formula>.</p>
</sec>
<sec id="s2_3">
<label>2.3</label>
<title>WELM Based Classification</title>
<p>Beforehand elaborating on the WELM, firstly presented the fundamental extreme learning machine (ELM). Using the mapping datasets <inline-formula id="ieqn-28">
<mml:math id="mml-ieqn-28"><mml:mo fence="false" stretchy="false">{</mml:mo><mml:msubsup><mml:mi>&#x03C7;</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:msubsup><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mo fence="false" stretchy="false">}</mml:mo><mml:mo>&#x2208;</mml:mo><mml:mrow><mml:msup><mml:mi mathvariant="normal">&#x211C;</mml:mi><mml:mi>p</mml:mi></mml:msup></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mrow><mml:msup><mml:mi mathvariant="normal">&#x211C;</mml:mi><mml:mi>c</mml:mi></mml:msup></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>
</inline-formula>, the output of generalized single layer feed forward network (SLFN) using activation function <inline-formula id="ieqn-29">
<mml:math id="mml-ieqn-29"><mml:mi>h</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msup><mml:mi>x</mml:mi><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:msup></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math>
</inline-formula> and <inline-formula id="ieqn-30">
<mml:math id="mml-ieqn-30"><mml:mi>q</mml:mi></mml:math>
</inline-formula> hidden node can be formulated by using the following equation. <xref ref-type="fig" rid="fig-2">Fig. 2</xref> demonstrates the structure of WELM.</p>
<fig id="fig-2">
<label>Figure 2</label>
<caption>
<title>Structure of WELM</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CSSE_27502-fig-2.png"/>
</fig>
<p><disp-formula id="eqn-4"><label>(4)</label>
<mml:math id="mml-eqn-4" display="block"><mml:mrow><mml:msub><mml:mi>o</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:msubsup><mml:mo movablelimits="false">&#x2211;</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>q</mml:mi></mml:msubsup><mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msubsup><mml:mi>&#x03C7;</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msubsup><mml:mo movablelimits="false">&#x2211;</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>q</mml:mi></mml:msubsup><mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mi>h</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mi>b</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:msubsup><mml:mrow><mml:mrow><mml:mi mathvariant="normal">x</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi></mml:mrow></mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:math>
</disp-formula></p>
<p>In which <inline-formula id="ieqn-31">
<mml:math id="mml-ieqn-31"><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy="false">[</mml:mo><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:msup><mml:mo stretchy="false">]</mml:mo><mml:mi>T</mml:mi></mml:msup></mml:mrow></mml:math>
</inline-formula> characterizes the input weight connect the kth hidden and input nodes, <inline-formula id="ieqn-32">
<mml:math id="mml-ieqn-32"><mml:mrow><mml:msub><mml:mi>b</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> signifies the bias of <inline-formula id="ieqn-33">
<mml:math id="mml-ieqn-33"><mml:mi>k</mml:mi><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math>
</inline-formula> hidden node, <inline-formula id="ieqn-34">
<mml:math id="mml-ieqn-34"><mml:mrow><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy="false">[</mml:mo><mml:mrow><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:msup><mml:mo stretchy="false">]</mml:mo><mml:mi>T</mml:mi></mml:msup></mml:mrow></mml:math>
</inline-formula> shows the output weight linking the kth hidden and output nodes, and <inline-formula id="ieqn-35">
<mml:math id="mml-ieqn-35"><mml:mrow><mml:msub><mml:mn>0</mml:mn><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> represents the predicted output of ith sample. The widely employed activation function in ELM includes multiquadric function, Gaussian RBF function, sigmoid function, and hard limit function [<xref ref-type="bibr" rid="ref-16">16</xref>].</p>
<p><disp-formula id="eqn-5"><label>(5)</label>
<mml:math id="mml-eqn-5" display="block"><mml:mi>H</mml:mi><mml:mi>&#x03B2;</mml:mi><mml:mo>=</mml:mo><mml:mi>O</mml:mi><mml:mo>,</mml:mo></mml:math>
</disp-formula></p>
<p>In which <inline-formula id="ieqn-36">
<mml:math id="mml-ieqn-36"><mml:mi>H</mml:mi></mml:math>
</inline-formula> represent the hidden neuron output matrix of SLFN</p>
<p><disp-formula id="eqn-6"><label>(6)</label>
<mml:math id="mml-eqn-6" display="block"><mml:mi>H</mml:mi><mml:mo>=</mml:mo><mml:mi>H</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi>q</mml:mi></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mi>b</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mi>b</mml:mi><mml:mi>q</mml:mi></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mn>1</mml:mn><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:msubsup><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mi>n</mml:mi><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mtable rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mrow><mml:mi>h</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mn>1</mml:mn><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:msubsup><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>&#x22EE;</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mi>h</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mi>n</mml:mi><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:msubsup><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:math>
</disp-formula></p>
<p><disp-formula id="ueqn-7">
<mml:math id="mml-ueqn-7" display="block"><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mtable rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mrow><mml:mi>h</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mi>b</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mn>1</mml:mn><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mtd><mml:mtd><mml:mo>&#x22EF;</mml:mo></mml:mtd><mml:mtd><mml:mrow><mml:mi>h</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi>q</mml:mi></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mi>b</mml:mi><mml:mi>q</mml:mi></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mn>1</mml:mn><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>&#x22EE;</mml:mo></mml:mtd><mml:mtd><mml:mo>&#x22F1;</mml:mo></mml:mtd><mml:mtd><mml:mo>&#x22EE;</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mi>h</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mi>b</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mn>1</mml:mn><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mtd><mml:mtd><mml:mo>&#x22EF;</mml:mo></mml:mtd><mml:mtd><mml:mrow><mml:mi>h</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi>q</mml:mi></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mi>b</mml:mi><mml:mi>q</mml:mi></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mn>1</mml:mn><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>
</disp-formula></p>
<p>Here, the <inline-formula id="ieqn-37">
<mml:math id="mml-ieqn-37"><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math>
</inline-formula> row of <inline-formula id="ieqn-38">
<mml:math id="mml-ieqn-38"><mml:mi>H</mml:mi></mml:math>
</inline-formula> represent the output of hidden node regarding the input samples <inline-formula id="ieqn-39">
<mml:math id="mml-ieqn-39"><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:msubsup></mml:math>
</inline-formula>, and the kth column of <inline-formula id="ieqn-40">
<mml:math id="mml-ieqn-40"><mml:mi>H</mml:mi></mml:math>
</inline-formula> shows the output of kth hidden node regarding the input sample <inline-formula id="ieqn-41">
<mml:math id="mml-ieqn-41"><mml:msubsup><mml:mi>x</mml:mi><mml:mn>1</mml:mn><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:msubsup><mml:mo>,</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mn>2</mml:mn><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:msubsup><mml:mo>,</mml:mo><mml:mo>,</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>,</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mi>n</mml:mi><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:msubsup></mml:math>
</inline-formula>.</p>
<p><inline-formula id="ieqn-42">
<mml:math id="mml-ieqn-42"><mml:mi>&#x03B2;</mml:mi></mml:math>
</inline-formula> indicates the weight matrix linking the output and hidden layers, as follows</p>
<p><disp-formula id="eqn-7"><label>(7)</label>
<mml:math id="mml-eqn-7" display="block"><mml:mi>&#x03B2;</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mtable rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd columnalign="left"><mml:mrow><mml:msubsup><mml:mi>&#x03B2;</mml:mi><mml:mn>1</mml:mn><mml:mi>T</mml:mi></mml:msubsup></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign="left"><mml:mo>&#x22EE;</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign="left"><mml:mrow><mml:msubsup><mml:mi>&#x03B2;</mml:mi><mml:mi>q</mml:mi><mml:mi>T</mml:mi></mml:msubsup></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mi>q</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>
</disp-formula></p>
<p><inline-formula id="ieqn-43">
<mml:math id="mml-ieqn-43"><mml:mi>O</mml:mi></mml:math>
</inline-formula> represents the predicted label matrix, and all the rows represent the output vector of single instance. <inline-formula id="ieqn-44">
<mml:math id="mml-ieqn-44"><mml:mi>O</mml:mi></mml:math>
</inline-formula> is determined by</p>
<p><disp-formula id="eqn-8"><label>(8)</label>
<mml:math id="mml-eqn-8" display="block"><mml:mi>O</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mtable rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd columnalign="left"><mml:mrow><mml:msubsup><mml:mi>o</mml:mi><mml:mn>1</mml:mn><mml:mi>T</mml:mi></mml:msubsup></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign="left"><mml:mo>&#x22EE;</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign="left"><mml:mrow><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mrow><mml:msub><mml:mi>O</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mtable rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mrow><mml:mrow><mml:msub><mml:mi>o</mml:mi><mml:mrow><mml:mn>11</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:mtd><mml:mtd><mml:mo>&#x22EF;</mml:mo></mml:mtd><mml:mtd><mml:mrow><mml:mrow><mml:msub><mml:mn>0</mml:mn><mml:mrow><mml:mn>1</mml:mn><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>&#x22EE;</mml:mo></mml:mtd><mml:mtd><mml:mo>&#x22F1;</mml:mo></mml:mtd><mml:mtd><mml:mo>&#x22EE;</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mrow><mml:msub><mml:mi>o</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:mtd><mml:mtd><mml:mo>&#x22EF;</mml:mo></mml:mtd><mml:mtd><mml:mrow><mml:mrow><mml:msub><mml:mn>0</mml:mn><mml:mrow><mml:mi>n</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:math>
</disp-formula></p>
<p>The aim of trained SLFN is to reduce the output errors, that is, approximate the input sample with zero error</p>
<p><disp-formula id="eqn-9"><label>(9)</label>
<mml:math id="mml-eqn-9" display="block"><mml:munderover><mml:mo>&#x2211;</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:munderover><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo><mml:msub><mml:mn>0</mml:mn><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo><mml:mo>=</mml:mo><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo><mml:mi>O</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>Y</mml:mi><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:math>
</disp-formula></p>
<p>Whereas <inline-formula id="ieqn-45">
<mml:math id="mml-ieqn-45"><mml:mi>y</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mtable rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd columnalign="left"><mml:mrow><mml:msubsup><mml:mi>y</mml:mi><mml:mn>1</mml:mn><mml:mi>T</mml:mi></mml:msubsup></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign="left"><mml:mo>&#x22EE;</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign="left"><mml:mrow><mml:mi>T</mml:mi><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mtable rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mrow><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mn>11</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:mtd><mml:mtd><mml:mo>&#x22EF;</mml:mo></mml:mtd><mml:mtd><mml:mrow><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>&#x22EE;</mml:mo></mml:mtd><mml:mtd><mml:mo>&#x22F1;</mml:mo></mml:mtd><mml:mtd><mml:mo>&#x22EE;</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:mtd><mml:mtd><mml:mo>&#x22EF;</mml:mo></mml:mtd><mml:mtd><mml:mrow><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:math>
</inline-formula> represents the target output matrix.</p>
<p><disp-formula id="eqn-10"><label>(10)</label>
<mml:math id="mml-eqn-10" display="block"><mml:mi>H</mml:mi><mml:mi>&#x03B2;</mml:mi><mml:mo>=</mml:mo><mml:mi>Y</mml:mi></mml:math>
</disp-formula></p>
<p>Aimed at ELM, the bias <inline-formula id="ieqn-46">
<mml:math id="mml-ieqn-46"><mml:mrow><mml:msub><mml:mi>b</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> of hidden neurons and the weight <inline-formula id="ieqn-47">
<mml:math id="mml-ieqn-47"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> of input connection is independently and arbitrarily chosen [<xref ref-type="bibr" rid="ref-17">17</xref>]. When this parameter is allocated, <xref ref-type="disp-formula" rid="eqn-10">Eq. (10)</xref> is transformed to linear method and the <inline-formula id="ieqn-48">
<mml:math id="mml-ieqn-48"><mml:mi>&#x03B2;</mml:mi></mml:math>
</inline-formula> output weight matrix is systematically defined by detecting the least-square solutions of linear method as</p>
<p><disp-formula id="eqn-11"><label>(11)</label>
<mml:math id="mml-eqn-11" display="block"><mml:munder><mml:mo movablelimits="true" form="prefix">min</mml:mo><mml:mrow><mml:mi>&#x03B2;</mml:mi></mml:mrow></mml:munder><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo><mml:mi>H</mml:mi><mml:mi>&#x03B2;</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>Y</mml:mi><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo></mml:math>
</disp-formula></p>
<p>The optimum solution of <xref ref-type="disp-formula" rid="eqn-11">Eq. (11)</xref> is</p>
<p><disp-formula id="eqn-12"><label>(12)</label>
<mml:math id="mml-eqn-12" display="block"><mml:mrow><mml:mover><mml:mi>&#x03B2;</mml:mi><mml:mo stretchy="false">&#x005E;</mml:mo></mml:mover></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:msup><mml:mi>H</mml:mi><mml:mo>&#x2020;</mml:mo></mml:msup></mml:mrow><mml:mi>Y</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msup><mml:mi>H</mml:mi><mml:mi>T</mml:mi></mml:msup></mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</disp-formula></p>
<p>Whereas <inline-formula id="ieqn-49">
<mml:math id="mml-ieqn-49"><mml:mi>H</mml:mi><mml:mo>&#x2020;</mml:mo></mml:math>
</inline-formula> means the Moore-Penrose generalized inverse of hidden neuron output matrix <inline-formula id="ieqn-50">
<mml:math id="mml-ieqn-50"><mml:mi>H</mml:mi></mml:math>
</inline-formula>. The attained <inline-formula id="ieqn-51">
<mml:math id="mml-ieqn-51"><mml:mrow><mml:mover><mml:mi>&#x03B2;</mml:mi><mml:mo stretchy="false">&#x005E;</mml:mo></mml:mover></mml:mrow></mml:math>
</inline-formula> could guarantee minimally trained error, attain optimum generalization capability, and prevent plunging to local optimal because <inline-formula id="ieqn-52">
<mml:math id="mml-ieqn-52"><mml:mrow><mml:mover><mml:mi>&#x03B2;</mml:mi><mml:mo stretchy="false">&#x005E;</mml:mo></mml:mover></mml:mrow></mml:math>
</inline-formula> is exclusive.</p>
<p><disp-formula id="eqn-13"><label>(13)</label>
<mml:math id="mml-eqn-13" display="block"><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msup><mml:mi>x</mml:mi><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:msup></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>h</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msup><mml:mi>x</mml:mi><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:msup></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mover><mml:mi>&#x03B2;</mml:mi><mml:mo stretchy="false">&#x005E;</mml:mo></mml:mover></mml:mrow><mml:mo>=</mml:mo><mml:mi>h</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msup><mml:mi>x</mml:mi><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:msup></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:msup><mml:mi>H</mml:mi><mml:mrow><mml:mo>&#x2020;</mml:mo><mml:mi>y</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>
</disp-formula></p>
<p>While constructing the ELM classification, we determine a <inline-formula id="ieqn-53">
<mml:math id="mml-ieqn-53"><mml:mi>n</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>n</mml:mi></mml:math>
</inline-formula> diagonal matrix <inline-formula id="ieqn-54">
<mml:math id="mml-ieqn-54"><mml:mi>W</mml:mi></mml:math>
</inline-formula>, that diagonal component <inline-formula id="ieqn-55">
<mml:math id="mml-ieqn-55"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>
</inline-formula> represents the weight of trained instance <inline-formula id="ieqn-56">
<mml:math id="mml-ieqn-56"><mml:msubsup><mml:mi>&#x03C7;</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:msubsup></mml:math>
</inline-formula>. Accurately, when <inline-formula id="ieqn-57">
<mml:math id="mml-ieqn-57"><mml:msubsup><mml:mi>&#x03C7;</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:msubsup></mml:math>
</inline-formula> belonging to the majority class, the <inline-formula id="ieqn-58">
<mml:math id="mml-ieqn-58"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>
</inline-formula> weight is comparatively lesser when compared to the samples that belong to the minority class.</p>
<p><disp-formula id="eqn-14"><label>(14)</label>
<mml:math id="mml-eqn-14" display="block"><mml:mrow><mml:mover><mml:mi>&#x03B2;</mml:mi><mml:mo stretchy="false">&#x005E;</mml:mo></mml:mover></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:msup><mml:mi>H</mml:mi><mml:mo>&#x2020;</mml:mo></mml:msup></mml:mrow><mml:mi>Y</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msup><mml:mi>H</mml:mi><mml:mi>T</mml:mi></mml:msup></mml:mrow><mml:mi>W</mml:mi><mml:mi>H</mml:mi><mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:msup><mml:mi>H</mml:mi><mml:mi>T</mml:mi></mml:msup></mml:mrow><mml:mi>W</mml:mi><mml:mi>T</mml:mi></mml:math>
</disp-formula></p>
<p>Next, <xref ref-type="disp-formula" rid="eqn-13">Eq. (13)</xref> becomes</p>
<p><disp-formula id="eqn-15"><label>(15)</label>
<mml:math id="mml-eqn-15" display="block"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msup><mml:mi>x</mml:mi><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:msup></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mi>h</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msup><mml:mi>x</mml:mi><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:msup></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mrow><mml:mover><mml:mi>&#x03B2;</mml:mi><mml:mo stretchy="false">&#x005E;</mml:mo></mml:mover></mml:mrow><mml:mo>=</mml:mo><mml:mi>h</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msup><mml:mi>x</mml:mi><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:msup></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msup><mml:mi>H</mml:mi><mml:mi>T</mml:mi></mml:msup></mml:mrow><mml:mi>W</mml:mi><mml:mi>H</mml:mi><mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:msup><mml:mi>H</mml:mi><mml:mi>T</mml:mi></mml:msup></mml:mrow><mml:mi>W</mml:mi><mml:mi>T</mml:mi></mml:math>
</disp-formula></p>
<p>Mainly, it consists of two systems to assign the weight to the sample of the two classes:</p>
<p><disp-formula id="eqn-16"><label>(16)</label>
<mml:math id="mml-eqn-16" display="block"><mml:mi>W</mml:mi><mml:mn>1</mml:mn><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mtable rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd columnalign="left"><mml:mrow><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi>P</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:mtd><mml:mtd columnalign="left"><mml:mrow><mml:mi>i</mml:mi><mml:mi>f</mml:mi><mml:mspace width="thickmathspace" /><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:msubsup><mml:mo>&#x2208;</mml:mo><mml:mrow><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">y</mml:mi></mml:mrow></mml:mrow><mml:mspace width="thickmathspace" /><mml:mrow><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:mrow></mml:mrow></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign="left"><mml:mrow><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi>N</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:mtd><mml:mtd columnalign="left"><mml:mrow><mml:mi>i</mml:mi><mml:mi>f</mml:mi><mml:mspace width="thickmathspace" /><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:msubsup><mml:mo>&#x2208;</mml:mo><mml:mrow><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">j</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">y</mml:mi></mml:mrow></mml:mrow><mml:mspace width="thickmathspace" /><mml:mrow><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:mrow></mml:mrow></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo></mml:mrow></mml:math>
</disp-formula></p>
<p>Or</p>
<p><disp-formula id="eqn-17"><label>(17)</label>
<mml:math id="mml-eqn-17" display="block"><mml:mi>W</mml:mi><mml:mn>2</mml:mn><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mtable rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd columnalign="left"><mml:mrow><mml:mn>0.618</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi>P</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:mtd><mml:mtd columnalign="left"><mml:mrow><mml:mi>i</mml:mi><mml:mi>f</mml:mi><mml:mspace width="thickmathspace" /><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:msubsup><mml:mo>&#x2208;</mml:mo><mml:mrow><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">y</mml:mi></mml:mrow></mml:mrow><mml:mspace width="thickmathspace" /><mml:mrow><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:mrow></mml:mrow></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign="left"><mml:mrow><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi>N</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:mtd><mml:mtd columnalign="left"><mml:mrow><mml:mi>i</mml:mi><mml:mi>f</mml:mi><mml:mspace width="thickmathspace" /><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:msubsup><mml:mo>&#x2208;</mml:mo><mml:mrow><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">j</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">y</mml:mi></mml:mrow></mml:mrow><mml:mspace width="thickmathspace" /><mml:mrow><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:mrow></mml:mrow></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:math>
</disp-formula></p>
<p>Here, <inline-formula id="ieqn-59">
<mml:math id="mml-ieqn-59"><mml:mi>W</mml:mi><mml:mi>l</mml:mi></mml:math>
</inline-formula> and <inline-formula id="ieqn-60">
<mml:math id="mml-ieqn-60"><mml:mi>W</mml:mi><mml:mn>2</mml:mn></mml:math>
</inline-formula> denotes weighting systems, <inline-formula id="ieqn-61">
<mml:math id="mml-ieqn-61"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi>P</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> &#x0026; <inline-formula id="ieqn-62">
<mml:math id="mml-ieqn-62"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi>N</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> indicates the amount of instances of the minority and majority classes, correspondingly.</p>
</sec>
<sec id="s2_4">
<label>2.4</label>
<title>Parameter Optimization Using CAS Algorithm</title>
<p>For tuning the weight values of the WELM model, the CAS is used. Recently, a SI optimization method named CAS approach is presented for solving the optimization issue according to chaos concept [<xref ref-type="bibr" rid="ref-18">18</xref>]. The CAS algorithm is mathematically modelled by the following equation:</p>
<p><disp-formula id="ueqn-19">
<mml:math id="mml-ueqn-19" display="block"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msup></mml:mrow><mml:mo>,</mml:mo></mml:math>
</disp-formula></p>
<p><disp-formula id="ueqn-20">
<mml:math id="mml-ueqn-20" display="block"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi mathvariant="normal">&#x0394;</mml:mi><mml:mi>exp</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mi>exp</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>a</mml:mi><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>3</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:msub><mml:mi mathvariant="normal">&#x03A8;</mml:mi><mml:mi>d</mml:mi></mml:msub></mml:mrow><mml:mi mathvariant="normal">&#x0394;</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo></mml:math>
</disp-formula></p>
<p><disp-formula id="eqn-18"><label>(18)</label>
<mml:math id="mml-eqn-18" display="block"><mml:mrow><mml:mfrac><mml:mrow><mml:mn>7.5</mml:mn></mml:mrow><mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="normal">&#x03A8;</mml:mi><mml:mi>d</mml:mi></mml:msub></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:mfrac></mml:mrow><mml:mo>+</mml:mo><mml:mi>exp</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mn>2</mml:mn><mml:mi>a</mml:mi><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo><mml:mi>b</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x00D7;</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mi>p</mml:mi><mml:mi>b</mml:mi><mml:mi>e</mml:mi><mml:mi>s</mml:mi><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi>d</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">)</mml:mo><mml:mo>,</mml:mo></mml:math>
</disp-formula></p>
<p>In which <inline-formula id="ieqn-63">
<mml:math id="mml-ieqn-63"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>
</inline-formula> represent the organization parameter of the CAS and <inline-formula id="ieqn-64">
<mml:math id="mml-ieqn-64"><mml:mi mathvariant="normal">&#x0394;</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo><mml:mn>7.5</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mi mathvariant="normal">&#x03A8;</mml:mi><mml:mi>d</mml:mi></mml:msub></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mrow><mml:msub><mml:mi>&#x03C6;</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math>
</inline-formula>. It handles chaotic behavior of one ant. <inline-formula id="ieqn-65">
<mml:math id="mml-ieqn-65"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> indicates the organization variances of one ant that is a positive constant lesser than 1. <inline-formula id="ieqn-66">
<mml:math id="mml-ieqn-66"><mml:mrow><mml:msub><mml:mi mathvariant="normal">&#x03A8;</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> defines the search array of <inline-formula id="ieqn-67">
<mml:math id="mml-ieqn-67"><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math>
</inline-formula> ant in <inline-formula id="ieqn-68">
<mml:math id="mml-ieqn-68"><mml:mi>d</mml:mi><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math>
</inline-formula> dimension. <inline-formula id="ieqn-69">
<mml:math id="mml-ieqn-69"><mml:mrow><mml:msub><mml:mi mathvariant="normal">&#x2205;</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> control the moving proportion of <inline-formula id="ieqn-70">
<mml:math id="mml-ieqn-70"><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math>
</inline-formula> ant search region. pbest <inline-formula id="ieqn-71">
<mml:math id="mml-ieqn-71"><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>
</inline-formula> denotes the optimal location that the single ant and neighbors have established with <inline-formula id="ieqn-72">
<mml:math id="mml-ieqn-72"><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:math>
</inline-formula> time step. Now the neighbor is fixed to be global neighbor; viz., each ant is the neighbor of one another. Usually, The ant exchanges data through direct or indirect transmission models. Owing to the efficient transmission, the effect of organization becomes robust as time changes. At last, each ant walks through the optimal route to forage food. As time grows, the impact of the organization parameter <inline-formula id="ieqn-73">
<mml:math id="mml-ieqn-73"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>
</inline-formula> on the behavior of all the ants become strong through the organization variable <inline-formula id="ieqn-74">
<mml:math id="mml-ieqn-74"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula>.</p>
<p>Lastly, with the impact of <inline-formula id="ieqn-75">
<mml:math id="mml-ieqn-75"><mml:mi>p</mml:mi><mml:mi>b</mml:mi><mml:mi>e</mml:mi><mml:mi>s</mml:mi><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi>d</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>
</inline-formula> and <inline-formula id="ieqn-76">
<mml:math id="mml-ieqn-76"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>
</inline-formula> , the state of <inline-formula id="ieqn-77">
<mml:math id="mml-ieqn-77"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>
</inline-formula> would converge to the global optimal location. <inline-formula id="ieqn-78">
<mml:math id="mml-ieqn-78"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> and <inline-formula id="ieqn-79">
<mml:math id="mml-ieqn-79"><mml:mrow><mml:msub><mml:mi mathvariant="normal">&#x03A8;</mml:mi><mml:mi>d</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> represent significant variables. <inline-formula id="ieqn-80">
<mml:math id="mml-ieqn-80"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> has an impact on the convergence rate of CAS approach. When <inline-formula id="ieqn-81">
<mml:math id="mml-ieqn-81"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> is smaller, the convergence rate of the CAS approach would be slower and the implementation time would take time. When <inline-formula id="ieqn-82">
<mml:math id="mml-ieqn-82"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> is larger, the convergence rate of CAS approach would be faster thereby the optimum solution mightn&#x2019;t be established. When <inline-formula id="ieqn-83">
<mml:math id="mml-ieqn-83"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> is fixed to be 0, the behavior of ant would be chaotic continually and the CAS approach could not converge to a certain location. Moreover, slight variation of organization impact is chosen, <inline-formula id="ieqn-84">
<mml:math id="mml-ieqn-84"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> is fixed to be <inline-formula id="ieqn-85">
<mml:math id="mml-ieqn-85"><mml:mn>0</mml:mn><mml:mo>&#x2264;</mml:mo><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>&#x2264;</mml:mo><mml:mn>0.5</mml:mn></mml:math>
</inline-formula>. The actual equation of <inline-formula id="ieqn-86">
<mml:math id="mml-ieqn-86"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> based on the runtime and certain issues.</p>
<p>To support ant to have a distinct organization variable, fix <inline-formula id="ieqn-87">
<mml:math id="mml-ieqn-87"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mn>0.1</mml:mn><mml:mo>+</mml:mo><mml:mn>0.2</mml:mn><mml:mo>&#x00D7;</mml:mo><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:math>
</inline-formula>, whereas rand represents a uniform distribution arbitrary value within <inline-formula id="ieqn-88">
<mml:math id="mml-ieqn-88"><mml:mo stretchy="false">[</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">]</mml:mo><mml:mo>.</mml:mo></mml:math>
</inline-formula> <inline-formula id="ieqn-89">
<mml:math id="mml-ieqn-89"><mml:mrow><mml:msub><mml:mi mathvariant="normal">&#x03A8;</mml:mi><mml:mi>d</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> has an impact on the search space of the CAS approach. When <inline-formula id="ieqn-90">
<mml:math id="mml-ieqn-90"><mml:mrow><mml:msub><mml:mi mathvariant="normal">&#x03A8;</mml:mi><mml:mi>d</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> is smaller, the search space would be larger. when the value of <inline-formula id="ieqn-91">
<mml:math id="mml-ieqn-91"><mml:mrow><mml:msub><mml:mi mathvariant="normal">&#x03A8;</mml:mi><mml:mi>d</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> is larger, the search space would be smaller. The search space is fixed to be <inline-formula id="ieqn-92">
<mml:math id="mml-ieqn-92"><mml:mo stretchy="false">[</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi>d</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi>d</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>2</mml:mn><mml:mo stretchy="false">]</mml:mo></mml:math>
</inline-formula>, and <italic>w<sub>d</sub></italic> &#x02242; <inline-formula id="ieqn-93">
<mml:math id="mml-ieqn-93"><mml:mn>7.5</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="normal">&#x03A8;</mml:mi><mml:mi>d</mml:mi></mml:msub></mml:mrow><mml:mo>.</mml:mo></mml:math>
</inline-formula></p>
</sec>
</sec>
<sec id="s3">
<label>3</label>
<title>Experimental Validation</title>
<p>The experimental result analysis of the CAS-WELM technique is validated using benchmark dataset. The initial dataset is named as ISOT Fake News Dataset [<xref ref-type="bibr" rid="ref-19">19</xref>] (Sample Set-1), comprising 44,898 articles (21,417 instances under truthful articles and 23,481 under fake articles). The second Kaggle dataset [<xref ref-type="bibr" rid="ref-20">20</xref>] (Sample Set-2) includes 20,386 articles employed to train the dataset and 5,126 articles are applied to test the dataset. The third dataset [<xref ref-type="bibr" rid="ref-21">21</xref>] (sample set-3) comprises 3,352 articles, both fake and true. The final dataset (Sample Set-4) includes the combination of the dataset.</p>
<p><xref ref-type="table" rid="table-1">Tab. 1</xref> and <xref ref-type="fig" rid="fig-3">Fig. 3</xref> demonstrate the accuracy analysis of the CAS-WELM technique with other ones [<xref ref-type="bibr" rid="ref-22">22</xref>]. The results indicated that the k-nearest neighbor (KNN) model has attained worse classification results than the other methods. In addition, the logistic regression (LR) model has obtained slightly improved classification performance over the KNN model. Moreover, the Localized Support Vector Machine (LSVM), MLP, and Bagging-decision tree (DT) model has accomplished moderately increased outcomes. Though the random forest (RF) model has resulted in competitive outcome, the CAS-WELM technique has outperformed the other methods with the higher accuracy of 99.46%, 96.32%, 96.58%, and 94.89% on the test sample sets 1&#x2013;4 respectively.</p>
<table-wrap id="table-1"><label>Table 1</label>
<caption>
<title>Accuracy analysis of CAS-WELM technique with existing methods on the test sample sets 1&#x2013;4</title></caption>
<table><colgroup>
<col/>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th colspan="5">Accuracy (%)</th>
</tr>
</thead>
<tbody>
<tr>
<td>Methods</td>
<td>Sample Set - 1</td>
<td>Sample Set - 2</td>
<td>Sample Set - 3</td>
<td>Sample Set - 4</td>
</tr>
<tr>
<td>LR Model</td>
<td>97.00</td>
<td>91.00</td>
<td>91.00</td>
<td>87.00</td>
</tr>
<tr>
<td>LSVM Model</td>
<td>98.00</td>
<td>37.00</td>
<td>53.00</td>
<td>86.00</td>
</tr>
<tr>
<td>MLP Model</td>
<td>98.00</td>
<td>35.00</td>
<td>94.00</td>
<td>90.00</td>
</tr>
<tr>
<td>KNN Model</td>
<td>88.00</td>
<td>28.00</td>
<td>82.00</td>
<td>77.00</td>
</tr>
<tr>
<td>RF Model</td>
<td>99.00</td>
<td>35.00</td>
<td>95.00</td>
<td>91.00</td>
</tr>
<tr>
<td>Bagging-DT</td>
<td>98.00</td>
<td>94.00</td>
<td>94.00</td>
<td>90.00</td>
</tr>
<tr>
<td>CAS-WELM</td>
<td>99.46</td>
<td>96.32</td>
<td>96.58</td>
<td>94.89</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="fig-3">
<label>Figure 3</label>
<caption>
<title>Accuracy analysis of CAS-WELM technique with existing approaches</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CSSE_27502-fig-3.png"/>
</fig>
<p><xref ref-type="table" rid="table-2">Tab. 2</xref> and <xref ref-type="fig" rid="fig-4">Fig. 4</xref> illustrate the precision analysis of the CAS-WELM approach with other ones. The results indicated that the KNN technique has attained least classification outcomes over the other methods. Besides, the LR approach has reached somewhat higher classification performance over the KNN technique. Moreover, the LSVM, MLP, and Bagging-DT methodology have accomplished moderately increased outcomes. Then, the RF system has resulted in competitive outcome, the CAS-WELM system has demonstrated the other methods with the superior precision of 99.61%, 95.74%, 99.24%, and 95.35% on the test sample sets 1&#x2013;4 correspondingly.</p>
<table-wrap id="table-2"><label>Table 2</label>
<caption>
<title>Precision analysis of CAS-WELM technique with existing methods on the test sample sets 1&#x2013;4</title></caption>
<table><colgroup>
<col/>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th colspan="5">Precision (%)</th>
</tr>
</thead>
<tbody>
<tr>
<td>Methods</td>
<td>Sample Set - 1</td>
<td>Sample Set - 2</td>
<td>Sample Set - 3</td>
<td>Sample Set - 4</td>
</tr>
<tr>
<td>LR Model</td>
<td>98.00</td>
<td>92.00</td>
<td>93.00</td>
<td>88.00</td>
</tr>
<tr>
<td>LSVM Model</td>
<td>98.00</td>
<td>31.00</td>
<td>54.00</td>
<td>88.00</td>
</tr>
<tr>
<td>MLP Model</td>
<td>97.00</td>
<td>32.00</td>
<td>93.00</td>
<td>92.00</td>
</tr>
<tr>
<td>KNN Model</td>
<td>91.00</td>
<td>22.00</td>
<td>85.00</td>
<td>80.00</td>
</tr>
<tr>
<td>RF Model</td>
<td>99.00</td>
<td>30.00</td>
<td>98.00</td>
<td>92.00</td>
</tr>
<tr>
<td>Bagging-DT</td>
<td>98.00</td>
<td>94.00</td>
<td>93.00</td>
<td>90.00</td>
</tr>
<tr>
<td>CAS-WELM</td>
<td>99.61</td>
<td>95.74</td>
<td>99.24</td>
<td>95.35</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="fig-4">
<label>Figure 4</label>
<caption>
<title>Precision analysis of CAS-WELM technique with existing approaches</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CSSE_27502-fig-4.png"/>
</fig>
<p><xref ref-type="table" rid="table-3">Tab. 3</xref> and <xref ref-type="fig" rid="fig-5">Fig. 5</xref> showcases the recall analysis of the CAS-WELM approach with other ones. The outcomes referred that the KNN algorithm has gained poor classification results over the other methods. Similarly, the LR technique has obtained slightly enhanced classification performance over the KNN technique. Likewise, the LSVM, MLP, and Bagging-DT approach has accomplished moderately increased outcomes. Eventually, the RF system has resulted in competitive outcome, the CAS-WELM method has exhibited the other techniques with the maximal recall of 100%, 98.24%, 100%, and 95.84% on the test sample sets 1&#x2013;4 correspondingly.</p>
<table-wrap id="table-3"><label>Table 3</label>
<caption>
<title>Recall analysis of CAS-WELM technique with existing methods on the test sample sets 1&#x2013;4</title></caption>
<table><colgroup>
<col/>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th colspan="5">Recall (%)</th>
</tr>
</thead>
<tbody>
<tr>
<td>Methods</td>
<td>Sample Set - 1</td>
<td>Sample Set - 2</td>
<td>Sample Set - 3</td>
<td>Sample Set - 4</td>
</tr>
<tr>
<td>LR Model</td>
<td>98.00</td>
<td>90.00</td>
<td>92.00</td>
<td>86.00</td>
</tr>
<tr>
<td>LSVM Model</td>
<td>98.00</td>
<td>32.00</td>
<td>100.00</td>
<td>86.00</td>
</tr>
<tr>
<td>MLP Model</td>
<td>100.00</td>
<td>36.00</td>
<td>96.00</td>
<td>88.00</td>
</tr>
<tr>
<td>KNN Model</td>
<td>87.00</td>
<td>24.00</td>
<td>81.00</td>
<td>74.00</td>
</tr>
<tr>
<td>RF Model</td>
<td>100.00</td>
<td>34.00</td>
<td>93.00</td>
<td>91.00</td>
</tr>
<tr>
<td>Bagging-DT</td>
<td>97.00</td>
<td>95.00</td>
<td>94.00</td>
<td>91.00</td>
</tr>
<tr>
<td>CAS-WELM</td>
<td>100.00</td>
<td>98.24</td>
<td>100.00</td>
<td>95.84</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="fig-5">
<label>Figure 5</label>
<caption>
<title>Recall analysis of CAS-WELM technique with existing approaches on test sample sets 1&#x2013;4</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CSSE_27502-fig-5.png"/>
</fig>
<p><xref ref-type="table" rid="table-4">Tab. 4</xref> and <xref ref-type="fig" rid="fig-6">Fig. 6</xref> illustrates the F-score analysis of the CAS-WELM technique with other ones. The results show that the KNN method has gained minimal classification outcomes over the other approaches. Besides, the LR technique has obtained somewhat enhanced classification performance over the KNN technique. Moreover, the LSVM, MLP, and Bagging-DT approach has accomplished moderately higher outcomes. At last, the RF system has resulted in competitive outcome, the CAS-WELM technique has outperformed the other methods with the increased F-score of 99.36%, 96.48%, 98.88%, and 96.23% on the test sample sets 1&#x2013;4 correspondingly.</p>
<table-wrap id="table-4"><label>Table 4</label>
<caption>
<title>F-score analysis of CAS-WELM technique with existing methods on the test sample sets 1&#x2013;4</title></caption>
<table><colgroup>
<col/>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th colspan="5">Precision (%)</th>
</tr>
</thead>
<tbody>
<tr>
<td>Methods</td>
<td>Sample Set - 1</td>
<td>Sample Set - 2</td>
<td>Sample Set - 3</td>
<td>Sample Set - 4</td>
</tr>
<tr>
<td>LR Model</td>
<td>98.00</td>
<td>91.00</td>
<td>92.00</td>
<td>87.00</td>
</tr>
<tr>
<td>LSVM Model</td>
<td>98.00</td>
<td>32.00</td>
<td>70.00</td>
<td>87.00</td>
</tr>
<tr>
<td>MLP Model</td>
<td>98.00</td>
<td>34.00</td>
<td>95.00</td>
<td>90.00</td>
</tr>
<tr>
<td>KNN Model</td>
<td>89.00</td>
<td>23.00</td>
<td>83.00</td>
<td>77.00</td>
</tr>
<tr>
<td>RF Model</td>
<td>99.00</td>
<td>32.00</td>
<td>95.00</td>
<td>91.00</td>
</tr>
<tr>
<td>Bagging-DT</td>
<td>98.00</td>
<td>94.00</td>
<td>94.00</td>
<td>90.00</td>
</tr>
<tr>
<td>CAS-WELM</td>
<td>99.36</td>
<td>96.48</td>
<td>98.88</td>
<td>96.23</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="fig-6">
<label>Figure 6</label>
<caption>
<title>F-score analysis of CAS-WELM technique with existing approaches on test sample sets 1&#x2013;4</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CSSE_27502-fig-6.png"/>
</fig>
<p><xref ref-type="fig" rid="fig-7">Fig. 7</xref> demonstrates the accuracy and loss graph analysis of the CAS-WELM technique on the test sample sets 1 and 2. The results show that the accuracy value tends to increase and loss value tends to decrease with an increase in epoch count. It is also observed that the training loss is low and validation accuracy is high on test sample sets 1 and 2.</p>
<fig id="fig-7">
<label>Figure 7</label>
<caption>
<title>Accuracy and loss analysis of CAS-WELM technique under test sample sets 1 and 2</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CSSE_27502-fig-7.png"/>
</fig>
<p><xref ref-type="fig" rid="fig-8">Fig. 8</xref> offers the accuracy and loss graph analysis of the CAS-WELM methodology on the test sample sets 3 and 4. The outcomes demonstrated that the accuracy value tends to be higher and loss value tends to lower with higher epoch count. It is also experiential that the training loss is minimum and validation accuracy is high on the test sample sets 3 and 4.</p>
<fig id="fig-8">
<label>Figure 8</label>
<caption>
<title>Accuracy and loss analysis of CAS-WELM technique under test sample sets 3 and 4</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CSSE_27502-fig-8.png"/>
</fig>
</sec>
<sec id="s4">
<label>4</label>
<title>Conclusion</title>
<p>In this study, a novel CAS-WELM technique has been developed for Cybersecurity Fake News Detection and Classification. The CAS-WELM technique mainly intends to discriminate news into fake and real. The CAS-WELM technique undergoes different stages of operations namely pre-processing, Glove based word embedding, N-gram based feature extraction, WELM based classification, and CAS based parameter optimization. Besides, the weight value of the WELM model can be optimally adjusted by the use of CAS algorithm. The performance validation of the CAS-WELM technique is carried out using the benchmark dataset and the results are inspected under several dimensions. The experimental results reported the enhanced outcomes of the CAS-WELM technique over the recent approaches. In the future, advanced deep learning models can be utilized to classify and detect fake news in social networking platform.</p>
</sec>
</body>
<back>
<ack>
<p>The authors deeply acknowledge the Researchers supporting program (TUMA-Project-2021-27) Almaarefa University, Riyadh, Saudi Arabia for supporting steps of this work. The authors would like to acknowledge the support of Prince Sultan University for paying the Article Processing Charges (APC) of this publication.</p>
</ack><fn-group>
<fn fn-type="other">
<p><bold>Funding Statement:</bold> This research was supported by the Researchers Supporting Program (TUMA-Project-2021-27) Almaarefa University, Riyadh, Saudi Arabia. Taif University Researchers Supporting Project number (TURSP-2020/161), Taif University, Taif, Saudi Arabia.</p>
</fn>
<fn fn-type="conflict">
<p><bold>Conflicts of Interest:</bold> The authors declare that they have no conflicts of interest to report regarding the present study.</p>
</fn>
</fn-group>
<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>S. A.</given-names> <surname>Garc&#x00ED;a</surname></string-name>, <string-name><given-names>G. G.</given-names> <surname>Garc&#x00ED;a</surname></string-name>, <string-name><given-names>M. S.</given-names> <surname>Prieto</surname></string-name>, <string-name><given-names>A. J. M.</given-names> <surname>Guerrero</surname></string-name> and <string-name><given-names>C. R.</given-names> <surname>Jim&#x00E9;nez</surname></string-name></person-group>, &#x201C;<article-title>The impact of term fake news on the scientific community scientific performance and mapping in web of science</article-title>,&#x201D; <source>Social Sciences</source>, vol. <volume>9</volume>, no. <issue>5</issue>, pp. <fpage>73</fpage>, <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>T.</given-names> <surname>Hopp</surname></string-name></person-group>, &#x201C;<article-title>Fake news self-efficacy, fake news identification, and content sharing on Facebook</article-title>,&#x201D; <source>Journal of Information Technology &#x0026; Politics</source>, pp. <fpage>1</fpage>&#x2013;<lpage>24</lpage>, <year>2021</year>. <uri>https://doi.org/10.1080/19331681.2021.1962778</uri>.</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>N. K.</given-names> <surname>Conroy</surname></string-name>, <string-name><given-names>V. L.</given-names> <surname>Rubin</surname></string-name> and <string-name><given-names>Y.</given-names> <surname>Chen</surname></string-name></person-group>, &#x201C;<article-title>Automatic deception detection: Methods for finding fake news</article-title>,&#x201D; <source>Proceedings of the American Society for Information Science and Technology</source>, vol. <volume>52</volume>, no. <issue>1</issue>, pp. <fpage>1</fpage>&#x2013;<lpage>4</lpage>, <year>2015</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>A.</given-names> <surname>Robb</surname></string-name></person-group>, &#x201C;<article-title>Anatomy of a fake news scandal</article-title>,&#x201D; <source>Rolling Stone</source>, vol. <volume>1301</volume>, pp. <fpage>28</fpage>&#x2013;<lpage>33</lpage>, <year>2017</year>.</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>H.</given-names> <surname>Allcott</surname></string-name> and <string-name><given-names>M.</given-names> <surname>Gentzkow</surname></string-name></person-group>, &#x201C;<article-title>Social media and fake news in the 2016 Election</article-title>,&#x201D; <source>Journal of Economic Perspectives</source>, vol. <volume>31</volume>, no. <issue>2</issue>, pp. <fpage>211</fpage>&#x2013;<lpage>236</lpage>, <year>2017</year>.</mixed-citation></ref>
<ref id="ref-6"><label>[6]</label><mixed-citation publication-type="conf-proc"><person-group person-group-type="author"><string-name><given-names>V.</given-names> <surname>Rubin</surname></string-name>, <string-name><given-names>N.</given-names> <surname>Conroy</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Chen</surname></string-name> and <string-name><given-names>S.</given-names> <surname>Cornwell</surname></string-name></person-group>, &#x201C;<article-title>Fake news or truth? using satirical cues to detect potentially misleading news</article-title>,&#x201D; in <conf-name>Proc. of the Second Workshop on Computational Approaches to Deception Detection</conf-name>, <publisher-loc>San Diego, California</publisher-loc>, pp. <fpage>7</fpage>&#x2013;<lpage>17</lpage>, <year>2016</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>K.</given-names> <surname>Shu</surname></string-name>, <string-name><given-names>A.</given-names> <surname>Sliva</surname></string-name>, <string-name><given-names>S.</given-names> <surname>Wang</surname></string-name>, <string-name><given-names>J.</given-names> <surname>Tang</surname></string-name> and <string-name><given-names>H.</given-names> <surname>Liu</surname></string-name></person-group>, &#x201C;<article-title>Fake news detection on social media: A data mining perspective</article-title>,&#x201D; <source>ACM SIGKDD Explorations Newsletter</source>, vol. <volume>19</volume>, no. <issue>1</issue>, pp. <fpage>22</fpage>&#x2013;<lpage>36</lpage>, <year>2017</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>S.</given-names> <surname>Kumar</surname></string-name>, <string-name><given-names>R.</given-names> <surname>Asthana</surname></string-name>, <string-name><given-names>S.</given-names> <surname>Upadhyay</surname></string-name>, <string-name><given-names>N.</given-names> <surname>Upreti</surname></string-name> and <string-name><given-names>M.</given-names> <surname>Akbar</surname></string-name></person-group>, &#x201C;<article-title>Fake news detection using deep learning models: A novel approach</article-title>,&#x201D; <source>Transactions on Emerging Telecommunications Technologies</source>, vol. <volume>31</volume>, no. <issue>2</issue>, pp. <fpage>1</fpage>&#x2013;<lpage>23</lpage>, <year>2020</year>.</mixed-citation></ref>
<ref id="ref-9"><label>[9]</label><mixed-citation publication-type="other"><person-group person-group-type="author"><string-name><given-names>A.</given-names> <surname>Roy</surname></string-name>, <string-name><given-names>K.</given-names> <surname>Basak</surname></string-name>, <string-name><given-names>A.</given-names> <surname>Ekbal</surname></string-name> and <string-name><given-names>P.</given-names> <surname>Bhattacharyya</surname></string-name></person-group>, &#x201C;<article-title>A deep ensemble framework for fake news detection and classification</article-title>,&#x201D; <comment>arXiv preprint arXiv: 1811.04670</comment>, <year>2018</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>N.</given-names> <surname>Aslam</surname></string-name>, <string-name><given-names>I. U.</given-names> <surname>Khan</surname></string-name>, <string-name><given-names>F.</given-names> <surname>Alotaibi</surname></string-name>, <string-name><given-names>L.</given-names> <surname>Aldaej</surname></string-name> and <string-name><given-names>A.</given-names> <surname>Aldubaikil</surname></string-name></person-group>, &#x201C;<article-title>Fake Detect: A deep learning ensemble model for fake news detection</article-title>,&#x201D; <source>Complexity</source>, vol. <volume>2021</volume>, no. <issue>4</issue>, pp. <fpage>1</fpage>&#x2013;<lpage>8</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>A.</given-names> <surname>Agarwal</surname></string-name>, <string-name><given-names>M.</given-names> <surname>Mittal</surname></string-name>, <string-name><given-names>A.</given-names> <surname>Pathak</surname></string-name> and <string-name><given-names>L. M.</given-names> <surname>Goyal</surname></string-name></person-group>, &#x201C;<article-title>Fake news detection using a blend of neural networks: An application of deep learning</article-title>,&#x201D; <source>SN Computer Science</source>, vol. <volume>1</volume>, no. <issue>3</issue>, pp. <fpage>143</fpage>, <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>Z.</given-names> <surname>Khanam</surname></string-name>, <string-name><given-names>B. N.</given-names> <surname>Alwasel</surname></string-name>, <string-name><given-names>H.</given-names> <surname>Siraf</surname></string-name> and <string-name><given-names>M.</given-names> <surname>Rashid</surname></string-name></person-group>, &#x201C;<article-title>Fake news detection using machine learning approaches</article-title>,&#x201D; <source>IOP Conference Series: Materials Science and Engineering</source>, vol. <volume>1099</volume>, no. <issue>1</issue>, pp. <fpage>012040</fpage>, <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. H.</given-names> <surname>Bangyal</surname></string-name>, <string-name><given-names>R.</given-names> <surname>Qasim</surname></string-name>, <string-name><given-names>N. U.</given-names> <surname>Rehman</surname></string-name>, <string-name><given-names>Z.</given-names> <surname>Ahmad</surname></string-name>, <string-name><given-names>H.</given-names> <surname>Dar</surname></string-name> <etal>et al.</etal></person-group><italic>,</italic> &#x201C;<article-title>Detection of fake news text classification on covid-19 using deep learning approaches</article-title>,&#x201D; <source>Computational and Mathematical Methods in Medicine</source>, vol. <volume>2021</volume>, no. <issue>12</issue>, pp. <fpage>1</fpage>&#x2013;<lpage>14</lpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-14"><label>[14]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>T.</given-names> <surname>Chauhan</surname></string-name> and <string-name><given-names>H.</given-names> <surname>Palivela</surname></string-name></person-group>, &#x201C;<article-title>Optimization and improvement of fake news detection using deep learning approaches for societal benefit</article-title>,&#x201D; <source>International Journal of Information Management Data Insights</source>, vol. <volume>1</volume>, no. <issue>2</issue>, pp. <fpage>100051</fpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-15"><label>[15]</label><mixed-citation publication-type="other"><person-group person-group-type="author"><string-name><given-names>C.</given-names> <surname>Zhou</surname></string-name>, <string-name><given-names>C.</given-names> <surname>Sun</surname></string-name>, <string-name><given-names>Z.</given-names> <surname>Liu</surname></string-name> and <string-name><given-names>F.</given-names> <surname>Lau</surname></string-name></person-group>, &#x201C;<article-title>A C-LSTM neural network for text classification</article-title>,&#x201D; <comment>arXiv preprint arXiv: 1511.08630</comment>, <year>2015</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>S.</given-names> <surname>Ding</surname></string-name>, <string-name><given-names>H.</given-names> <surname>Zhao</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Zhang</surname></string-name>, <string-name><given-names>X.</given-names> <surname>Xu</surname></string-name> and <string-name><given-names>R.</given-names> <surname>Nie</surname></string-name></person-group>, &#x201C;<article-title>Extreme learning machine: Algorithm, theory and applications</article-title>,&#x201D; <source>Artificial Intelligence Review</source>, vol. <volume>44</volume>, no. <issue>1</issue>, pp. <fpage>103</fpage>&#x2013;<lpage>115</lpage>, <year>2015</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>Z.</given-names> <surname>Xu</surname></string-name>, <string-name><given-names>J.</given-names> <surname>Liu</surname></string-name>, <string-name><given-names>X.</given-names> <surname>Luo</surname></string-name>, <string-name><given-names>Z.</given-names> <surname>Yang</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Zhang</surname></string-name> <etal>et al.</etal></person-group><italic>,</italic> &#x201C;<article-title>Software defect prediction based on kernel PCA and weighted extreme learning machine</article-title>,&#x201D; <source>Information and Software Technology</source>, vol. <volume>106</volume>, no. <issue>6</issue>, pp. <fpage>182</fpage>&#x2013;<lpage>200</lpage>, <year>2019</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>M.</given-names> <surname>Wan</surname></string-name>, <string-name><given-names>C.</given-names> <surname>Wang</surname></string-name>, <string-name><given-names>L.</given-names> <surname>Li</surname></string-name> and <string-name><given-names>Y.</given-names> <surname>Yang</surname></string-name></person-group>, &#x201C;<article-title>Chaotic ant swarm approach for data clustering</article-title>,&#x201D; <source>Applied Soft Computing</source>, vol. <volume>12</volume>, no. <issue>8</issue>, pp. <fpage>2387</fpage>&#x2013;<lpage>2393</lpage>, <year>2012</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>H.</given-names> <surname>Ahmed</surname></string-name>, <string-name><given-names>I.</given-names> <surname>Traore</surname></string-name> and <string-name><given-names>S.</given-names> <surname>Saad</surname></string-name></person-group>, &#x201C;<article-title>Detecting opinion spams and fake news using text classification</article-title>,&#x201D; <source>Security and Privacy</source>, vol. <volume>1</volume>, no. <issue>1</issue>, pp. <fpage>e9</fpage>, <year>2018</year>.</mixed-citation></ref>
<ref id="ref-20"><label>[20]</label><mixed-citation publication-type="other"><person-group person-group-type="author"><collab>Kaggle</collab></person-group>, <article-title>Fake News, Kaggle</article-title>. <publisher-loc>San Francisco, CA, USA</publisher-loc>, <year>2018</year>. [Online]. Available: <uri>https://www.kaggle.com/c/fake-news</uri>.</mixed-citation></ref>
<ref id="ref-21"><label>[21]</label><mixed-citation publication-type="other"><person-group person-group-type="author"><collab>Kaggle</collab></person-group>, <article-title>Fake News Detection, Kaggle</article-title>. <publisher-loc>San Francisco, CA, USA</publisher-loc>, <year>2018</year>. [Online]. Available: <uri>https://www.kaggle.com/jruvika/fake-news-detection</uri>.</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>I.</given-names> <surname>Ahmad</surname></string-name>, <string-name><given-names>M.</given-names> <surname>Yousaf</surname></string-name>, <string-name><given-names>S.</given-names> <surname>Yousaf</surname></string-name> and <string-name><given-names>M. O.</given-names> <surname>Ahmad</surname></string-name></person-group>, &#x201C;<article-title>Fake news detection using machine learning ensemble methods</article-title>,&#x201D; <source>Complexity</source>, vol. <volume>2020</volume>, no. <issue>5</issue>, pp. <fpage>1</fpage>&#x2013;<lpage>11</lpage>, <year>2020</year>.</mixed-citation></ref>
</ref-list>
</back>
</article>