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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">37580</article-id>
<article-id pub-id-type="doi">10.32604/csse.2023.037580</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Spotted Hyena Optimizer Driven Deep Learning-Based Drug-Drug Interaction Prediction in Big Data Environment</article-title>
<alt-title alt-title-type="left-running-head">Spotted Hyena Optimizer Driven Deep Learning-Based Drug-Drug Interaction Prediction in Big Data Environment</alt-title>
<alt-title alt-title-type="right-running-head">Spotted Hyena Optimizer Driven Deep Learning-Based Drug-Drug Interaction Prediction in Big Data Environment</alt-title>
</title-group>
<contrib-group>
<contrib id="author-1" contrib-type="author">
<name name-style="western"><surname>Mohammed Jasim</surname><given-names>Mohammed Jasim</given-names></name><xref ref-type="aff" rid="aff-1">1</xref></contrib>
<contrib id="author-2" contrib-type="author">
<name name-style="western"><surname>Kak</surname><given-names>Shakir Fattah</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>Ageed</surname><given-names>Zainab Salih</given-names></name><xref ref-type="aff" rid="aff-3">3</xref></contrib>
<contrib id="author-4" contrib-type="author" corresp="yes">
<name name-style="western"><surname>Zeebaree</surname><given-names>Subhi R. M.</given-names></name><xref ref-type="aff" rid="aff-4">4</xref><email>subhi.rafeeq@dpu.edu.krd</email></contrib>
<aff id="aff-1"><label>1</label><institution>Engineering College, Al-Kitab University</institution>, <addr-line>Kirkuk</addr-line>, <country>Iraq</country></aff>
<aff id="aff-2"><label>2</label><institution>Information Technology Department, Technical College of Informatics-Akre, Duhok Polytechnic University</institution>, <addr-line>Duhok</addr-line>, <country>Iraq</country></aff>
<aff id="aff-3"><label>3</label><institution>Computer Science Department, College of Science, Nawroz University</institution>, <addr-line>Duhok</addr-line>, <country>Iraq</country></aff>
<aff id="aff-4"><label>4</label><institution>Energy Engineering Department, Technical College of Engineering, Duhok Polytechnic University</institution>, <addr-line>Duhok</addr-line>, <country>Iraq</country></aff>
</contrib-group>
<author-notes>
<corresp id="cor1"><label>&#x002A;</label>Corresponding Author: Subhi R. M. Zeebaree. Email: <email>subhi.rafeeq@dpu.edu.krd</email></corresp>
</author-notes>
<pub-date date-type="collection" publication-format="electronic">
<year>2023</year></pub-date>
<pub-date date-type="pub" publication-format="electronic">
<day>31</day>
<month>3</month>
<year>2023</year>
</pub-date>
<volume>46</volume>
<issue>3</issue>
<fpage>3831</fpage>
<lpage>3845</lpage>
<history>
<date date-type="received"><day>09</day><month>11</month><year>2022</year></date>
<date date-type="accepted"><day>09</day><month>2</month><year>2023</year></date>
</history>
<permissions>
<copyright-statement>&#x00A9; 2023 Mohammed Jasim et al.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Mohammed Jasim 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_37580.pdf"></self-uri>
<abstract>
<p>Nowadays, smart healthcare and biomedical research have marked a substantial growth rate in terms of their presence in the literature, computational approaches, and discoveries, owing to which a massive quantity of experimental datasets was published and generated (Big Data) for describing and validating such novelties. Drug-drug interaction (DDI) significantly contributed to drug administration and development. It continues as the main obstacle in offering inexpensive and safe healthcare. It normally happens for patients with extensive medication, leading them to take many drugs simultaneously. DDI may cause side effects, either mild or severe health problems. This reduced victims&#x2019; quality of life and increased hospital healthcare expenses by increasing their recovery time. Several efforts were made to formulate new methods for DDI prediction to overcome this issue. In this aspect, this study designs a new Spotted Hyena Optimizer Driven Deep Learning based Drug-Drug Interaction Prediction (SHODL-DDIP) model in a big data environment. In the presented SHODL-DDIP technique, the relativity and characteristics of the drugs can be identified from different sources for prediction. The input data is preprocessed at the primary level to improve its quality. Next, the salp swarm optimization algorithm (SSO) is used to select features. In this study, the deep belief network (DBN) model is exploited to predict the DDI accurately. The SHO algorithm is involved in improvising the DBN model&#x2019;s predictive outcomes, showing the novelty of the work. The experimental result analysis of the SHODL-DDIP technique is tested using drug databases, and the results signified the improvements of the SHODL-DDIP technique over other recent models in terms of different performance measures.</p>
</abstract>
<kwd-group kwd-group-type="author">
<kwd>Drug-drug interaction</kwd>
<kwd>deep learning</kwd>
<kwd>spotted hyena optimization</kwd>
<kwd>feature selection</kwd>
<kwd>classification</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1"><label>1</label><title>Introduction</title>
<p>Drug repositioning is a potential technique for identifying new utility for existing drugs [<xref ref-type="bibr" rid="ref-1">1</xref>]. There exist many drug repositioning techniques; forecasting drug-drug interactions (DDIs) are a helpful method for exploring the pharmacologic function of drugs, which can be used to identify effective drugs for new treatment [<xref ref-type="bibr" rid="ref-2">2</xref>,<xref ref-type="bibr" rid="ref-3">3</xref>]. DDI refers to drug mixtures&#x2019; clinical and pharmacological responses, dissimilar to the familiar effect of utilizing one drug separately [<xref ref-type="bibr" rid="ref-4">4</xref>]. In certain circumstances, DDIs may lead to adverse drug reactions (ADR), a serious health risk that affects the patient&#x2019;s health condition and may cause death [<xref ref-type="bibr" rid="ref-5">5</xref>,<xref ref-type="bibr" rid="ref-6">6</xref>]. Thus, DDI recognition is becoming crucial before the medical use of drugs compiling many drugs to cure severe illnesses such as tumours, AIDS, and so on. Tuns out to be a common and promising method in the modern era [<xref ref-type="bibr" rid="ref-7">7</xref>]. This is because utilizing many drugs to cure a disease increases treatment efficiency, and various drugs can manage a diverse part of the treatment process [<xref ref-type="bibr" rid="ref-8">8</xref>,<xref ref-type="bibr" rid="ref-9">9</xref>]. Thus, the significance of forecasting DDIs in human health was huge. Organizations and Researchers worldwide have used ample money and time to find DDI pairs utilizing several In Vitro and In Vivo experimental approaches [<xref ref-type="bibr" rid="ref-10">10</xref>]. The experimental technique to determine DDI can be extremely slow, demanding more money and time. Such techniques generally lead to low throughput, resulting in certain communications going unnoticed [<xref ref-type="bibr" rid="ref-11">11</xref>]. Since this process was extremely expensive and slow, it was impossible to find large compounds of drugs.</p>
<p>Conventional experimental techniques, like identifying transporter-based communications, were time-consuming and costly [<xref ref-type="bibr" rid="ref-12">12</xref>]. Also, just a few DDIs can be found during drug development, whereas many DDIs were reported after drug approval and discovered in post-marketing surveillance. In the meantime, computing methods render a promising alternative for finding effective DDIs on a large scale for further screening and grabbed much more interest from both industry and academia [<xref ref-type="bibr" rid="ref-13">13</xref>]. DDIs are determined as an attributed graph, in which nodes signify drugs and edges denote reported communications. There were attributes linked with nodes and edges. Node attributes were from drug profiles, like targets, chemical structures, pathways, enzymes, and side effects, whereas edge attributes will describe DDI types [<xref ref-type="bibr" rid="ref-14">14</xref>]. Individuals often adopted feature-based machine learning (ML) and pattern-related approaches in the initial days. Still, techniques related to patterns need the annotator to have some field knowledge, and the main disadvantage of this technique is that it can be both inefficient and time-consuming [<xref ref-type="bibr" rid="ref-15">15</xref>]. Deep learning (DL) is the most commonly implemented and effective technique to solve this issue.</p>
<p>Zhang et al. [<xref ref-type="bibr" rid="ref-16">16</xref>] present the implementation and construction of the knowledge graph based on the DL method. The relationship extraction and entity recognition are performed on the text of the social networking dataset. Next, the graph database is utilized to construct the knowledge graph (KG) and store medical knowledge. A DDI predictive model can be developed by integrating KG and bidirectional long short-term memory (Bi-LSTM) with attention. The multiple DDI resources are incorporated with the help of KG, and later they are converted into vectors by the knowledge representation module HolE. Lastly, the implicit feature of DDI is extracted through BiLSTM, and DDI is recognized by Softmax classification. Hung et al. [<xref ref-type="bibr" rid="ref-17">17</xref>] developed a machine learning (ML) method for predicting the outcome of interaction amongst drugs utilized for Paget&#x2019;s treatment and osteoporosis that assist in mitigating the cost and time for enforcing the better integration of medication in medical practice. The presented method gathered DDI data from the DrugBank dataset about Paget diseases and osteoporosis. Next, chemical features are extracted from the simplified molecular-input line-entry system (SMILES) of determining drug pairs communicating with one another. Lastly, an ML algorithm was executed to learn the extracted feature.</p>
<p>Noor [<xref ref-type="bibr" rid="ref-18">18</xref>] designs a data-driven model to conduct knowledge-driven data analysis, which integrates the enrichment analysis and semantic inference system for identifying possible ADE mechanisms. The architecture has been exploited for ranking mechanisms based on the relevance for DDI and also to classify ADE depending on the number of DDI mechanisms association recognized through enrichment analysis. Chen et al. [<xref ref-type="bibr" rid="ref-19">19</xref>] derived two signed graph filtering-oriented neural networks (SGFNN) that incorporate signed graph structure and drug node attribute. Furthermore, we utilized the end-to-end architecture for learning DDI, whereby a discriminator and the SGFNN are collectively trained under a problem-specific loss function. The experiment outcome on two predictive issues shows that the architecture could improve considerably compared to the baseline. Su et al. [<xref ref-type="bibr" rid="ref-20">20</xref>] developed a novel architecture named KG2ECapsule which explicitly modelled the multi-relational DDI dataset relying on a biomedical knowledge graph in an end-to-end manner. Firstly, it produces a higher-quality negative sample according to an average number of head and tail entities for all the relations to reduce the false-negative sample to a certain range. Then, KG2ECapsule refines the representation of an entity by recursively broadcasting the embedding from the attention-related receptive field of the entities. Feature selection methods can be used to improve the performance of the ML classification model [<xref ref-type="bibr" rid="ref-21">21</xref>&#x2013;<xref ref-type="bibr" rid="ref-25">25</xref>].</p>
<p>This study designs a new Spotted Hyena Optimizer Driven Deep Learning based Drug-Drug Interaction Prediction (SHODL-DDIP) model in a big data environment. In the presented SHODL-DDIP technique, the relativity and characteristics of the drugs can be identified from different sources for prediction. The input data is preprocessed at the primary level to improve its quality. Next, the salp swarm optimization algorithm (SSO) is used to select features. In this study, the deep belief network (DBN) model is exploited to predict the DDI accurately. The SHO algorithm is involved in improvising the DBN model&#x2019;s predictive outcomes. The experimental result analysis of the SHODL-DDIP technique is tested using drug databases.</p>
</sec>
<sec id="s2"><label>2</label><title>The Proposed DDI Prediction Model</title>
<p>In this study, an automated SHODL-DDIP model has been developed to predict DDI in a big-data environment. In the presented SHODL-DDIP technique, the relativity and characteristics of the drugs can be identified from different sources for prediction. <xref ref-type="fig" rid="fig-1">Fig. 1</xref> depicts the workflow of the SHODL-DDIP approach.</p>
<fig id="fig-1"><label>Figure 1</label><caption><title>Workflow of SHODL-DDIP approach</title></caption><graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_37580-fig-1.tif"/></fig>
<sec id="s2_1"><label>2.1</label><title>Data Pre-Processing</title>
<p>Standard text cleaning and preprocessing processes were executed on sentences involving but unrestricted to lemmatization. All drugs are discussed in a sentence labelled to communicate with others. The number of drug pairs (DP) in a sentence can be evaluated below:
<disp-formula id="eqn-1"><label>(1)</label><mml:math id="mml-eqn-1" display="block"><mml:mi>D</mml:mi><mml:mi>r</mml:mi><mml:mi>u</mml:mi><mml:mi>g</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mrow><mml:mtext mathvariant="italic">Pairs</mml:mtext></mml:mrow><mml:mtext>&#x00A0;</mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mi>D</mml:mi><mml:mi>P</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>m</mml:mi><mml:mrow><mml:mtext>ax&#xA0;</mml:mtext></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:msubsup><mml:mrow><mml:mo>&#x2211;</mml:mo></mml:mrow><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:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula>where <italic>n</italic> specifies the number of drugs in a sentence, drug blinding has been employed, in which every drug name can be allotted to the label. Afterwards, the processed sentence was given to the method for detecting and classifying DDI. At Word Embedding, all words can be transformed into real value vectors. This word mapping into a matrix is done through Word2Vec and embedding the dataset utilizing the extract of PubMed comprising the drugs.</p>
</sec>
<sec id="s2_2"><label>2.2</label><title>SSO-Based Feature Selection</title>
<p>Here, the SSO algorithm is used for the optimal selection of features. The SSO is a newly presented technique simulated by the forging and swarming performance of salps (aquatic organisms) [<xref ref-type="bibr" rid="ref-26">26</xref>]. The salps procedure chain for foraging and navigating in seas and oceans. As with other SI techniques, the SSO technique depended upon the arbitrary initialization of populations with an existing count of individuals (solutions). To assist the search, the salps separate themselves into 2 types followers and leaders. The leader was a primary salp from the chain (optimum solution) that pilots follower drive. All the swarms <italic>X</italic> contain <italic>n</italic> salps and are determined in <inline-formula id="ieqn-1"><mml:math id="mml-ieqn-1"><mml:mn>2</mml:mn><mml:mi>D</mml:mi></mml:math></inline-formula>-matrix as:
<disp-formula id="eqn-2"><label>(2)</label><mml:math id="mml-eqn-2" display="block"><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mtable columnalign="left center left left" rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:msubsup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:mtd><mml:mtd><mml:msubsup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:mtd><mml:mtd><mml:mo>&#x2026;</mml:mo></mml:mtd><mml:mtd><mml:msubsup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msubsup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup></mml:mtd><mml:mtd><mml:msubsup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup></mml:mtd><mml:mtd><mml:mo>&#x2026;</mml:mo></mml:mtd><mml:mtd><mml:msubsup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup></mml:mtd></mml:mtr><mml:mtr><mml:mtd /><mml:mtd><mml:mo>&#x22EE;</mml:mo></mml:mtd><mml:mtd /><mml:mtd /></mml:mtr><mml:mtr><mml:mtd><mml:msubsup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msubsup></mml:mtd><mml:mtd><mml:msubsup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msubsup></mml:mtd><mml:mtd><mml:mo>&#x2026;</mml:mo></mml:mtd><mml:mtd><mml:msubsup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msubsup></mml:mtd></mml:mtr></mml:mtable><mml:mo>]</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>The swarms&#x2019; purpose is to define the food source (optimum solution) from the whole searching space. Next mathematical process of salps chain with upgrade principle of leader position:
<disp-formula id="eqn-3"><label>(3)</label><mml:math id="mml-eqn-3" display="block"><mml:msubsup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mml:mtr><mml:mtd><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mi>u</mml:mi><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:mi>l</mml:mi><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi>l</mml:mi><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2265;</mml:mo><mml:mn>0.5</mml:mn></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mi>u</mml:mi><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:mi>l</mml:mi><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi>l</mml:mi><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo>&#x003C;</mml:mo><mml:mn>0.5</mml:mn></mml:mtd></mml:mtr></mml:mtable><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>whereas the leader position was represented by <inline-formula id="ieqn-2"><mml:math id="mml-ieqn-2"><mml:msubsup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:math></inline-formula>, the position of food sources can be represented by <inline-formula id="ieqn-3"><mml:math id="mml-ieqn-3"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> from the <inline-formula id="ieqn-4"><mml:math id="mml-ieqn-4"><mml:msup><mml:mi>j</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> dimensional. The parameter <inline-formula id="ieqn-5"><mml:math id="mml-ieqn-5"><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> is provided as:
<disp-formula id="eqn-4"><label>(4)</label><mml:math id="mml-eqn-4" display="block"><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mfrac><mml:mrow><mml:mn>4</mml:mn><mml:mi>t</mml:mi></mml:mrow><mml:mi>T</mml:mi></mml:mfrac><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:msup></mml:math></disp-formula></p>
<p><inline-formula id="ieqn-6"><mml:math id="mml-ieqn-6"><mml:mi>T</mml:mi></mml:math></inline-formula> signifies the present iteration, and <italic>T</italic> implies the maximal count of iterations. With enhancement under the iterations, the <inline-formula id="ieqn-7"><mml:math id="mml-ieqn-7"><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> reduces, ensuring the appropriate exploitation of searching space. The <inline-formula id="ieqn-8"><mml:math id="mml-ieqn-8"><mml:mi>u</mml:mi><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-9"><mml:math id="mml-ieqn-9"><mml:mi>l</mml:mi><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> signify the upper and lower bounds of the <inline-formula id="ieqn-10"><mml:math id="mml-ieqn-10"><mml:msup><mml:mi>j</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> dimensional. The parameters <inline-formula id="ieqn-11"><mml:math id="mml-ieqn-11"><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-12"><mml:math id="mml-ieqn-12"><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> are the arbitrary numbers drawn in the interval of zero and one. The position of follower&#x2019;s salps can upgrade as:
<disp-formula id="eqn-5"><label>(5)</label><mml:math id="mml-eqn-5" display="block"><mml:msubsup><mml:mrow><mml:mi>&#x03C7;</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mn>0.5</mml:mn><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mrow><mml:mi>X</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mrow><mml:mi>X</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>The position of the <inline-formula id="ieqn-13"><mml:math id="mml-ieqn-13"><mml:msup><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> follower from the <inline-formula id="ieqn-14"><mml:math id="mml-ieqn-14"><mml:msup><mml:mi>j</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> dimensional was demonstrated by <inline-formula id="ieqn-15"><mml:math id="mml-ieqn-15"><mml:msubsup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> with <inline-formula id="ieqn-16"><mml:math id="mml-ieqn-16"><mml:mi>i</mml:mi><mml:mo>&#x003E;</mml:mo><mml:mn>1.</mml:mn></mml:math></inline-formula></p>
<p>The fitness function (FF) employed in the presented method was modelled to maintain a balance among the number of selected features in all solutions (min) and classifier accuracy (max) acquired through such selected features. <xref ref-type="disp-formula" rid="eqn-6">Eq. (6)</xref> signifies the FF for evaluating solutions.
<disp-formula id="eqn-6"><label>(6)</label><mml:math id="mml-eqn-6" display="block"><mml:mrow><mml:mtext mathvariant="italic">Fitness</mml:mtext></mml:mrow><mml:mo>=</mml:mo><mml:mi>&#x03B1;</mml:mi><mml:msub><mml:mi>&#x03B3;</mml:mi><mml:mrow><mml:mi>R</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>D</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>&#x03B2;</mml:mi><mml:mfrac><mml:mrow><mml:mo>|</mml:mo><mml:mi>R</mml:mi><mml:mo>|</mml:mo></mml:mrow><mml:mrow><mml:mo>|</mml:mo><mml:mi>C</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:mfrac></mml:math></disp-formula></p>
<p>Here <inline-formula id="ieqn-17"><mml:math id="mml-ieqn-17"><mml:mrow><mml:mo>|</mml:mo><mml:mi>R</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:math></inline-formula> is the cardinality of the selected subset, <inline-formula id="ieqn-18"><mml:math id="mml-ieqn-18"><mml:msub><mml:mi>&#x03B3;</mml:mi><mml:mrow><mml:mi>R</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> signifies the classification error rate of a given classier (the K-nearest neighbor (KNN) classifier), and <inline-formula id="ieqn-19"><mml:math id="mml-ieqn-19"><mml:mrow><mml:mo>|</mml:mo><mml:mi>C</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:math></inline-formula> designates the total features in the dataset, <inline-formula id="ieqn-20"><mml:math id="mml-ieqn-20"><mml:mi>&#x03B2;</mml:mi><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext></mml:math></inline-formula> and <inline-formula id="ieqn-21"><mml:math id="mml-ieqn-21"><mml:mi>&#x03B1;</mml:mi></mml:math></inline-formula> are 2 parameters matching the significance of classifier quality and subset length. &#x2208; [1, 0] and <inline-formula id="ieqn-22"><mml:math id="mml-ieqn-22"><mml:mi>&#x03B2;</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mi>&#x03B1;</mml:mi><mml:mo>.</mml:mo></mml:math></inline-formula></p>
</sec>
<sec id="s2_3"><label>2.3</label><title>Optimal DBN-Based DDI Prediction Process</title>
<p>The DBN model is used at this stage to predict the DDI proficiently. The DBN approach contains four layers of pre-training RBM and resultant layers (Softmax Regression) [<xref ref-type="bibr" rid="ref-27">27</xref>]. The parameter can be projected by a trained approach previously employing DBN for classifying and representing assaults. The DBN trained is categorized as pre-train for presenting and fine-tuning for classifiers. At the same time, the resulting DBN is transmitted to inputted Softmax Regression and comprised in DBN, which includes stacked RBM. Primarily, DBN was training to reconfigure untagged training databases and therefore executed unsupervised. Edata [.] and Emodel [.] can be expectations of possibilities.
<disp-formula id="eqn-7"><label>(7)</label><mml:math id="mml-eqn-7" display="block"><mml:mfrac><mml:mrow><mml:mi mathvariant="normal">&#x2202;</mml:mi><mml:mrow><mml:mtext>&#x00A0;log&#x00A0;</mml:mtext></mml:mrow><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2202;</mml:mi><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>d</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">[</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">]</mml:mo><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">model</mml:mtext></mml:mrow></mml:mrow></mml:msub><mml:mo stretchy="false">[</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">]</mml:mo></mml:math></disp-formula>
<disp-formula id="eqn-8"><label>(8)</label><mml:math id="mml-eqn-8" display="block"><mml:mfrac><mml:mrow><mml:mi mathvariant="normal">&#x2202;</mml:mi><mml:mrow><mml:mtext>&#x00A0;log&#x00A0;</mml:mtext></mml:mrow><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2202;</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>d</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>]</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">model</mml:mtext></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>]</mml:mo></mml:mrow></mml:math></disp-formula>
<disp-formula id="eqn-9"><label>(9)</label><mml:math id="mml-eqn-9" display="block"><mml:mfrac><mml:mrow><mml:mi mathvariant="normal">&#x2202;</mml:mi><mml:mrow><mml:mtext>&#x00A0;log&#x00A0;</mml:mtext></mml:mrow><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2202;</mml:mi><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>d</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>]</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">model</mml:mtext></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>]</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>During this case, three techniques <xref ref-type="disp-formula" rid="eqn-7">(Eqs. (7)</xref>&#x2013;<xref ref-type="disp-formula" rid="eqn-9">(9)</xref>) primarily comprised in classical DBN network, the second term can only be indirectly obtained. At the same time, it can be possible in distribution which is studied utilizing the DBN. Gibb&#x2019;s sampling was utilized to calculate this probability. But, this approach is time-consuming and is utilized in real-time. The contrastive divergence (CD) system was utilized to determine optimum solutions, a fast-learning technique. A trained sample can be employed to finish the Markov chain&#x2019;s beginning. Afterwards, instances are obtained, and then <inline-formula id="ieqn-23"><mml:math id="mml-ieqn-23"><mml:mi>t</mml:mi><mml:mi>h</mml:mi><mml:mi>e</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>k</mml:mi></mml:math></inline-formula> steps of Gibb&#x2019;s selection. This approach is termed CD-k. Noticeably the efficiency of CD is suitable if <inline-formula id="ieqn-24"><mml:math id="mml-ieqn-24"><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math></inline-formula>. <xref ref-type="fig" rid="fig-2">Fig. 2</xref> exhibits the framework of DBN.</p>
<fig id="fig-2"><label>Figure 2</label><caption><title>Architecture of DBN</title></caption><graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_37580-fig-2.tif"/></fig>
<p>During this work, for training, stacked RBM layer-wise to generate DBN, <italic>b</italic>, and <italic>W</italic> parameters can be upgraded dependent upon CD-1.
<disp-formula id="eqn-10"><label>(10)</label><mml:math id="mml-eqn-10" display="block"><mml:msup><mml:mi>W</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:msup><mml:mi>W</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:mi>&#x03B5;</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mfrac><mml:mi>h</mml:mi><mml:msup><mml:mi>x</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msup></mml:mfrac><mml:mo>)</mml:mo></mml:mrow><mml:mo stretchy="false">[</mml:mo><mml:msup><mml:mi>x</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mo stretchy="false">]</mml:mo><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msup><mml:mo>&#x2212;</mml:mo><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mfrac><mml:mi>h</mml:mi><mml:msup><mml:mi>x</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msup></mml:mfrac><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">[</mml:mo><mml:msup><mml:mi>x</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mo stretchy="false">]</mml:mo><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:msup><mml:mi>a</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:msup><mml:mi>a</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:mi>&#x03B5;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mi>x</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msup><mml:mo>&#x2212;</mml:mo><mml:msup><mml:mi>x</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula>
<disp-formula id="ueqn-1">
<mml:math id="mml-ueqn-1" display="block"><mml:msup><mml:mi>b</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:msup><mml:mi>b</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:mi>&#x03B5;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mfrac><mml:mi>h</mml:mi><mml:msup><mml:mi>x</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msup></mml:mfrac><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mfrac><mml:mi>h</mml:mi><mml:msup><mml:mi>x</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msup></mml:mfrac><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>In this formula, <inline-formula id="ieqn-25"><mml:math id="mml-ieqn-25"><mml:mo>&#x2208;</mml:mo></mml:math></inline-formula> represents the learning rate, and <italic>t</italic> signifies the time step. The visible variable is represented as <inline-formula id="ieqn-26"><mml:math id="mml-ieqn-26"><mml:mi>h</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mi>h</mml:mi><mml:mo>}</mml:mo></mml:mrow></mml:math></inline-formula> and the hidden variable as <inline-formula id="ieqn-27"><mml:math id="mml-ieqn-27"><mml:mi>x</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo>}</mml:mo></mml:mrow></mml:math></inline-formula>. At this point, <italic>M</italic> and <italic>N</italic> nodes and hidden layers are visible. The weighted feature vector was introduced arbitrarily in the network by selection from the CD system.</p>
<p>The stages of executing greedy layer-wise trained processes to every layer of DBN can be provided.</p>
<p>A primary RBM trained, the data appropriate to <inline-formula id="ieqn-28"><mml:math id="mml-ieqn-28"><mml:mi>t</mml:mi><mml:mi>h</mml:mi><mml:mi>e</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> parameter was assumed that input <inline-formula id="ieqn-29"><mml:math id="mml-ieqn-29"><mml:mi>x</mml:mi><mml:mo>.</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> is frozen and executed to train RBM <inline-formula id="ieqn-30"><mml:math id="mml-ieqn-30"><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> as <inline-formula id="ieqn-31"><mml:math id="mml-ieqn-31"><mml:mi>Q</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mi>v</mml:mi></mml:mfrac></mml:mstyle><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> to train RBM and the subsequent binary feature layer. <inline-formula id="ieqn-32"><mml:math id="mml-ieqn-32"><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> that defines 2-layered features can be frozen, and the database vital to train binary features at 3 layers can be obtained in <inline-formula id="ieqn-33"><mml:math id="mml-ieqn-33"><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> as <inline-formula id="ieqn-34"><mml:math id="mml-ieqn-34"><mml:mrow><mml:mo>(</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mfrac></mml:mstyle><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. This process constantly repeats across all the layers. LR was employed in traditional binary classifiers. Conversely, the study chose Softmax as it is several classifiers from the DBN.</p>
<p>While the trained set <inline-formula id="ieqn-35"><mml:math id="mml-ieqn-35"><mml:mo fence="false" stretchy="false">{</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mrow><mml:mi>z</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, <inline-formula id="ieqn-36"><mml:math id="mml-ieqn-36"><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mrow><mml:mi>z</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, <inline-formula id="ieqn-37"><mml:math id="mml-ieqn-37"><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mrow><mml:mi>z</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo fence="false" stretchy="false">}</mml:mo></mml:math></inline-formula>, <italic>m</italic> stands for the count of instances from the trained set and <inline-formula id="ieqn-38"><mml:math id="mml-ieqn-38"><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mrow><mml:mi>z</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:msubsup><mml:mrow><mml:mi>z</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> illustrates hidden vector of top RBM. The Softmax function &#x03D5; in a resultant layer, <inline-formula id="ieqn-39"><mml:math id="mml-ieqn-39"><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mi>k</mml:mi></mml:math></inline-formula> for every class, the conditional probability of <inline-formula id="ieqn-40"><mml:math id="mml-ieqn-40"><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>y</mml:mi><mml:mo>=</mml:mo><mml:mi>j</mml:mi><mml:mo fence="false" stretchy="false">|</mml:mo><mml:msup><mml:mi>z</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> was estimated by the following formula.
<disp-formula id="eqn-11"><label>(11)</label><mml:math id="mml-eqn-11" display="block"><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>=</mml:mo><mml:mi>j</mml:mi><mml:mo fence="false" stretchy="false">|</mml:mo><mml:msup><mml:mi>z</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>&#x03D5;</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">softma</mml:mtext></mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mi>z</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mrow><mml:msup><mml:mi>z</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:msup><mml:mrow><mml:msubsup><mml:mrow><mml:mo>&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msubsup><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:msubsup><mml:mrow><mml:mi>z</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:mrow></mml:msup></mml:mrow></mml:mfrac></mml:math></disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-11">Eq. (11)</xref>, <inline-formula id="ieqn-41"><mml:math id="mml-ieqn-41"><mml:msub><mml:mi>z</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>&#x2208;</mml:mo></mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> depicts the topmost confidential vector, and it can be provided in subsequent:
<disp-formula id="eqn-12"><label>(12)</label><mml:math id="mml-eqn-12" display="block"><mml:mi>z</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>+</mml:mo><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msubsup><mml:mrow><mml:mo>&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>l</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msubsup><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mi>w</mml:mi><mml:mrow><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>X</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:msup></mml:math></disp-formula></p>
<p>The SHO algorithm is involved in hyperparameter tuning to improve the predictive outcomes of the DBN model. The presented SHO method comprises four major stages stimulated by the natural behavior of spotted hyenas [<xref ref-type="bibr" rid="ref-28">28</xref>]. They are attacking, searching, encircling, and hunting for prey that is mathematically formulated below.</p>
<p>The better solution was regarded as the target prey to encircle the prey, and the other spotted hyenas or searching agents upgraded the location based on the optimum solution as follows:
<disp-formula id="eqn-13"><label>(13)</label><mml:math id="mml-eqn-13" display="block"><mml:msub><mml:mover><mml:mi>D</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mi>M</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo>|</mml:mo><mml:mover><mml:mi>B</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mo>&#x00D7;</mml:mo><mml:msub><mml:mover><mml:mi>P</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mover><mml:mi>P</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>|</mml:mo></mml:mrow></mml:math></disp-formula>
<disp-formula id="eqn-14"><label>(14)</label><mml:math id="mml-eqn-14" display="block"><mml:mover><mml:mi>P</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mover><mml:mi>P</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mover><mml:mi>E</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mo>&#x00D7;</mml:mo><mml:msub><mml:mover><mml:mi>D</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub></mml:math></disp-formula></p>
<p>whereas <inline-formula id="ieqn-42"><mml:math id="mml-ieqn-42"><mml:msub><mml:mover><mml:mi>D</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> represents the distance vector amongst spotted hyena and prey, <italic>y</italic> represents the current iteration, <inline-formula id="ieqn-43"><mml:math id="mml-ieqn-43"><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> indicates the location vector of prey, <inline-formula id="ieqn-44"><mml:math id="mml-ieqn-44"><mml:msub><mml:mover><mml:mi>P</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> symbolizes the position vector of spotted hyena, <inline-formula id="ieqn-45"><mml:math id="mml-ieqn-45"><mml:mover><mml:mi>B</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:math></inline-formula> and <inline-formula id="ieqn-46"><mml:math id="mml-ieqn-46"><mml:mover><mml:mi>E</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:math></inline-formula> indicate the coefficient vector:
<disp-formula id="eqn-15"><label>(15)</label><mml:math id="mml-eqn-15" display="block"><mml:mover><mml:mi>B</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mo>&#x00D7;</mml:mo><mml:mi>r</mml:mi><mml:msub><mml:mover><mml:mi>d</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></disp-formula>
<disp-formula id="eqn-16"><label>(16)</label><mml:math id="mml-eqn-16" display="block"><mml:mover><mml:mi>E</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mo>&#x00D7;</mml:mo><mml:mover><mml:mi>m</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mo>&#x00D7;</mml:mo><mml:mi>r</mml:mi><mml:msub><mml:mover><mml:mi>d</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:mover><mml:mi>m</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:math></disp-formula>
<disp-formula id="eqn-17"><label>(17)</label><mml:math id="mml-eqn-17" display="block"><mml:mover><mml:mi>m</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mn>5</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mtext mathvariant="italic">Iteration</mml:mtext></mml:mrow><mml:mtext>&#x00A0;</mml:mtext><mml:mo>&#x00D7;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mfrac><mml:mn>5</mml:mn><mml:msub><mml:mrow><mml:mtext>Max</mml:mtext></mml:mrow><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">Iteration</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:mfrac><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula>where, Iteration <inline-formula id="ieqn-47"><mml:math id="mml-ieqn-47"><mml:mo>=</mml:mo><mml:mn>0</mml:mn><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:msub><mml:mrow><mml:mtext>Max</mml:mtext></mml:mrow><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">Iteration</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula></p>
<p>The hunting phase makes a cluster of the optimum solution against the better searching agent and upgrades the position of other searching agents:
<disp-formula id="eqn-18"><label>(18)</label><mml:math id="mml-eqn-18" display="block"><mml:msub><mml:mover><mml:mi>D</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo>|</mml:mo><mml:mover><mml:mi>B</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mo>&#x00D7;</mml:mo><mml:msub><mml:mover><mml:mi>P</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mover><mml:mi>P</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>|</mml:mo></mml:mrow></mml:math></disp-formula>
<disp-formula id="eqn-19"><label>(19)</label><mml:math id="mml-eqn-19" display="block"><mml:msub><mml:mover><mml:mi>P</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mover><mml:mi>P</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:mover><mml:mi>E</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mo>&#x00D7;</mml:mo><mml:msub><mml:mover><mml:mi>D</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub></mml:math></disp-formula>
<disp-formula id="eqn-20"><label>(20)</label><mml:math id="mml-eqn-20" display="block"><mml:msub><mml:mover><mml:mi>C</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mover><mml:mi>P</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mover><mml:mi>P</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>+</mml:mo><mml:msub><mml:mover><mml:mi>P</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mi>N</mml:mi></mml:mrow></mml:msub></mml:math></disp-formula></p>
<p>whereas <inline-formula id="ieqn-48"><mml:math id="mml-ieqn-48"><mml:msub><mml:mover><mml:mi>P</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> describes the location of the initial optimal spotted hyena, <inline-formula id="ieqn-49"><mml:math id="mml-ieqn-49"><mml:msub><mml:mover><mml:mi>P</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> represent the location of other spotted hyenas, and <italic>N</italic> indicates the number of spotted hyenas:
<disp-formula id="eqn-21"><label>(21)</label><mml:math id="mml-eqn-21" display="block"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>u</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mover><mml:mi>P</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mover><mml:mi>P</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mi>m</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mover><mml:mi>P</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mi>m</mml:mi><mml:mo>+</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mo>&#x2026;</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mover><mml:mi>P</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mover><mml:mi>M</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-21">Eq. (21)</xref>, <inline-formula id="ieqn-50"><mml:math id="mml-ieqn-50"><mml:mover><mml:mi>M</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:math></inline-formula> represent a random parameter within [0.5, 1], <inline-formula id="ieqn-51"><mml:math id="mml-ieqn-51"><mml:mi>n</mml:mi><mml:mi>s</mml:mi></mml:math></inline-formula> indicates the number of solutions, and <inline-formula id="ieqn-52"><mml:math id="mml-ieqn-52"><mml:msub><mml:mover><mml:mi>C</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> denotes the group of <italic>N</italic> amount of optimum solutions. It is essential to decrease the value of vector <inline-formula id="ieqn-53"><mml:math id="mml-ieqn-53"><mml:mover><mml:mi>m</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:math></inline-formula>. But the variation in <inline-formula id="ieqn-54"><mml:math id="mml-ieqn-54"><mml:mover><mml:mi>E</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:math></inline-formula> has reduced because of the changes in the value in <italic>m</italic> that could reduce from 5 to <inline-formula id="ieqn-55"><mml:math id="mml-ieqn-55"><mml:mn>0</mml:mn></mml:math></inline-formula>, and it is mathematically expressed as follows:
<disp-formula id="eqn-22"><label>(22)</label><mml:math id="mml-eqn-22" display="block"><mml:mover><mml:mi>P</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mover><mml:mi>C</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mi>N</mml:mi></mml:mfrac></mml:math></disp-formula></p>
<p>whereas <inline-formula id="ieqn-56"><mml:math id="mml-ieqn-56"><mml:mover><mml:mi>P</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover><mml:mrow><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> stores the better solution and upgrades the location of other searching agents. The search model defines the exploration ability. The presented technique thus guarantees the ability to use <italic>E</italic> with the random value greater or lesser than 1. Also, vector <inline-formula id="ieqn-57"><mml:math id="mml-ieqn-57"><mml:mover><mml:mi>B</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:math></inline-formula> is accountable to demonstrate the randomized behaviors of SHO and prevent local optima.</p>
</sec>
</sec>
<sec id="s3"><label>3</label><title>Results and Discussion</title>
<p>The proposed model is simulated using Python 3.6.5 tool on PC i5-8600k, GeForce 1050Ti 4 GB, 16 GB RAM, 250 GB SSD, and 1 TB HDD. The parameter settings are given as follows: learning rate: 0.01, dropout: 0.5, batch size: 5, epoch count: 50, and activation: ReLU. In this section, the DDI prediction results of the SHODL-DDIP model are investigated on four datasets. The class distribution of the datasets is given in <xref ref-type="table" rid="table-1">Table 1</xref> and <xref ref-type="fig" rid="fig-3">Fig. 3</xref>.</p>
<table-wrap id="table-1"><label>Table 1</label><caption><title>Details of datasets</title></caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left">Database</th>
<th align="left">Drug</th>
<th align="left">Target</th>
<th align="left">Interactions</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">Enzyme-dataset</td>
<td align="left">445</td>
<td align="left">664</td>
<td align="left">2926</td>
</tr>
<tr>
<td align="left">Ion channel-dataset</td>
<td align="left">210</td>
<td align="left">204</td>
<td align="left">1467</td>
</tr>
<tr>
<td align="left">GPCR-dataset</td>
<td align="left">223</td>
<td align="left">95</td>
<td align="left">635</td>
</tr>
<tr>
<td align="left">Nuclear receptor-dataset</td>
<td align="left">54</td>
<td align="left">26</td>
<td align="left">90</td>
</tr>
</tbody>
</table>
</table-wrap><fig id="fig-3"><label>Figure 3</label><caption><title>Dataset details</title></caption><graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_37580-fig-3.tif"/></fig>
<p>In <xref ref-type="table" rid="table-2">Table 2</xref> and <xref ref-type="fig" rid="fig-4">Fig. 4</xref>, the performance of the SSODL-DDIP approach under unlabelled and labelled samples on top k&#x0025; values is given. The outcomes exhibited that the SSODL-DDIP method has effectively labelled the samples. For instance, on the enzyme dataset with the top 10&#x0025; samples, the SHODL-DDIP model has properly identified 384 samples from 28969 unlabeled samples.</p>
<table-wrap id="table-2"><label>Table 2</label><caption><title>Result analysis of the SSODL-DDIP approach under unlabelled and labelled samples</title></caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th align="center" colspan="3">Enzyme dataset</th>
<th align="center" colspan="3">GPCR dataset</th>
</tr>
<tr>
<th align="left">Top k (&#x0025;)</th>
<th align="left">Unlabelled</th>
<th align="left">Labelled</th>
<th align="left">Top k (&#x0025;)</th>
<th align="left">Unlabelled</th>
<th align="left">Labelled</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">10</td>
<td align="left">28969</td>
<td align="left">384</td>
<td align="left">10</td>
<td align="left">1860</td>
<td align="left">367</td>
</tr>
<tr>
<td align="left">20</td>
<td align="left">58109</td>
<td align="left">542</td>
<td align="left">20</td>
<td align="left">3860</td>
<td align="left">502</td>
</tr>
<tr>
<td align="left">30</td>
<td align="left">87359</td>
<td align="left">582</td>
<td align="left">30</td>
<td align="left">5908</td>
<td align="left">555</td>
</tr>
<tr>
<td align="left">40</td>
<td align="left">116682</td>
<td align="left">561</td>
<td align="left">40</td>
<td align="left">7956</td>
<td align="left">605</td>
</tr>
<tr>
<td align="left">50</td>
<td align="left">145909</td>
<td align="left">611</td>
<td align="left">50</td>
<td align="left">9994</td>
<td align="left">656</td>
</tr>
<tr>
<td align="left">60</td>
<td align="left">175154</td>
<td align="left">640</td>
<td align="left">60</td>
<td align="left">12024</td>
<td align="left">713</td>
</tr>
<tr>
<td align="left">70</td>
<td align="left">204402</td>
<td align="left">679</td>
<td align="left">70</td>
<td align="left">14035</td>
<td align="left">762</td>
</tr>
<tr>
<td align="left">80</td>
<td align="left">233673</td>
<td align="left">690</td>
<td align="left">80</td>
<td align="left">16102</td>
<td align="left">760</td>
</tr>
<tr>
<td align="left">90</td>
<td align="left">262904</td>
<td align="left">745</td>
<td align="left">90</td>
<td align="left">18152</td>
<td align="left">765</td>
</tr>
<tr>
<td align="left">100</td>
<td align="left">292138</td>
<td align="left">794</td>
<td align="left">100</td>
<td align="left">20228</td>
<td align="left">783</td>
</tr>
<tr>
<td align="center" colspan="3">ION channel dataset</td>
<td align="center" colspan="3">Nuclear receptor dataset</td>
</tr>
<tr>
<td align="left">Top k (&#x0025;)</td>
<td align="left">Unlabelled</td>
<td align="left">Labelled</td>
<td align="left">Top k (&#x0025;)</td>
<td align="left">Unlabelled</td>
<td align="left">Labelled</td>
</tr>
<tr>
<td align="left">10</td>
<td align="left">3969</td>
<td align="left">452</td>
<td align="left">10</td>
<td align="left">68</td>
<td align="left">76</td>
</tr>
<tr>
<td align="left">20</td>
<td align="left">7983</td>
<td align="left">805</td>
<td align="left">20</td>
<td align="left">178</td>
<td align="left">99</td>
</tr>
<tr>
<td align="left">30</td>
<td align="left">12171</td>
<td align="left">850</td>
<td align="left">30</td>
<td align="left">305</td>
<td align="left">105</td>
</tr>
<tr>
<td align="left">40</td>
<td align="left">16368</td>
<td align="left">853</td>
<td align="left">40</td>
<td align="left">444</td>
<td align="left">97</td>
</tr>
<tr>
<td align="left">50</td>
<td align="left">20317</td>
<td align="left">1131</td>
<td align="left">50</td>
<td align="left">581</td>
<td align="left">90</td>
</tr>
<tr>
<td align="left">60</td>
<td align="left">24402</td>
<td align="left">1240</td>
<td align="left">60</td>
<td align="left">720</td>
<td align="left">81</td>
</tr>
<tr>
<td align="left">70</td>
<td align="left">28547</td>
<td align="left">1281</td>
<td align="left">70</td>
<td align="left">822</td>
<td align="left">109</td>
</tr>
<tr>
<td align="left">80</td>
<td align="left">32659</td>
<td align="left">1331</td>
<td align="left">80</td>
<td align="left">959</td>
<td align="left">102</td>
</tr>
<tr>
<td align="left">90</td>
<td align="left">36757</td>
<td align="left">1412</td>
<td align="left">90</td>
<td align="left">1069</td>
<td align="left">122</td>
</tr>
<tr>
<td align="left">100</td>
<td align="left">40871</td>
<td align="left">1462</td>
<td align="left">100</td>
<td align="left">1215</td>
<td align="left">106</td>
</tr>
</tbody>
</table>
</table-wrap><fig id="fig-4"><label>Figure 4</label><caption><title>Result analysis of SHODL-DDIP system (a) Enzyme, (b) GPCR, (c) ION, and (d) Nuclear receptor</title></caption><graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_37580-fig-4a.tif"/><graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_37580-fig-4b.tif"/></fig>
<p>In addition, on the GPCR dataset with the top 10&#x0025; samples, the SHODL-DDIP model has properly identified 367 samples from 1860 unlabeled samples. Also, on the ION dataset with the top 10&#x0025; samples, the SHODL-DDIP method has properly identified 452 samples from 3969 unlabeled samples. Furthermore, on the nuclear receptor dataset with the top 10&#x0025; samples, the SHODL-DDIP technique has properly identified 76 samples from 68 unlabeled samples. At last, on the nuclear receptor dataset with the top 100&#x0025; samples, the SHODL-DDIP method has properly identified 106 samples from 1215 unlabeled samples.</p>
<p><xref ref-type="table" rid="table-3">Table 3</xref> and <xref ref-type="fig" rid="fig-5">Fig. 5</xref> report the AUC and AUPR analysis of the SHODL-DDIP model. The results show the SHODL-DDIP method has enhanced values of AUC and AUPR under different CV_Seed values. For instance, on the enzyme dataset with 3201 CV_SEED, the SHODL-DDIP model has obtained AUC and AUPR of 94.55&#x0025; and 61.92&#x0025;, respectively. Moreover, on the GPCR dataset with 3201 CV_SEED, the SHODL-DDIP method has acquired AUC and AUPR of 88.67&#x0025; and 64.08&#x0025;, correspondingly. Concurrently, on the ION dataset with 3201 CV_SEED, the SHODL-DDIP approach has acquired AUC and AUPR of 85.11&#x0025; and 62.50&#x0025;, correspondingly. Additionally, on the nuclear receptor dataset with 3201 CV_SEED, the SHODL-DDIP method has gained AUC and AUPR of 93.27&#x0025; and 76.49&#x0025;, respectively.</p>
<table-wrap id="table-3"><label>Table 3</label><caption><title>AUC and AUPR analysis of SHODL-DDIP approach under distinct datasets</title></caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th align="center" colspan="3">Enzyme dataset</th>
<th align="center" colspan="3">GPCR dataset</th>
</tr>
<tr>
<th align="left">CV_SEED</th>
<th align="left">AUC</th>
<th align="left">AUPR</th>
<th align="left">CV_SEED</th>
<th align="left">AUC</th>
<th align="left">AUPR</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">3201</td>
<td align="left">94.55</td>
<td align="left">61.92</td>
<td align="left">3201</td>
<td align="left">88.67</td>
<td align="left">64.08</td>
</tr>
<tr>
<td align="left">2033</td>
<td align="left">98.90</td>
<td align="left">69.79</td>
<td align="left">2033</td>
<td align="left">85.67</td>
<td align="left">62.89</td>
</tr>
<tr>
<td align="left">5179</td>
<td align="left">98.10</td>
<td align="left">67.68</td>
<td align="left">5179</td>
<td align="left">88.62</td>
<td align="left">64.38</td>
</tr>
<tr>
<td align="left">2931</td>
<td align="left">89.32</td>
<td align="left">55.73</td>
<td align="left">2931</td>
<td align="left">89.67</td>
<td align="left">68.08</td>
</tr>
<tr>
<td align="left">9117</td>
<td align="left">98.60</td>
<td align="left">72.94</td>
<td align="left">9117</td>
<td align="left">93.93</td>
<td align="left">69.96</td>
</tr>
<tr>
<td align="center" colspan="3">ION channel dataset</td>
<td align="center" colspan="3">Nuclear receptor dataset</td>
</tr>
<tr>
<td align="left">CV_SEED</td>
<td align="left">AUC</td>
<td align="left">AUPR</td>
<td align="left">CV_SEED</td>
<td align="left">AUC</td>
<td align="left">AUPR</td>
</tr>
<tr>
<td align="left">3201</td>
<td align="left">85.11</td>
<td align="left">62.50</td>
<td align="left">3201</td>
<td align="left">93.27</td>
<td align="left">76.49</td>
</tr>
<tr>
<td align="left">2033</td>
<td align="left">89.17</td>
<td align="left">68.33</td>
<td align="left">2033</td>
<td align="left">96.08</td>
<td align="left">77.55</td>
</tr>
<tr>
<td align="left">5179</td>
<td align="left">93.34</td>
<td align="left">68.35</td>
<td align="left">5179</td>
<td align="left">98.56</td>
<td align="left">84.07</td>
</tr>
<tr>
<td align="left">2931</td>
<td align="left">85.48</td>
<td align="left">64.80</td>
<td align="left">2931</td>
<td align="left">98.97</td>
<td align="left">87.37</td>
</tr>
<tr>
<td align="left">9117</td>
<td align="left">93.04</td>
<td align="left">71.46</td>
<td align="left">9117</td>
<td align="left">99.08</td>
<td align="left">89.09</td>
</tr>
</tbody>
</table>
</table-wrap><fig id="fig-5"><label>Figure 5</label><caption><title>AUC and AUPR analysis of SHODL-DDIP system (a) Enzyme, (b) GPCR, (c) ION, and (d) Nuclear receptor</title></caption><graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_37580-fig-5.tif"/></fig>
<p><xref ref-type="table" rid="table-4">Table 4</xref> and <xref ref-type="fig" rid="fig-6">Fig. 6</xref> show a comparative AUC study of the SHODL-DDIP model on four datasets. The figure exhibited that the SHODL-DDIP method has reached improved values of AUC under each dataset. For instance, on the enzyme dataset, the SHODL-DDIP model has gained an increased AUC of 98.90&#x0025;, whereas the UDTPP, Bi-gram PSSM, Nearest Neighbour, IFB Model, KBMF2K, DBSI, and DTIP-ORNN models have reported reduced AUC of 86.76&#x0025;, 94.79&#x0025;, 89.51&#x0025;, 84.52&#x0025;, 82.77&#x0025;, 80.29&#x0025;, and 96.53&#x0025; respectively. Meanwhile, on the GPCR dataset, the SHODL-DDIP methodology has attained an increased AUC of 93.93&#x0025;. In contrast, the UDTPP, Bi-gram PSSM, Nearest Neighbour, IFB Model, KBMF2K, DBSI, and DTIP-ORNN techniques have reported reduced AUC of 87.15&#x0025;, 89.47&#x0025;, 88.53&#x0025;, 81.48&#x0025;, 85.89&#x0025;, 80.19&#x0025;, and 92.22&#x0025; correspondingly. Eventually, on the ION dataset, the SHODL-DDIP approach has acquired an increased AUC of 93.34&#x0025;, whereas the UDTPP, Bi-gram PSSM, Nearest Neighbour, IFB Model, KBMF2K, DBSI, and DTIP-ORNN methods have reported reduced AUC of 77.49&#x0025;, 87.98&#x0025;, 85.08&#x0025;, 73.33&#x0025;, 80.30&#x0025;, 73.33&#x0025;, and 80.51&#x0025; correspondingly.</p>
<table-wrap id="table-4"><label>Table 4</label><caption><title>AUC analysis of the SHODL-DDIP approach with other techniques under 4 distinct datasets</title></caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th align="center" colspan="5">AUC (&#x0025;)</th>
</tr>
<tr>
<th align="left">Methods</th>
<th align="left">Enzyme</th>
<th align="left">GPCR</th>
<th align="left">ION channel</th>
<th align="left">Nuclear receptor</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">UDTPP</td>
<td align="left">86.76</td>
<td align="left">87.15</td>
<td align="left">77.49</td>
<td align="left">79.70</td>
</tr>
<tr>
<td align="left">Bi-gram PSSM</td>
<td align="left">94.79</td>
<td align="left">89.47</td>
<td align="left">87.98</td>
<td align="left">87.06</td>
</tr>
<tr>
<td align="left">Nearest neighbour</td>
<td align="left">89.51</td>
<td align="left">88.53</td>
<td align="left">85.08</td>
<td align="left">82.19</td>
</tr>
<tr>
<td align="left">IFB model</td>
<td align="left">84.52</td>
<td align="left">81.48</td>
<td align="left">73.33</td>
<td align="left">83.34</td>
</tr>
<tr>
<td align="left">KBMF2K</td>
<td align="left">82.77</td>
<td align="left">85.89</td>
<td align="left">80.30</td>
<td align="left">82.59</td>
</tr>
<tr>
<td align="left">DBSI</td>
<td align="left">80.29</td>
<td align="left">80.19</td>
<td align="left">80.51</td>
<td align="left">75.55</td>
</tr>
<tr>
<td align="left">DTIP-ORNN</td>
<td align="left">96.53</td>
<td align="left">92.22</td>
<td align="left">90.77</td>
<td align="left">98.68</td>
</tr>
<tr>
<td align="left">SHODL-DDIP</td>
<td align="left">98.90</td>
<td align="left">93.93</td>
<td align="left">93.34</td>
<td align="left">99.08</td>
</tr>
</tbody>
</table>
</table-wrap><fig id="fig-6"><label>Figure 6</label><caption><title>AUC analysis of the SHODL-DDIP approach with other techniques</title></caption><graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_37580-fig-6.tif"/></fig>
<p><xref ref-type="table" rid="table-5">Table 5</xref> and <xref ref-type="fig" rid="fig-7">Fig. 7</xref> show a comparative AUPR study of the SHODL-DDIP method on four datasets. The outcomes show the SHODL-DDIP method has reached improved values of AUPR under each dataset. For example, on the enzyme dataset, the SHODL-DDIP method has acquired an increased AUPR of 72.94&#x0025;, whereas the BLM, SELF-BLM, PULBLM-3, PULBLM-5, PULBLM-7, and DTIP-ORNN approaches have reported reduced AUPR of 56.56&#x0025;, 63.04&#x0025;, 67.13&#x0025;, 67.34&#x0025;, 66.75&#x0025;, and 70.19&#x0025; correspondingly.</p>
<table-wrap id="table-5"><label>Table 5</label><caption><title>AUPR analysis of the SHODL-DDIP approach with other techniques under 4 distinct datasets</title></caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th align="center" colspan="5">AUPR (&#x0025;)</th>
</tr>
<tr>
<th align="left">Methods</th>
<th align="left">Enzyme</th>
<th align="left">GPCR</th>
<th align="left">ION channel</th>
<th align="left">Nuclear receptor</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">BLM</td>
<td align="left">56.56</td>
<td align="left">54.59</td>
<td align="left">48.18</td>
<td align="left">42.92</td>
</tr>
<tr>
<td align="left">SELF-BLM</td>
<td align="left">63.04</td>
<td align="left">59.69</td>
<td align="left">52.08</td>
<td align="left">44.51</td>
</tr>
<tr>
<td align="left">PULBLM-3</td>
<td align="left">67.13</td>
<td align="left">64.57</td>
<td align="left">59.63</td>
<td align="left">58.42</td>
</tr>
<tr>
<td align="left">PULBLM-5</td>
<td align="left">67.34</td>
<td align="left">64.55</td>
<td align="left">61.25</td>
<td align="left">58.53</td>
</tr>
<tr>
<td align="left">PULBLM-7</td>
<td align="left">66.75</td>
<td align="left">64.62</td>
<td align="left">64.07</td>
<td align="left">59.33</td>
</tr>
<tr>
<td align="left">DTIP-ORNN</td>
<td align="left">70.19</td>
<td align="left">67.39</td>
<td align="left">68.31</td>
<td align="left">86.10</td>
</tr>
<tr>
<td align="left">SHODL-DDIP</td>
<td align="left">72.94</td>
<td align="left">69.96</td>
<td align="left">71.46</td>
<td align="left">89.09</td>
</tr>
</tbody>
</table>
</table-wrap><fig id="fig-7"><label>Figure 7</label><caption><title>AUPR analysis of SHODL-DDIP approach with other techniques</title></caption><graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_37580-fig-7.tif"/></fig>
<p>In the meantime, on the GPCR dataset, the SHODL-DDIP algorithm has gained an increased AUPR of 69.96&#x0025;, whereas the BLM, SELF-BLM, PULBLM-3, PULBLM-5, PULBLM-7, and DTIP-ORNN approaches have reported reduced AUPR of 54.59&#x0025;, 59.69&#x0025;, 64.57&#x0025;, 64.55&#x0025;, 64.62&#x0025;, and 67.39&#x0025; correspondingly. Parallelly, on the ION dataset, the SHODL-DDIP technique has attained an increased AUPR of 71.46&#x0025;, whereas the BLM, SELF-BLM, PULBLM-3, PULBLM-5, PULBLM-7, and DTIP-ORNN methods have reported reduced AUPR of 48.18&#x0025;, 52.08&#x0025;, 59.63&#x0025;, 61.25&#x0025;, 64.07&#x0025;, and 68.31&#x0025; correspondingly.</p>
</sec>
<sec id="s4"><label>4</label><title>Conclusion</title>
<p>In this study, an automated SHODL-DDIP model has been developed to predict DDI in big data environments. In the presented SHODL-DDIP technique, the relativity and characteristics of the drugs can be identified from different sources for prediction. The input data is preprocessed at the primary level to improve its quality. Next, the SSO algorithm is used for the optimal selection of features. To predict the DDI accurately, in this study, the DBN model is exploited. The SHO algorithm is involved in improvising the DBN model&#x2019;s predictive outcomes. The experimental result analysis of the SHODL-DDIP technique is tested using drug databases, and the results signified the improvements of the SHODL-DDIP technique over other recent models in terms of different performance measures. In future, a hybrid DL model can be employed for improved predictive performance.</p>
</sec>
</body>
<back>
<sec><title>Funding Statement</title>
<p>The authors received no specific funding for this study.</p></sec>
<sec sec-type="COI-statement"><title>Conflicts of Interest</title>
<p>The authors declare that they have no conflicts of interest to report regarding the present study.</p></sec>
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