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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">34213</article-id>
<article-id pub-id-type="doi">10.32604/csse.2023.034213</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Statistical Data Mining with Slime Mould Optimization for Intelligent Rainfall Classification</article-title>
<alt-title alt-title-type="left-running-head">Statistical Data Mining with Slime Mould Optimization for Intelligent Rainfall Classification</alt-title>
<alt-title alt-title-type="right-running-head">Statistical Data Mining with Slime Mould Optimization for Intelligent Rainfall Classification</alt-title>
</title-group>
<contrib-group>
<contrib id="author-1" contrib-type="author">
<name name-style="western"><surname>Nemani</surname><given-names>Ramya</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>Jose Moses</surname><given-names>G.</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>Alenezi</surname><given-names>Fayadh</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>Vijaya Kumar</surname><given-names>K.</given-names></name><xref ref-type="aff" rid="aff-4">4</xref></contrib>
<contrib id="author-5" contrib-type="author" corresp="yes">
<name name-style="western"><surname>Kadry</surname><given-names>Seifedine</given-names></name><xref ref-type="aff" rid="aff-5">5</xref><xref ref-type="aff" rid="aff-6">6</xref><xref ref-type="aff" rid="aff-7">7</xref><email>skadry@gmail.com</email></contrib>
<contrib id="author-6" contrib-type="author">
<name name-style="western"><surname>Kim</surname><given-names>Jungeun</given-names></name><xref ref-type="aff" rid="aff-8">8</xref></contrib>
<contrib id="author-7" contrib-type="author">
<name name-style="western"><surname>Han</surname><given-names>Keejun</given-names></name><xref ref-type="aff" rid="aff-9">9</xref></contrib>
<aff id="aff-1"><label>1</label><institution>Department of Mathematics, Vignan&#x2019;s Institute of Information Technology</institution>, <addr-line>Visakhapatnam, 530049</addr-line>, <country>India</country></aff>
<aff id="aff-2"><label>2</label><institution>Department of Computer Science and Engineering, University Institute of Engineering and Technology (UIET),Guru Nanak University</institution>, <addr-line>Hyderabad</addr-line>, <country>India</country></aff>
<aff id="aff-3"><label>3</label><institution>Department of Electrical Engineering, College of Engineering, Jouf University</institution>, <country>Saudi Arabia</country></aff>
<aff id="aff-4"><label>4</label><institution>Department of Computer Science and Engineering, GITAM School of Technology, Vishakhapatnam Campus, GITAM (Deemed to be a University)</institution>, <addr-line>Vishakhapatnam</addr-line>, <country>India</country></aff>
<aff id="aff-5"><label>5</label><institution>Department of Applied Data Science, Noroff University College</institution>, <addr-line>Kristiansand</addr-line>, <country>Norway</country></aff>
<aff id="aff-6"><label>6</label><institution>Artificial Intelligence Research Center (AIRC), College of Engineering and Information Technology, Ajman University</institution>, <addr-line>Ajman</addr-line>, <country>United Arab Emirates</country></aff>
<aff id="aff-7"><label>7</label><institution>Department of Electrical and Computer Engineering, Lebanese American University</institution>, <addr-line>Byblos</addr-line>, <country>Lebanon</country></aff>
<aff id="aff-8"><label>8</label><institution>Department of Software, Kongju National University</institution>, <addr-line>Cheonan, 31080</addr-line>, <country>Korea</country></aff>
<aff id="aff-9"><label>9</label><institution>Division of Computer Engineering, Hansung University</institution>, <addr-line>Seoul, 02876</addr-line>, <country>Korea</country></aff>
</contrib-group>
<author-notes>
<corresp id="cor1"><label>&#x002A;</label>Corresponding Author: Seifedine Kadry. Email: <email>skadry@gmail.com</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>26</day><month>5</month><year>2023</year></pub-date>
<volume>47</volume>
<issue>1</issue>
<fpage>919</fpage>
<lpage>935</lpage>
<history>
<date date-type="received"><day>09</day><month>7</month><year>2022</year></date>
<date date-type="accepted"><day>10</day><month>3</month><year>2023</year></date>
</history>
<permissions>
<copyright-statement>&#x00A9; 2023 Nemani et al.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Nemani 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_34213.pdf"></self-uri>
<abstract>
<p>Statistics are most crucial than ever due to the accessibility of huge counts of data from several domains such as finance, medicine, science, engineering, and so on. Statistical data mining (SDM) is an interdisciplinary domain that examines huge existing databases to discover patterns and connections from the data. It varies in classical statistics on the size of datasets and on the detail that the data could not primarily be gathered based on some experimental strategy but conversely for other resolves. Thus, this paper introduces an effective statistical Data Mining for Intelligent Rainfall Prediction using Slime Mould Optimization with Deep Learning (SDMIRP-SMODL) model. In the presented SDMIRP-SMODL model, the feature subset selection process is performed by the SMO algorithm, which in turn minimizes the computation complexity. For rainfall prediction. Convolution neural network with long short-term memory (CNN-LSTM) technique is exploited. At last, this study involves the pelican optimization algorithm (POA) as a hyperparameter optimizer. The experimental evaluation of the SDMIRP-SMODL approach is tested utilizing a rainfall dataset comprising 23682 samples in the negative class and 1865 samples in the positive class. The comparative outcomes reported the supremacy of the SDMIRP-SMODL model compared to existing techniques.</p>
</abstract>
<kwd-group kwd-group-type="author">
<kwd>Statistical data mining</kwd>
<kwd>predictive models</kwd>
<kwd>deep learning</kwd>
<kwd>rainfall prediction</kwd>
<kwd>parameter tuning</kwd>
</kwd-group>
<funding-group>
<award-group id="awg1">
<funding-source>Technology Development Program of MSS</funding-source>
<award-id>S3033853</award-id>
</award-group>
<award-group id="awg2">
<funding-source>National Research Foundation of Korea (NRF)</funding-source>
</award-group>
<award-group id="awg3">
<funding-source>Korea government (MSIT)</funding-source>
<award-id>2021R1A4A1031509</award-id>
</award-group>
</funding-group>
</article-meta>
</front>
<body>
<sec id="s1"><label>1</label><title>Introduction</title>
<p>Data mining represents extracting or mining knowledge from massive quantities of data. In other words, data mining is the science, art, and technology of discovering huge and complex bodies of data for beneficial patterns. Practitioners and Theoreticians are constantly searching for more appropriate approaches to make the process accurate, more efficient, and cost-effective [<xref ref-type="bibr" rid="ref-1">1</xref>]. The statistical data mining (SDM) technique is established for effectively processing massive quantities of data that are usually multi-dimensional and probably of many complex types [<xref ref-type="bibr" rid="ref-2">2</xref>]. Some traditional statistical methods for data analysis, particularly for numerical data. This method has been extensively used for scientific records (viz., records from experiments in manufacturing, physics, engineering, medicine, and psychology) and data from the social sciences and economics. Rainfall prediction remains a serious concern and has drawn the consideration of industries, governments, the scientific community, and risk management entities [<xref ref-type="bibr" rid="ref-3">3</xref>]. Rainfall is a climatic factor that affects several human events, such as construction, agricultural production, forestry and tourism, and power generation, amongst others [<xref ref-type="bibr" rid="ref-4">4</xref>]. In that regard, rainfall prediction is crucial since this parameter has the maximum correlation with adversarial natural disasters like flooding, landslides, avalanches, and mass movements. This incident has adversely impacted society in recent years. As a result, having an improved technique for rainfall prediction could allow taking mitigation and preventive measures for these natural phenomena [<xref ref-type="bibr" rid="ref-5">5</xref>].</p>
<p>Besides, this prediction facilitates the supervision of construction, agriculture activities, transport, health, and tourism, amongst others [<xref ref-type="bibr" rid="ref-6">6</xref>]. For events accountable for disaster prevention, providing precise meteorological prediction helps decision-making despite the probable occurrence of natural events [<xref ref-type="bibr" rid="ref-7">7</xref>]. To achieve this prediction, there exist different methodologies, which ranges from naive method to those that use complicated approaches like artificial intelligence (AI), and artificial neural network (ANN), has been the most attractive and valuable approaches for the prediction task [<xref ref-type="bibr" rid="ref-8">8</xref>]. ANN, <italic>vs.</italic> conventional approaches in meteorology, depends on a self-adaptive mechanism that learns from examples and captures functional relationships amongst data. However, the relationship still needs to be determined or explained [<xref ref-type="bibr" rid="ref-9">9</xref>]. Recently, the Deep Learning (DL) algorithm has been used as an effective method in ANN for resolving difficult challenges. DL is a common term used to represent a sequence of multi-layer architecture that can be trained using unsupervised algorithms [<xref ref-type="bibr" rid="ref-10">10</xref>]. The major development is learning a valid, non-linear, and compact presentation of data through unsupervised methods, hoping that the novel data presentation contributed to the prediction technique.</p>
<p>Suparta et al. [<xref ref-type="bibr" rid="ref-11">11</xref>] intend to forecast rainfall by exploring the implementation of AI methods like Adaptive NeuroFuzzy Inference System (ANFIS). The modelled approach compiles NN learning capabilities having transparent linguistic representations of fuzzy systems. The ANFIS approach has several input structures and membership functions tested, constructed, and trained to evaluate the model&#x2019;s ability. Dada et al. [<xref ref-type="bibr" rid="ref-12">12</xref>] presented 4 non-linear approaches like Artificial Neural Networks (ANN) for predicting rainfall. ANN is capable of mapping various output and input patterns. The Elman Neural Network (ENN), FFNN, RNN, and Cascade Forward Neural Network (CFNN) are employed for rainfall prediction. Wang et al. [<xref ref-type="bibr" rid="ref-13">13</xref>] inspect the applicability of numerous predicting methods based on wavelet packet decomposition (WPD) in the annual prediction of rainfall, and a novel hybrid precipitation prediction structure (WPD-ELM) was devised with WPD and ELM. These works are described as follows: WPD can be employed for decomposing creative precipitation data into numerous sublayers; ELM method, BPNN, and ARIMA were used to realize the decomposed sequences&#x2019; forecasting computation.</p>
<p>Manoj et al. [<xref ref-type="bibr" rid="ref-14">14</xref>] modelled the rainfall predictive method related to the DL network, the convolutional LSTM (convLSTM) method that promises to forecast related to the spatial-and-temporal paradigms. The convLSTM weights were fine-tuned utilizing the projected Salp-stochastic gradient descent algorithm (S-SGD) that can be the amalgamation of the Salp swarm algorithm (SSA) presented in stochastic gradient descent (SGD) approach for facilitating the global fine-tuning of the weights and for assuring a superior predictive accuracy. In contrast, the formulated DL structure can be constructed in the MapReduce structure, allowing the potential big data management. Liyew et al. [<xref ref-type="bibr" rid="ref-15">15</xref>] study was to find the related atmospheric features which might cause rainfall and forecast the intensity of daily rainfall utilizing ML approaches. The Pearson correlation method has been utilized for selecting related environmental parameters employed as input for the ML approach. The dataset has been gathered for measuring the performances of 3 ML methods (Extreme Gradient Boost (XGBoost), Multivariate Linear Regression, and Random Forest (RF)).</p>
<p>This paper introduces an effective statistical Data Mining for Intelligent Rainfall Prediction using Slime Mould Optimization with Deep Learning (SDMIRP-SMODL) model. In the presented SDMIRP-SMODL model, the feature subset selection process is performed by the SMO algorithm, which in turn minimizes the computation complexity. For rainfall prediction. Convolution neural network with long short-term memory (CNN-LSTM) approach is exploited. At last, this study involves the pelican optimization algorithm (POA) as a hyperparameter optimizer. A wide-ranging simulation analysis was executed to highlight the betterment of the SDMIRP-SMODL model. The comparative outcomes reported the supremacy of the SDMIRP-SMODL model compared to existing techniques.</p>
</sec>
<sec id="s2"><label>2</label><title>The Proposed Rainfall Prediction Model</title>
<p>This study established a new SDMIRP-SMODL system for rainfall prediction systems. The SDMIRP-SMODL technique comprises SMO based on feature subset selection, CNN-LSTM prediction, and POA hyperparameter tuning. <xref ref-type="fig" rid="fig-1">Fig. 1</xref> illustrates the overall process of the SDMIRP-SMODL approach.</p>
<fig id="fig-1"><label>Figure 1</label><caption><title>Overall process of the PODTL-BIR approach</title></caption><graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_34213-fig-1.tif"/></fig>
<sec id="s2_1"><label>2.1</label><title>SMO-Based Feature Selection</title>
<p>In the presented SDMIRP-SMODL method, the feature subset selection process was performed by the SMO algorithm. The projected SMO encompasses many distinctive characteristics involving mathematical modelling, which employs adaptive weight to mimic the procedure of generating positive and negative feedback in slime mold propagative waves [<xref ref-type="bibr" rid="ref-16">16</xref>]. The feature depends on a bio-oscillator, creating the optimal pathway to interconnect food with highly exploring capability and exploitation tendency. A summary of the SMO algorithm is shown as follows:</p>
<p>Approach Food: The following rules are provided to characterize the behaviour of SM as an arithmetical formula for replicating the contraction method:
<disp-formula id="eqn-1"><label>(1)</label><mml:math id="mml-eqn-1" display="block"><mml:mover><mml:mrow><mml:mi>X</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mtable rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mover><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>+</mml:mo><mml:mover><mml:mrow><mml:mi>v</mml:mi><mml:mi>b</mml:mi></mml:mrow><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>.</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mover><mml:mi>W</mml:mi><mml:mo stretchy="false">&#x27F6;</mml:mo></mml:mover><mml:mo>&#x22C5;</mml:mo><mml:mover><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>A</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>&#x2212;</mml:mo><mml:mover><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>B</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mi>r</mml:mi><mml:mo>&#x003C;</mml:mo><mml:mi>p</mml:mi></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mtext>&#x00A0;</mml:mtext><mml:mover><mml:mrow><mml:mi>v</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mo stretchy="false">&#x27F6;</mml:mo></mml:mover><mml:mo>&#x22C5;</mml:mo><mml:mover><mml:mrow><mml:mi>X</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mi>r</mml:mi><mml:mo>&#x2265;</mml:mo><mml:mi>p</mml:mi></mml:mtd></mml:mtr></mml:mtable><mml:mtext>&#x00A0;</mml:mtext><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-1">Eq. (1)</xref>, <inline-formula id="ieqn-1"><mml:math id="mml-ieqn-1"><mml:mover><mml:mi>W</mml:mi><mml:mo stretchy="false">&#x27F6;</mml:mo></mml:mover></mml:math></inline-formula> indicates the weight of SM, <inline-formula id="ieqn-2"><mml:math id="mml-ieqn-2"><mml:mover><mml:mrow><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>v</mml:mi></mml:mrow><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mi>b</mml:mi></mml:math></inline-formula> denotes a variable within <inline-formula id="ieqn-3"><mml:math id="mml-ieqn-3"><mml:mrow><mml:mo>[</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mi>a</mml:mi><mml:mo>]</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mover><mml:mrow><mml:mtext>&#x00A0;</mml:mtext><mml:mi>v</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mo stretchy="false">&#x27F6;</mml:mo></mml:mover></mml:math></inline-formula> linearly reduces from [0, 1]. <italic>t</italic> characterizes the current iteration, <inline-formula id="ieqn-4"><mml:math id="mml-ieqn-4"><mml:mover><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">&#x27F6;</mml:mo></mml:mover></mml:math></inline-formula> characterizes the different positions with the maximum odor smell, <italic>X</italic> embodies the SM position, <inline-formula id="ieqn-5"><mml:math id="mml-ieqn-5"><mml:mover><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>A</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">&#x27F6;</mml:mo></mml:mover></mml:math></inline-formula> and <inline-formula id="ieqn-6"><mml:math id="mml-ieqn-6"><mml:mover><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>B</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">&#x27F6;</mml:mo></mml:mover></mml:math></inline-formula> characterize two individuals arbitrarily chosen from the swarm, and <inline-formula id="ieqn-7"><mml:math id="mml-ieqn-7"><mml:mover><mml:mi>W</mml:mi><mml:mo stretchy="false">&#x27F6;</mml:mo></mml:mover></mml:math></inline-formula> denotes the SM weight. The formulation of <italic>p</italic> is shown below:
<disp-formula id="eqn-2"><label>(2)</label><mml:math id="mml-eqn-2" display="block"><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mtext>tanh</mml:mtext></mml:mrow><mml:mrow><mml:mo>|</mml:mo><mml:mi>S</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>D</mml:mi><mml:mi>F</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:math></disp-formula>where <inline-formula id="ieqn-8"><mml:math id="mml-ieqn-8"><mml:mi>i</mml:mi><mml:mo>&#x2208;</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:math></inline-formula>, <inline-formula id="ieqn-9"><mml:math id="mml-ieqn-9"><mml:mi>S</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> signifies fitness of <inline-formula id="ieqn-10"><mml:math id="mml-ieqn-10"><mml:mover><mml:mi>X</mml:mi><mml:mo stretchy="false">&#x27F6;</mml:mo></mml:mover></mml:math></inline-formula>. The optimal fitness attained in every iteration is represented as the <inline-formula id="ieqn-11"><mml:math id="mml-ieqn-11"><mml:mi>D</mml:mi><mml:mi>F</mml:mi></mml:math></inline-formula>. And it is given in the following:
<disp-formula id="eqn-3"><label>(3)</label><mml:math id="mml-eqn-3" display="block"><mml:mover><mml:mrow><mml:mi>v</mml:mi><mml:mi>b</mml:mi></mml:mrow><mml:mo stretchy="false">&#x27F6;</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>a</mml:mi><mml:mo>]</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:math></disp-formula>
<disp-formula id="eqn-4"><label>(4)</label><mml:math id="mml-eqn-4" display="block"><mml:mi>a</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mtext mathvariant="italic">arctanh</mml:mtext></mml:mrow><mml:mtext>&#x00A0;</mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mfrac><mml:mi>t</mml:mi><mml:mrow><mml:munder><mml:mo movablelimits="true" form="prefix">max</mml:mo><mml:mrow><mml:mo>&#x2212;</mml:mo></mml:mrow></mml:munder><mml:mi>t</mml:mi></mml:mrow></mml:mfrac><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:math></disp-formula></p>
<p>The equation of <inline-formula id="ieqn-12"><mml:math id="mml-ieqn-12"><mml:mover><mml:mi>W</mml:mi><mml:mo stretchy="false">&#x27F6;</mml:mo></mml:mover></mml:math></inline-formula> is represented in the following:
<disp-formula id="eqn-5"><label>(5)</label><mml:math id="mml-eqn-5" display="block"><mml:mover><mml:mrow><mml:mi>W</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mtext mathvariant="italic">SmellIndex</mml:mtext></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mml:mtr><mml:mtd><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mi>r</mml:mi><mml:mo>&#x22C5;</mml:mo><mml:mrow><mml:mtext>log</mml:mtext></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:mrow><mml:mi>b</mml:mi><mml:mi>F</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>S</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>b</mml:mi><mml:mi>F</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>w</mml:mi><mml:mi>F</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mrow><mml:mtext mathvariant="italic">condition</mml:mtext></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mtext>&#x00A0;</mml:mtext><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mi>r</mml:mi><mml:mo>&#x22C5;</mml:mo><mml:mrow><mml:mtext>log</mml:mtext></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:mrow><mml:mi>b</mml:mi><mml:mi>F</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>S</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>b</mml:mi><mml:mi>F</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>w</mml:mi><mml:mi>F</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mrow><mml:mtext mathvariant="italic">others</mml:mtext></mml:mrow></mml:mtd></mml:mtr></mml:mtable><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo></mml:mrow></mml:math></disp-formula>
<disp-formula id="eqn-6"><label>(6)</label><mml:math id="mml-eqn-6" display="block"><mml:mrow><mml:mtext mathvariant="italic">Smell</mml:mtext></mml:mrow><mml:mtext>&#x00A0;</mml:mtext><mml:mrow><mml:mtext mathvariant="italic">Index</mml:mtext></mml:mrow><mml:mo>=</mml:mo><mml:mi>s</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>t</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>S</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>Now, the condition signifies that <inline-formula id="ieqn-13"><mml:math id="mml-ieqn-13"><mml:mi>S</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> ranks the initial half of the population, <italic>r</italic> symbolizes the arbitrary integer within <inline-formula id="ieqn-14"><mml:math id="mml-ieqn-14"><mml:mrow><mml:mo>[</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>]</mml:mo></mml:mrow></mml:math></inline-formula>, <inline-formula id="ieqn-15"><mml:math id="mml-ieqn-15"><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>b</mml:mi><mml:mi>F</mml:mi></mml:math></inline-formula> and <inline-formula id="ieqn-16"><mml:math id="mml-ieqn-16"><mml:mi>w</mml:mi><mml:mi>F</mml:mi></mml:math></inline-formula> signify the optimum and worst fitness attained in the existing iteration method, correspondingly. The smell Index characterizes the series of fitness values arranged.</p>
<p>Wrap Food: The subsequent defines the updating location of SM:
<disp-formula id="eqn-7"><label>(7)</label><mml:math id="mml-eqn-7" display="block"><mml:msup><mml:mi>X</mml:mi><mml:mrow><mml:mover><mml:mo>&#x2217;</mml:mo><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mml:mtr><mml:mtd><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mo>.</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mi>U</mml:mi><mml:mi>B</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>L</mml:mi><mml:mi>B</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>L</mml:mi><mml:mi>B</mml:mi><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mo>&#x003C;</mml:mo><mml:mi>z</mml:mi></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mover><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>+</mml:mo><mml:mover><mml:mrow><mml:mi>v</mml:mi><mml:mi>b</mml:mi></mml:mrow><mml:mo stretchy="false">&#x27F6;</mml:mo></mml:mover><mml:mo>&#x22C5;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mi>W</mml:mi><mml:mo>&#x22C5;</mml:mo><mml:mover><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>A</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>&#x2212;</mml:mo><mml:mover><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>B</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mi>r</mml:mi><mml:mo>&#x003C;</mml:mo><mml:mi>p</mml:mi></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mover><mml:mrow><mml:mi>v</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mo stretchy="false">&#x27F6;</mml:mo></mml:mover><mml:mo>&#x22C5;</mml:mo><mml:mover><mml:mrow><mml:mi>X</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>&#x2192;</mml:mo></mml:mover><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mi>r</mml:mi><mml:mo>&#x2265;</mml:mo><mml:mi>p</mml:mi></mml:mtd></mml:mtr></mml:mtable><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>Here <inline-formula id="ieqn-17"><mml:math id="mml-ieqn-17"><mml:mi>L</mml:mi><mml:mi>B</mml:mi></mml:math></inline-formula> and <inline-formula id="ieqn-18"><mml:math id="mml-ieqn-18"><mml:mi>U</mml:mi><mml:mi>B</mml:mi></mml:math></inline-formula> characterize the lower and upper limits, <inline-formula id="ieqn-19"><mml:math id="mml-ieqn-19"><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:math></inline-formula> and <italic>r</italic> represent the arbitrary number in <inline-formula id="ieqn-20"><mml:math id="mml-ieqn-20"><mml:mrow><mml:mo>[</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>]</mml:mo></mml:mrow><mml:mo>.</mml:mo></mml:math></inline-formula></p>
<p>Grabble Food: As the iteration count rises, the value of <inline-formula id="ieqn-21"><mml:math id="mml-ieqn-21"><mml:mover><mml:mrow><mml:mi>v</mml:mi><mml:mi>b</mml:mi></mml:mrow><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:math></inline-formula> oscillates arbitrarily within <inline-formula id="ieqn-22"><mml:math id="mml-ieqn-22"><mml:mrow><mml:mo>[</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mi>a</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:math></inline-formula> and eventually tends to zero. The value of <inline-formula id="ieqn-23"><mml:math id="mml-ieqn-23"><mml:mover><mml:mrow><mml:mi>v</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mo stretchy="false">&#x2192;</mml:mo></mml:mover></mml:math></inline-formula> oscillates amongst [1, 1] and progressively approaches zero.</p>
<p>The fitness function (FF) employed from the SMO system is to contain a balance amongst the count of particular features from every solution (min) and classifier accuracy (max) attained by employing these chosen features, <xref ref-type="disp-formula" rid="eqn-8">Eq. (8)</xref> signifies the FF for measuring solutions.
<disp-formula id="eqn-8"><label>(8)</label><mml:math id="mml-eqn-8" 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>where <inline-formula id="ieqn-24"><mml:math id="mml-ieqn-24"><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> denotes the classifier error rate of the presented classification. <inline-formula id="ieqn-25"><mml:math id="mml-ieqn-25"><mml:mo fence="false" stretchy="false">|</mml:mo><mml:mi>R</mml:mi><mml:mo fence="false" stretchy="false">|</mml:mo></mml:math></inline-formula> stands for the cardinality of chosen subset, and <inline-formula id="ieqn-26"><mml:math id="mml-ieqn-26"><mml:mrow><mml:mo>|</mml:mo><mml:mi>C</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:math></inline-formula> signifies the entire amount of features from the dataset &#x03B1; and <inline-formula id="ieqn-27"><mml:math id="mml-ieqn-27"><mml:mi>&#x03B2;</mml:mi></mml:math></inline-formula> are 2 parameters equivalent to the significance of classifier quality and subset length. &#x2208; [1, 0] and <inline-formula id="ieqn-28"><mml:math id="mml-ieqn-28"><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_2"><label>2.2</label><title>CNN-LSTM-Based Rainfall Prediction</title>
<p>In this work, the CNN-LSTM model is exploited to predict rainfall. Long short-term memory is the development of recurrent neural networks (RNN) [<xref ref-type="bibr" rid="ref-17">17</xref>]. LSTM presents a memory block instead of a traditional RNN unit to overcome gradient exploding and vanishing problems. Then, a cell state is added to store the long-term state, that is, its major dissimilarity from RNN. An LSTM connects and remembers preceding data to the dataset attained in the present. LSTM is coupled with 3 gates. Namely, input, forget, and output gates, whereby <inline-formula id="ieqn-29"><mml:math id="mml-ieqn-29"><mml:msub><mml:mi>&#x03C7;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> represent the existing inputs; <inline-formula id="ieqn-30"><mml:math id="mml-ieqn-30"><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-31"><mml:math id="mml-ieqn-31"><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> denote the previous and new cell states, correspondingly; and <inline-formula id="ieqn-32"><mml:math id="mml-ieqn-32"><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-33"><mml:math id="mml-ieqn-33"><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> indicate the current and preceding outputs, correspondingly. The standard of input gates of LSTM is presented in the succeeding formula.
<disp-formula id="eqn-9"><label>(9)</label><mml:math id="mml-eqn-9" display="block"><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>&#x03C3;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>&#x22C5;</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msub><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>]</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula>
<disp-formula id="eqn-10"><label>(10)</label><mml:math id="mml-eqn-10" display="block"><mml:mrow><mml:mover><mml:mi>C</mml:mi><mml:mo>&#x007E;</mml:mo></mml:mover></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mtext>tanh</mml:mtext></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>&#x22C5;</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>]</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula>
<disp-formula id="eqn-11"><label>(11)</label><mml:math id="mml-eqn-11" display="block"><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mover><mml:mi>c</mml:mi><mml:mo>&#x007E;</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></disp-formula></p>
<p>For passing <inline-formula id="ieqn-34"><mml:math id="mml-ieqn-34"><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-35"><mml:math id="mml-ieqn-35"><mml:msub><mml:mi>&#x03C7;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> via a sigmoid layer for deciding where part of the dataset needs to be appended using <xref ref-type="disp-formula" rid="eqn-9">Eq. (9)</xref>. Consequently, to achieve novel data afterwards, <inline-formula id="ieqn-36"><mml:math id="mml-ieqn-36"><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-37"><mml:math id="mml-ieqn-37"><mml:msub><mml:mi>&#x03C7;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> are passed by the <inline-formula id="ieqn-38"><mml:math id="mml-ieqn-38"><mml:mi>t</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> layer using <xref ref-type="disp-formula" rid="eqn-10">(10)</xref>. The present moment dataset, <inline-formula id="ieqn-39"><mml:math id="mml-ieqn-39"><mml:mrow><mml:mover><mml:mi>C</mml:mi><mml:mo>&#x007E;</mml:mo></mml:mover></mml:mrow></mml:math></inline-formula> and long-term memory dataset <inline-formula id="ieqn-40"><mml:math id="mml-ieqn-40"><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> into <inline-formula id="ieqn-41"><mml:math id="mml-ieqn-41"><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> are integrated with <xref ref-type="disp-formula" rid="eqn-11">(11)</xref>, <inline-formula id="ieqn-42"><mml:math id="mml-ieqn-42"><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> represents a sigmoid output, and <inline-formula id="ieqn-43"><mml:math id="mml-ieqn-43"><mml:mrow><mml:mover><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>&#x007E;</mml:mo></mml:mover></mml:mrow></mml:math></inline-formula> denotes a <inline-formula id="ieqn-44"><mml:math id="mml-ieqn-44"><mml:mi>t</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> output. Now, <inline-formula id="ieqn-45"><mml:math id="mml-ieqn-45"><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> represents the weight matrix, and <inline-formula id="ieqn-46"><mml:math id="mml-ieqn-46"><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> epitomizes the input gate bias of LSTM. Next, the LSTM forget gate enables data extraction using a dot product and a sigmoid layer. <xref ref-type="disp-formula" rid="eqn-12">Eq. (12)</xref> is used to decide whether forgetting a relevant dataset from a primary cell with a specific probability is implemented. <inline-formula id="ieqn-47"><mml:math id="mml-ieqn-47"><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi>f</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> denotes the weight matrix, <inline-formula id="ieqn-48"><mml:math id="mml-ieqn-48"><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>f</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> represents the offset, and <inline-formula id="ieqn-49"><mml:math id="mml-ieqn-49"><mml:mi>&#x03C3;</mml:mi></mml:math></inline-formula> characterizes the sigmoid operation.
<disp-formula id="eqn-12"><label>(12)</label><mml:math id="mml-eqn-12" display="block"><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>&#x03C3;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi>f</mml:mi></mml:mrow></mml:msub><mml:mo>&#x22C5;</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msub><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>]</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>f</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>The LSTM output gate determines the state essential for continuance by <inline-formula id="ieqn-50"><mml:math id="mml-ieqn-50"><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-51"><mml:math id="mml-ieqn-51"><mml:msub><mml:mi>&#x03C7;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> inputs. The concluding output is attained and multiplied with the state decision vector that passes novel Ct data via the <inline-formula id="ieqn-52"><mml:math id="mml-ieqn-52"><mml:mi>t</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> layer.
<disp-formula id="eqn-13"><label>(13)</label><mml:math id="mml-eqn-13" display="block"><mml:msub><mml:mi>O</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>&#x03C3;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi>o</mml:mi></mml:mrow></mml:msub><mml:mo>&#x22C5;</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>]</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>o</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula>
<disp-formula id="eqn-14"><label>(14)</label><mml:math id="mml-eqn-14" display="block"><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>O</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mtext>tanh</mml:mtext></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>From the expression, <inline-formula id="ieqn-53"><mml:math id="mml-ieqn-53"><mml:mi>b</mml:mi><mml:mi>o</mml:mi></mml:math></inline-formula> and <inline-formula id="ieqn-54"><mml:math id="mml-ieqn-54"><mml:mi>W</mml:mi><mml:mi>o</mml:mi></mml:math></inline-formula> correspondingly, the LSTM bias and output gate weighted matrices. <xref ref-type="fig" rid="fig-2">Fig. 2</xref> demonstrates the structure of CNN-LSTM.</p>
<fig id="fig-2"><label>Figure 2</label><caption><title>Structure of CNN-LSTM</title></caption><graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_34213-fig-2.tif"/></fig>
<p>An integrated approach has been intended for automatic rainfall detection and combining LSTM and CNN networks from which the CNN is applied to extract complicated features from an image. LSTM is also employed as a classification. The network has twenty layers: 1 LSTM layer, 1 FC layer, 5 pooling layers, twelve convolution layers, and 1 output layer using the <inline-formula id="ieqn-55"><mml:math id="mml-ieqn-55"><mml:mrow><mml:mtext mathvariant="italic">softmax</mml:mtext></mml:mrow></mml:math></inline-formula> operation. Every convolutional block is integrated into 1 pooling layer and multiple 2D-CNNs. Subsequently, a dropout layer is considered a twenty-five percent dropout rate. A size of <inline-formula id="ieqn-56"><mml:math id="mml-ieqn-56"><mml:mn>3</mml:mn><mml:mo>&#x00D7;</mml:mo></mml:math></inline-formula> 3 convolution kernel layers is exploited to extract features activated through the ReLU operation. The <inline-formula id="ieqn-57"><mml:math id="mml-ieqn-57"><mml:mrow><mml:mtext>max</mml:mtext></mml:mrow><mml:mo>&#x2212;</mml:mo></mml:math></inline-formula> pooling function with a size of <inline-formula id="ieqn-58"><mml:math id="mml-ieqn-58"><mml:mn>2</mml:mn><mml:mo>&#x00D7;</mml:mo><mml:mn>2</mml:mn></mml:math></inline-formula> convolution layers is applied to reduce the dimension of the input image. In the final portion, the mapping function is transported to the LSTM for extracting time data. Afterwards, the convolution blocks, the output form, are considered as (none, 7, 7, and 512).</p>
</sec>
<sec id="s2_3"><label>2.3</label><title>POA-Based Hyperparameter Tuning</title>
<p>At the final stage, the POA as a hyperparameter optimizer of the CNN-LSTM model helps enhance classification output. POA is a population-based methodology whereby the pelican is a member of the population [<xref ref-type="bibr" rid="ref-18">18</xref>]. In this work, every population member implies a solution candidate. All the population members propose a value for the optimization variable along with the location of the problem. Initially, the population member is initialized randomly, as stated by the lower and upper bounds of the searching domain,
<disp-formula id="eqn-15"><label>(15)</label><mml:math id="mml-eqn-15" display="block"><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mo>&#x22C5;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><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:mtext>&#x00A0;</mml:mtext><mml:mi>N</mml:mi><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mi>j</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>m</mml:mi><mml:mo>,</mml:mo></mml:math></disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-15">Eq. (15)</xref>, <inline-formula id="ieqn-59"><mml:math id="mml-ieqn-59"><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> indicates the value of <inline-formula id="ieqn-60"><mml:math id="mml-ieqn-60"><mml:mi>t</mml:mi><mml:mi>h</mml:mi><mml:mi>e</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>j</mml:mi></mml:math></inline-formula>-<inline-formula id="ieqn-61"><mml:math id="mml-ieqn-61"><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> parameter specified by the <inline-formula id="ieqn-62"><mml:math id="mml-ieqn-62"><mml:mi>i</mml:mi></mml:math></inline-formula>-<inline-formula id="ieqn-63"><mml:math id="mml-ieqn-63"><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> solution candidate, <italic>N</italic> indicates population member count, <italic>m</italic> illustrates the parameter number, <inline-formula id="ieqn-64"><mml:math id="mml-ieqn-64"><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:math></inline-formula> indicates an arbitrary integer within [0, 1], <inline-formula id="ieqn-65"><mml:math id="mml-ieqn-65"><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-66"><mml:math id="mml-ieqn-66"><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> show the <inline-formula id="ieqn-67"><mml:math id="mml-ieqn-67"><mml:mi>j</mml:mi></mml:math></inline-formula>-<inline-formula id="ieqn-68"><mml:math id="mml-ieqn-68"><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> lower, and <inline-formula id="ieqn-69"><mml:math id="mml-ieqn-69"><mml:mi>j</mml:mi></mml:math></inline-formula>-<inline-formula id="ieqn-70"><mml:math id="mml-ieqn-70"><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> upper bounds in the search space. The population member of pelicans in the projected POA is recognized by a matrix named population matrix in <xref ref-type="disp-formula" rid="eqn-16">Eq. (16)</xref>. The matrix column signifies the suggested value in the search space. In contrast, every row of the matrix characterizes a solution candidate.
<disp-formula id="eqn-16"><label>(16)</label><mml:math id="mml-eqn-16" display="block"><mml:mi>X</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:mtable columnalign="left" rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>&#x22EE;</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mrow><mml:mtext>i</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>&#x22EE;</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mrow><mml:mtext>N</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mi>N</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:mtable columnalign="center center center center center" rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:msub><mml:mi>&#x03C7;</mml:mi><mml:mrow><mml:mrow><mml:msub><mml:mn>1</mml:mn><mml:mrow><mml:mrow><mml:mtext>^{'}</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:mo>&#x2026;</mml:mo></mml:mtd><mml:mtd><mml:msub><mml:mi>&#x03C7;</mml:mi><mml:mrow><mml:mrow><mml:msub><mml:mn>1</mml:mn><mml:mrow><mml:mrow><mml:mtext>^{'}</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:mo>&#x2026;</mml:mo></mml:mtd><mml:mtd><mml:msub><mml:mi>&#x03C7;</mml:mi><mml:mrow><mml:mrow><mml:msub><mml:mn>1</mml:mn><mml:mrow><mml:mrow><mml:mtext>^{'}</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub></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:mtd><mml:mtext>&#x00A0;</mml:mtext></mml:mtd><mml:mtd><mml:mo>&#x22EE;</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mi>&#x03C7;</mml:mi><mml:mrow><mml:mrow><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mrow><mml:mtext>^{'}</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:mo>&#x2026;</mml:mo></mml:mtd><mml:mtd><mml:msub><mml:mi>&#x03C7;</mml:mi><mml:mrow><mml:mrow><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mrow><mml:mtext>^{'}</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:mo>&#x2026;</mml:mo></mml:mtd><mml:mtd><mml:msub><mml:mi>&#x03C7;</mml:mi><mml:mrow><mml:mrow><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mrow><mml:mtext>^{'}</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>&#x22EE;</mml:mo></mml:mtd><mml:mtd><mml:mtext>&#x00A0;</mml:mtext></mml:mtd><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:msub><mml:mi>x</mml:mi><mml:mrow><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mrow><mml:mtext>^{'}</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:mo>&#x22EF;</mml:mo></mml:mtd><mml:mtd><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>N</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:mo>&#x2026;</mml:mo></mml:mtd><mml:mtd><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>N</mml:mi><mml:mo>,</mml:mo><mml:mi>m</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mi>N</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>m</mml:mi></mml:mrow></mml:msub></mml:math></disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-16">Eq. (16)</xref>, <italic>X</italic> indicates the population matrix of pelicans, and <inline-formula id="ieqn-71"><mml:math id="mml-ieqn-71"><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> shows the <inline-formula id="ieqn-72"><mml:math id="mml-ieqn-72"><mml:mi>i</mml:mi></mml:math></inline-formula>-<inline-formula id="ieqn-73"><mml:math id="mml-ieqn-73"><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> pelican.</p>
<p>In this work, all the population members are a pelican whose solution candidate is given to the problem. As a result, an objective function is measured according to the solution candidate. The value attained for the objective function is defined by the vector named objective function vector, as given below.
<disp-formula id="eqn-17"><label>(17)</label><mml:math id="mml-eqn-17" display="block"><mml:mi>F</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:mtable columnalign="left" rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>&#x22EE;</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext>i</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>&#x22EE;</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext>N</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mi>N</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:mtable rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mtext>&#x00A0;</mml:mtext><mml:mo>&#x22EE;</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mtext>&#x00A0;</mml:mtext><mml:mo>&#x22EE;</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mi>N</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:mrow></mml:msub></mml:math></disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-17">Eq. (17)</xref>, <italic>F</italic> indicates the objective function vector, and <inline-formula id="ieqn-74"><mml:math id="mml-ieqn-74"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> represents the objective function value of the <inline-formula id="ieqn-75"><mml:math id="mml-ieqn-75"><mml:mi>i</mml:mi></mml:math></inline-formula>-<inline-formula id="ieqn-76"><mml:math id="mml-ieqn-76"><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> solution candidate [<xref ref-type="bibr" rid="ref-19">19</xref>,<xref ref-type="bibr" rid="ref-20">20</xref>].</p>
<p>The projected approach simulates the strategy and behavior of pelicans while hunting and attacking targets to upgrade the solution candidate, and it can be given in the following steps:
<list list-type="simple">
<list-item><label>i.</label><p>Moving to the target (exploration stage).</p></list-item>
<list-item><label>ii.</label><p>Flying on the water surface (exploitation stage).</p></list-item>
</list></p>
<p>Afterwards, each population member has been upgraded according to the first and second stages according to the original status of the population and values of an objective function, and the optimal candidate solution would be upgraded. Lastly, the optimal solution candidate is characterized by a quasi-optimum solution in the search space.</p>
</sec>
</sec>
<sec id="s3"><label>3</label><title>Results and Discussion</title>
<p>The SDMIRP-SMODL approach is simulated utilizing Python 3.6.5 on PC i5-8600k, 1TB HDD, GeForce 1050Ti 4&#x2005;GB, 250&#x2005;GB SSD, and 16&#x2005;GB RAM. The following are the parameter settings: learning rate: 0.01, dropout: 0.5, batch size: 5, activation: ReLU and epoch count: 50. The experimental evaluation of the SDMIRP-SMODL approach is tested utilizing a dataset comprising 23682 instances in the negative class and 1865 instances in the positive class, as depicted in <xref ref-type="table" rid="table-1">Table 1</xref>. The dataset holds 18 features, and the proposed model has chosen a set of 12 features. The dataset is split into 70:30 and 80:20 training (TR) and testing (TS) data for experimental validation.</p>
<table-wrap id="table-1"><label>Table 1</label><caption><title>Dataset details</title></caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left">Class</th>
<th align="left">No. of instances</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">Negative</td>
<td align="left">23682</td>
</tr>
<tr>
<td align="left">Positive</td>
<td align="left">1865</td>
</tr>
<tr>
<td align="left">Total number of samples</td>
<td align="left">25547</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The confusion matrix produced by the SDMIRP-SMODL system under varying training set (TRS) and testing set (TSS) data is given in <xref ref-type="fig" rid="fig-3">Fig. 3</xref>. On 80&#x0025; of the TRS, the SDMIRP-SMODL technique has identified 18619 instances into negative class and 1082 instances into positive class. Meanwhile, on 20&#x0025; of TSS, the SDMIRP-SMODL approach identified 4645 instances as negative and 294 as positive classes. Eventually, on 70&#x0025; of TRS, the SDMIRP-SMODL approach identified 16369 instances as negative and 926 as positive classes. At last, on 30&#x0025; of the TSS, the SDMIRP-SMODL methodology has identified 7046 instances as a negative class and 399 as a positive class.</p>
<fig id="fig-3"><label>Figure 3</label><caption><title>Confusion matrix of SDMIRP-SMODL methodology (a) 80&#x0025; of TRS, (b) 20&#x0025; of TSS,(c) 70&#x0025; of TRS, and (d) 30&#x0025; of TSS</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_34213-fig-3a.tif"/>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_34213-fig-3b.tif"/></fig>
<p><xref ref-type="table" rid="table-2">Table 2</xref> provides an overall classification outcome of the SDMIRP-SMODL approach with 80:20 of TRS/TSS.</p>
<table-wrap id="table-2"><label>Table 2</label><caption><title>Rainfall classification outcomes of SDMIRP-SMODL technique on 80:20 of TRS/TSS</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="left">Labels</th>
<th align="left"><inline-formula id="ieqn-77"><mml:math id="mml-ieqn-77"><mml:mrow><mml:mi>A</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
<th align="left"><inline-formula id="ieqn-78"><mml:math id="mml-ieqn-78"><mml:mrow><mml:mi>P</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
<th align="left"><inline-formula id="ieqn-79"><mml:math id="mml-ieqn-79"><mml:mrow><mml:mi>R</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
<th align="left"><inline-formula id="ieqn-80"><mml:math id="mml-ieqn-80"><mml:mrow><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
<th align="left">ER</th>
</tr>
</thead>
<tbody>
<tr>
<td align="center" colspan="6">Training set (80&#x0025;)</td>
</tr>
<tr>
<td align="left">Negative</td>
<td align="left">96.40</td>
<td align="left">97.94</td>
<td align="left">98.19</td>
<td align="left">73.41</td>
<td align="left">03.60</td>
</tr>
<tr>
<td align="left">Positive</td>
<td align="left">96.40</td>
<td align="left">75.88</td>
<td align="left">73.41</td>
<td align="left">98.19</td>
<td align="left">03.60</td>
</tr>
<tr>
<td align="left"><bold>Average</bold></td>
<td align="left"><bold>96.40</bold></td>
<td align="left"><bold>86.91</bold></td>
<td align="left"><bold>85.80</bold></td>
<td align="left"><bold>85.80</bold></td>
<td align="left"><bold>03.60</bold></td>
</tr>
<tr>
<td align="center" colspan="6">Testing set (20&#x0025;)</td>
</tr>
<tr>
<td align="left">Negative</td>
<td align="left">96.65</td>
<td align="left">97.95</td>
<td align="left">98.43</td>
<td align="left">75.19</td>
<td align="left">03.35</td>
</tr>
<tr>
<td align="left">Positive</td>
<td align="left">96.65</td>
<td align="left">79.89</td>
<td align="left">75.19</td>
<td align="left">98.43</td>
<td align="left">03.35</td>
</tr>
<tr>
<td align="left"><bold>Average</bold></td>
<td align="left"><bold>96.65</bold></td>
<td align="left"><bold>88.92</bold></td>
<td align="left"><bold>86.81</bold></td>
<td align="left"><bold>86.81</bold></td>
<td align="left"><bold>03.35</bold></td>
</tr>
</tbody>
</table>
</table-wrap>
<p><xref ref-type="fig" rid="fig-4">Fig. 4</xref> reports the rainfall classification outcome of the SDMIRP-SMODL model on 80&#x0025; of the TRS. The SDMIRP-SMODL method has recognized negative samples with <inline-formula id="ieqn-81"><mml:math id="mml-ieqn-81"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-82"><mml:math id="mml-ieqn-82"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-83"><mml:math id="mml-ieqn-83"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-84"><mml:math id="mml-ieqn-84"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, and ER of 96.40&#x0025;, 97.97&#x0025;, 98.19&#x0025;, 73.41&#x0025;, and 3.60&#x0025;, respectively. Also, the SDMIRP-SMODL model has categorized positive samples with <inline-formula id="ieqn-85"><mml:math id="mml-ieqn-85"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-86"><mml:math id="mml-ieqn-86"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-87"><mml:math id="mml-ieqn-87"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-88"><mml:math id="mml-ieqn-88"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, and ER of 96.40&#x0025;, 75.88&#x0025;, 73.41&#x0025;, 98.19&#x0025;, and 3.60&#x0025;, respectively. Besides, the SDMIRP-SMODL model has obtained average <inline-formula id="ieqn-89"><mml:math id="mml-ieqn-89"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-90"><mml:math id="mml-ieqn-90"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-91"><mml:math id="mml-ieqn-91"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-92"><mml:math id="mml-ieqn-92"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, and ER of 96.40&#x0025;, 86.91&#x0025;, 85.80&#x0025;, 85.80&#x0025;, and 3.60&#x0025;, respectively.</p>
<fig id="fig-4"><label>Figure 4</label><caption><title>Result analysis of SDMIRP-SMODL method on 80&#x0025; of TR data</title></caption><graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_34213-fig-4.tif"/></fig>
<p><xref ref-type="fig" rid="fig-5">Fig. 5</xref> demonstrates a detailed classification outcome of the SDMIRP-SMODL model on 20&#x0025; of TSS. The SDMIRP-SMODL algorithm has recognized negative samples with <inline-formula id="ieqn-93"><mml:math id="mml-ieqn-93"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-94"><mml:math id="mml-ieqn-94"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-95"><mml:math id="mml-ieqn-95"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-96"><mml:math id="mml-ieqn-96"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, and ER of 96.65&#x0025;, 97.95&#x0025;, 98.43&#x0025;, 75.19&#x0025;, and 3.35&#x0025; correspondingly. Also, the SDMIRP-SMODL system has categorized positive samples with <inline-formula id="ieqn-97"><mml:math id="mml-ieqn-97"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-98"><mml:math id="mml-ieqn-98"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-99"><mml:math id="mml-ieqn-99"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-100"><mml:math id="mml-ieqn-100"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, and ER of 96.65&#x0025;, 79.89&#x0025;, 75.19&#x0025;, 98.43&#x0025;, and 3.35&#x0025;, respectively. Moreover, the SDMIRP-SMODL methodology has achieved average <inline-formula id="ieqn-101"><mml:math id="mml-ieqn-101"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-102"><mml:math id="mml-ieqn-102"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-103"><mml:math id="mml-ieqn-103"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-104"><mml:math id="mml-ieqn-104"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, and ER of 96.65&#x0025;, 88.92&#x0025;, 86.81&#x0025;, 86.81&#x0025;, and 3.35&#x0025;, correspondingly.</p>
<fig id="fig-5"><label>Figure 5</label><caption><title>Rainfall classification results of SDMIRP-SMODL approach under 20&#x0025; of the TSS</title></caption><graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_34213-fig-5.tif"/></fig>
<p><xref ref-type="table" rid="table-3">Table 3</xref> offers an overall classification outcome of the SDMIRP-SMODL technique with a 70:30 TRS/TSS.</p>
<table-wrap id="table-3"><label>Table 3</label><caption><title>Overall rainfall classification results of SDMIRP-SMODL algorithm on 70:30 of TRS/TSS</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="left">Labels</th>
<th align="left"><inline-formula id="ieqn-117"><mml:math id="mml-ieqn-117"><mml:mrow><mml:mi>A</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
<th align="left"><inline-formula id="ieqn-118"><mml:math id="mml-ieqn-118"><mml:mrow><mml:mi>P</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
<th align="left"><inline-formula id="ieqn-119"><mml:math id="mml-ieqn-119"><mml:mrow><mml:mi>R</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
<th align="left"><inline-formula id="ieqn-120"><mml:math id="mml-ieqn-120"><mml:mrow><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
<th align="left">ER</th>
</tr>
</thead>
<tbody>
<tr>
<td align="center" colspan="6">Training set (70&#x0025;)</td>
</tr>
<tr>
<td align="left">Negative</td>
<td align="left">96.72</td>
<td align="left">97.61</td>
<td align="left">98.88</td>
<td align="left">69.78</td>
<td align="left">03.28</td>
</tr>
<tr>
<td align="left">Positive</td>
<td align="left">96.72</td>
<td align="left">83.27</td>
<td align="left">69.78</td>
<td align="left">98.88</td>
<td align="left">03.28</td>
</tr>
<tr>
<td align="left"><bold>Average</bold></td>
<td align="left"><bold>96.72</bold></td>
<td align="left"><bold>90.44</bold></td>
<td align="left"><bold>84.33</bold></td>
<td align="left"><bold>84.33</bold></td>
<td align="left"><bold>03.28</bold></td>
</tr>
<tr>
<td align="center" colspan="6">Testing set (30&#x0025;)</td>
</tr>
<tr>
<td align="left">Negative</td>
<td align="left">97.13</td>
<td align="left">98.07</td>
<td align="left">98.86</td>
<td align="left">74.16</td>
<td align="left">02.87</td>
</tr>
<tr>
<td align="left">Positive</td>
<td align="left">97.13</td>
<td align="left">83.13</td>
<td align="left">74.16</td>
<td align="left">98.86</td>
<td align="left">02.87</td>
</tr>
<tr>
<td align="left"><bold>Average</bold></td>
<td align="left"><bold>97.13</bold></td>
<td align="left"><bold>90.60</bold></td>
<td align="left"><bold>86.51</bold></td>
<td align="left"><bold>86.51</bold></td>
<td align="left"><bold>02.87</bold></td>
</tr>
</tbody>
</table>
</table-wrap>
<p><xref ref-type="fig" rid="fig-6">Fig. 6</xref> depict a brief classification outcome of the SDMIRP-SMODL method on 70&#x0025; of the TRS. The SDMIRP-SMODL methodology has recognized negative samples with <inline-formula id="ieqn-105"><mml:math id="mml-ieqn-105"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-106"><mml:math id="mml-ieqn-106"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-107"><mml:math id="mml-ieqn-107"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-108"><mml:math id="mml-ieqn-108"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, and ER of 96.72&#x0025;, 97.61&#x0025;, 98.88&#x0025;, 69.78&#x0025;, and 3.28&#x0025;, respectively. The SDMIRP-SMODL approach has categorized positive samples with <inline-formula id="ieqn-109"><mml:math id="mml-ieqn-109"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-110"><mml:math id="mml-ieqn-110"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-111"><mml:math id="mml-ieqn-111"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-112"><mml:math id="mml-ieqn-112"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, and ER of 96.72&#x0025;, 83.27&#x0025;, 69.78&#x0025;, 98.88&#x0025;, and 3.28&#x0025; correspondingly. In addition, the SDMIRP-SMODL technique has obtained average <inline-formula id="ieqn-113"><mml:math id="mml-ieqn-113"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-114"><mml:math id="mml-ieqn-114"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-115"><mml:math id="mml-ieqn-115"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-116"><mml:math id="mml-ieqn-116"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, and ER of 96.72&#x0025;, 90.44&#x0025;, 84.33&#x0025;, 84.33&#x0025;, and 3.28&#x0025; correspondingly.</p>
<fig id="fig-6"><label>Figure 6</label><caption><title>Rainfall classification results of SDMIRP-SMODL system on 70&#x0025; of TR data</title></caption><graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_34213-fig-6.tif"/></fig>
<p><xref ref-type="fig" rid="fig-7">Fig. 7</xref> showcases a detailed classification outcome of the SDMIRP-SMODL approach on 30&#x0025; of TSS. The SDMIRP-SMODL model has recognized negative samples with <inline-formula id="ieqn-121"><mml:math id="mml-ieqn-121"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-122"><mml:math id="mml-ieqn-122"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-123"><mml:math id="mml-ieqn-123"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-124"><mml:math id="mml-ieqn-124"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, and ER of 97.13&#x0025;, 98.07&#x0025;, 98.86&#x0025;, 74.16&#x0025;, and 2.87&#x0025; correspondingly. Simultaneously, the SDMIRP-SMODL technique has categorized positive samples with <inline-formula id="ieqn-125"><mml:math id="mml-ieqn-125"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-126"><mml:math id="mml-ieqn-126"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-127"><mml:math id="mml-ieqn-127"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-128"><mml:math id="mml-ieqn-128"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, and ER of 97.13&#x0025;, 83.13&#x0025;, 74.16&#x0025;, 98.86&#x0025;, and 2.87&#x0025;, respectively. Moreover, the SDMIRP-SMODL algorithm has gained average <inline-formula id="ieqn-129"><mml:math id="mml-ieqn-129"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-130"><mml:math id="mml-ieqn-130"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-131"><mml:math id="mml-ieqn-131"><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-132"><mml:math id="mml-ieqn-132"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, and ER of 97.13&#x0025;, 90.60&#x0025;, 86.51&#x0025;, 86.51&#x0025;, and 2.87&#x0025;, correspondingly.</p>
<fig id="fig-7"><label>Figure 7</label><caption><title>Rainfall classification results of SDMIRP-SMODL system on 30&#x0025; of the TS database</title></caption><graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_34213-fig-7.tif"/></fig>
<p>The training accuracy (TRAY) and validation accuracy (VLAY) achieved by the SDMIRP-SMODL technique on the TSS is illustrated in <xref ref-type="fig" rid="fig-8">Fig. 8</xref>. The results revealed that the SDMIRP-SMODL approach had achieved superior values of TRAY and VLAY. Mostly the VLAY appeared greater than TRAY.</p>
<fig id="fig-8"><label>Figure 8</label><caption><title>TRAY and VLAY study of SDMIRP-SMODL methodology</title></caption><graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_34213-fig-8.tif"/></fig>
<p>The training loss (TRLS) and validation loss (VLLS) executed by the SDMIRP-SMODL approach on the TSS are shown in <xref ref-type="fig" rid="fig-9">Fig. 9</xref>. The experimental result stated that the SDMIRP-SMODL technique had realized lower values of TRLS and VLLS. The VLLS is lesser than TRLS.</p>
<fig id="fig-9"><label>Figure 9</label><caption><title>TRLS and VLLS study of SDMIRP-SMODL methodology</title></caption><graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_34213-fig-9.tif"/></fig>
<p>A clear <inline-formula id="ieqn-133"><mml:math id="mml-ieqn-133"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> study of the SDMIRP-SMODL methodology on the TSS is revealed in <xref ref-type="fig" rid="fig-10">Fig. 10</xref>. The obtained result exposed that the SDMIRP-SMODL technique has improved <inline-formula id="ieqn-134"><mml:math id="mml-ieqn-134"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> values under every class.</p>
<fig id="fig-10"><label>Figure 10</label><caption><title><inline-formula id="ieqn-135"><mml:math id="mml-ieqn-135"><mml:mi>P</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> study of SDMIRP-SMODL approach</title></caption><graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_34213-fig-10.tif"/></fig>
<p>A brief ROC analysis of the SDMIRP-SMODL system on the TSS is illustrated in <xref ref-type="fig" rid="fig-11">Fig. 11</xref>. The outcome revealed the SDMIRP-SMODL approach had presented its ability to categorize several classes on TSS.</p>
<fig id="fig-11"><label>Figure 11</label><caption><title>ROC study of SDMIRP-SMODL approach</title></caption><graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_34213-fig-11.tif"/></fig>
<p><xref ref-type="table" rid="table-4">Table 4</xref> provides a detailed accuracy and miss rate analysis of the SDMIRP-SMODL system with recent models. <xref ref-type="fig" rid="fig-12">Fig. 12</xref> provides an accurate comparative rate (ACR) analysis of the SDMIRP-SMODL system with contemporary techniques. The results implied that the DTSLIQ, NV, and PRNN-10 Neuron models had poor performance with lower ACR values of 72.21&#x0025;, 78.55&#x0025;, and 82.3&#x0025;, respectively. Next, the INBC and Bayesian approaches have shown slightly enhanced ACR values of 90.17&#x0025; and 90.93&#x0025;, correspondingly. Likewise, the DT and SVM methods have reported reasonable ACR values of 91&#x0025; and 92&#x0025;, respectively. Though the fused ML model has accomplished a considerable ACR value of 94.22&#x0025;, the SDMIRP-SMODL system has outperformed higher performance with a maximal ACR of 97.13&#x0025;.</p>
<table-wrap id="table-4"><label>Table 4</label><caption><title>Comparison study of SDMIRP-SMODL method and other approaches</title></caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left">Method</th>
<th align="left">ACR</th>
<th align="left">Miss rate</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">SDMIRP-SMODL</td>
<td align="left">97.13</td>
<td align="left">2.87</td>
</tr>
<tr>
<td align="left">SVM model</td>
<td align="left">92.00</td>
<td align="left">8.00</td>
</tr>
<tr>
<td align="left">Na&#x00EF;ve bayes</td>
<td align="left">78.55</td>
<td align="left">21.45</td>
</tr>
<tr>
<td align="left">DT model</td>
<td align="left">91.00</td>
<td align="left">9.00</td>
</tr>
<tr>
<td align="left">PRNN-10 neuron</td>
<td align="left">82.30</td>
<td align="left">17.70</td>
</tr>
<tr>
<td align="left">Bayesian model</td>
<td align="left">90.93</td>
<td align="left">9.07</td>
</tr>
<tr>
<td align="left">INBC technique</td>
<td align="left">90.17</td>
<td align="left">9.83</td>
</tr>
<tr>
<td align="left">DTSLIQ model</td>
<td align="left">72.21</td>
<td align="left">27.79</td>
</tr>
<tr>
<td align="left">Fused-ML</td>
<td align="left">94.22</td>
<td align="left">5.78</td>
</tr>
</tbody>
</table>
</table-wrap><fig id="fig-12"><label>Figure 12</label><caption><title>ACR analysis of SDMIRP-SMODL approach with existing methodologies</title></caption><graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_34213-fig-12.tif"/></fig>
<p><xref ref-type="fig" rid="fig-13">Fig. 13</xref> offers a comparative miss rate (MSR) inspection of the SDMIRP-SMODL approach with recent algorithms. The outcomes revealed that the DTSLIQ, NV, and PRNN-10 Neuron techniques had worse performance with higher MSR values of 27.79&#x0025;, 21.45&#x0025;, and 17.7&#x0025;, respectively. Next, the INBC and Bayesian methods have exhibited somewhat enhanced MSR values of 9.83&#x0025; and 9.07&#x0025;, respectively. Similarly, the DT and SVM techniques have correspondingly obtained reasonable MSR values of 9&#x0025; and 8&#x0025;. But, the fused ML system has accomplished a considerable MSR value of 5.78&#x0025;, and the SDMIRP-SMODL approach has demonstrated higher performance with a lesser MSR of 2.87&#x0025;.</p>
<fig id="fig-13"><label>Figure 13</label><caption><title>MSR analysis of SDMIRP-SMODL approach with existing methodologies</title></caption><graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_34213-fig-13.tif"/></fig>
<p>From these discussions, it can be assured that the SDMIRP-SMODL technique has shown improved performance over other models.</p>
</sec>
<sec id="s4"><label>4</label><title>Conclusion</title>
<p>This study established a new SDMIRP-SMODL system for rainfall prediction systems. The SDMIRP-SMODL technique comprises SMO based on feature subset selection, CNN-LSTM prediction, and POA hyperparameter tuning. In the presented SDMIRP-SMODL algorithm, the feature subset selection process is performed by the SMO algorithm, which minimizes the computation complexity. At the same time, the POA, as a hyperparameter optimizer of the CNN-LSTM model, helps accomplish enhanced classification output. A wide-ranging simulation analysis was applied to highlight the betterment of the SDMIRP-SMODL approach, and the comparative outcomes reported the supremacy of the SDMIRP-SMODL model compared to existing techniques with maximum accuracy of 97.13&#x0025;. In the future, the presented model will be extended to the design of ensemble learning-based classification models with optimal clustering techniques.</p>
</sec>
</body>
<back>
<sec><title>Funding Statement</title>
<p>This research was partly supported by the Technology Development Program of MSS [No. S3033853] and by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2021R1A4A1031509).</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>
<ref-list content-type="authoryear">
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