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<front>
<journal-meta>
<journal-id journal-id-type="pmc">CMC</journal-id>
<journal-id journal-id-type="nlm-ta">CMC</journal-id>
<journal-id journal-id-type="publisher-id">CMC</journal-id>
<journal-title-group>
<journal-title>Computers, Materials &#x0026; Continua</journal-title>
</journal-title-group>
<issn pub-type="epub">1546-2226</issn>
<issn pub-type="ppub">1546-2218</issn>
<publisher>
<publisher-name>Tech Science Press</publisher-name>
<publisher-loc>USA</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">33054</article-id>
<article-id pub-id-type="doi">10.32604/cmc.2023.033054</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Automated Deep Learning Driven Crop Classification on Hyperspectral Remote Sensing Images</article-title>
<alt-title alt-title-type="left-running-head">Automated Deep Learning Driven Crop Classification on Hyperspectral Remote Sensing Images</alt-title>
<alt-title alt-title-type="right-running-head">Automated Deep Learning Driven Crop Classification on Hyperspectral Remote Sensing Images</alt-title>
</title-group>
<contrib-group content-type="authors">
<contrib id="author-1" contrib-type="author" corresp="yes">
<name name-style="western"><surname>Duhayyim</surname><given-names>Mesfer Al</given-names></name><xref ref-type="aff" rid="aff-1">1</xref><email>m.alduhayyim@psau.edu.sa</email></contrib>
<contrib id="author-2" contrib-type="author">
<name name-style="western"><surname>Alsolai</surname><given-names>Hadeel</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>Haj Hassine</surname><given-names>Siwar Ben</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>Alzahrani</surname><given-names>Jaber S.</given-names></name><xref ref-type="aff" rid="aff-4">4</xref></contrib>
<contrib id="author-5" contrib-type="author">
<name name-style="western"><surname>Salama</surname><given-names>Ahmed S.</given-names></name><xref ref-type="aff" rid="aff-5">5</xref></contrib>
<contrib id="author-6" contrib-type="author">
<name name-style="western"><surname>Motwakel</surname><given-names>Abdelwahed</given-names></name><xref ref-type="aff" rid="aff-6">6</xref></contrib>
<contrib id="author-7" contrib-type="author">
<name name-style="western"><surname>Yaseen</surname><given-names>Ishfaq</given-names></name><xref ref-type="aff" rid="aff-6">6</xref></contrib>
<contrib id="author-8" contrib-type="author">
<name name-style="western"><surname>Zamani</surname><given-names>Abu Sarwar</given-names></name><xref ref-type="aff" rid="aff-6">6</xref></contrib>
<aff id="aff-1"><label>1</label><institution>Department of Computer Science, College of Sciences and Humanities-Aflaj, Prince Sattam bin Abdulaziz University</institution>, <country>Saudi Arabia</country></aff>
<aff id="aff-2"><label>2</label><institution>Department of Information Systems, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University</institution>, <addr-line>P. O. Box 84428, Riyadh, 11671</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-3"><label>3</label><institution>Department of Computer Science, College of Science &#x0026; Art at Mahayil, King Khalid University</institution>, <country>Saudi Arabia</country></aff>
<aff id="aff-4"><label>4</label><institution>Department of Industrial Engineering, College of Engineering at Alqunfudah, Umm Al-Qura University</institution>, <country>Saudi Arabia</country></aff>
<aff id="aff-5"><label>5</label><institution>Department of Electrical Engineering, Faculty of Engineering &#x0026; Technology, Future University in Egypt</institution>,&#x00A0; <addr-line>New Cairo, 11845</addr-line>, <country>Egypt</country></aff>
<aff id="aff-6"><label>6</label><institution>Department of Computer and Self Development, Preparatory Year Deanship, Prince Sattam bin Abdulaziz University</institution>, <addr-line>AlKharj</addr-line>, <country>Saudi Arabia</country></aff>
</contrib-group>
<author-notes>
<corresp id="cor1"><label>&#x002A;</label>Corresponding Author: Mesfer Al Duhayyim. Email: <email>m.alduhayyim@psau.edu.sa</email></corresp>
</author-notes>
<pub-date pub-type="epub" date-type="pub" iso-8601-date="2022-10-28"><day>28</day>
<month>10</month>
<year>2022</year></pub-date>
<volume>74</volume>
<issue>2</issue>
<fpage>3167</fpage>
<lpage>3181</lpage>
<history>
<date date-type="received"><day>06</day><month>6</month><year>2022</year></date>
<date date-type="accepted"><day>12</day><month>7</month><year>2022</year></date>
</history>
<permissions>
<copyright-statement>&#x00A9; 2023 Duhayyim et al.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Duhayyim et al.</copyright-holder>
<license xlink:href="https://creativecommons.org/licenses/by/4.0/">
<license-p>This work is licensed under a <ext-link ext-link-type="uri" xlink:type="simple" xlink:href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International License</ext-link>, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</license-p>
</license>
</permissions>
<self-uri content-type="pdf" xlink:href="TSP_CMC_33054.pdf"></self-uri>
<abstract>
<p>Hyperspectral remote sensing/imaging spectroscopy is a novel approach to reaching a spectrum from all the places of a huge array of spatial places so that several spectral wavelengths are utilized for making coherent images. Hyperspectral remote sensing contains acquisition of digital images from several narrow, contiguous spectral bands throughout the visible, Thermal Infrared (TIR), Near Infrared (NIR), and Mid-Infrared (MIR) regions of the electromagnetic spectrum. In order to the application of agricultural regions, remote sensing approaches are studied and executed to their benefit of continuous and quantitative monitoring. Particularly, hyperspectral images (HSI) are considered the precise for agriculture as they can offer chemical and physical data on vegetation. With this motivation, this article presents a novel Hurricane Optimization Algorithm with Deep Transfer Learning Driven Crop Classification (HOADTL-CC) model on Hyperspectral Remote Sensing Images. The presented HOADTL-CC model focuses on the identification and categorization of crops on hyperspectral remote sensing images. To accomplish this, the presented HOADTL-CC model involves the design of HOA with capsule network (CapsNet) model for generating a set of useful feature vectors. Besides, Elman neural network (ENN) model is applied to allot proper class labels into the input HSI. Finally, glowworm swarm optimization (GSO) algorithm is exploited to fine tune the ENN parameters involved in this article. The experimental result scrutiny of the HOADTL-CC method can be tested with the help of benchmark dataset and the results are assessed under distinct aspects. Extensive comparative studies stated the enhanced performance of the HOADTL-CC model over recent approaches with maximum accuracy of 99.51&#x0025;.</p>
</abstract>
<kwd-group kwd-group-type="author">
<kwd>Hyperspectral images</kwd>
<kwd>remote sensing</kwd>
<kwd>deep learning</kwd>
<kwd>hurricane optimization algorithm</kwd>
<kwd>crop classification</kwd>
<kwd>parameter tuning</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1"><label>1</label><title>Introduction</title>
<p>With the technological advancement in remote sensing image (RSI) acquisition mechanism and the greater accessibility of rich spatial and spectral datasets through a collection of sensors, hyperspectral imaging technique has become increasingly important. Particularly, Hyperspectral Image (HSI) classification has become a great source for real-time application in fields such as forestry, environment, mineral mapping, agriculture, and so on [<xref ref-type="bibr" rid="ref-1">1</xref>]. HSI classification (assigning all the pixels to one specific class depending upon their spectral features) was a most active research topic in the HSI and attracted considerable attention in the remote sensing fields [<xref ref-type="bibr" rid="ref-2">2</xref>]. In HSI classification task, there are 2 major challenges one is the limited available training samples against the high dimensionalities of hyperspectral data and another one is the large spatial variability of spectral signs. Initially, it is often brought by several components including variations in environmental, illumination, temporal, and atmospheric conditions [<xref ref-type="bibr" rid="ref-3">3</xref>]. Next, it results in ill posed problems for certain techniques and minimizes the generalizing capability of classification.</p>
<p>Conventional technique obtains crop classification outcomes by using field investigation, statistics, and measurement, which are money-consuming, time-taking, and labor-consuming [<xref ref-type="bibr" rid="ref-4">4</xref>]. Remote sensing technique advanced by bounds and leaps, timeliness and resolution of RSI has been developed, and hyperspectral remote sensing information is extensively applied [<xref ref-type="bibr" rid="ref-5">5</xref>,<xref ref-type="bibr" rid="ref-6">6</xref>]. In particular, hyperspectral information plays a significant role in agricultural surveys and is utilized for agricultural yield estimation, pest monitoring, crop condition monitoring, etc. In agriculture surveys, the fine classifying of HIS provide the data on crop distribution [<xref ref-type="bibr" rid="ref-7">7</xref>]. Fine classifying of crop needs image with higher spectral and spatial resolution. In recent times, as a significant part of machine learning, deep learning (DL) has gained considerable attention as a result of its stronger abilities in feature extraction and analysis [<xref ref-type="bibr" rid="ref-8">8</xref>]. By extracting features of the input dataset from the bottom to the top of the networks, DL model forms the higher-level abstract feature appropriate for pattern categorization [<xref ref-type="bibr" rid="ref-9">9</xref>].</p>
<p>Out of several DL methods, a convolutional neural network (CNN) contains a comparatively smaller amount of weights due to sharing weights and local connections [<xref ref-type="bibr" rid="ref-10">10</xref>]. A quantity of DL structures was suggested and admired by neuro-science researchers. The CNN is regarded as an unusual case of deep neural networks (DNN) which are advanced for processing images but also utilized for other kinds of data such as audio [<xref ref-type="bibr" rid="ref-11">11</xref>]. It could scan multi-dimensional input piece-by-piece with a convolutional window that means a neuron set having typical weights. The output respective to single convolutional window was known as a feature map and was taken as a map of activities of a provided feature over entire inputs [<xref ref-type="bibr" rid="ref-12">12</xref>]. The CNN serves as one such most famous architectures for DLNN categorization in recent times.</p>
<p>This article presents a novel Hurricane Optimization Algorithm with Deep Transfer Learning Driven Crop Classification (HOADTL-CC) model on Hyperspectral RSIs. The presented HOADTL-CC model uses HOA with capsule network (CapsNet) model for generating useful feature vectors set. Moreover, Elman neural network (ENN) model is applied to allot proper class labels into the input HSI. Lastly, glowworm swarm optimization (GSO) algorithm is exploited to fine tune the ENN parameters involved in this paper. The experimental result examination of the HOADTL-CC approach can be tested with the use of a benchmark dataset.</p>
</sec>
<sec id="s2"><label>2</label><title>Literature Review</title>
<p>Bhosle&#x00A0;et&#x00A0;al.&#x00A0;[<xref ref-type="bibr" rid="ref-13">13</xref>] examine an estimation of CNN for crop classifier utilizing the Indian Pines standard dataset attained in the AVIRIS sensor and the research region dataset reached in the EO-1hyperion sensor. An optimization CNN was adapted by training the method on distinct parameters. It is related to 2 classifier techniques such as DNN and Convolutional Auto-encoder (AE). The author [<xref ref-type="bibr" rid="ref-14">14</xref>] utilizes a new 3D deep CNN (DCNN) technique which directly integrates the hyperspectral information. Besides, the authors examine the learned method for producing physiologically meaningful clarifications. The authors concentrate on an economically vital disease, charcoal rot that is a soil borne fungal disease which affected the yield of soybean crops worldwide. In [<xref ref-type="bibr" rid="ref-15">15</xref>], the morphological profiles, GLCM texture, and endmember abundance features were leveraged for exploiting the spatial data of HSI. Afterward, several spatial data were fused with original spectral data for generating classifier outcomes by utilizing the DNN with conditional random field (DNN&#x002B;CRF) approach. Especially, the DNN is a deep detection method that is extracting depth features and mine the potential data. As a discriminant method, the CRF assumes both spatial as well as contextual data for reducing the misclassified noises while holding the object boundary.</p>
<p>In [<xref ref-type="bibr" rid="ref-16">16</xref>], the authors provide a distinct viewpoint on solving the hyperspectral pixel-level classifier tasks. The recent approaches employ difficult methods for this task, however, the efficacy of these approaches is frequently ignored. According to this observation, the authors present an effectual small method for spectral-spatial classifier on HSIs dependent upon a single gated recurrent unit (GRU). During this method, an essential GRU is learned spectral correlation in an entire spectrum input, and spatial data are fused as the primary hidden state of GRU. Han et al. [<xref ref-type="bibr" rid="ref-17">17</xref>] present minimum redundancy and maximum relevance (mRMR) FS approach for directly choosing important raw bands in HSIs. Besides, a DNN was offered for classifying the hyperspectral information with decreased dimensional that contains CNN than a fully connected network (FCN). In [<xref ref-type="bibr" rid="ref-18">18</xref>], a quick and non-destructive approach utilizing HSI coupled with DL classifier has been executed to the quality estimate of unblanched kernel from Canarium indicum classified by peroxide value (PV). The group of 2300 sub-images of 289 C. indicum instances was utilized for training a CNN for estimating quality level.</p>
</sec>
<sec id="s3"><label>3</label><title>The Proposed Model</title>
<p>In this study, a new HOADTL-CC approach was advanced for the identification and categorization of crops on the hyperspectral RSIs. The proposed HOADTL-CC model incorporates a series of processes namely CapsNet feature extractor, HOA based hyperparameter optimizer, ENN classification, and GSO based parameter optimization. Here, the GSO algorithm is exploited to fine tune the ENN parameters involved in this study. <xref ref-type="fig" rid="fig-1">Fig. 1</xref> depicts the block diagram of HOADTL-CC approach.</p>
<fig id="fig-1"><label>Figure 1</label><caption><title>Block diagram of HOADTL-CC approach</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_33054-fig-1.png"/></fig>
<sec id="s3_1"><label>3.1</label><title>Feature Extraction</title>
<p>In this study, the CapsNet model is used to generate a set of useful feature vectors. A CapsNet is a new form of CNN which aims at providing data regarding the presence or spatial relationships of features (scales, locations, orientations, brightness, and so on.) in an image [<xref ref-type="bibr" rid="ref-19">19</xref>]. The basis of network depends on the addition of concept named &#x201C;capsules&#x201D;. A capsule is a set of neurons that include probability of certain object presence and useful value related to instantiation parameters including pose, rotation, slope, posture, direction, position, scale, and thickness. Different from CNN modules such as convolution and pooling that cause data loss, capsules can able to hold further details.</p>
<p><xref ref-type="fig" rid="fig-2">Fig. 2</xref> depicts the structure of CapsNet method. The novelty in CapsNets is the &#x201C;routing by agreement&#x201D; concept that can be replaced by pooling. Based on these concepts, output is transferred to each parent capsule in the next layer, but the coupling coefficient is not the same. All the capsules try to evaluate the output of parental capsule, and if this estimate matches the original output of parental capsule, the coupling coefficients among the two capsules rise. Consider <inline-formula id="ieqn-1"><mml:math id="mml-ieqn-1"><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> as the output of <inline-formula id="ieqn-2"><mml:math id="mml-ieqn-2"><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>capsules, their prediction for <inline-formula id="ieqn-3"><mml:math id="mml-ieqn-3"><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> parental capsules are evaluated by
<disp-formula id="eqn-1"><label>(1)</label><mml:math id="mml-eqn-1" display="block"><mml:msub><mml:mrow><mml:mover><mml:mi>u</mml:mi><mml:mo stretchy="false">&#x005E;</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo fence="false" stretchy="false">|</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></disp-formula></p>
<fig id="fig-2"><label>Figure 2</label><caption><title>Structure of CapsNet</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_33054-fig-2.png"/></fig>
<p>In <xref ref-type="disp-formula" rid="eqn-1">Eq. (1)</xref>, <inline-formula id="ieqn-4"><mml:math id="mml-ieqn-4"><mml:msub><mml:mrow><mml:mover><mml:mi>u</mml:mi><mml:mo stretchy="false">&#x005E;</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo fence="false" stretchy="false">|</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> refers to the predictive vector of the output of <italic>j</italic>-<italic>th</italic> capsules at a high level calculated using <inline-formula id="ieqn-5"><mml:math id="mml-ieqn-5"><mml:mi>i</mml:mi></mml:math></inline-formula>-<inline-formula id="ieqn-6"><mml:math id="mml-ieqn-6"><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> capsules, and <inline-formula id="ieqn-7"><mml:math id="mml-ieqn-7"><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> denotes the weighting matrix that should be learned in the backward pass. According to the degree of confirmation among the capsules and the parental capsules, <inline-formula id="ieqn-8"><mml:math id="mml-ieqn-8"><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> coupling coefficient is evaluated by the subsequent softmax function
<disp-formula id="eqn-2"><label>(2)</label><mml:math id="mml-eqn-2" display="block"><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:mrow><mml:mi>exp</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="normal">&#x03A3;</mml:mi><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mi>exp</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:mstyle></mml:math></disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-2">Eq. (2)</xref>, <inline-formula id="ieqn-9"><mml:math id="mml-ieqn-9"><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> represents the <inline-formula id="ieqn-10"><mml:math id="mml-ieqn-10"><mml:mi>log</mml:mi></mml:math></inline-formula> likelihood that capsule <italic>i</italic> needs to be combined with <inline-formula id="ieqn-11"><mml:math id="mml-ieqn-11"><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> capsules and set to zero. Therefore, the input vector to parental capsule <italic>j</italic> is calculated by using the <xref ref-type="disp-formula" rid="eqn-3">Eq. (3)</xref>
<disp-formula id="eqn-3"><label>(3)</label><mml:math id="mml-eqn-3" display="block"><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mo>&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x22C5;</mml:mo><mml:msub><mml:mrow><mml:mover><mml:mi>u</mml:mi><mml:mo stretchy="false">&#x005E;</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo fence="false" stretchy="false">|</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></disp-formula></p>
<p>At last, the no-linear squashing function is utilized for preventing the output vector of capsule from above one and form the last output of every capsule as follows
<disp-formula id="eqn-4"><label>(4)</label><mml:math id="mml-eqn-4" display="block"><mml:msub><mml:mi>&#x03B8;</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:mrow><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo fence="false" stretchy="false">|</mml:mo><mml:msup><mml:mo fence="false" stretchy="false">|</mml:mo><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mfrac></mml:mstyle><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo></mml:mrow></mml:mfrac></mml:mstyle></mml:math></disp-formula></p>
<p>The new framework accomplishes considerably better, current performance accuracy with MNIST dataset.</p>
<p>To summarize the capsule network process, the capsule determines the feature parameter in certain objects. In the object identification process, capsule determines the absence or presence of an object and considers the corresponding parameter, where the object feature is organized. This implies the method identifies the object once the feature identified by capsule is existing in the correct sequence. The working process of the capsule is given below:
<list list-type="bullet">
<list-item><p>Initially, capsule proceeds with the matrix multiplication of input vector with weight matrix that characterize the spatial relationship of lower-level feature with higher-level feature;</p></list-item>
<list-item><p>Capsule decides the parental capsules. This can be accomplished by the dynamic routing algorithm. For instance, the system tries to identify an image of a house from diverse perspectives. Capsule extracts the data regarding the walls and roof, but this doesn&#x2019;t mean any roof can be a house. As a result, the capsule analyzes the reliable part in the image. To decide whether the object is a house (or else), prediction is made by using roofs and walls. Such predictions are later transferred to the high-level capsules. Once the prediction is right, the object is allocated as a house;</p></list-item>
<list-item><p>Afterward the parent capsule decision, the process proceeds by summing each vector eventually squashed to 0 and 1 while preserving the direction. Squashing can be done by norm calculation as the probability of presence and cosine distance as a degree of agreement.</p></list-item>
</list></p>
</sec>
<sec id="s3_2"><label>3.2</label><title>HOA Based Parameter Tuning</title>
<p>To adjust the hyperparameters [<xref ref-type="bibr" rid="ref-20">20</xref>&#x2013;<xref ref-type="bibr" rid="ref-22">22</xref>] indulged in the CapsNet model, the HOA was utilized. The HOA follows the communication of the natural forces of hurricanes and wind parcels initiate there, making them for moving nearby the distinct regions of hurricane [<xref ref-type="bibr" rid="ref-23">23</xref>]. The HOA work with primary population collected by wind parcels arbitrarily distributed from the hurricane, this permits the technique for starting with their exploration as well as exploitation procedures from the solution spaces. A primary population of wind parcels gets the infrastructure demonstrated in <xref ref-type="disp-formula" rid="eqn-5">Eq. (5)</xref>:
<disp-formula id="eqn-5"><label>(5)</label><mml:math id="mml-eqn-5" display="block"><mml:msup><mml:mi>P</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mtable columnalign="center center center center" rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:msubsup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mn>11</mml:mn></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup></mml:mtd><mml:mtd><mml:msubsup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mn>12</mml:mn></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup></mml:mtd><mml:mtd><mml:mo>&#x22EF;</mml:mo></mml:mtd><mml:mtd><mml:msubsup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>v</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msubsup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mn>21</mml:mn></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup></mml:mtd><mml:mtd><mml:msubsup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mn>22</mml:mn></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup></mml:mtd><mml:mtd><mml:mo>&#x22EF;</mml:mo></mml:mtd><mml:mtd><mml:msubsup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>v</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>&#x22EE;</mml:mo></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:msubsup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup></mml:mtd><mml:mtd><mml:msubsup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup></mml:mtd><mml:mtd><mml:mo>&#x22EF;</mml:mo></mml:mtd><mml:mtd><mml:msubsup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>v</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup></mml:mtd></mml:mtr></mml:mtable><mml:mo>]</mml:mo></mml:mrow></mml:math></disp-formula>whereas <inline-formula id="ieqn-12"><mml:math id="mml-ieqn-12"><mml:msup><mml:mi>P</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> refers the wind parcels population from the iteration <italic>t</italic>, if <inline-formula id="ieqn-13"><mml:math id="mml-ieqn-13"><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:math></inline-formula> the primary population of individuals is attained. <inline-formula id="ieqn-14"><mml:math id="mml-ieqn-14"><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> signifies the amount of wind parcels (individuals) and <inline-formula id="ieqn-15"><mml:math id="mml-ieqn-15"><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>v</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> denotes the amount of variables or the dimensional of solution spaces, conversely, the amount of parameters of a single phase transformer.</p>
<p>For creating the primary population of individuals it can be utilized in <xref ref-type="disp-formula" rid="eqn-6">Eq. (6)</xref> that creates a matrix of arbitrary numbers in the upper as well as lower limits which comprises feasible solution to problem in this case.
<disp-formula id="eqn-6"><label>(6)</label><mml:math id="mml-eqn-6" display="block"><mml:msup><mml:mi>P</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:msup><mml:mi>y</mml:mi><mml:mrow><mml:mo movablelimits="true" form="prefix">min</mml:mo></mml:mrow></mml:msup><mml:mi>o</mml:mi><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mi>s</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>v</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mi>y</mml:mi><mml:mrow><mml:mo movablelimits="true" form="prefix">max</mml:mo></mml:mrow></mml:msup><mml:mo>&#x2212;</mml:mo><mml:msup><mml:mi>y</mml:mi><mml:mrow><mml:mo movablelimits="true" form="prefix">min</mml:mo></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>v</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula>whereas ones <inline-formula id="ieqn-16"><mml:math id="mml-ieqn-16"><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>v</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>v</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:msup></mml:math></inline-formula> implies the all-ones matrix. <inline-formula id="ieqn-17"><mml:math id="mml-ieqn-17"><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>v</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>v</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:msup></mml:math></inline-formula> indicates the all-random numbers matrix in [0, 1] created in a normal distribution. At last, <inline-formula id="ieqn-18"><mml:math id="mml-ieqn-18"><mml:msup><mml:mi>y</mml:mi><mml:mrow><mml:mo movablelimits="true" form="prefix">min</mml:mo></mml:mrow></mml:msup><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>i</mml:mi><mml:mi>m</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mi>y</mml:mi><mml:msup><mml:mi>y</mml:mi><mml:mrow><mml:mo movablelimits="true" form="prefix">max</mml:mo></mml:mrow></mml:msup><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>v</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> were vectors which signify the upper as well as lower limits of solution spaces. Because of the communication of wind parcels with natural force of hurricanes, it can be displaced from its primary point to distinct point of solution spaces. This movement is demonstrated mathematically in 2 distinct approaches because of rotation offered by hurricane winds as demonstrated in <xref ref-type="disp-formula" rid="eqn-7">Eqs. (7)</xref> and <xref ref-type="disp-formula" rid="eqn-8">(8)</xref>.
<disp-formula id="eqn-7"><label>(7)</label><mml:math id="mml-eqn-7" display="block"><mml:msubsup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><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:msubsup><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:mrow><mml:mtext>sin</mml:mtext></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mrow><mml:mi>&#x03D5;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mrow><mml:mi>&#x03D5;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msubsup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>H</mml:mi><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>&#x003C;</mml:mo><mml:mn>0.5</mml:mn></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msubsup><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:mrow><mml:mtext>cos</mml:mtext></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mrow><mml:mi>&#x03D5;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mrow><mml:mi>&#x03D5;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msubsup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>H</mml:mi><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2265;</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>
<disp-formula id="eqn-8"><label>(8)</label><mml:math id="mml-eqn-8" display="block"><mml:msubsup><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mtext>exp</mml:mtext></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msubsup><mml:mrow><mml:mi>&#x03D5;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>In which <inline-formula id="ieqn-19"><mml:math id="mml-ieqn-19"><mml:msubsup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:math></inline-formula> signifies the novel place of wind parcels <italic>i</italic> if the evolution condition of the technique was executed, being <inline-formula id="ieqn-20"><mml:math id="mml-ieqn-20"><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>.</p>
<p>The parameter <inline-formula id="ieqn-21"><mml:math id="mml-ieqn-21"><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> are an arbitrary variable amongst <inline-formula id="ieqn-22"><mml:math id="mml-ieqn-22"><mml:mi>z</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>o</mml:mi></mml:math></inline-formula> and one that ensures the equity of commuting among the sine and cosine trigonometric functions referred to in <xref ref-type="disp-formula" rid="eqn-7">Eq. (7)</xref>. <inline-formula id="ieqn-23"><mml:math id="mml-ieqn-23"><mml:msubsup><mml:mrow><mml:mi>&#x03D5;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:math></inline-formula> implies the primary angular co-ordinate of wind parcels <italic>i</italic> that gets arbitrary values amongst [0, 2&#x03C0;]. <inline-formula id="ieqn-24"><mml:math id="mml-ieqn-24"><mml:msubsup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>H</mml:mi><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> denotes the hurricane eye from the iteration <italic>t</italic>. <inline-formula id="ieqn-25"><mml:math id="mml-ieqn-25"><mml:msubsup><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> and <inline-formula id="ieqn-26"><mml:math id="mml-ieqn-26"><mml:msubsup><mml:mrow><mml:mi>&#x03D5;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> signifies the radial and angular coordinates from polar representation correspondingly. In <xref ref-type="disp-formula" rid="eqn-8">Eq. (8)</xref> if <inline-formula id="ieqn-27"><mml:math id="mml-ieqn-27"><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:msubsup><mml:mrow><mml:mi>&#x03D5;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> is an all-zeros vector, where <inline-formula id="ieqn-28"><mml:math id="mml-ieqn-28"><mml:msubsup><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> is obtain the value of <inline-formula id="ieqn-29"><mml:math id="mml-ieqn-29"><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula>. Being <inline-formula id="ieqn-30"><mml:math id="mml-ieqn-30"><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> the radius of hurricane eye that gets the value of <inline-formula id="ieqn-31"><mml:math id="mml-ieqn-31"><mml:mn>1</mml:mn><mml:mo>&#x00D7;</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mn>5</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. Eventually, <inline-formula id="ieqn-32"><mml:math id="mml-ieqn-32"><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> demonstrates the arbitrary number amongst <inline-formula id="ieqn-33"><mml:math id="mml-ieqn-33"><mml:mi>z</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>o</mml:mi></mml:math></inline-formula> and one. While the wind parcel <inline-formula id="ieqn-34"><mml:math id="mml-ieqn-34"><mml:msubsup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:math></inline-formula> requires the velocity for starting move and keep in the movement, it can be assumed that change rate from the angular displacement (angular velocity) summed to their angular co-ordinate <inline-formula id="ieqn-35"><mml:math id="mml-ieqn-35"><mml:msubsup><mml:mrow><mml:mi>&#x03D5;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula>, as depicted in <xref ref-type="disp-formula" rid="eqn-9">Eq. (9)</xref>.
<disp-formula id="eqn-9"><label>(9)</label><mml:math id="mml-eqn-9" display="block"><mml:msubsup><mml:mrow><mml:mi>&#x03D5;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><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:msubsup><mml:mrow><mml:mi>&#x03D5;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:mi>w</mml:mi></mml:mtd><mml:mtd><mml:msubsup><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:mo>&#x2264;</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mo movablelimits="true" form="prefix">max</mml:mo></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msubsup><mml:mrow><mml:mi>&#x03D5;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:mi>w</mml:mi><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mrow><mml:mtext>max</mml:mtext></mml:mrow></mml:mrow></mml:msub><mml:msubsup><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup></mml:mfrac></mml:mstyle><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:msup></mml:mtd><mml:mtd><mml:msubsup><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:mo>&#x003E;</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mo movablelimits="true" form="prefix">max</mml:mo></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo></mml:mrow></mml:math></disp-formula>whereas, <italic>w</italic> represents the angular velocity that is considered constant with value of <inline-formula id="ieqn-36"><mml:math id="mml-ieqn-36"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:mi>&#x03C0;</mml:mi><mml:mn>10</mml:mn></mml:mfrac></mml:mstyle></mml:math></inline-formula> and <inline-formula id="ieqn-37"><mml:math id="mml-ieqn-37"><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mo movablelimits="true" form="prefix">max</mml:mo></mml:mrow></mml:msub></mml:math></inline-formula> is the radius whereas the maximal wind velocity was established that is obtained as 0.2. Lastly, <inline-formula id="ieqn-38"><mml:math id="mml-ieqn-38"><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> signifies the arbitrary value amongst <inline-formula id="ieqn-39"><mml:math id="mml-ieqn-39"><mml:mi>z</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>o</mml:mi></mml:math></inline-formula> and one. For making the solutions possible, novel places of wind parcels produced by communication of hurricane forces, take that in the limit of solution spaces.</p>
<p>In this sense, the upper as well as lower limits were confirmed for all the individuals restricted from the group of novel places <inline-formula id="ieqn-40"><mml:math id="mml-ieqn-40"><mml:msup><mml:mi>P</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, as displayed in <xref ref-type="disp-formula" rid="eqn-10">Eq. (10)</xref>.
<disp-formula id="eqn-10"><label>(10)</label><mml:math id="mml-eqn-10" display="block"><mml:msubsup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><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:msubsup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:mtd><mml:mtd><mml:msup><mml:mi>y</mml:mi><mml:mrow><mml:mo movablelimits="true" form="prefix">min</mml:mo></mml:mrow></mml:msup><mml:mo>&#x2264;</mml:mo><mml:msubsup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>&#x2264;</mml:mo><mml:msup><mml:mi>y</mml:mi><mml:mrow><mml:mo movablelimits="true" form="prefix">max</mml:mo></mml:mrow></mml:msup></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msup><mml:mi>y</mml:mi><mml:mrow><mml:mo movablelimits="true" form="prefix">min</mml:mo></mml:mrow></mml:msup><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:mrow><mml:mo>(</mml:mo><mml:msup><mml:mi>y</mml:mi><mml:mrow><mml:mo movablelimits="true" form="prefix">max</mml:mo></mml:mrow></mml:msup><mml:mo>&#x2212;</mml:mo><mml:msup><mml:mi>y</mml:mi><mml:mrow><mml:mo movablelimits="true" form="prefix">min</mml:mo></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mtext mathvariant="italic">otherwise</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>whereas <inline-formula id="ieqn-41"><mml:math id="mml-ieqn-41"><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:math></inline-formula> offers arbitrary numbers with normal distribution amongst <inline-formula id="ieqn-42"><mml:math id="mml-ieqn-42"><mml:mi>z</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>o</mml:mi></mml:math></inline-formula> and one. Some individuals in the group of candidate solutions <inline-formula id="ieqn-43"><mml:math id="mml-ieqn-43"><mml:msup><mml:mi>P</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> is chosen as the novel hurricane eye if, and only if, the value of their objective function was superior to the present hurricane eye <inline-formula id="ieqn-44"><mml:math id="mml-ieqn-44"><mml:msubsup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>H</mml:mi><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula>. This upgrade was determined in <xref ref-type="disp-formula" rid="eqn-11">Eq. (11)</xref>.
<disp-formula id="eqn-11"><label>(11)</label><mml:math id="mml-eqn-11" display="block"><mml:msubsup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>H</mml:mi><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><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:msubsup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mi>I</mml:mi><mml:mi>f</mml:mi><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x003C;</mml:mo><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>H</mml:mi><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msubsup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>H</mml:mi><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:mrow><mml:mtext mathvariant="italic">otherwise</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>whereas <inline-formula id="ieqn-45"><mml:math id="mml-ieqn-45"><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mo>&#x22C5;</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> implies the objective function.</p>
</sec>
<sec id="s3_3"><label>3.3</label><title>Optimal ENN Based Classification</title>
<p>Once the feature vectors are derived, the next stage is the classification process using the ENN model. Elman proposed an ENN was the standard local recursion delay FFNN [<xref ref-type="bibr" rid="ref-24">24</xref>]. The ENN adds a context layer as internal feedback according to BPNN and also it could store state data. Especially, ENN stores the output values of hidden state at <italic>t</italic> time in the context layers, the input of hidden state at <inline-formula id="ieqn-46"><mml:math id="mml-ieqn-46"><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math></inline-formula> time includes the input of the hidden state at <inline-formula id="ieqn-47"><mml:math id="mml-ieqn-47"><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math></inline-formula> time, and the output of hidden layer at <italic>t</italic> time. Consequently, ENN is very suitable for determining time series predictive method. The mathematical expression of ENN is given below:
<disp-formula id="eqn-12"><label>(12)</label><mml:math id="mml-eqn-12" display="block"><mml:mrow><mml:mo>{</mml:mo><mml:mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mml:mtr><mml:mtd><mml:mi>x</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mi>w</mml:mi><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msup><mml:mi>w</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mrow><mml:mtext>u</mml:mtext></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</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:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>&#x03B1;</mml:mi><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>x</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mi>y</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>g</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mi>w</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mi>x</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-12">Eq. (12)</xref>, <italic>u</italic> refers to the input value, the <italic>k</italic> represents at <inline-formula id="ieqn-48"><mml:math id="mml-ieqn-48"><mml:mi>k</mml:mi></mml:math></inline-formula>-<inline-formula id="ieqn-49"><mml:math id="mml-ieqn-49"><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> iteration steps. <inline-formula id="ieqn-50"><mml:math id="mml-ieqn-50"><mml:msup><mml:mi>w</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, <inline-formula id="ieqn-51"><mml:math id="mml-ieqn-51"><mml:msup><mml:mi>w</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> and <inline-formula id="ieqn-52"><mml:math id="mml-ieqn-52"><mml:msup><mml:mi>w</mml:mi><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> denotes the connection weight of input to the hidden layers, the hidden to output layers, and context to hidden layers, correspondingly. <inline-formula id="ieqn-53"><mml:math id="mml-ieqn-53"><mml:msup><mml:mi>b</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, <inline-formula id="ieqn-54"><mml:math id="mml-ieqn-54"><mml:msup><mml:mi>b</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> and <inline-formula id="ieqn-55"><mml:math id="mml-ieqn-55"><mml:msup><mml:mi>b</mml:mi><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> indicates the threshold of the hidden, output, and context layers, correspondingly. <inline-formula id="ieqn-56"><mml:math id="mml-ieqn-56"><mml:mi>&#x03B1;</mml:mi></mml:math></inline-formula> refers to self-connected feedback gain factor. The activation function of hidden state utilized the sigmoid function and the linear function was utilized as activation function for the output layer. <inline-formula id="ieqn-57"><mml:math id="mml-ieqn-57"><mml:mi>y</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> indicates the target output.</p>
<p>For effectual adjustment of the ENN parameters, the GSO algorithm has been exploited. Here, a set of glowworms is distributed and initialized in a random manner from the solution space [<xref ref-type="bibr" rid="ref-25">25</xref>]. The intensity of emitted light was associated with the luciferin count, i.e., strongly associated with it, while the glowworm was situated from the movement and had a dynamic decision range <inline-formula id="ieqn-58"><mml:math id="mml-ieqn-58"><mml:msubsup><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> constraint using a spherical sensor range <inline-formula id="ieqn-59"><mml:math id="mml-ieqn-59"><mml:mi>r</mml:mi><mml:mi>s</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>0</mml:mn><mml:mo>&#x003C;</mml:mo><mml:msubsup><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup><mml:mo>&#x003C;=</mml:mo><mml:msubsup><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>. At first, the glowworm encompasses an equal number of luciferins, <inline-formula id="ieqn-60"><mml:math id="mml-ieqn-60"><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula>. According to the similarity of luciferin value, the <italic>i</italic> glowworm chooses their neighboring one <italic>j</italic> with <inline-formula id="ieqn-61"><mml:math id="mml-ieqn-61"><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> possibility and shift from the direction of decision range <inline-formula id="ieqn-62"><mml:math id="mml-ieqn-62"><mml:mi>r</mml:mi><mml:mi>s</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>0</mml:mn><mml:mo>&#x003C;</mml:mo><mml:msubsup><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup><mml:mo>&#x003C;=</mml:mo><mml:msubsup><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>, while the location of the glowworm <italic>i</italic> is characterized as <inline-formula id="ieqn-63"><mml:math id="mml-ieqn-63"><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mo>&#x2208;</mml:mo><mml:mi>R</mml:mi><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mrow><mml:mtext>i</mml:mtext></mml:mrow><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.</p>
<p>A luciferin update phase is impacted using the function value in the glowworm position:
<disp-formula id="eqn-13"><label>(13)</label><mml:math id="mml-eqn-13" display="block"><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><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:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mi>&#x03C1;</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>&#x03B3;</mml:mi><mml:mi>J</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:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><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-13">Eq. (13)</xref>, <inline-formula id="ieqn-64"><mml:math id="mml-ieqn-64"><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> indicates the luciferin level interconnected with a glowworm <italic>i</italic> at time <italic>t</italic>, <inline-formula id="ieqn-65"><mml:math id="mml-ieqn-65"><mml:mi>&#x03C1;</mml:mi></mml:math></inline-formula> denotes the luciferin decay constant <inline-formula id="ieqn-66"><mml:math id="mml-ieqn-66"><mml:mn>0</mml:mn><mml:mo>&#x003C;</mml:mo><mml:mi>&#x03C1;</mml:mi><mml:mo>&#x003C;</mml:mo><mml:mn>1</mml:mn></mml:math></inline-formula>, <inline-formula id="ieqn-67"><mml:math id="mml-ieqn-67"><mml:mi>&#x03B3;</mml:mi></mml:math></inline-formula> indicates the luciferin constant, and <inline-formula id="ieqn-68"><mml:math id="mml-ieqn-68"><mml:mi>J</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:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> indicates the value of major function at agent <inline-formula id="ieqn-69"><mml:math id="mml-ieqn-69"><mml:mi>i</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> location at time <inline-formula id="ieqn-71"><mml:math id="mml-ieqn-71"><mml:mi>t</mml:mi><mml:mo>.</mml:mo></mml:math></inline-formula></p>
<p>Also, in the process included in the GSO approach, glowworm is fascinated using the neighbor that glows brightly. Therefore, the results during the movement stage, the glowworms use the probabilistic method for moving toward the neighbor that has a maximal luciferin intensity. Especially for every <italic>i</italic> glowworms, the moving possibility over a neighborhod glowworm is denoted by:
<disp-formula id="eqn-14"><label>(14)</label><mml:math id="mml-eqn-14" display="block"><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mtext>t</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:mrow><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mi>j</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:msub><mml:mi mathvariant="normal">&#x03A3;</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mo>&#x2208;</mml:mo><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msub></mml:mfrac></mml:mstyle></mml:math></disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-14">Eq. (14)</xref>, <inline-formula id="ieqn-72"><mml:math id="mml-ieqn-72"><mml:mi>j</mml:mi><mml:mo>&#x2208;</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, <inline-formula id="ieqn-73"><mml:math id="mml-ieqn-73"><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mo fence="false" stretchy="false">{</mml:mo><mml:mi>j</mml:mi><mml:mrow><mml:mo>:</mml:mo></mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x003C;</mml:mo><mml:msubsup><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x003C;</mml:mo><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo fence="false" stretchy="false">}</mml:mo></mml:math></inline-formula> embodies the set of neighboring glowworms <italic>i</italic> at time <italic>t</italic>, <inline-formula id="ieqn-74"><mml:math id="mml-ieqn-74"><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> refers to the Euclidean distance among the <italic>i</italic> and <italic>j</italic> glowworms at time <italic>t</italic>, <inline-formula id="ieqn-75"><mml:math id="mml-ieqn-75"><mml:msubsup><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> indicates the parameter neighboring range associated with <italic>i</italic> glowworm at <italic>t</italic> time. The parameter controlled by a radial sensor ranges from (<inline-formula id="ieqn-76"><mml:math id="mml-ieqn-76"><mml:mn>0</mml:mn><mml:mo>&#x003C;</mml:mo><mml:msubsup><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup><mml:mo>&#x003C;</mml:mo><mml:mi>r</mml:mi><mml:mi>s</mml:mi></mml:math></inline-formula>).
<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:mrow></mml:msub><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:mo>=</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>s</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mtext>t</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mtext>t</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mo fence="false" stretchy="false">|</mml:mo><mml:mo fence="false" stretchy="false">|</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mtext>t</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mtext>t</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo fence="false" stretchy="false">|</mml:mo><mml:mo fence="false" stretchy="false">|</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>]</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-15">Eq. (15)</xref>, <italic>s</italic><inline-formula id="ieqn-77"><mml:math id="mml-ieqn-77"><mml:mo stretchy="false">(</mml:mo><mml:mo>&#x003E;</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> indicates the step size, and <inline-formula id="ieqn-78"><mml:math id="mml-ieqn-78"><mml:mo fence="false" stretchy="false">|</mml:mo><mml:mo fence="false" stretchy="false">|</mml:mo><mml:mo fence="false" stretchy="false">|</mml:mo><mml:mo fence="false" stretchy="false">|</mml:mo></mml:math></inline-formula> denotes the Euclidean norm operator. Furthermore, <inline-formula id="ieqn-79"><mml:math id="mml-ieqn-79"><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mi>R</mml:mi><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> denotes the position of <italic>i</italic> glowworm at <inline-formula id="ieqn-80"><mml:math id="mml-ieqn-80"><mml:mi>t</mml:mi></mml:math></inline-formula> time from <inline-formula id="ieqn-81"><mml:math id="mml-ieqn-81"><mml:mrow><mml:mtext>m</mml:mtext></mml:mrow></mml:math></inline-formula> dimension real space <inline-formula id="ieqn-82"><mml:math id="mml-ieqn-82"><mml:msup><mml:mrow><mml:mtext>R</mml:mtext></mml:mrow><mml:mrow><mml:mrow><mml:mtext>m</mml:mtext></mml:mrow></mml:mrow></mml:msup></mml:math></inline-formula>. Then, consider <inline-formula id="ieqn-83"><mml:math id="mml-ieqn-83"><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> represent the initialized neighborhood range of each glowworm (i.e., <inline-formula id="ieqn-84"><mml:math id="mml-ieqn-84"><mml:msubsup><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula id="ieqn-85"><mml:math id="mml-ieqn-85"><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mi>i</mml:mi></mml:math></inline-formula>):
<disp-formula id="eqn-16"><label>(16)</label><mml:math id="mml-eqn-16" display="block"><mml:msubsup><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup><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:mo>=</mml:mo><mml:mrow><mml:mtext>min</mml:mtext></mml:mrow><mml:mrow><mml:mo>{</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mrow><mml:mtext>max</mml:mtext></mml:mrow><mml:mrow><mml:mo>{</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:msubsup><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mrow><mml:mtext>r</mml:mtext></mml:mrow></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mo>|</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>|</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow><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-16">Eq. (16)</xref> <inline-formula id="ieqn-86"><mml:math id="mml-ieqn-86"><mml:mi>&#x03B2;</mml:mi></mml:math></inline-formula> refers to a constant, and <inline-formula id="ieqn-87"><mml:math id="mml-ieqn-87"><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> determines a variable employed for controlling the degree.</p>
<p>The GSO system develops a fitness function (FF) for achieving superior classifier efficiency. It defines a positive integer for representing the best efficiency of candidate solutions. During this case, the minimized classifier error rate was supposed that FF is providing in <xref ref-type="disp-formula" rid="eqn-17">Eq. (17)</xref>.
<disp-formula id="eqn-17"><label>(17)</label><mml:math id="mml-eqn-17" display="block"><mml:mrow><mml:mtext mathvariant="italic">fitness</mml:mtext></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mtext mathvariant="italic">Classifier</mml:mtext></mml:mrow><mml:mrow><mml:mtext mathvariant="italic">Error</mml:mtext></mml:mrow><mml:mrow><mml:mtext mathvariant="italic">Rate</mml:mtext></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">number</mml:mtext></mml:mrow><mml:mi>o</mml:mi><mml:mi>f</mml:mi><mml:mrow><mml:mtext mathvariant="italic">misclassified</mml:mtext></mml:mrow><mml:mrow><mml:mtext mathvariant="italic">samples</mml:mtext></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">Total</mml:mtext></mml:mrow><mml:mrow><mml:mtext mathvariant="italic">number</mml:mtext></mml:mrow><mml:mi>o</mml:mi><mml:mi>f</mml:mi><mml:mrow><mml:mtext mathvariant="italic">samples</mml:mtext></mml:mrow></mml:mrow></mml:mfrac></mml:mstyle><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow><mml:mn>100</mml:mn></mml:math></disp-formula></p>
</sec>
</sec>
<sec id="s4"><label>4</label><title>Result and Discussion</title>
<p>In this section, the experimental validation of the suggested method was carried out against dataset-1 [<xref ref-type="bibr" rid="ref-26">26</xref>] (WHU-Hi-LongKou). It comprised total of 9,000 samples with 9 class labels, holding 1000 samples under every class as shown in <xref ref-type="table" rid="table-1">Tab. 1</xref>. <xref ref-type="fig" rid="fig-3">Fig. 3</xref> depict the sample HSIs from various classes involved in dataset 1.</p>
<table-wrap id="table-1"><label>Table 1</label><caption><title>Dataset-1 details</title></caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left">Classes No.</th>
<th align="left">Description</th>
<th align="left">No. of images</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">1</td>
<td align="left">Corn</td>
<td align="left">1000</td>
</tr>
<tr>
<td align="left">2</td>
<td align="left">Cotton</td>
<td align="left">1000</td>
</tr>
<tr>
<td align="left">3</td>
<td align="left">Sesame</td>
<td align="left">1000</td>
</tr>
<tr>
<td align="left">4</td>
<td align="left">Broad-leaf soybean</td>
<td align="left">1000</td>
</tr>
<tr>
<td align="left">5</td>
<td align="left">Narrow-leaf soybean</td>
<td align="left">1000</td>
</tr>
<tr>
<td align="left">6</td>
<td align="left">Rice</td>
<td align="left">1000</td>
</tr>
<tr>
<td align="left">7</td>
<td align="left">Water</td>
<td align="left">1000</td>
</tr>
<tr>
<td align="left">8</td>
<td align="left">Roads and houses</td>
<td align="left">1000</td>
</tr>
<tr>
<td align="left">9</td>
<td align="left">Mixed weed</td>
<td align="left">1000</td>
</tr>
</tbody>
</table>
</table-wrap><fig id="fig-3"><label>Figure 3</label><caption><title>Sample images on dataset-1</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_33054-fig-3.png"/></fig>
<p><xref ref-type="fig" rid="fig-4">Fig. 4</xref> showcases the confusion matrix offered by the HOADTL-CC model on dataset-1. The figure implied that the HOADTL-CC model has proficiently recognized 985 samples into class 1, 983 samples into class 2, 963 samples into class 3, 990 samples into class 4, 991 samples into class 5, 979 samples into class 6, 979 samples into class 7, 946 samples into class 8, and 986 samples into class 9.</p>
<fig id="fig-4"><label>Figure 4</label><caption><title>Confusion matrices of HOADTL-CC approach on dataset-1</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_33054-fig-4.png"/></fig>
<p>A brief crop classifier outcome of the presented HOADTL-CC model on dataset-1 is demonstrated in <xref ref-type="table" rid="table-2">Tab. 2</xref> and <xref ref-type="fig" rid="fig-5">Fig. 5</xref>. The results indicated that the presented HOADTL-CC model has shown effectual results under every class label. For instance, the HOADTL-CC model has recognized images under corn class with <inline-formula id="ieqn-88"><mml:math id="mml-ieqn-88"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 99.50&#x0025;, <inline-formula id="ieqn-89"><mml:math id="mml-ieqn-89"><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> of 98.50&#x0025;, <inline-formula id="ieqn-90"><mml:math id="mml-ieqn-90"><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> of 99.62&#x0025;, and <inline-formula id="ieqn-91"><mml:math id="mml-ieqn-91"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">score</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> of 97.77&#x0025;. Meanwhile, the HOADTL-CC technique has recognized images under rice class with <inline-formula id="ieqn-92"><mml:math id="mml-ieqn-92"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 99.69&#x0025;, <inline-formula id="ieqn-93"><mml:math id="mml-ieqn-93"><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> of 97.90&#x0025;, <inline-formula id="ieqn-94"><mml:math id="mml-ieqn-94"><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> of 99.91&#x0025;, and <inline-formula id="ieqn-95"><mml:math id="mml-ieqn-95"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">score</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> of 98.59&#x0025;. Eventually, the HOADTL-CC approach has recognized images under mixed weed class with <inline-formula id="ieqn-96"><mml:math id="mml-ieqn-96"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 99.76&#x0025;, <inline-formula id="ieqn-97"><mml:math id="mml-ieqn-97"><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> of 98.60&#x0025;, <inline-formula id="ieqn-98"><mml:math id="mml-ieqn-98"><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> of 99.90&#x0025;, and <inline-formula id="ieqn-99"><mml:math id="mml-ieqn-99"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">score</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> of 98.90&#x0025;.</p>
<table-wrap id="table-2"><label>Table 2</label><caption><title>Result analysis of HOADTL-CC method with distinct class labels and measures on dataset-1</title></caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left">Class labels</th>
<th align="left">Accuracy</th>
<th align="left">Recall</th>
<th align="left">Specificity</th>
<th align="left">F-score</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">Corn</td>
<td align="left">99.50</td>
<td align="left">98.50</td>
<td align="left">99.62</td>
<td align="left">97.77</td>
</tr>
<tr>
<td align="left">Cotton</td>
<td align="left">98.82</td>
<td align="left">98.30</td>
<td align="left">98.89</td>
<td align="left">94.88</td>
</tr>
<tr>
<td align="left">Sesame</td>
<td align="left">99.51</td>
<td align="left">96.30</td>
<td align="left">99.91</td>
<td align="left">97.77</td>
</tr>
<tr>
<td align="left">Broad-leaf soybean</td>
<td align="left">99.76</td>
<td align="left">99.00</td>
<td align="left">99.85</td>
<td align="left">98.90</td>
</tr>
<tr>
<td align="left">Narrow-leaf soybean</td>
<td align="left">99.66</td>
<td align="left">99.10</td>
<td align="left">99.72</td>
<td align="left">98.46</td>
</tr>
<tr>
<td align="left">Rice</td>
<td align="left">99.69</td>
<td align="left">97.90</td>
<td align="left">99.91</td>
<td align="left">98.59</td>
</tr>
<tr>
<td align="left">Water</td>
<td align="left">99.60</td>
<td align="left">97.90</td>
<td align="left">99.81</td>
<td align="left">98.19</td>
</tr>
<tr>
<td align="left">Roads and houses</td>
<td align="left">99.31</td>
<td align="left">94.60</td>
<td align="left">99.90</td>
<td align="left">96.83</td>
</tr>
<tr>
<td align="left">Mixed weed</td>
<td align="left">99.76</td>
<td align="left">98.60</td>
<td align="left">99.90</td>
<td align="left">98.90</td>
</tr>
<tr>
<td align="left">Average</td>
<td align="left">99.51</td>
<td align="left">97.80</td>
<td align="left">99.73</td>
<td align="left">97.81</td>
</tr>
</tbody>
</table>
</table-wrap><fig id="fig-5"><label>Figure 5</label><caption><title>Average analysis of HOADTL-CC method with distinct class labels on dataset-1</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_33054-fig-5.png"/></fig>
<p>The training accuracy (TA) and validation accuracy (VA) gained by the HOADTL-CC method on dataset-1 is established in <xref ref-type="fig" rid="fig-6">Fig. 6</xref>. The experimental outcome revealed that the HOADTL-CC approach has acquired maximum values of TA and VA. In specific, the VA is performed that higher than TA.</p>
<fig id="fig-6"><label>Figure 6</label><caption><title>TA and VA analysis of HOADTL-CC algorithm on dataset-1</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_33054-fig-6.png"/></fig>
<p>The training loss (TL) and validation loss (VL) obtained by the HOADTL-CC system on dataset-1 are recognized in <xref ref-type="fig" rid="fig-7">Fig. 7</xref>. The experimental outcome represented that the HOADTL-CC methodology has accomplished least values of TL and VL. In specific, the VL appeared to be lower than TL.</p>
<fig id="fig-7"><label>Figure 7</label><caption><title>TL and VL analysis of HOADTL-CC algorithm on dataset-1</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_33054-fig-7.png"/></fig>
<p>A brief precision-recall examination of the HOADTL-CC model under dataset-1 is portrayed in <xref ref-type="fig" rid="fig-8">Fig. 8</xref>. By observing the figure, it is noticed that the HOADTL-CC model has accomplished maximum precision-recall performance under all classes.</p>
<fig id="fig-8"><label>Figure 8</label><caption><title>Precision-recall curve analysis of HOADTL-CC algorithm on dataset-1</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_33054-fig-8.png"/></fig>
<p>To ensure the enhanced performance of the HOADTL-CC model, a comparative analysis with existing methods [<xref ref-type="bibr" rid="ref-27">27</xref>] on dataset-1 is made in <xref ref-type="table" rid="table-3">Tab. 3</xref> and <xref ref-type="fig" rid="fig-9">Fig. 9</xref>. The figure demonstrated that the SVM, FNEA-OO, and SVRFMC models have obtained lower <inline-formula id="ieqn-100"><mml:math id="mml-ieqn-100"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 96.18&#x0025;, 97.57&#x0025;, and 97.99&#x0025; respectively. Besides, the CNN and CNN-CRF models have attained closer <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> values of 98.38&#x0025; and 98.94&#x0025; respectively. However, the HOADTL-CC model has shown effectual performance over other models with maximum <inline-formula id="ieqn-102"><mml:math id="mml-ieqn-102"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 99.51&#x0025;.</p>
<table-wrap id="table-3"><label>Table 3</label><caption><title>Comparative analysis of HOADTL-CC approach with recent methodologies on dataset-1</title></caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left">Methods</th>
<th align="left">Accuracy (&#x0025;)</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">SVM model</td>
<td align="left">96.18</td>
</tr>
<tr>
<td align="left">FNEA-OO model</td>
<td align="left">97.57</td>
</tr>
<tr>
<td align="left">SVRFMC model</td>
<td align="left">97.99</td>
</tr>
<tr>
<td align="left">CNN model</td>
<td align="left">98.38</td>
</tr>
<tr>
<td align="left">CNN-CRF model</td>
<td align="left">98.94</td>
</tr>
<tr>
<td align="left">HOADTL-CC</td>
<td align="left">99.51</td>
</tr>
</tbody>
</table>
</table-wrap><fig id="fig-9"><label>Figure 9</label><caption><title>Comparative analysis of HOADTL-CC approach on dataset-1</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_33054-fig-9.png"/></fig>
</sec>
<sec id="s5"><label>5</label><title>Conclusion</title>
<p>In this study, a new HOADTL-CC model was advanced for the identification and categorization of crops on the hyperspectral RSIs. The proposed HOADTL-CC model includes a series of processes namely CapsNet feature extractor, HOA based hyperparameter optimizer, ENN classification, and GSO based parameter optimization. Here, the GSO algorithm is exploited to fine tune the ENN parameters involved in this study. The experimental result scrutiny of the HOADTL-CC method was tested with the help of a benchmark dataset and the results are assessed under distinct aspects. The extensive comparative studies stated the enhanced performance of the HOADTL-CC model over recent approaches. Thus, the presented HOADTL-CC model can be exploited as an effectual tool to classify crops. In future, ensemble of DL based fusion methods can be applied to boost the classification results.</p>
</sec>
</body>
<back>
<fn-group>
<fn fn-type="other"><p><bold>Funding Statement:</bold> The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through Large Groups Project under Grant Number (25/43). Princess Nourah bint Abdulrahman University Researchers Supporting Project Number (PNURSP2022R303), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia. The authors would like to thank the Deanship of Scientific Research at Umm Al-Qura University for supporting this work by Grant Code: 22UQU4340237DSR28.</p></fn>
<fn fn-type="conflict"><p><bold>Conflicts of Interest:</bold> The authors declare that they have no conflicts of interest to report regarding the present study.</p></fn>
</fn-group>
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