<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.1 20151215//EN" "http://jats.nlm.nih.gov/publishing/1.1/JATS-journalpublishing1.dtd">
<article xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" article-type="research-article" dtd-version="1.1">
<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">27327</article-id>
<article-id pub-id-type="doi">10.32604/cmc.2022.027327</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Arithmetic Optimization with Deep Learning Enabled Anomaly Detection in&#x00A0;Smart City</article-title>
<alt-title alt-title-type="left-running-head">Arithmetic Optimization with Deep Learning Enabled Anomaly Detection in Smart City</alt-title>
<alt-title alt-title-type="right-running-head">Arithmetic Optimization with Deep Learning Enabled Anomaly Detection in Smart City</alt-title>
</title-group>
<contrib-group content-type="authors">
<contrib id="author-1" contrib-type="author" corresp="yes">
<name name-style="western"><surname>Ragab</surname><given-names>Mahmoud</given-names>
</name><xref ref-type="aff" rid="aff-1">1</xref>
<xref ref-type="aff" rid="aff-2">2</xref>
<xref ref-type="aff" rid="aff-3">3</xref><email>mragab@kau.edu.sa</email></contrib>
<contrib id="author-2" contrib-type="author">
<name name-style="western"><surname>Sabir</surname><given-names>Maha Farouk S.</given-names>
</name><xref ref-type="aff" rid="aff-4">4</xref></contrib>
<aff id="aff-1"><label>1</label><institution>Information Technology Department, Faculty of Computing and Information Technology, King Abdulaziz University</institution>, <addr-line>Jeddah, 21589</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-2"><label>2</label><institution>Centre of Artificial Intelligence for Precision Medicines, King Abdulaziz University</institution>, <addr-line>Jeddah, 21589</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-3"><label>3</label><institution>Mathematics Department, Faculty of Science, Al-Azhar University</institution>, <addr-line>Naser City, 11884, Cairo</addr-line>, <country>Egypt</country></aff>
<aff id="aff-4"><label>4</label><institution>Information Systems Department, Faculty of Computing and Information Technology King Abdulaziz University</institution>, <addr-line>Jeddah, 21589</addr-line>, <country>Saudi Arabia</country></aff>
</contrib-group>
<author-notes>
<corresp id="cor1"><label>&#x002A;</label>Corresponding Author: Mahmoud Ragab. Email: <email>mragab@kau.edu.sa</email></corresp>
</author-notes>
<pub-date pub-type="epub" date-type="pub" iso-8601-date="2022-05-16"><day>16</day>
<month>05</month>
<year>2022</year></pub-date>
<volume>73</volume>
<issue>1</issue>
<fpage>381</fpage>
<lpage>395</lpage>
<history>
<date date-type="received">
<day>14</day>
<month>1</month>
<year>2022</year>
</date>
<date date-type="accepted">
<day>30</day>
<month>3</month>
<year>2022</year>
</date>
</history>
<permissions>
<copyright-statement>&#x00A9; 2022 Ragab and Sabir</copyright-statement>
<copyright-year>2022</copyright-year>
<copyright-holder>Ragab and Sabir</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_27327.pdf"></self-uri>
<abstract>
<p>In recent years, Smart City Infrastructures (SCI) have become familiar whereas intelligent models have been designed to improve the quality of living in smart cities. Simultaneously, anomaly detection in SCI has become a hot research topic and is widely explored to enhance the safety of pedestrians. The increasing popularity of video surveillance system and drastic increase in the amount of collected videos make the conventional physical investigation method to identify abnormal actions, a laborious process. In this background, Deep Learning (DL) models can be used in the detection of anomalies found through video surveillance systems. The current research paper develops an Internet of Things Assisted Deep Learning Enabled Anomaly Detection Technique for Smart City Infrastructures, named (IoTAD-SCI) technique. The aim of the proposed IoTAD-SCI technique is to mainly identify the existence of anomalies in smart city environment. Besides, IoTAD-SCI technique involves Deep Consensus Network (DCN) model design to detect the anomalies in input video frames. In addition, Arithmetic Optimization Algorithm (AOA) is executed to tune the hyperparameters of the DCN model. Moreover, ID3 classifier is also utilized to classify the identified objects in different classes. The experimental analysis was conducted for the proposed IoTAD-SCI technique upon benchmark UCSD anomaly detection dataset and the results were inspected under different measures. The simulation results infer the superiority of the proposed IoTAD-SCI technique under different metrics.</p>
</abstract>
<kwd-group kwd-group-type="author">
<kwd>Object detection</kwd>
<kwd>anomaly detection</kwd>
<kwd>smart city infrastructure</kwd>
<kwd>deep learning</kwd>
<kwd>parameter tuning</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1">
<label>1</label>
<title>Introduction</title>
<p>Video surveillance systems have been widely installed in the recent years for monitoring the crowd at public places. The video information generated by such systems is complex, huge and in different formats while Traditional manual analysis to label abnormal events in such data is challenging and time-consuming in nature. Thus, a smart surveillance scheme and a hotspot of Computer Vision (CV) applications and researches are immediately required to detect and recognize anomalies [<xref ref-type="bibr" rid="ref-1">1</xref>]. But localization and anomaly detection remain a challenge in smart video surveillance. However, considerable development has occurred in the recent years in terms of behavior modeling, anomaly measuring, and feature extraction. One of the primary challenges in anomaly detection is that the description of the anomaly is indeterminate in almost all real-time surveillance videos. Generally, an event that is considerably distinct from general event is classified as anomaly. In other terms, anomalies are determined as common events rather than details of themselves or classifications [<xref ref-type="bibr" rid="ref-2">2</xref>]. An event which is anomalous in one scene (people running) may not be necessarily anomalous in another scene. This is because the common event in another scene might include the person running, while the initial scene does not. Thus, anomaly is composed of inadequate similarities and sizes to be efficiently modelled. Essentially, anomaly detection for crowd scenes has an innovation detection that is called a one-class, semi-supervised learning problem [<xref ref-type="bibr" rid="ref-3">3</xref>]. This is because the training data of the current dataset comprises of common events, where the information to be confirmed has abnormal as well as normal events. <xref ref-type="fig" rid="fig-1">Fig. 1</xref> illustrates the structure of smart city.</p>
<fig id="fig-1">
<label>Figure 1</label>
<caption>
<title>Smart city infrastructure</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_27327-fig-1.png"/>
</fig>
<p>Several CV methods that depends upon work, have been presented earlier. These methods focus on the operation including scene learning, data acquisition, behavioural learning, feature extraction, activity learning, etc [<xref ref-type="bibr" rid="ref-4">4</xref>]. The main objective is to calculate the operation that includes video processing model, anomaly predictive approach, scene detection, human behavior learning, vehicle prediction, multiple camera-based challenges and schemes, vehicle observation, traffic observation, activity examination, etc. Now, anomalous prediction is considered as a sub-region of behavioral learning in the captured visual scene [<xref ref-type="bibr" rid="ref-5">5</xref>]. The availability of video captured in public places has led to anomalous prediction and the simulation of video analysis. Furthermore, anomaly prediction methods understand to differentiate the normal behavior through training. Any important changes that deviate from common behavior are considered as anomalous. Sudden dispersion of people from a crowd, presence of vehicles on pathways, jaywalking, person fainting when walking, U-turn of vehicles at red signals and signal bypasses at a traffic junction are some of the instances of anomalies [<xref ref-type="bibr" rid="ref-6">6</xref>]. Recently, Deep Learning (DL) method has attained an outstanding achievement in a number of CV methods that include object detection and classification since the application depends upon supervised learning.</p>
<p>The current research work develops an Internet of Things Assisted Deep Learning Enabled Anomaly Detection Technique for Smart City Infrastructures, abbreviated as (IoTAD-SCI) technique. The proposed IoTAD-SCI technique involves the design of Deep Consensus Network (DCN) model to detect the anomalies in input video frames. In addition, Arithmetic Optimization Algorithm (AOA) is implemented to fine tune the hyperparameters of DCN technique. Moreover, ID3 classifier is also utilized to classify the identified objects under different classes. The experimental analysis was conducted for IoTAD-SCI technique upon benchmark UCSD anomaly detection dataset and the results were inspected under different measures.</p>
</sec>
<sec id="s2">
<label>2</label>
<title>Related works</title>
<p>Li et al. [<xref ref-type="bibr" rid="ref-7">7</xref>] proposed an anomaly detection model and video anomaly event feature. At first, dense optical flow of video was attained and the data of optical flow was converted into histogram features of the optical flow. Next, the space-time cube of video was created using space-time relation of the video. At last, sparse depiction technique was utilized to model the entire procedure. Font et al. [<xref ref-type="bibr" rid="ref-8">8</xref>] used real-time information from smart cities of Barcelona to identify typical attacks and simulate WSN as and when required. Next, the researchers compared the commonly-utilized anomaly detection methods that disclose such attacks. The algorithm was evaluated under distinct necessities on access network data.</p>
<p>Alrashdi et al. [<xref ref-type="bibr" rid="ref-9">9</xref>] presented an Anomalous Detection-IoT (AD-IoT) method i.e., a smart anomalous detection-based RF-ML method. The presented method was able to identify the compromised IoT devices in distribution fog nodes efficiently. To estimate the presented method, the study employed current datasets to demonstrate the accuracy of the algorithm. Chackravarthy et al. [<xref ref-type="bibr" rid="ref-10">10</xref>] introduced a NN approach as well as a Hybrid Deep Learning method to analyze the video stream data. The presented method was capable of identifying and assessing the criminal activities quickly. This sequentially reduced the manual workload on supervisors. While the method was executed through smart city framework, it also allowed one to an adaptable and efficient crime detection method.</p>
<p>Kang et al. [<xref ref-type="bibr" rid="ref-11">11</xref>] introduced an NN-based model which integrates the idea of AUC using Multi-Instance Learning (MIL) model. The authors created MI-AUC method which forecasts high anomaly scores for anomalous segments. Moreover, sparsity and temporal smoothness limitations were also employed in this study from loss function for effective anomalous detection. Chen et al. [<xref ref-type="bibr" rid="ref-12">12</xref>] designed an architecture-based bi-directional prediction that forecasts a similar target frame by both forward and backward predictive subsystems, correspondingly. Next, the loss function is formulated on the basis of bi-directional predictive frame and real-time target frame. Additionally, an anomaly score assessment model-based sliding window system was presented in this study that focuses on the foreground of predictive error map.</p>
<p>Ullah et al. [<xref ref-type="bibr" rid="ref-13">13</xref>] developed an effective deep feature-based intelligent anomaly detection method. In the presented method, the spatiotemporal features were initially extracted from a sequence of frames by passing everyone to a pre-trained CNN method. The feature extracted from the series of frames is beneficial in terms of capturing anomalous actions. Next, the extracted deep feature is passed onto multilayer Bi-LSTM method that could precisely categorize the ongoing normal or anomalous events in complicated surveillance scenes.</p>
</sec>
<sec id="s3">
<label>3</label>
<title>The Proposed Model</title>
<p>In current study, an effective IoTAD-SCI technique is developed to identify the presence of anomalies in smart city environment. The proposed IoTAD-SCI technique involves the design of DCN technique to detect anomalies in input video frames. Followed by, AOA is applied to fine tune the hyperparameters of DCN technique whereas ID3 classifier is utilized to classify the identified objects under different classes.</p>
<sec id="s3_1">
<label>3.1</label>
<title>Object Detection Using DCN Model</title>
<p>In initial stage, DCN model is applied for the identification of objects that exist in input video frame. DCN has an analogous structure alike RetinaNet [<xref ref-type="bibr" rid="ref-14">14</xref>]. It makes use of Feature Pyramid Network (FPN) for feature extraction at different scales from ResNet-50 mainstream by following squeeze-and-excite method for the residual. In order to detect smaller objects, higher-resolution variants of FPN is employed in this study. It is utilized for Leaky ReLU activation function and group normalization. The feature extraction maps, at all the scales, are transmitted to Centroid Proposal Network (CPN). In comparison with Region Proposal Network (RPN) that predicts the bounding boxes, CPN forecasts a subset of centroids <inline-formula id="ieqn-1"><mml:math id="mml-ieqn-1"><mml:msup><mml:mi>v</mml:mi><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:msup></mml:math></inline-formula> with respective confidence score <inline-formula id="ieqn-2"><mml:math id="mml-ieqn-2"><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mi>v</mml:mi><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>. When compared with RetinaNet, CPN does not share the weight at all the scales to capture distinct representations. This is because each image within the microscopy data sets has a similar magnification. Like RPN in RetinaNet, anchor is utilized in this study as prior, but with a distinct configuration.</p>
<p>For every spatial location in a <inline-formula id="ieqn-3"><mml:math id="mml-ieqn-3"><mml:mn>2</mml:mn><mml:mi>D</mml:mi></mml:math></inline-formula> grid, <inline-formula id="ieqn-4"><mml:math id="mml-ieqn-4"><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>a</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>17</mml:mn></mml:math></inline-formula> anchors are employed in overall that involves 8 anchors at a length of 0.5 pixels, 8 anchors with a length of one pixel, and one anchor without any offset. The anchor vector is rotated thus they are able to cover a unit disk. The <inline-formula id="ieqn-5"><mml:math id="mml-ieqn-5"><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> anchor <inline-formula id="ieqn-6"><mml:math id="mml-ieqn-6"><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> is employed to the <inline-formula id="ieqn-7"><mml:math id="mml-ieqn-7"><mml:mi>i</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> predicted vector, <inline-formula id="ieqn-8"><mml:math id="mml-ieqn-8"><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msubsup><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>:</p>
<p><disp-formula id="eqn-1"><label>(1)</label><mml:math id="mml-eqn-1" display="block"><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>s</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>p</mml:mi><mml:mi>o</mml:mi><mml:mi>s</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msubsup><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>Whereas <inline-formula id="ieqn-9"><mml:math id="mml-ieqn-9"><mml:mi>p</mml:mi><mml:mi>o</mml:mi><mml:mi>s</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msubsup><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> represents the spatial location from the grid and <inline-formula id="ieqn-10"><mml:math id="mml-ieqn-10"><mml:mi>s</mml:mi></mml:math></inline-formula> signifies a scaling factor to standardize the distribution of <inline-formula id="ieqn-11"><mml:math id="mml-ieqn-11"><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula>. Therefore, every probable anchor in anchor configuration is included in each position of the grid [<xref ref-type="bibr" rid="ref-15">15</xref>]. In order to encourage the network to favor the matching anchor, the confidence score <inline-formula id="ieqn-12"><mml:math id="mml-ieqn-12"><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msubsup><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> of larger regression value for the magnitude of <inline-formula id="ieqn-13"><mml:math id="mml-ieqn-13"><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> is penalized so as to compute the confidence score of <inline-formula id="ieqn-14"><mml:math id="mml-ieqn-14"><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>. The network regresses the offset vector from this position. So, both anchor and spatial position are combined in the grid assisted individual neuron, since they emphasize the forecasting of smaller offset of centroid position:</p>
<p><disp-formula id="eqn-2"><label>(2)</label><mml:math id="mml-eqn-2" display="block"><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msubsup><mml:mo stretchy="false">)</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>ln</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msubsup><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo></mml:mrow></mml:msup></mml:math></disp-formula></p>
<p>For mathematical reason, CPN predicts the logit (logarithm of odds) <inline-formula id="ieqn-15"><mml:math id="mml-ieqn-15"><mml:msubsup><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mrow><mml:mi mathvariant="italic">L</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">g</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">t</mml:mi></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msubsup><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x2208;</mml:mo><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow></mml:math></inline-formula> rather than forecasting the confidence score directly, <inline-formula id="ieqn-16"><mml:math id="mml-ieqn-16"><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msubsup><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><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:mrow></mml:msup></mml:math></inline-formula>. Therefore, the normalization in <xref ref-type="disp-formula" rid="eqn-2">(2)</xref> is implemented in logit space yield where the normalized logit <inline-formula id="ieqn-17"><mml:math id="mml-ieqn-17"><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2208;</mml:mo><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow></mml:math></inline-formula>:<disp-formula id="eqn-3"><label>(3)</label><mml:math id="mml-eqn-3" display="block"><mml:mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mml:mtr><mml:mtd><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:mi></mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mi mathvariant="italic">L</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">g</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">t</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>v</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:mo>=</mml:mo><mml:mrow><mml:mi mathvariant="italic">L</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">g</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">t</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:msubsup><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>ln</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msubsup><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd /><mml:mtd><mml:mi></mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mi mathvariant="italic">L</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">g</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">t</mml:mi></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msubsup><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo><mml:mrow><mml:mi mathvariant="italic">L</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">g</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">t</mml:mi></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>ln</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msubsup><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo></mml:mrow></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd /><mml:mtd><mml:mi></mml:mi><mml:mo>=</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:mi>ln</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>ln</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msubsup><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>ln</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>ln</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msubsup><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd /><mml:mtd><mml:mi></mml:mi><mml:mo>=</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:msubsup><mml:mo>&#x2212;</mml:mo><mml:mi>ln</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:msubsup><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mi>ln</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>ln</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo symmetric="true">&#x2016;</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msubsup><mml:mo symmetric="true">&#x2016;</mml:mo></mml:mrow></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula></p>
</sec>
<sec id="s3_2">
<label>3.2</label>
<title>Hyperparameter Tuning Using AOA</title>
<p>In order to proficiently adjust the hyperparameters of DCN model, AOA is utilized. AOA is stimulated on the basis of basic arithmetic operators used in mathematics. In line with other optimization algorithms, AOA mainly operates on two searching processes namely, exploration and exploration [<xref ref-type="bibr" rid="ref-16">16</xref>], depending upon the arithmetic operators like <inline-formula id="ieqn-18"><mml:math id="mml-ieqn-18"><mml:mo>&#x2212;</mml:mo><mml:mo>,</mml:mo><mml:mo>+</mml:mo><mml:mo>,</mml:mo><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mrow><mml:mo>/</mml:mo></mml:mrow></mml:math></inline-formula>. Initially, AOA produces a collection of <inline-formula id="ieqn-19"><mml:math id="mml-ieqn-19"><mml:mi>N</mml:mi></mml:math></inline-formula> solutions (agent). And every individual solution indicates a solution for the applied problem. Therefore, the solution or agent indicates <inline-formula id="ieqn-20"><mml:math id="mml-ieqn-20"><mml:mi>X</mml:mi></mml:math></inline-formula> population which is given below:</p>
<p><disp-formula id="eqn-4"><label>(4)</label><mml:math id="mml-eqn-4" display="block"><mml:mi>X</mml:mi><mml:mo>=</mml:mo><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>x</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><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:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mrow><mml:mtext>j</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mrow><mml:mtext>n</mml:mtext></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mo>,</mml:mo><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:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mrow><mml:mtext>j</mml:mtext></mml:mrow></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:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>&#x22EF;</mml:mo></mml:mtd><mml:mtd><mml:mo>&#x22EF;</mml:mo></mml:mtd><mml:mtd><mml:mo>&#x22EF;</mml:mo></mml:mtd><mml:mtd><mml:mo>&#x22EF;</mml:mo></mml:mtd><mml:mtd><mml:mo>&#x22EF;</mml:mo></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>&#x22EE;</mml:mo></mml:mtd><mml:mtd><mml:mo>&#x22EE;</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:mi>N</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><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>&#x2212;</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mrow><mml:mtext>j</mml:mtext></mml:mrow></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>&#x2212;</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mrow><mml:mtext>n</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>N</mml:mi><mml:mo>,</mml:mo><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:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>N</mml:mi><mml:mo>,</mml:mo><mml:mrow><mml:mtext>n</mml:mtext></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>N</mml:mi><mml:mo>,</mml:mo><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:math></disp-formula></p>
<p>Then, the fitness values of all the solutions are determined to identify the optimal solution, <inline-formula id="ieqn-21"><mml:math id="mml-ieqn-21"><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>. Afterward, based on Math Optimizer Accelerated <inline-formula id="ieqn-22"><mml:math id="mml-ieqn-22"><mml:mo stretchy="false">(</mml:mo><mml:mi>M</mml:mi><mml:mi>O</mml:mi><mml:mi>A</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> value, AOA conducted exploration or exploitation process. Subsequently, MOA is upgraded using the <xref ref-type="disp-formula" rid="eqn-5">Eq. (5)</xref>:</p>
<p><disp-formula id="eqn-5"><label>(5)</label><mml:math id="mml-eqn-5" display="block"><mml:mi>M</mml:mi><mml:mi>O</mml:mi><mml:mi>A</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mrow><mml:mtext>&#xA0;Min&#xA0;</mml:mtext></mml:mrow><mml:mo>+</mml:mo><mml:mi>t</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mrow><mml:mtext>Max</mml:mtext></mml:mrow><mml:mrow><mml:mi>M</mml:mi><mml:mi>O</mml:mi><mml:mi>A</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mrow><mml:mtext>Min</mml:mtext></mml:mrow><mml:mrow><mml:mi>M</mml:mi><mml:mi>O</mml:mi><mml:mi>A</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula>where <inline-formula id="ieqn-23"><mml:math id="mml-ieqn-23"><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> signifies the maximum iteration count. <inline-formula id="ieqn-24"><mml:math id="mml-ieqn-24"><mml:msub><mml:mrow><mml:mtext>Min</mml:mtext></mml:mrow><mml:mrow><mml:mi>M</mml:mi><mml:mi>O</mml:mi><mml:mi>A</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-25"><mml:math id="mml-ieqn-25"><mml:msub><mml:mrow><mml:mtext>Max</mml:mtext></mml:mrow><mml:mrow><mml:mi>O</mml:mi><mml:mi>A</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> signify the lower and higher values of the accelerated function, correspondingly. Also, both multiplication (M) and division (D) can be utilized at the time of exploration, as given below.</p>
<p><disp-formula id="eqn-6"><label>(6)</label><mml:math id="mml-eqn-6" 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 stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mml:mtr><mml:mtd><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x00F7;</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mi>O</mml:mi><mml:mi>P</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mo>&#x2208;</mml:mo><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x00D7;</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mi>U</mml:mi><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:mi>L</mml:mi><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x00D7;</mml:mo><mml:mi>&#x03BC;</mml:mi><mml:mo>+</mml:mo><mml:mi>L</mml:mi><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>,</mml:mo></mml:mtd><mml:mtd><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mn>2</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:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x00D7;</mml:mo><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mi>O</mml:mi><mml:mi>P</mml:mi></mml:mrow></mml:msub><mml:mo>&#x00D7;</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mi>U</mml:mi><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:mi>L</mml:mi><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x00D7;</mml:mo><mml:mi>&#x03BC;</mml:mi><mml:mo>+</mml:mo><mml:mi>L</mml:mi><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>,</mml:mo></mml:mtd><mml:mtd><mml:mrow><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">t</mml:mi><mml:mi mathvariant="italic">h</mml:mi><mml:mi mathvariant="italic">e</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">w</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mtd></mml:mtr></mml:mtable><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo></mml:mrow></mml:math></disp-formula>where <inline-formula id="ieqn-26"><mml:math id="mml-ieqn-26"><mml:mi>e</mml:mi></mml:math></inline-formula> indicates the least integer, <inline-formula id="ieqn-27"><mml:math id="mml-ieqn-27"><mml:mi>U</mml:mi><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-28"><mml:math id="mml-ieqn-28"><mml:mi>L</mml:mi><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> denote the maximum and minimum bounds of the searching region at <inline-formula id="ieqn-29"><mml:math id="mml-ieqn-29"><mml:mi>j</mml:mi><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> dimension. <inline-formula id="ieqn-30"><mml:math id="mml-ieqn-30"><mml:mi>&#x03BC;</mml:mi><mml:mo>=</mml:mo><mml:mn>0.5</mml:mn></mml:math></inline-formula> indicates the control function. Besides, Math Optimizer <inline-formula id="ieqn-31"><mml:math id="mml-ieqn-31"><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mi>O</mml:mi><mml:mi>P</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> is represented as follows</p>
<p><disp-formula id="eqn-7"><label>(7)</label><mml:math id="mml-eqn-7" display="block"><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mi>O</mml:mi><mml:mi>P</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mfrac><mml:msup><mml:mi>t</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>&#x03B1;</mml:mi></mml:mrow></mml:msup><mml:msubsup><mml:mi>M</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>&#x03B1;</mml:mi></mml:mrow></mml:msubsup></mml:mfrac></mml:math></disp-formula></p>
<p><inline-formula id="ieqn-32"><mml:math id="mml-ieqn-32"><mml:mi>&#x03B1;</mml:mi><mml:mo>=</mml:mo><mml:mn>5</mml:mn></mml:math></inline-formula> denotes the dynamic variable in determining the accuracy of the exploitation process after several rounds of operations. In addition, add operator (A) and subtract operator (D) can be utilized to perform AOA exploitation process [<xref ref-type="bibr" rid="ref-17">17</xref>].</p>
<p><disp-formula id="eqn-8"><label>(8)</label><mml:math id="mml-eqn-8" 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 stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mml:mtr><mml:mtd><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mi>O</mml:mi><mml:mi>P</mml:mi></mml:mrow></mml:msub><mml:mo>&#x00D7;</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mi>U</mml:mi><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:mi>L</mml:mi><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x00D7;</mml:mo><mml:mi>&#x03BC;</mml:mi><mml:mo>+</mml:mo><mml:mi>L</mml:mi><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo>&#x003C;</mml:mo><mml:mn>0.5</mml:mn></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mi>O</mml:mi><mml:mi>P</mml:mi></mml:mrow></mml:msub><mml:mo>&#x00D7;</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mi>U</mml:mi><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:mi>L</mml:mi><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x00D7;</mml:mo><mml:mi>&#x03BC;</mml:mi><mml:mo>+</mml:mo><mml:mi>L</mml:mi><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>,</mml:mo><mml:mrow><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">t</mml:mi><mml:mi mathvariant="italic">h</mml:mi><mml:mi mathvariant="italic">e</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">w</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mtd></mml:mtr></mml:mtable><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo></mml:mrow></mml:math></disp-formula>where <inline-formula id="ieqn-33"><mml:math id="mml-ieqn-33"><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> indicates an arbitrary number in the range of zero and one. Then, the agent update procedure is carried out using AOA operators. The process involved in AOA is shown in Algorithm 1.</p>
<fig id="fig-11">
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_27327-fig-11.png"/>
</fig>
</sec>
<sec id="s3_3">
<label>3.3</label>
<title>ID3 Based Classification Model</title>
<p>Once the objects are detected in input frame, ID3 classifier is applied to classify the objects as either anomalies or non-anomalies. Id3 method selects the testing features by comparing and calculating their data gains. Here, <inline-formula id="ieqn-54"><mml:math id="mml-ieqn-54"><mml:mi>S</mml:mi></mml:math></inline-formula> represents the subset of data instances. Assume the class attribute <inline-formula id="ieqn-55"><mml:math id="mml-ieqn-55"><mml:mi>C</mml:mi></mml:math></inline-formula> has <inline-formula id="ieqn-56"><mml:math id="mml-ieqn-56"><mml:mi>m</mml:mi></mml:math></inline-formula> distinct values that denote <inline-formula id="ieqn-57"><mml:math id="mml-ieqn-57"><mml:mi>m</mml:mi></mml:math></inline-formula> distinct class label, <inline-formula id="ieqn-58"><mml:math id="mml-ieqn-58"><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mi>m</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>. Here, <inline-formula id="ieqn-59"><mml:math id="mml-ieqn-59"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> represents the number of samples from class <inline-formula id="ieqn-60"><mml:math id="mml-ieqn-60"><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mi>m</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>. The predicted number of data required to classify <inline-formula id="ieqn-61"><mml:math id="mml-ieqn-61"><mml:mi>S</mml:mi></mml:math></inline-formula> is shown below.</p>
<p><disp-formula id="eqn-9"><label>(9)</label><mml:math id="mml-eqn-9" display="block"><mml:mi>I</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mo>&#x2212;</mml:mo><mml:munderover><mml:mo>&#x2211;</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:munderover><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>log</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2061;</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></disp-formula></p>
<p>Here, <inline-formula id="ieqn-62"><mml:math id="mml-ieqn-62"><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> implies the probability of samples in <inline-formula id="ieqn-63"><mml:math id="mml-ieqn-63"><mml:mi>S</mml:mi></mml:math></inline-formula> that belongs to the class <inline-formula id="ieqn-64"><mml:math id="mml-ieqn-64"><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>.</mml:mo></mml:math></inline-formula> <inline-formula id="ieqn-65"><mml:math id="mml-ieqn-65"><mml:mi>I</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> shows the average amount of data needed to identify the class label for each sample in S [<xref ref-type="bibr" rid="ref-18">18</xref>].</p>
<p>Consider <inline-formula id="ieqn-66"><mml:math id="mml-ieqn-66"><mml:mi>A</mml:mi></mml:math></inline-formula> attribute has <inline-formula id="ieqn-67"><mml:math id="mml-ieqn-67"><mml:mi>v</mml:mi></mml:math></inline-formula> distinct values <inline-formula id="ieqn-68"><mml:math id="mml-ieqn-68"><mml:mo fence="false" stretchy="false">{</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>&#x03BD;</mml:mi></mml:mrow></mml:msub><mml:mo fence="false" stretchy="false">}</mml:mo></mml:math></inline-formula> from the trained data set, S. When <inline-formula id="ieqn-69"><mml:math id="mml-ieqn-69"><mml:mi>A</mml:mi></mml:math></inline-formula> represents a nominal attribute, the attributes split <inline-formula id="ieqn-70"><mml:math id="mml-ieqn-70"><mml:mi>S</mml:mi></mml:math></inline-formula> to <inline-formula id="ieqn-71"><mml:math id="mml-ieqn-71"><mml:mi>v</mml:mi></mml:math></inline-formula> subset as <inline-formula id="ieqn-72"><mml:math id="mml-ieqn-72"><mml:mo fence="false" stretchy="false">{</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>&#x03BD;</mml:mi></mml:mrow></mml:msub><mml:mo fence="false" stretchy="false">}</mml:mo></mml:math></inline-formula>, where <inline-formula id="ieqn-73"><mml:math id="mml-ieqn-73"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> indicates the subsets of <inline-formula id="ieqn-74"><mml:math id="mml-ieqn-74"><mml:mi>S</mml:mi></mml:math></inline-formula> in which the samples in <inline-formula id="ieqn-75"><mml:math id="mml-ieqn-75"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> have the similar attribute value <inline-formula id="ieqn-76"><mml:math id="mml-ieqn-76"><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> on <inline-formula id="ieqn-77"><mml:math id="mml-ieqn-77"><mml:mi>A</mml:mi></mml:math></inline-formula>. But, the sample in <inline-formula id="ieqn-78"><mml:math id="mml-ieqn-78"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> might have distinct class labels. Consider <inline-formula id="ieqn-79"><mml:math id="mml-ieqn-79"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> to represent a set of samples with class label being <inline-formula id="ieqn-80"><mml:math id="mml-ieqn-80"><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> in the subsets of <inline-formula id="ieqn-81"><mml:math id="mml-ieqn-81"><mml:mo fence="false" stretchy="false">{</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mi>A</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:math></inline-formula> <inline-formula id="ieqn-82"><mml:math id="mml-ieqn-82"><mml:mi>j</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:math></inline-formula> <inline-formula id="ieqn-83"><mml:math id="mml-ieqn-83"><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo></mml:math></inline-formula> <inline-formula id="ieqn-84"><mml:math id="mml-ieqn-84"><mml:mi>&#x03BD;</mml:mi><mml:mo>,</mml:mo></mml:math></inline-formula> <inline-formula id="ieqn-85"><mml:math id="mml-ieqn-85"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2208;</mml:mo><mml:mi>S</mml:mi><mml:mo fence="false" stretchy="false">}</mml:mo></mml:math></inline-formula> whereas attribute <inline-formula id="ieqn-86"><mml:math id="mml-ieqn-86"><mml:mi>A</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>. The required data amount of attribute <inline-formula id="ieqn-87"><mml:math id="mml-ieqn-87"><mml:mi>A</mml:mi></mml:math></inline-formula> splits the trained data set <inline-formula id="ieqn-88"><mml:math id="mml-ieqn-88"><mml:mi>S</mml:mi></mml:math></inline-formula> which is estimated as follows.</p>
<p><disp-formula id="eqn-10"><label>(10)</label><mml:math id="mml-eqn-10" display="block"><mml:mi>E</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>A</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:munderover><mml:mo>&#x2211;</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>&#x03BD;</mml:mi></mml:mrow></mml:munderover><mml:mo stretchy="false">(</mml:mo><mml:mfrac><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>+</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mi>s</mml:mi></mml:mfrac><mml:mo>&#x00D7;</mml:mo><mml:mi>I</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:math></disp-formula></p>
<p>The less data amount needed; the more purity of sub-data set is.</p>
<p><disp-formula id="eqn-11"><label>(11)</label><mml:math id="mml-eqn-11" display="block"><mml:mi>I</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mo>&#x2212;</mml:mo><mml:munderover><mml:mo>&#x2211;</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:munderover><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>log</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2061;</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:math></disp-formula></p>
<p>While <inline-formula id="ieqn-89"><mml:math id="mml-ieqn-89"><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> denotes the probability of samples in <inline-formula id="ieqn-90"><mml:math id="mml-ieqn-90"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> that belongs to the class <inline-formula id="ieqn-91"><mml:math id="mml-ieqn-91"><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>.</mml:mo></mml:math></inline-formula> <inline-formula id="ieqn-92"><mml:math id="mml-ieqn-92"><mml:mi>I</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> implies the average number of data required to identify the class labels for each instance in <inline-formula id="ieqn-93"><mml:math id="mml-ieqn-93"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>. The data gain of <inline-formula id="ieqn-94"><mml:math id="mml-ieqn-94"><mml:mi>A</mml:mi></mml:math></inline-formula> is determined as follows.</p>
<p><disp-formula id="eqn-12"><label>(12)</label><mml:math id="mml-eqn-12" display="block"><mml:mrow><mml:mi mathvariant="italic">I</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">f</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">G</mml:mi><mml:mi mathvariant="italic">a</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">n</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>I</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>E</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula>viz., the number of new data needed minus the number of original data needed. Choose the attributes with maximal <inline-formula id="ieqn-95"><mml:math id="mml-ieqn-95"><mml:mrow><mml:mi mathvariant="italic">I</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">f</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">G</mml:mi><mml:mi mathvariant="italic">a</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">n</mml:mi></mml:mrow></mml:math></inline-formula> (A) as testing attributes that are allocated as internal node in a decision tree. In this method, the required amount of data to classify the samples is minimal.</p>
</sec>
</sec>
<sec id="s4">
<label>4</label>
<title>Experimental Results and Discussion</title>
<p>The experimental analysis was conducted upon the proposed IoTAD-SCI technique using UCSD dataset [<xref ref-type="bibr" rid="ref-19">19</xref>]. In this study, two testbeds namely, Test007 and Test005 were used for simulation and these datasets comprise a total of 360 frames with 12 s duration. <xref ref-type="fig" rid="fig-2">Fig. 2</xref> demonstrates the sample test images with ground truth of the anomalies that exist in the image.</p>
<fig id="fig-2">
<label>Figure 2</label>
<caption>
<title>Sample images (a and c) ground truth (b and d)</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_27327-fig-2a.png"/><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_27327-fig-2b.png"/>
</fig>
<p><xref ref-type="fig" rid="fig-3">Fig. 3</xref> visualizes the outcome of the proposed IoTAD-SCI technique on test image. From the figure, it can be understood that the presented IoTAD-SCI technique identified the presence of two anomalies namely &#x2018;bicycle and truck&#x2019; in an efficient manner.</p>
<fig id="fig-3">
<label>Figure 3</label>
<caption>
<title>Anomaly detected image</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_27327-fig-3.png"/>
</fig>
<p><xref ref-type="table" rid="table-1">Tab. 1</xref> provides the results of detection analysis accomplished by IoTAD-SCI technique on Test004 testbed. The results indicate that the presented IoTAD-SCI technique effectually identified all the anomalies with maximum accuracy. For instance, on 142 frames, IoTAD-SCI technique identified anomalies [<xref ref-type="bibr" rid="ref-1">1</xref>,<xref ref-type="bibr" rid="ref-2">2</xref>] with <inline-formula id="ieqn-96"><mml:math id="mml-ieqn-96"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> values such as 99.69% and 99.68% respectively. Likewise, on 146 frames, the presented IoTAD-SCI technique recognized the anomalies 1 and 2 with accuracy values such as 99.08% and 98.99% correspondingly. Moreover, on 179 frames, the proposed IoTAD-SCI technique categorized the anomalies [<xref ref-type="bibr" rid="ref-1">1</xref>,<xref ref-type="bibr" rid="ref-2">2</xref>] with <inline-formula id="ieqn-97"><mml:math id="mml-ieqn-97"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> values such as 99.86% and 99.78% respectively. At last, on 180 frames, IoTAD-SCI technique identified the anomalies [<xref ref-type="bibr" rid="ref-1">1</xref>,<xref ref-type="bibr" rid="ref-2">2</xref>] with <inline-formula id="ieqn-98"><mml:math id="mml-ieqn-98"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> values such as 99.76% and 99.91% correspondingly.</p>
<table-wrap id="table-1">
<label>Table 1</label>
<caption>
<title>Accuracy of anomalies in Test004 sequences</title>
</caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th>Frame number</th>
<th>Anomaly&#x00A0;1</th>
<th>Anomaly&#x00A0;2</th>
</tr>
</thead>
<tbody>
<tr>
<td>142</td>
<td>99.69</td>
<td>99.68</td>
</tr>
<tr>
<td>146</td>
<td>99.08</td>
<td>98.99</td>
</tr>
<tr>
<td>147</td>
<td>99.83</td>
<td>99.80</td>
</tr>
<tr>
<td>148</td>
<td>99.75</td>
<td>99.82</td>
</tr>
<tr>
<td>150</td>
<td>99.73</td>
<td>99.80</td>
</tr>
<tr>
<td>178</td>
<td>99.76</td>
<td>99.84</td>
</tr>
<tr>
<td>179</td>
<td>99.86</td>
<td>99.78</td>
</tr>
<tr>
<td>180</td>
<td>99.76</td>
<td>99.91</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>A brief comparative anomaly detection analysis was conducted between the proposed IoTAD-SCI technique and other methods and the results are shown in <xref ref-type="fig" rid="fig-4">Fig. 4</xref>. The outcomes report that the proposed IoTAD-SCI approach achieved effectual outcomes under all the frames. For instance, with 142 frames, IoTAD-SCI technique offered a high accuracy of 99.69% whereas DLAD, RSCNN, FRCNN, and MDT techniques obtained the least accuracy values namely, 99.37%, 98.49%, 93.21%, and 81.39%. Concurrently, with 180 frames, the proposed IoTAD-SCI technique achieved an increased accuracy of 99.84%, whereas DLAD, RSCNN, FRCNN, and MDT techniques reached low accuracy values such as 99.19%, 99.14%, 86.08%, and 85.84% respectively.</p>
<fig id="fig-4">
<label>Figure 4</label>
<caption>
<title>Accuracy analysis of IoTAD-SCI technique under test004 testbed</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_27327-fig-4.png"/>
</fig>
<p><xref ref-type="fig" rid="fig-5">Fig. 5</xref> highlights the ROC analysis results achieved by IoTAD-SCI technique on test004 testbed. The figure reports the enhanced anomaly detection outcomes of IoTAD-SCI technique with an increased ROC value of 99.9452.</p>
<fig id="fig-5">
<label>Figure 5</label>
<caption>
<title>ROC analysis of IoTAD-SCI technique under test004 testbed</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_27327-fig-5.png"/>
</fig>
<p><xref ref-type="table" rid="table-2">Tab. 2</xref> offers the results of detection analysis accomplished by IoTAD-SCI approach on Test007 testbed. The results indicate that the proposed IoTAD-SCI technique effectually identified all the anomalies with maximum accuracy. For instance, on 040 frames, IoTAD-SCI methodology identified the anomalies [<xref ref-type="bibr" rid="ref-1">1</xref>,<xref ref-type="bibr" rid="ref-2">2</xref>] with <inline-formula id="ieqn-99"><mml:math id="mml-ieqn-99"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> values such as 98.47% and 98.47% correspondingly. Besides, on 075 frames, IoTAD-SCI algorithm recognized the anomalies [<xref ref-type="bibr" rid="ref-1">1</xref>,<xref ref-type="bibr" rid="ref-2">2</xref>] with <inline-formula id="ieqn-100"><mml:math id="mml-ieqn-100"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> values being 96.49% and 96.59% correspondingly. Furthermore, on 135 frames, the proposed IoTAD-SCI technique categorized the anomalies [<xref ref-type="bibr" rid="ref-1">1</xref>,<xref ref-type="bibr" rid="ref-2">2</xref>] with the accuracy values such as 99.75% and 99.67% respectively. Eventually, on 180 frames, IoTAD-SCI approach identified the anomalies 1 and 2 with <inline-formula id="ieqn-101"><mml:math id="mml-ieqn-101"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> values such as 89.68% and 89.65% correspondingly.</p>
<table-wrap id="table-2">
<label>Table 2</label>
<caption>
<title>Accuracy of anomalies in Test007 Sequences</title>
</caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th>Frame number</th>
<th>Anomaly&#x00A0;1</th>
<th>Anomaly&#x00A0;2</th>
</tr>
</thead>
<tbody>
<tr>
<td>040</td>
<td>98.47</td>
<td>98.47</td>
</tr>
<tr>
<td>051</td>
<td>98.95</td>
<td>99.09</td>
</tr>
<tr>
<td>075</td>
<td>96.49</td>
<td>96.59</td>
</tr>
<tr>
<td>106</td>
<td>88.99</td>
<td>89.00</td>
</tr>
<tr>
<td>123</td>
<td>99.56</td>
<td>99.86</td>
</tr>
<tr>
<td>135</td>
<td>99.75</td>
<td>99.67</td>
</tr>
<tr>
<td>158</td>
<td>95.89</td>
<td>95.84</td>
</tr>
<tr>
<td>180</td>
<td>89.68</td>
<td>89.65</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>A detailed comparative anomaly detection analysis was conducted upon IoTAD-SCI approach against other techniques and the results are shown in <xref ref-type="fig" rid="fig-6">Fig. 6</xref>. The outcomes demonstrate that the proposed IoTAD-SCI system produced effective outcomes under all the frames. For sample, with 042 frames, the presented IoTAD-SCI technique offered a high accuracy of 98.47%, whereas DLAD, RSCNN, FRCNN, and MDT techniques attained the minimal accuracy values namely, 97.52%, 94.62%, 89.98%, and 85.17% respectively. In addition, with 180 frames, IoTAD-SCI approach offered a maximum accuracy of 89.67%, whereas DLAD, RSCNN, FRCNN, and MDT methodologies reached low accuracy values such as 88.58%, 83.65%, 81.65%, and 80.88% correspondingly.</p>
<fig id="fig-6">
<label>Figure 6</label>
<caption>
<title>Accuracy analysis of IoTAD-SCI technique under test007 testbed</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_27327-fig-6.png"/>
</fig>
<p><xref ref-type="fig" rid="fig-7">Fig. 7</xref> demonstrates the ROC analysis graph generated by IoTAD-SCI approach upon test007 testbed. The figure reveals the improved anomaly detection outcomes of IoTAD-SCI approach with a maximum ROC of 99.9452.</p>
<fig id="fig-7">
<label>Figure 7</label>
<caption>
<title>ROC analysis of IoTAD-SCI technique under test007 testbed</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_27327-fig-7.png"/>
</fig>
<p><xref ref-type="fig" rid="fig-8">Figs. 8</xref> and <xref ref-type="fig" rid="fig-9">9</xref> show the average anomaly detection outcomes of the presented IoTAD-SCI technique against recent methods on two testbeds. The figure reports that the proposed IoTAD-SCI technique has the ability to effectively identify the anomalies on both testbeds. For instance, with Test004 testbed, IoTAD-SCI technique reached a high average accuracy value i.e., 99.70% whereas DLAD, RSCNN, FRCNN, and MDT techniques obtained low average accuracy values such as 99.22%, 98.84%, 86.60%, and 81.27% respectively. Similarly, with Test007 testbed, the proposed IoTAD-SCI technique reached an increased average accuracy of 96%, whereas DLAD, RSCNN, FRCNN, and MDT techniques achieved low average accuracy values namely, 95.01%, 91.84%, 88.34%, and 84.03%.</p>
<fig id="fig-8">
<label>Figure 8</label>
<caption>
<title>Average accuracy analysis results of IoTAD-SCI technique under test004 testbed</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_27327-fig-8.png"/>
</fig>
<fig id="fig-9">
<label>Figure 9</label>
<caption>
<title>Average accuracy analysis results of IoTAD-SCI technique under test007 testbed</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_27327-fig-9.png"/>
</fig>
<p>Finally, running time analysis was conducted between the proposed IoTAD-SCI system and the existing models and the results are shown in <xref ref-type="table" rid="table-3">Tab. 3</xref> and <xref ref-type="fig" rid="fig-10">Fig. 10</xref> [<xref ref-type="bibr" rid="ref-20">20</xref>&#x2013;<xref ref-type="bibr" rid="ref-22">22</xref>]. The results demonstrate that the presented IoTAD-SCI technique required minimal running time compared to other techniques. For instance, with Test004 testbed, the IoTAD-SCI technique offered a minimum running time of 10.159 s, whereas DLAD, RSCNN, FRCNN, and MDT techniques demanded the maximum running times such as 10.825, 12.355, 12.403 and 12.463 s respectively. At the same time, with Test007 testbed, the proposed IoTAD-SCI technique produced a low running time of 10.504s, whereas DLAD, RSCNN, FRCNN, and MDT techniques attained a maximum running time of 11.043, 11.480, 11.876 and 12.000 s respectively. Based on the results and discussion made above, it can be understood that the proposed IoTAD-SCI technique is superior compared to existing techniques.</p>
<table-wrap id="table-3">
<label>Table 3</label>
<caption>
<title>Running time analysis results of IoTAD-SCI technique against existing methods</title>
</caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th colspan="3" align="center">Running time (sec)</th>
</tr>
</thead>
<tbody>
<tr>
<td>Methods</td>
<td>Test004</td>
<td>Test007</td>
</tr>
<tr>
<td>IOTAD-SCI</td>
<td>10.159</td>
<td>10.504</td>
</tr>
<tr>
<td>DLAD Model</td>
<td>10.825</td>
<td>11.043</td>
</tr>
<tr>
<td>RSCNN</td>
<td>12.355</td>
<td>11.480</td>
</tr>
<tr>
<td>FRCNN Model</td>
<td>12.403</td>
<td>11.876</td>
</tr>
<tr>
<td>MDT Model</td>
<td>12.463</td>
<td>12.000</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="fig-10">
<label>Figure 10</label>
<caption>
<title>Running time analysis of IoTAD-SCI technique with recent algorithms</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_27327-fig-10.png"/>
</fig>
</sec>
<sec id="s5">
<label>5</label>
<title>Conclusion</title>
<p>In current study, an effective IoTAD-SCI technique has been developed to identify the presence of anomalies in smart city environment. The proposed IoTAD-SCI technique involves the design of DCN technique to detect the anomalies from input video frames. Followed by, AOA is applied to fine tune the hyperparameters of DCN technique whereas ID3 classifier is utilized to classify the identified objects under different classes. The experimental analysis results of IoTAD-SCI technique against the benchmark UCSD anomaly detection dataset were inspected under different measures. The simulation outcomes infer the superiority of the proposed IoTAD-SCI technique under different metrics compared to other recent approaches. As a part of future work, IoTAD-SCI technique can be realized in real time environment.</p>
</sec>
</body>
<back>
<ack>
<p>The authors extend their appreciation to the Deputyship for Research &#x0026; Innovation, Ministry of Education in Saudi Arabia for funding this research work through the project number (IFPIP-1308-612-1442) and King Abdulaziz University, DSR, Jeddah, Saudi Arabia.</p>
</ack>
<fn-group>
<fn fn-type="other"><p><bold>Funding Statement:</bold> This project was supported financially by Institution Fund projects under grant no. (IFPIP-1308-612-1442).</p>
</fn>
<fn fn-type="conflict"><p><bold>Conflicts of Interest:</bold> The authors declare that they have no conflicts of interest to report regarding the present study.</p>
</fn>
</fn-group>
<ref-list content-type="authoryear">
<title>References</title>
<ref id="ref-1"><label>[1]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>Q.</given-names> <surname>Sun</surname></string-name>, <string-name><given-names>H.</given-names> <surname>Liu</surname></string-name> and <string-name><given-names>T.</given-names> <surname>Harada</surname></string-name></person-group>, &#x201C;<article-title>Online growing neural gas for anomaly detection in changing surveillance scenes</article-title>,&#x201D; <source>Pattern Recognition</source>, vol. <volume>64</volume>, no. <issue>3</issue>, pp. <fpage>187</fpage>&#x2013;<lpage>201</lpage>, <year>2017</year>.</mixed-citation></ref>
<ref id="ref-2"><label>[2]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>X. R.</given-names> <surname>Zhang</surname></string-name>, <string-name><given-names>X.</given-names> <surname>Sun</surname></string-name>, <string-name><given-names>X. M.</given-names> <surname>Sun</surname></string-name>, <string-name><given-names>W.</given-names> <surname>Sun</surname></string-name> and <string-name><given-names>S. K.</given-names> <surname>Jha</surname></string-name></person-group>, &#x201C;<article-title>Robust reversible audio watermarking scheme for telemedicine and privacy protection</article-title>,&#x201D; <source>Computers Materials &#x0026; Continua</source>, vol. <volume>71</volume>, no. <issue>2</issue>, pp. <fpage>3035</fpage>&#x2013;<lpage>3050</lpage>, <year>2022</year>.</mixed-citation></ref>
<ref id="ref-3"><label>[3]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>T.</given-names> <surname>Xiao</surname></string-name>, <string-name><given-names>C.</given-names> <surname>Zhang</surname></string-name> and <string-name><given-names>H.</given-names> <surname>Zha</surname></string-name></person-group>, &#x201C;<article-title>Learning to detect anomalies in surveillance video</article-title>,&#x201D; <source>IEEE Signal Processing Letters</source>, vol. <volume>22</volume>, no. <issue>9</issue>, pp. <fpage>1477</fpage>&#x2013;<lpage>1481</lpage>, <year>2015</year>.</mixed-citation></ref>
<ref id="ref-4"><label>[4]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>X. R.</given-names> <surname>Zhang</surname></string-name>, <string-name><given-names>W. F.</given-names> <surname>Zhang</surname></string-name>, <string-name><given-names>W.</given-names> <surname>Sun</surname></string-name>, <string-name><given-names>X. M.</given-names> <surname>Sun</surname></string-name> and <string-name><given-names>S. K.</given-names> <surname>Jha</surname></string-name></person-group>, &#x201C;<article-title>A robust 3-D medical watermarking based on wavelet transform for data protection</article-title>,&#x201D; <source>Computer Systems Science &#x0026; Engineering</source>, vol. <volume>41</volume>, no. <issue>3</issue>, pp. <fpage>1043</fpage>&#x2013;<lpage>1056</lpage>, <year>2022</year>.</mixed-citation></ref>
<ref id="ref-5"><label>[5]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>S.</given-names> <surname>Biswas</surname></string-name> and <string-name><given-names>V.</given-names> <surname>Gupta</surname></string-name></person-group>, &#x201C;<article-title>Abnormality detection in crowd videos by tracking sparse components</article-title>,&#x201D; <source>Machine Vision and Applications</source>, vol. <volume>28</volume>, no. <issue>1&#x2013;2</issue>, pp. <fpage>35</fpage>&#x2013;<lpage>48</lpage>, <year>2017</year>.</mixed-citation></ref>
<ref id="ref-6"><label>[6]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>I. R.</given-names> <surname>de Almeida</surname></string-name>, <string-name><given-names>V. J.</given-names> <surname>Cassol</surname></string-name>, <string-name><given-names>N. I.</given-names> <surname>Badler</surname></string-name>, <string-name><given-names>S. R.</given-names> <surname>Musse</surname></string-name> and <string-name><given-names>C. R.</given-names> <surname>Jung</surname></string-name></person-group>, &#x201C;<article-title>Detection of global and local motion changes in human crowds</article-title>,&#x201D; <source>IEEE Transactions on Circuits and Systems for Video Technology</source>, vol. <volume>27</volume>, no. <issue>3</issue>, pp. <fpage>603</fpage>&#x2013;<lpage>612</lpage>, <year>2017</year>.</mixed-citation></ref>
<ref id="ref-7"><label>[7]</label><mixed-citation publication-type="conf-proc"><person-group person-group-type="author"><string-name><given-names>A.</given-names> <surname>Li</surname></string-name>, <string-name><given-names>Z.</given-names> <surname>Miao</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Cen</surname></string-name> and <string-name><given-names>Q.</given-names> <surname>Liang</surname></string-name></person-group>, &#x201C;<article-title>Abnormal event detection based on sparse reconstruction in crowded scenes</article-title>,&#x201D; in <conf-name>2016 IEEE Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP)</conf-name>, Shanghai, China, pp. <fpage>1786</fpage>&#x2013;<lpage>1790</lpage>, <year>2016</year>. </mixed-citation></ref>
<ref id="ref-8"><label>[8]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>V. G.</given-names> <surname>Font</surname></string-name>, <string-name><given-names>C.</given-names> <surname>Garrigues</surname></string-name> and <string-name><given-names>H.</given-names> <surname>Rif&#x00E0;-Pous</surname></string-name></person-group>, &#x201C;<article-title>A comparative study of anomaly detection techniques for smart city wireless sensor networks</article-title>,&#x201D; <source>Sensors</source>, vol. <volume>16</volume>, no. <issue>6</issue>, pp. <fpage>868</fpage>, <year>2016</year>.</mixed-citation></ref>
<ref id="ref-9"><label>[9]</label><mixed-citation publication-type="conf-proc"><person-group person-group-type="author"><string-name><given-names>I.</given-names> <surname>Alrashdi</surname></string-name>, <string-name><given-names>A.</given-names> <surname>Alqazzaz</surname></string-name>, <string-name><given-names>E.</given-names> <surname>Aloufi</surname></string-name>, <string-name><given-names>R.</given-names> <surname>Alharthi</surname></string-name>, <string-name><given-names>M.</given-names> <surname>Zohdy</surname></string-name> <etal>et al.</etal></person-group><italic>,</italic> &#x201C;<article-title>sAD-IoT: Anomaly detection of IoT cyberattacks in smart city using machine learning</article-title>,&#x201D; in <conf-name>2019 IEEE 9th Annual Computing and Communication Workshop and Conf. (CCWC)</conf-name>, Las Vegas, NV, USA, pp. <fpage>305</fpage>&#x2013;<lpage>310</lpage>, <year>2019</year>. </mixed-citation></ref>
<ref id="ref-10"><label>[10]</label><mixed-citation publication-type="conf-proc"><person-group person-group-type="author"><string-name><given-names>S.</given-names> <surname>Chackravarthy</surname></string-name>, <string-name><given-names>S.</given-names> <surname>Schmitt</surname></string-name> and <string-name><given-names>L.</given-names> <surname>Yang</surname></string-name></person-group>, &#x201C;<article-title>Intelligent crime anomaly detection in smart cities using deep learning</article-title>,&#x201D; in <conf-name>2018 IEEE 4th Int. Conf. on Collaboration and Internet Computing (CIC)</conf-name>, <publisher-loc>Philadelphia, PA</publisher-loc>, pp. <fpage>399</fpage>&#x2013;<lpage>404</lpage>, <year>2018</year>. </mixed-citation></ref>
<ref id="ref-11"><label>[11]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>L.</given-names> <surname>Kang</surname></string-name>, <string-name><given-names>S.</given-names> <surname>Liu</surname></string-name>, <string-name><given-names>H.</given-names> <surname>Zhang</surname></string-name> and <string-name><given-names>D.</given-names> <surname>Gong</surname></string-name></person-group>, &#x201C;<article-title>Person anomaly detection-based videos surveillance system in urban integrated pipe gallery</article-title>,&#x201D; <source>Building Research &#x0026; Information</source>, vol. <volume>49</volume>, no. <issue>1</issue>, pp. <fpage>55</fpage>&#x2013;<lpage>68</lpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-12"><label>[12]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>D.</given-names> <surname>Chen</surname></string-name>, <string-name><given-names>P.</given-names> <surname>Wang</surname></string-name>, <string-name><given-names>L.</given-names> <surname>Yue</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Zhang</surname></string-name> and <string-name><given-names>T.</given-names> <surname>Jia</surname></string-name></person-group>, &#x201C;<article-title>Anomaly detection in surveillance video based on bidirectional prediction</article-title>,&#x201D; <source>Image and Vision Computing</source>, vol. <volume>98</volume>, pp. <fpage>103915</fpage>, <year>2020</year>.</mixed-citation></ref>
<ref id="ref-13"><label>[13]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>W.</given-names> <surname>Ullah</surname></string-name>, <string-name><given-names>A.</given-names> <surname>Ullah</surname></string-name>, <string-name><given-names>I. U.</given-names> <surname>Haq</surname></string-name>, <string-name><given-names>K.</given-names> <surname>Muhammad</surname></string-name>, <string-name><given-names>M.</given-names> <surname>Sajjad</surname></string-name> <etal>et al.</etal></person-group><italic>,</italic> &#x201C;<article-title>CNN features with bi-directional LSTM for real-time anomaly detection in surveillance networks</article-title>,&#x201D; <source>Multimedia Tools and Applications</source>, vol. <volume>80</volume>, no. <issue>11</issue>, pp. <fpage>16979</fpage>&#x2013;<lpage>16995</lpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-14"><label>[14]</label><mixed-citation publication-type="conf-proc"><person-group person-group-type="author"><string-name><given-names>T. Y.</given-names> <surname>Lin</surname></string-name>, <string-name><given-names>P.</given-names> <surname>Dollar</surname></string-name>, <string-name><given-names>R.</given-names> <surname>Girshick</surname></string-name>, <string-name><given-names>K.</given-names> <surname>He</surname></string-name>, <string-name><given-names>B.</given-names> <surname>Hariharan</surname></string-name> <etal>et al.</etal></person-group><italic>,</italic> &#x201C;<article-title>Feature pyramid networks for object detection</article-title>,&#x201D; in <conf-name>2017 IEEE Conf. on Computer Vision and Pattern Recognition (CVPR)</conf-name>, <publisher-loc>Honolulu, HI</publisher-loc>, pp. <fpage>936</fpage>&#x2013;<lpage>944</lpage>, <year>2017</year>. </mixed-citation></ref>
<ref id="ref-15"><label>[15]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>T.</given-names> <surname>Wollmann</surname></string-name> and <string-name><given-names>K.</given-names> <surname>Rohr</surname></string-name></person-group>, &#x201C;<article-title>Deep consensus network: Aggregating predictions to improve object detection in microscopy images</article-title>,&#x201D; <source>Medical Image Analysis</source>, vol. <volume>70</volume>, no. <issue>4</issue>, pp. <fpage>102019</fpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-16"><label>[16]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>L.</given-names> <surname>Abualigah</surname></string-name>, <string-name><given-names>A.</given-names> <surname>Diabat</surname></string-name>, <string-name><given-names>S.</given-names> <surname>Mirjalili</surname></string-name>, <string-name><given-names>M. A.</given-names> <surname>Elaziz</surname></string-name> and <string-name><given-names>A. H.</given-names> <surname>Gandomi</surname></string-name></person-group>, &#x201C;<article-title>The arithmetic optimization algorithm</article-title>,&#x201D; <source>Computer Methods in Applied Mechanics and Engineering</source>, vol. <volume>376</volume>, no. <issue>2</issue>, pp. <fpage>113609</fpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-17"><label>[17]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>A.</given-names> <surname>Ewees</surname></string-name>, <string-name><given-names>M. A. A.</given-names> <surname>Al-qaness</surname></string-name>, <string-name><given-names>L.</given-names> <surname>Abualigah</surname></string-name>, <string-name><given-names>D.</given-names> <surname>Oliva</surname></string-name>, <string-name><given-names>Z. Y.</given-names> <surname>Algamal</surname></string-name> <etal>et al.</etal></person-group><italic>,</italic> &#x201C;<article-title>Boosting arithmetic optimization algorithm with genetic algorithm operators for feature selection: Case study on cox proportional hazards model</article-title>,&#x201D; <source>Mathematics</source>, vol. <volume>9</volume>, no. <issue>18</issue>, pp. <fpage>2321</fpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-18"><label>[18]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>S.</given-names> <surname>Yang</surname></string-name>, <string-name><given-names>J. Z.</given-names> <surname>Guo</surname></string-name> and <string-name><given-names>J. W.</given-names> <surname>Jin</surname></string-name></person-group>, &#x201C;<article-title>An improved Id3 algorithm for medical data classification</article-title>,&#x201D; <source>Computers &#x0026; Electrical Engineering</source>, vol. <volume>65</volume>, no. <issue>4</issue>, pp. <fpage>474</fpage>&#x2013;<lpage>487</lpage>, <year>2018</year>.</mixed-citation></ref>
<ref id="ref-19"><label>[19]</label><mixed-citation publication-type="other"><uri>http://www.svcl.ucsd.edu/projects/anomaly/dataset.htm</uri>.</mixed-citation></ref>
<ref id="ref-20"><label>[20]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>I. V.</given-names> <surname>Pustokhina</surname></string-name>, <string-name><given-names>D. A.</given-names> <surname>Pustokhin</surname></string-name>, <string-name><given-names>T.</given-names> <surname>Vaiyapuri</surname></string-name>, <string-name><given-names>D.</given-names> <surname>Gupta</surname></string-name>, <string-name><given-names>S.</given-names> <surname>Kumar</surname></string-name> <etal>et al.</etal></person-group><italic>,</italic> &#x201C;<article-title>An automated deep learning based anomaly detection in pedestrian walkways for vulnerable road users safety</article-title>,&#x201D; <source>Safety Science</source>, vol. <volume>142</volume>, no. <issue>11</issue>, pp. <fpage>105356</fpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-21"><label>[21]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>M.</given-names> <surname>Xu</surname></string-name>, <string-name><given-names>X.</given-names> <surname>Yu</surname></string-name>, <string-name><given-names>D.</given-names> <surname>Chen</surname></string-name>, <string-name><given-names>C.</given-names> <surname>Wu</surname></string-name> and <string-name><given-names>Y.</given-names> <surname>Jiang</surname></string-name></person-group>, &#x201C;<article-title>An efficient anomaly detection system for crowded scenes using variational autoencoders</article-title>,&#x201D; <source>Applied Sciences</source>, vol. <volume>9</volume>, no. <issue>16</issue>, pp. <fpage>3337</fpage>, <year>2019</year>.</mixed-citation></ref>
<ref id="ref-22"><label>[22]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>B. S.</given-names> <surname>Murugan</surname></string-name>, <string-name><given-names>M.</given-names> <surname>Elhoseny</surname></string-name>, <string-name><given-names>K.</given-names> <surname>Shankar</surname></string-name> and <string-name><given-names>J.</given-names> <surname>Uthayakumar</surname></string-name></person-group>, &#x201C;<article-title>Region-based scalable smart system for anomaly detection in pedestrian walkways</article-title>,&#x201D; <source>Computers &#x0026; Electrical Engineering</source>, vol. <volume>75</volume>, no. <issue>3</issue>, pp. <fpage>146</fpage>&#x2013;<lpage>160</lpage>, <year>2019</year>.</mixed-citation></ref>
</ref-list>
</back>
</article>
