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\begin{frontmatter}

\title{Beetle Swarm-based Multi Verse Optimization for the Autism Spectrum Disorder Detection via EEG Signal Analysis: A Novel Hybrid Deep Learning Concept 
}
% Title, preferably not more than 10 words.



\author[First]{K. Nagendran} 
\author[Second]{E. Mohanraj} 


\address[First]{Information and Communication Engineering, Anna University, Chennai.).}
\address[Second]{Department of Computer Science and Engineering,K.S. Rangasamy College of Technology, Tiruchengode, Namakkal, Tamil Nadu, India
)}(nagendrankcse@gmail.com , mohanrajcse1982@gmail.com)


\begin{abstract}                % Abstract of 50--100 words
children having ASD from those who were typically developing without reaching the severity of their autistic traits. Using EEG research to identify possible variations among children having mild and severe ASD is a serious challenge. Hence, this paper plans to detect the ASD via the EEG signal processing and analysis. The dataset is first gathered from the ASD dataset. After that, median filtering and normalization are used to complete the pre-processing. The signals are then transformed to images using the STFT method. GLCM is used to extract features from the transformed images. Because the retrieved features are long, PCA is used to pick significant features. The categorization is done using a hybrid deep learning model based on these ideally picked features. SVM takes the place of CNN's fully connected layer in this case. Novel BS-MVO by merging BSO and MVO optimizes the learning rate in CNN and iteration in SVM with the goal of accuracy maximization as the fitness or objective function, resulting in enhanced CNN. The final output is classified using this enhanced CNN. The accuracy of the proposed BS-MVO at 90\% learning percentage is higher with 94.49\% in comparison to GA with 92.90\%, WOA with 89.99\%, MVO with 93.91\%, and BSO with 91.60\% respectively.  Simulation findings demonstrate the superiority of the proposed method by comparing with traditional methods in terms of various measures.
\end{abstract}

\begin{keyword}
autism spectrum disorder; EEG Signal Analysis; Novel Hybrid Deep Learning Model; Beetle Swarm-based Multi Verse Optimization
\end{keyword}

\end{frontmatter}
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\section{Introduction}
The ability to describe and diagnose a variety of neurological illnesses has been demonstrated by representing the brain's information processing systems as a huge network \cite{Ibrahim2018}. ASDs are one instance of abnormalities in this network's normal operation \cite{Sheikhani2012}. The existence of compulsive movements of narrow impairment and interests in socio-communicative capabilities are the basic signs of an ASD \cite{Sheikhani2008}. Because ASDs represent a wider range of illnesses rather than a singular diagnosis, treatment must be tailored to every kid individually. For determining the success of a therapy, one should preferably depend on objective metrics that quantitatively represent physiological variations in the brain \cite{Ahmadlou2012}. Presently, the success of a therapy is determined by behavioral method (i.e., seeing if any change happens as a result of the treatment), which is susceptible to subjective assessment and hence may add systematic bias \cite{Alhaddad2012}. DTI, resting-state fMRI, fMRI, or EEG have all been used to measure the impact of intensive behavioral therapy on the function and brain structure of ASD patients \cite{Vissers2012}. This explains how brain connection analysis might be employed to provide a group of objective measurements for defining an autistic child's true patho physiological condition. 

When choosing an imaging approach, it is critical for knowing the basic processes of illnesses like ASD \cite{Fan2015}. As a result, the knowledge on brain networks offered by fMRI is inadequate for a complete and appropriate characterization, necessitating the use of EEG data \cite{Billeci2016}. True ubiquitous EEG systems, like the ENOBIO system, have recently appeared, including wireless data transfer and dry electrodes. This enables EEG recorded as much as needed at home \cite{Ahmadlou2012b}. Nevertheless, there are no convergent results, necessitating a multimodal investigation to establish a technique that may disclose network alterations comparable to those discovered by DTI or fMRI \cite{Bosl2011}. Prior research, on the other hand, was confined to just distinguishing children having autism from those who were developing normally on the basis of the ASD - (DSM) and without considering the symptoms\cite{Alsaggaf2014}. Even though the DSM defines the gold standard for distinguishing children having autism from those who are normally developing, earlier studies have suggested that much socio-behavioral scales, like the CARS or the ATEC, be used instead \cite{Jamal2014}. Furthermore \cite{Kang2020b}, it is critical to investigate a variety of analytic approaches. Since EEG signals contain both non stationary and nonlinear characteristics, a novel approach on the basis of EMD, SODP, and ellipse area was developed to evaluate non stationary and nonlinear EEG signals\cite{Kana2011}. The novel SODP and EMD approach has been shown to be quite helpful in distinguishing among several non-neurological and neurological illnesses, although it has yet to be used to ASD \cite{Dawson2012}. 

This article is summarized as Section II explains the related works; Section III describes the proposed model and pre-processing for ASD detection; Section IV discusses signal to image conversion and feature extraction for ASD detection; Section V elucidates hybrid deep learning model-based EEG signal processing for ASD detection with results and discussion in Section VI and Section VII concludes with future work.

\section{LITERATURE SURVEY}

In 2018, Cociu et al. \cite{Cociu2018} have developed a unique method for characterizing an autistic brain by combining several neuro imaging methods. Various methodologies have historically been utilized to know the neurobiological basis of ASD using a multimodal or combined technique of fMRI, EEG, and DTI. Here, we look at how only those can reveal the information shared by the two. Initially, source localization from EEG was performed utilizing ICA and dipole fitting. This enables time changing to be estimated using EEG's high temporal resolution. The predicted functional connection among two active areas can be associated according to the findings. This defines an initial step toward employing ubiquitous EEG without having to do costly DTI or fMRI studies on a regular basis. 

In 2021, Alturki et al.\cite{Alturki2021} the examination and analysis of EEGs has been employed to diagnose epilepsy and ASDs. Artifacts were eliminated from EEG datasets employing ICA, while noise and interference were eliminated utilizing a fifth-order band-pass Butterworth filter. Then, employing a CSP, novel approaches were employed to extract the characteristics of EEGs. The usage of variance in traditional CSP is well recognized. Nevertheless, to extract features from EEGs, the usage of energy, entropy, and band power having CSP was recommended. Furthermore, in the study, four classification approaches were used: LDA, SVM, KNN, and ANN, with the goal of evaluating the techniques and selecting the best combination for ASD and epilepsy diagnosis. Furthermore, we looked at the impacts of frequency band, segment length, and reduction count on the findings. The suggested approaches were tested using two EEG datasets. 

In 2020, Ghahari et al. \cite{Ghahari2020} youngsters having autism and healthy children had their resting-state EEG data compared. The functional connectivity was calculated using the dDTF approach. The directed temporal network metrics were established and employed to measure the functional brain connections in the frequency bands. The findings revealed that every one among the global measurements was successful in establishing a substantial difference. In the entire groups, the burstiness differed across complete frequency ranges. In every group, the important nodes and edges were also identified. In the Alpha, Beta1, Delta, and Theta bands, the count of important bursty was lower than in the healthy group. 

In 2021, Shillington and Capal \cite{Shillington2021} in children having abnormal EEGs and ASD, the genetic test technique was investigated. Data was gathered from the medical records of an earlier reported cohort of kids with very well ASD who were evaluated by Developmental Pediatrics at CCHMC. ASD without epilepsy but having aberrant EEG data was split into two groups: ASD with epilepsy and ASD without epilepsy. Data on EEG was extracted from reports. We investigated genetic testing data in this follow-up research, specifically the percentage of this cohort. 

In 2021, Lavanga et al. \cite{Lavanga2021} have looked at the ability of early-life EEG backdrop anomalies or "dysmature" qualities to forecast ASD or neuro developmental success in newborns with TSC. During the EPISTOP experiment, EEG data from TSC patients were obtained continuously (NCT02098759). Neuro developmental performance and ASD risk were measured at the age of two years in subjects who were less than four months. MSE, MFA were used to assess the EEG at the initial visit. Applying LDA, these characteristics were linked to both abnormal Bayley and ASD outcomes in the babies. 

In 2020, Vettori et al.\cite{Vettori2020} to resolve this concern, researcher observed eye tracking and EEG. While both groups had stronger frequency-tagged neural activity to features than to concurrently displayed homes, this impact was substantially higher. After 5 seconds of sensory stimulation, there exists a substantial variation in group sensitivity of social vs non-social processing, which persists all via the experiment. Eye tracking as well as EEG values were substantially associated. We suggest that frequency-tagging EEG offered a quick, objective, and computed the real of reduced desire for social information in ASD by permitting tracking of both hidden and overt processes. 

In 2019, Hadoush et al. \cite{Hadoush2019} have utilized EEG analysis and EMD and SODP methods. The IMFs features, elliptical area, SODP patterns, and CTM values were identified using EMD research on their EEG data. The accuracy of this method's primary finding in discriminating among the two ASD groups was then determined using an ANN. 

In 2018, Capal et al. \cite{Capal2018} have discovered a link among seizures and/or abnormalities in EEG data, as well as disease-related deficits in children having ASD. Data was gathered from the medical records of kids having well-defined ASD at CCHMC. The assessments included formative (MSEL), as well as medications, developmental and birth histories, and medical comorbidities. The existence, type, and location of anomalies in EEG data were extracted from reports. 

In 2020, Abdolzadegan et al.\cite{Abdolzadegan2020} the goal of this study was to offer a reliable approach for detecting ASD early in the EEG data. Some of the nonlinear and linear properties were used to describe the EEG signal in the suggested method. Furthermore, for artefact removal and resilience, Density-oriented Clustering was used. Furthermore, other criteria like IG, MI, mRMR, and GA are used to pick features. For the final choice, the KNN and SVM classifiers were utilized. As a consequence, the inquiry found that the strategy employing SVM has a classification accuracy of 90.57 percent, whereas KNN has a classification accuracy of 72.77 percent. Furthermore, the suggested technique has a sensitivity of 99.91 percent for SVM and 91.96 percent for KNN. Experiments also reveal that DFA, Entropy, LE, and SL characteristics contained a significant impact on classification accuracy. 

In 2020, Kang et al. \cite{Kang2020} we employed characteristics collected from two modalities (eye-tracking and EEG) as input to SVM to identify autistic toddlers. The current study included 97 children ranging in age from 3 to 6. For the categorization of autistic vs generally functioning youngsters, the MRMR feature selection approach was paired with SVM classifiers.

The findings allow for the association of the anticipated functional relationship between two active zones. This outlines a first step towards using ubiquitous EEG without needing to regularly do expensive DTI or fMRI experiments. The results showed that every single worldwide measurement had been able to demonstrate a sizable difference. The burstiness varied across all frequency ranges in the full groupings. The number of significant bursts was lower than in the group of healthy people. We argue that by enabling the surveillance of both covert and overt activities, frequency-tagging EEG provided a rapid, accurate, and computed the actual of diminished need for social information in ASD. These impacts lead to develop a novel hybrid methodology together with intelligent deep learning models for the ASD detection via EEG signal. The major contributions of the work are,

\begin{itemize}
    \item To detect the ASD via the EEG signal processing and analysis using novel hybrid deep learning methodology.
    \item To perform the classification using enhanced CNN, where the fully connected layer of CNN is replaced by SVM and the learning rate in CNN and the iteration in SVM is optimized with the intention of accuracy maximization.
    \item To propose a novel form of optimization algorithm called BS-MVO for enhancing the classification phase of the developed EEG model and to compare the proposed model with existing methods to describe the superiority.
\end{itemize}

\section{PROPOSED MODEL AND PRE-PROCESSING FOR AUTISM SPECTRUM DISORDER DETECTION}
\begin{enumerate}[A]
    \item Proposed Model
\end{enumerate}

The proposed model mainly consists of six phases such as data collection, pre processing, signal to image conversion, feature extraction, optimal feature selection, and classification. First, the dataset is collected from ASD dataset. Next, the pre processing is accomplished using median filtering and normalization. Then, the signals are converted to image using STFT. From the converted images, the features are extracted employing GLCM. As the extracted features are lengthy, significant features are selected from it using PCA. From these optimally selected features, the classification is done using hybrid deep learning model. Here, the fully connected layer of CNN is replaced by SVM. The learning rate in CNN as well as iteration in SVM is optimized by BS-MVO with the intention of accuracy maximization as the fitness or objective function thus referred as enhanced CNN. This enhanced CNN classifies the final output. The developed model for the EEG signal-based autism spectrum disorder is shown in Fig. 1. 


\begin{figure}[htbp]
  \centering
  \includegraphics[width=5cm]{Picture1.png}
  \caption{Proposed architectural model for EEG signal-based ASD}
\end{figure}

\begin{enumerate}[B.]
    \item Pre processing
\end{enumerate}

The pre processing of the introduced ASD model is done by the median filtering and normalization techniques. 


\textbf{Median filtering:}The median filter\cite{Zhu2012}describes a statistically oriented nonlinear signal processing method. The median filtering result is $h(y, z) = \text{med}\{g(y - j \cdot z - k) \mid j, k \in X\}$where$(y, z),h(y, z)$respectively, describes the original as well as output images. The 2D mask is$X$: The mask size is $0×0$in which $O$ is usually odd); the mask form is square, linear, cross, circular, and so on. 

The statistical modelling of the median filter for the image having random noise is quite hard since it defines a nonlinear filter filter \cite{Chen1994}.

\begin{equation}
   \sigma_{\text {med }}^{2}=\frac{1}{4 \operatorname{cg}^{2} \overline{(o)}} \approx \frac{\sigma_{j}^{2}}{o+\frac{\pi}{2}-1} \cdot \frac{\pi}{\ddot{2}} 
\end{equation}
Here, $\sigma_{j}^{2}$ shows the variance linked with the input noise power, oshows the size linked with the median filtering mask, and $g(\bar{o})$ shows the noise density function. And the average filtering's noise variance is 
\begin{equation}
    \sigma_{0}^{2}=\frac{1}{o} \sigma_{j}^{2} 
\end{equation}
When comparing (1) and (2), the median filtering impacts are determined by two factors: the noise distribution and the mask size. \\
\textbf{Normalization \cite{Chen1994}\cite{Patro2015}:}Different forms of normalization exist. Min-Mix Normalization \cite{Peketi2023} [30] [31] [32] describes an approach that delivers linear transformation on an initial range of data. It is used to normalize data. 
\begin{equation}
\begin{split}
     B^{\prime}=\left(\frac{B-\min \text { value of } B}{\max \text { value of } B-\min \text { value of } B}\right) \\ *(E-D)+D 
     \end{split}
\end{equation}

Here, A' is a set of Min-Max Normalized data. If the predetermined border is [C, D], then If A shows the original data range and B shows the mapped data range, then Z-score Normalization \cite{Patro2015} \cite{Peketi2023} \cite{Sen2014} \cite{Eslami2019} defines the approach that delivers the normalized values or range of data from the original unstructured data utilizing notions such as standard deviation and mean. As a result, the unstructured data may be normalized employing the z-score parameter, as seen below: 


\begin{equation}
     w_{j}^{\prime}=\frac{w_{j}-\bar{F}}{\operatorname{std}(F)} 
\end{equation}
Here, $w_{j}$ shows the normalised Z-score one value. $w_{j}$defines the value of the $ j^{t h}$ column's row F. 
\begin{equation}
   \operatorname{std}(F)=\sqrt{\frac{1}{(o-1)} \sum_{j=1}^{o}\left(w_{j}-\bar{F}\right)^{2}} 
\end{equation}
The mean value is shown as follows.
\begin{equation}
   \bar{F}=\frac{1}{o} \sum_{j=1}^{o} w_{j} 
\end{equation}
Decimal Scaling \cite{peketi2023machine} \cite{sen2014comparative}\cite{eslami2019asd} \cite{craddock2012whole} represents the approach that offers the range among -1 and 1. As a result of the decimal scaling method,
\begin{equation}
 w^{j}=\frac{w}{10^{k}} 
\end{equation}


The scaled values are represented by $w^{j}$. The range of values is denoted by w.  The smallest integer is shown by $ k \cdot \operatorname{Max}\left(\left|w^{j}\right|\right)<1 $. 

\section{SIGNAL TO IMAGE ONVERSION AND FEATURE EXTRACTION FOR AUTISM SPECTRUM DISORDER DETECTION }

\begin{enumerate}[A]
    \item Signal to image conversion
\end{enumerate}

The signal is converted to image in this step by STFT. The Fourier transform linked with overlapping windowed chunks of a signal is called the STFT \cite{selesnick2009stft}. In this section, we calculate the perfect reconstruction condition for the window function, designated$\omega(0)$.  For $ o=0, \cdots, O-1 $ is considered to be supported (non-zero). The window in this case is a symmetric half-cycle sine window. The half-cycle sine window for Opoints is defined by 
\begin{equation}
     \omega(o)=\sin \left(\frac{\pi}{o}(o+0.5)\right), \quad o=0, \cdots, 0-1 
\end{equation}
The relocated windows have been moved by half their length.$ y(o) \cdot \omega(o-n \cdot 0 / 2) $ represents the $ n^{t h} $ thwindowed block of the signal $ y(o) . t(n, o) $ denotes the $n^{t h}$ windowed block: 
\begin{equation}
     t(n, o):=y(o) \cdot \omega(o-n \cdot 0 / 2) 
\end{equation}
Taking the DTFT of every windowed block yields the STFT: 
\begin{equation}
  T(n, \omega):=\operatorname{DTFT}\{y(o) \cdot \omega(o-n \cdot o / 2)\} 
\end{equation}
The STFT related with a discrete-time signal y(o)is specified by 
\begin{equation}
    T(n, \omega)=\operatorname{STFT}\{y(o)\} 
\end{equation}

\begin{enumerate}[B]
    \item Feature Extraction
\end{enumerate}

The features are extracted in the developed ASD model utilizing GLCM. The GLCM approach \cite{Craddock2012}describes a technique for obtaining statistical texture features linked with second order. The method has been applied in a variety of situations. The count of rows and columns in a GLCM matrix equals the count of grey levels $H$ in the image. The matrix member $Q(j, k \mid \Delta y, \Delta z)$represents the relative frequency, where two pixels spaced by a pixel distance$(\Delta y, \Delta z)$ , one having intensity $j$ and the other having intensity $k$, appear inside a specified neighbourhood. The second order statistical probability values for variations among grey levels $j$and $k$at a certain displacement distance $e$ and at a specific angle $(0)$ are contained in the matrix element onsider $g(n;o)$ 

be the intensity at sample$n$, line $o$of a $N$ x $o$ Oneighbourhood of an input image having $H$ grey levels ranging from 0 to H-1. Hence, 

\begin{equation}
     Q(j, k \mid \Delta y, \Delta z)=X R(j, k \mid \Delta y, \Delta z) 
\end{equation}
\\
\begin{equation}
     X=\frac{1}{(N-\Delta y)(O-\Delta z)} 
\end{equation}
\\
\begin{equation}
    R(j, k \mid \Delta y, \Delta z)=\sum_{o=1}^{O-\Delta z} \sum_{n=1}^{N-\Delta y} B 
\end{equation}
\\
\begin{equation}
     B=\left\{\begin{array}{c}1 \text { if } g(n, o)=j \text { and } g(n+\Delta y, o+\Delta z)=k \\ 0 \text { elsewhere }\end{array}\right. 
\end{equation}
Various features that are utilized are as below.\\\\
\textbf{Homogeneity, ASM:}It defines a metric for image uniformity. A homogenous image will have some grey levels, resulting in a GLCM having few but greater values $Q(j,k)$. As a result, the sum of squares would be large. 
\begin{equation}
   A S M=\sum_{j=0}^{H-1} \sum_{k=0}^{H-1}\{Q(j, k)\}^{2} 
\end{equation}
\textbf{Contrast:}$Q(j,k)$ contributions distant from the diagonal, $ j\neq k$, will be favoured by this metric of contrast or local intensity fluctuation. \\\\
\textbf{Local Homogeneity, IDM:}The uniformity of the image has an impact on IDM. IDM will receive minimal benefits from inhomogeneous locations $ j\neq k$ due to the weighting factor $\left(1+(j-k)^{2}\right)^{-1} $ . As a consequence, inhomogeneous images have a lower IDM value, whereas homogeneous images have a significantly greater value. 
\begin{equation}
    I D M=\sum_{j=0}^{H-1} \sum_{k=0}^{H-1} \frac{1}{1+(j-k)^{2}} Q(j, k) 
\end{equation}
\textbf{Entropy:}The entropy of inhomogeneous situations is small, whereas the entropy of homogeneous scenes is large. 
\begin{equation}
    Entropy =-\sum_{j=0}^{H-1} \sum_{k=0}^{H-1} Q(j, k) \times \log (Q(j, k)) 
\end{equation}
\textbf{Correlation:}The grey level linear dependency among the pixels at the given places relative to one another is measured via correlation. 
\begin{equation}
    Correlation  =\sum_{j=0}^{H-1} \sum_{k=0}^{H-1} \frac{\{j \times k\} \times Q(j, k)-\left\{\mu_{y} \times \mu_{z}\right\}}{\sigma_{y} \times \sigma_{z}} 
\end{equation}
\textbf{Sum of Squares, Variance:}This feature gives the items that deviate from the average value of $Q(j,k)a$ lot of weight.
\begin{equation}
    Variance =\sum_{j=0}^{H-1} \sum_{k=0}^{H-1}(j-\mu)^{2} Q(j, k) 
\end{equation}
\textbf{Sum Average:}
\begin{equation}
    Aver  =\sum_{j=0}^{2 H-2} j Q_{y+z}(j) 
\end{equation}
\textbf{Sum Entropy:}
\begin{equation}
    Sent  =-\sum_{j=0}^{2 H-2} Q_{y+z}(j) \log \left(Q_{y+z}(j)\right) 
\end{equation}
\textbf{Difference Entropy:}
\begin{equation}
    Dent =-\sum_{j=0}^{H-1} Q_{y+z}(j) \log \left(Q_{y+z}(j)\right) 
\end{equation}
\textbf{Inertia:}
\begin{equation}
    Inertia  =\sum_{j=0}^{H-1} \sum_{k=0}^{H-1}\{j-k\}^{2} \times Q(j, k) 
\end{equation}
\textbf{Cluster Shade:}
\begin{equation}
    Shade  =\sum_{j=0}^{H-1} \sum_{k=0}^{H-1}\left\{j+k-\mu_{y}-\mu_{z}\right\}^{3} \times Q(j, k) 
\end{equation}
\textbf{Cluster Prominence:}
\begin{equation}
    Prom  =\sum_{j=0}^{H-1} \sum_{k=0}^{H-1}\left\{j+k-\mu_{y}-\mu_{z}\right\}^{4} \times Q(j, k) 
\end{equation}


\begin{enumerate}[C]
    \item Optimal feature selection
\end{enumerate}

The optimal features are selected from the extracted features using PCA. PCA \cite{Selesnick2009} employs n×odimensional vectors to describe an image of size n×opixels and utilizes those vectors to compute the mean of vectors, which shows the average throughout all dimensions. The vector mean is removed from the entire vectors. The covariance matrix Ddefines the product matrix of the subtracted mean vector together with its transpose. It is written as follows: 

\begin{equation}
     D=Y^{\prime} Y^{\prime T} 
\end{equation}
Here, $ Y^{\prime} $ defines the subtracted mean data matrix, and the trained vectors are the column.  The covariance matrix is used to calculate the eigenvectors as well as eigen values. For Lvector, the eigenvectors having the greatest eigenvalue are chosen. Eigenfaces describes the names given to these eigenvectors. These eigenfaces are used to create the transformation matrix in a row fashion. The below equation may be used to determine the extracted feature, $z_j$ of the input data, $y_j$. 
\begin{equation}
    z_{j}=X\left(y_{j}-\bar{y}\right) 
\end{equation}
Here, $X$ denotes the transformation matrix and y denotes the data as well as its mean value. 

\section{HYBRID DEEP LEARNING MODEL-BASED EEG SIGNAL PROCESSING FOR AUTISM SPECTRUM DISORDER DETECTION}

\begin{enumerate}[A]
    \item CNN
\end{enumerate}
A typical CNN is made up of one or multiple convolutions as well as subsampling layers, followed by one or multiple fully connected layers, and finally an output layer. \\
Convolutional Layer: \\
The essential portion of a CNN \cite{Albregtsen2008} defines the convolutional layer (conv layer). In reality, images are usually static. That would be to say, the formation of one portion of the image is like the formation of any remaining part. As a result, a feature learned in one location may be used to match a pattern in another. We consider a tiny segment of a huge image and pass it via entire of the points in the large image (Input). We condense them into a single position when traveling through any location (Output). Filters are tiny sections of an image that pass across a larger image (Kernel). The back propagation approach is then used to construct the filters. 

Pooling or sub-sampling layer:

Down sampling associated with an image is referred to as pooling. It sub-samples a tiny section of the convolutional output as input to create a single output. There exist several pooling strategies available, like mean pooling, maximum pooling, and average pooling. The biggest of a region's pixel values is used in max pooling. Pooling decreases the count of parameters that must be calculated while also making the network insensitive to changes in size, form, and scale. Here, the fully connected layer is replaced by SVM. 

\begin{enumerate}[B]
    \item SVM
\end{enumerate}

SVMsSVMs\cite{Puyati2008} define a collection of supervised learning techniques for classification as well as regression \cite{Sultana2018}.  Data points of the type $ \left\{\left(y_{1}, z_{1}\right),\left(y_{2}, z_{2}\right),\left(y_{3}, z_{3}\right),\left(y_{4}, z_{4}\right) \cdots \cdots \cdots,\left(y_{0}, z_{o}\right)\right\} $ are considered. Here,$ z_{o}=1 /-1 $ is a constant indicating the class that $y_o$corresponds to. ois the count of samples taken. Every $y_o$ represents a q-dimensional real vector. The scaling is necessary to avoid variables (attributes) having a lot of variation. We can see this Training data by using the dividing (or separating) hyperplane, which divides the data into two halves. 
\begin{equation}
     x \cdot y+c=0 
\end{equation}
Here, x shows a q-dimensional Vector and cdefines a scalar. The separating hyperplane is perpendicular to the vectorx. We may extend the margin by using the offset parameter c. The hyperplane is forced to pass via the origin in the absence of c, limiting the solution.
\begin{equation}
  x \cdot y+c=1 
\end{equation}
\begin{equation}
    x \cdot y+c=-1 
\end{equation}
The distance among the hyperplane is$2 /|x|$ , as determined by geometry. As a result, we aim to keep $ |x| $to a minimum. To pique the interest of data points, we must guarantee that for every jeither 
\begin{equation}
    x \cdot y_{j}-c \geq 1 \quad or \quad x \cdot y_{j}-c \leq-1 
\end{equation}
This can be expressed as:
\begin{equation}
    z_{j}\left(x \cdot y_{j}-c\right) \geq 1, \quad 1 \leq j \leq o 
\end{equation}

\begin{enumerate}[C]
    \item Hybrid Deep Learning Model
\end{enumerate}
The hybrid deep learning model for the introduced ASD is performed by enhanced CNN. Here, the fully connected layer of CNN is replaced by SVM thus called as enhanced CNN. The major objective of hybrid deep learning model is to optimize the learning rate of CNN as well as iteration of SVM with the intention of accuracy maximization. This is shown as below.
\begin{equation}
    fit \ =\underbrace{\operatorname{argmax}}_{\left\{L R_{C N N}, I T_{S V M}\right\}}  (Accuracy)
\end{equation}
Here, the fitness or the objective function is revealed byfit, learning rate of CNN is given by $ L R_{C N N}$, iteration of SVM is given by$I T_{S V M}$, and accuracy is shown byAccuracy respectively. Accuracy is formulated as below.
\begin{equation}
    Accuracy =\frac{T^{P E}+T^{N E}}{T^{P E}+T^{N E}+F^{P E}+F^{N E}} 
\end{equation}
Here, the true positive, true negative, false positive, and false negative is shown $\operatorname{by} T^{P E}, T^{N E}, F^{P E} ,$and $F^{N E}$ respectively.

\begin{enumerate}[D]
    \item Proposed BS-MVO
\end{enumerate}

The proposed BS-MVO is used for enhancing the classification phase of the introduced ASD model with the aid of hybrid deep learning model. It optimizes the learning rate of ANN as well as iteration of SVM with the intention of accuracy maximization. MVO \cite{Srivastava2009} algorithm's major influences are three cosmological concepts: white hole, black hole, and wormhole. These three notions have statistical formulas that are used to execute exploitation, exploration, and local search, accordingly. The MVO has various advantages such as better exploitation, exploration, and convergence. But, it limits from binary as well as multi objective versions. Hence, to overcome its shortcomings, BSO is integrated into it and the resulting algorithm is called as BS-MVO. 

BSO\cite{Vapnik1995}, which is dependent on the BAS \cite{Mirjalili2016MVO} and the conventional PSO \cite{Chen2018}, is drawn from PSO, but the update criteria for every particle come from BAS. 

Hence, BS-MVO is designed on the basis of random concept. If$rand\geq 0.5$,then the update takes place by BSO as below. 

\begin{equation}
    w c_{j}=-\delta^{u} \cdot \vec{c} \cdot \operatorname{sign}\left(g\left(y_{\text {right }}\right)-g\left(y_{\text {left }}\right)\right) 
\end{equation}
Here, the update rate is shown by $w c_{j}$, particle is shown by $j$, fitness function value of left and right side is shown by $ g\left(y_{l e f t}\right)$and $g\left(y_{right}\right)$, iteration is shown by $u$, step size is shown by$delta$, and the symbolic function is shown by sign respectively. \\
Otherwise, if $rand<0.5$, then the update takes place by MVO as in Eq. (37).
\begin{equation}
\begin{split}
  w c_{u}^{j}=\left\{\begin{array}{rrr}W C_{j}+T D R \times\left(\left(u d_{j}-l d_{j}\right) \times q 4+l d_{j}\right) & \\ q 3<0.5 & \\ q 2<W E P \\ w c_{u}^{j} W C_{j}-T D R \times\left(\left(u d_{j}-l d_{j}\right) \times q 4+l d_{j}\right) & \\ q 3 \geq 0.5 & \\ q 2 \geq W E P\end{array}\right. 
  \end{split}
\end{equation}
Here,  $W C_{j}$ defines the $j^{\text {th }}$ parameter of best universe,  W E P  and T D R are coefficients, upper and lower bound is revealed by $ u d_{j}, l d_{j} ,$ random numbers are $q 2, q 3 $, and  $q 4, j^{\text {th }}$  parameter of  $u^{\text {th }}$ universe is depicted by  $w c_{u}^{j}$  respectively. The BS-MVO pseudo code is in Algorithm 1.
The flowchart of proposed BS-MVO is shown in Figure 2 \\\\

\begin{table}[htbp]
\centering
\begin{tabular}{|l|}
\hline
Algorithm 1: BS-MVO                     \\ \hline
Start                                   \\
Parameter and population initialization \\
Fitness calculation                     \\
if rand $ \geq 0.5 $                    \\
$ w c_{j}=-\delta^{u} \cdot \vec{c} \cdot \operatorname{sign}\left(g\left(y_{\text {right }}\right)-g\left(y_{\text {left }}\right)\right) $ \\
else                                    \\
$w c_{u}^{j}=\left\{\begin{array}{rrr}W C_{j}+T D R \times\left(\left(u d_{j}-l d_{j}\right) \times q 4+l d_{j}\right) & \\ q 3<0.5 & \\ q 2<W E P \\ w c_{u}^{j} W C_{j}-T D R \times\left(\left(u d_{j}-l d_{j}\right) \times q 4+l d_{j}\right) & \\ q 3 \geq 0.5 & \\ q 2 \geq W E P\end{array}\right.$ \\
Return best solution                    \\
Stop                                    \\ \hline
\end{tabular}
\end{table}

\begin{figure}[htbp]
  \centering
  \includegraphics[width=5cm]{Picture2.png}
  \caption{Flowchart of proposed BS-MVO}
\end{figure}    

\section{RESULTS}

\begin{enumerate}[A]
    \item Experimental Setup
\end{enumerate}
TThe proposed EEG signal classification-based ASD was implemented and analyzed. The dataset regarding the proposed work is gathered from standard online sources. The suggested ASD model was compared with different heuristic-based algorithms like GA \cite{Jiang2017}, WOA \cite{Eberhart1995}, MVO [39], and BSO [40] with respect to analysis such as accuracy, sensitivity, TPR, specificity, and MCC to describe the betterment of the introduced method. and BSO [40] with respect to analysis such as accuracy, sensitivity, TPR, specificity, and MCC to describe the betterment of the introduced method. 

\begin{enumerate}[B]
    \item Accuracy Analysis
\end{enumerate}
The accuracy analysis \cite{McCall2005} of different heuristic-based algorithms for the introduced ASD model is shown here. It can be seen that BS-MVO outperforms other methods at various learning percentages. Hence, it can be revealed clearly that the proposed BS-MVO is better than the other methods for the developed ASD model.

\begin{figure}[htbp]
  \centering
  \includegraphics[width=5cm]{Picture3.png}
  \caption{Accuracy analysis}
\end{figure}  

\begin{table*}[htbp]
\centering
\caption{ACCURACY ANALYSIS}
\label{tab:learning-percentages}
\begin{tabular}{|c|c|c|c|c|}
\hline
Methods & Learning 30\% & Learning 50\% & Learning 70\% & Learning 90\% \\
\hline
GA [43] & 93.16 & 97.85 & 91.87 & 92.90 \\ \hline
WOA \cite{mccall2005genetic} & 96.62 & 96.96 & 93.40 & 89.99 \\ \hline
MVO [39] & 97.73 & 97.84 & 93.43 & 93.91 \\ \hline
BSO [40] & 97.24 & 95.52 & 90.10 & 91.60 \\ \hline
BS-MVO & 98.81 & 99.53 & 94.47 & 94.49 \\  
\hline
\end{tabular}
\end{table*}
\begin{enumerate}[C]
    \item Sensitivity Analysis
\end{enumerate}
The sensitivity \cite{Mirjalili2016WOA} of several heuristic-oriented methods for the proposed ASD model is examined in this paper. At various learning percentages, it can be demonstrated that BS-MVO beats other approaches. As a result, it is obvious that the suggested BS-MVO is superior to the other approaches in terms of the created ASD model for sensitivity.

\begin{figure}[htbp]
    \centering
    \includegraphics[width=0.5\linewidth]{Picture4.png}
    \caption{Sensitivity Analysis}
    \label{fig:enter-label}
\end{figure}
\begin{table*}[htbp]
\centering
\caption{SENSITIVITY ANALYSIS}
\label{tab:learning-percentages}
\begin{tabular}{|c|c|c|c|c|}
\hline
Methods & Learning 30\% & Learning 50\% & Learning 70\% & Learning 90\% \\
\hline
GA [43] & 92.89 & 95.71 & 97.21 & 91.12 \\ \hline
WOA [44] & 96.96 & 97.98 & 96.70 & 91.39 \\ \hline
MVO [39] & 94.93 & 96.95 & 97.23 & 94.95 \\ \hline
BSO [40] & 94.90 & 97.98 & 96.97 & 90.85 \\ \hline
BS-MVO & 97.72 & 98.81 & 98.80 & 95.56 \\ 
\hline
\end{tabular}
\end{table*}

\begin{enumerate}[D]
    \item TPR Analysis
\end{enumerate}
This research investigates the TPR of multiple heuristic-oriented strategies for the suggested ASD model. It can be proved that BS-MVO outperforms other techniques at various learning percentages. As a consequence, the proposed BS-MVO is clearly superior to the other techniques in terms of the ASD model for TPR generated. 

\begin{figure}[htbp]
    \centering
    \includegraphics[width=0.5\linewidth]{Picture5.png}
    \caption{TPR Analysis}
    \label{fig:enter-label}
\end{figure}

\begin{table*}[htbp]
\centering
\caption{TPR ANALYSIS}
\label{tab:learning-percentages}
\begin{tabular}{|c|c|c|c|c|}
\hline
Methods & Learning 30\% & Learning 50\% & Learning 70\% & Learning 90\% \\
\hline
GA [43] & 94.18 & 94.86 & 95.23 & 96.59 \\ \hline
WOA [44] & 91.36 & 93.84 & 94.55 & 92.83 \\ \hline
MVO [39] & 93.18 & 91.43 & 92.80 & 97.95 \\ \hline
BSO [40] & 92.93 & 94.88 & 96.25 & 94.88 \\ \hline
BS-MVO & 95.51 & 95.59 & 97.77 & 98.18 \\
\hline
\end{tabular}
\end{table*}

\begin{enumerate}[E]
    \item Specificity Analysis
\end{enumerate}

The specificity \cite{Jayachitra2021}\cite{Jayachitra2020} of several heuristic-oriented techniques for the proposed ASD model is investigated in this study. At various learning percentages, it can be demonstrated that BS-MVO outperforms other approaches. As a result, in terms of the ASD model for specificity produced, the suggested BS-MVO obviously outperforms the other strategies.

\begin{figure}
    \centering
    \includegraphics[width=0.5\linewidth]{Picture6.png}
    \caption{Specificity Analysis}
    \label{fig:enter-label}
\end{figure}

\begin{table*}[htbp]
\centering
\caption{SPECIFICITY ANALYSIS}
\label{tab:learning-percentages}
\begin{tabular}{|c|c|c|c|c|}
\hline
Methods & Learning 30\% & Learning 50\% & Learning 70\% & Learning 90\% \\
\hline
GA [43] & 90.83 & 93.65 & 91.12 & 90.40 \\ \hline
WOA [44] & 93.39 & 93.89 & 92.64 & 92.18 \\ \hline
MVO [39] & 92.37 & 95.94 & 94.17 & 93.19 \\ \hline
BSO [40] & 93.94 & 90.12 & 95.46 & 91.43 \\ \hline
BS-MVO & 94.41 & 96.67 & 96.12 & 95.11 \\
\hline
\end{tabular}
\end{table*}

\begin{enumerate}[F]
    \item MCC Analysis
\end{enumerate}
This study investigates the MCC of numerous heuristic-oriented strategies for the suggested ASD model. It has been established that BS-MVO outperforms other techniques at various learning percentages. As a consequence, the recommended BS-MVO clearly beats the other techniques in terms of the ASD model for MCC created.

\begin{figure}
    \centering
    \includegraphics[width=0.5\linewidth]{Picture7.png}
    \caption{MCC Analysis}
    \label{fig:enter-label}
\end{figure}

\begin{table*}[htbp]
\centering
\caption{MCC ANALYSIS}
\label{tab:learning-percentages}
\begin{tabular}{|c|c|c|c|c|}
\hline
Methods & Learning 30\% & Learning 50\% & Learning 70\% & Learning 90\% \\
\hline
GA [43]   & 91.78 & 97.62 & 91.80 & 92.40 \\ \hline
WOA [44]  & 96.95 & 97.63 & 93.86 & 92.47 \\ \hline
MVO [39]  & 96.97 & 97.64 & 90.81 & 91.46 \\ \hline
BSO [40]  & 97.65 & 98.65 & 94.22 & 93.50 \\ \hline
BS-MVO    & 98.80 & 98.90 & 95.14 & 94.99 \\ 
\hline
\end{tabular}
\end{table*}

\section {CONCLUSION}
The goal of this study was to use EEG signal processing and analysis to detect ASD. The ASD dataset was used to create the dataset. The pre-processing was then completed using median filtering and normalization. The STFT technique was then used to convert the signals to images. To extract features from altered images, the GLCM was employed. PCA was used to choose relevant characteristics from the recovered features since they are lengthy. Based on these carefully selected characteristics, a hybrid deep learning model was used to categorize the data. In this scenario, the fully connected layer of CNN was replaced with SVM. By combining BSO with MVO, the novel BS-MVO optimized CNN learning rate and SVM iteration with the goal of accuracy maximization as the fitness or objective function, resulting in enhanced CNN. This upgraded CNN was used to classify the final output. By comparing the suggested technique to established techniques on a variety of criteria, simulation results showed that it was superior. In the future, the proposed methodology can be better improved by considering different forms of deep learning models together with novel optimization algorithms for reducing the computational complexity to the extended level.
\\\\

\begin{table*}[htbp]
\centering
\begin{tabular}{|l|l|}
\hline
Abbreviation & Description                                                                                \\ \hline
GLCM         & \begin{tabular}[c]{@{}l@{}}Grey Level   Co-occurrence \\ Matrix\end{tabular}               \\ \hline
ASD          & Autism   Spectrum Disorder                                                                 \\ \hline
GA           & Genetic   Algorithm                                                                        \\ \hline
STFT         & Short Time   Fourier Transform                                                             \\ \hline
MCC          & Matthews   Correlation Coefficient                                                         \\ \hline
BS-MVO       & \begin{tabular}[c]{@{}l@{}}Beetle   Swarm-based\\  Multi Verse Optimization\end{tabular}   \\ \hline
DTI          & Diffusion   Tensor Imaging                                                                 \\ \hline
EEG          & Electro   Encephalo Gram                                                                   \\ \hline
DSM          & \begin{tabular}[c]{@{}l@{}}Diagnostic   and Statistical\\  Manual\end{tabular}             \\ \hline
CARS         & \begin{tabular}[c]{@{}l@{}}Childhood   Autism Rating\\  Scale\end{tabular}                 \\ \hline
BSO          & Beetle Swarm   Optimization                                                                \\ \hline
PCA          & Principal   Component Analysis                                                             \\ \hline
fMRI         & \begin{tabular}[c]{@{}l@{}}functional   Magnetic\\  Resonance Imaging\end{tabular}         \\ \hline
ATEC         & \begin{tabular}[c]{@{}l@{}}Autism   Treatment \\ Evaluation Checklist\end{tabular}         \\ \hline
ICA          & \begin{tabular}[c]{@{}l@{}}Independent   Component \\ Analysis\end{tabular}                \\ \hline
CSP          & Common   Spatial Pattern                                                                   \\ \hline
MVO          & Multi Verse   Optimization                                                                 \\ \hline
EMD          & Empirical   Mode Decomposition                                                             \\ \hline
LDA          & Linear   Discriminant Analysis                                                             \\ \hline
dDTF         & \begin{tabular}[c]{@{}l@{}}direct   Directed Transfer \\ Function\end{tabular}             \\ \hline
CCHMC        & \begin{tabular}[c]{@{}l@{}}Cincinnati Children's   \\ Hospital Medical Center\end{tabular} \\ \hline
SODP         & \begin{tabular}[c]{@{}l@{}}Second-Order   Difference\\  Plotting\end{tabular}              \\ \hline
KNN          & k-Nearest   Neighbour                                                                      \\ \hline
TSC          & Tuberous   Sclerosis Complex                                                               \\ \hline
MFA          & Multi   FrActality                                                                         \\ \hline
TD           & Typically   Developing                                                                     \\ \hline
ANN          & Artificial   Neural Network                                                                \\ \hline
MSE          & Multi Scale   Entropy                                                                      \\ \hline
IMFs         & Intrinsic   Mode Functions                                                                 \\ \hline
MSEL         & Mullen   Scales of Early Learning                                                          \\ \hline
FFT          & Fast Fourier   Transform                                                                   \\ \hline
PSO          & Particle   Swarm Optimization                                                              \\ \hline
AOI          & Areas Of   Interest                                                                        \\ \hline
CTM          & Central   Tendency Measure                                                                 \\ \hline
WOA          & Whale   Optimization Algorithm                                                             \\ \hline
mRMR         & \begin{tabular}[c]{@{}l@{}}minimum-Redundancy   \\ Maximum-Relevancy\end{tabular}          \\ \hline
ASM          & Angular   Second moment                                                                    \\ \hline
CNN          & Convolutional   Neural Network                                                             \\ \hline
VABS         & \begin{tabular}[c]{@{}l@{}}Vineland   Adaptive Behavior \\ Scales\end{tabular}             \\ \hline
MI           & Mutual   Information                                                                       \\ \hline
IDM          & Inverse   Difference Moment                                                                \\ \hline
SRM          & Structural   Risk Minimization                                                             \\ \hline
PLS          & Preschool   Language Scales                                                                \\ \hline
SVM          & Support   Vector Machine                                                                   \\ \hline
IG           & Information   Gain                                                                         \\ \hline
BAS          & Beetle   Antennae Search                                                                   \\ \hline
TPR          & True   Positive Rate                                                                       \\ \hline
\end{tabular}
\end{table*}






\begin{ack}
We acknowledge DST-File No.368. DST - FIST (SR/FIST/
College - 235/2014 dated 21 - 11 - 2014) for financial support  and  DBT-STAR-College-Scheme-ref.no:  BT/HRD/11
/09/2018 for providing infrastructure support.
\end{ack}

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\end{document}
