Optimal Ensemble learning model for COVID-19 detection using chest X-ray images

COVID-19 pandemic is the main outbreak in the world, which has shown a bad impact on people's lives in more than 150 countries. The major steps in fighting COVID-19 are identifying the affected patients as early as possible and locating them with special care. Images from radiology and radiography are among the most effective tools for determining a patient's ailment. Recent studies have shown detailed abnormalities of affected patients with COVID-19 in the chest radiograms. The purpose of this work is to present a COVID-19 detection system with three key steps: “(i) preprocessing, (ii) Feature extraction, (iii) Classification.” Originally, the input image is given to the preprocessing step as its input, extracting the deep features and texture features from the preprocessed image. Particularly, it extracts the deep features by inceptionv3. Then, the features like proposed Local Vector Patterns (LVP) and Local Binary Pattern (LBP) are extracted from the preprocessed image. Moreover, the extracted features are subjected to the proposed ensemble model based classification phase, including Support Vector Machine (SVM), Convolutional Neural Network (CNN), Optimized Neural Network (NN), and Random Forest (RF). A novel Self Adaptive Kill Herd Optimization (SAKHO) approach is used to properly tune the weight of NN to improve classification accuracy and precision. The performance of the proposed method is then compared to the performance of the conventional approaches using a variety of metrics, including recall, FNR, MCC, FDR, Thread score, FPR, precision, FOR, accuracy, specificity, NPV, FMS, and sensitivity, accordingly.


Introduction
The SARS-CoV-2 (Corona Virus) started spreading from the Wuhan city of China and has shown its bad impact on several countries since December 2019 [1]. It is observed that early diagnosis is the only option to minimize the infection possibility in healthy people and should need sudden isolation of the infected person. Moreover, gene sequencing, blood specimens, or RT-PCR are the major screening techniques for COVID-19 [2 3]. However, the TPR of RT-PCR is reported as 30 to 60 % for the throat swab samples [4 5].
Moreover, chest radiography images (i.e.), CT or X-ray imaging are routine tools to execute with the quick diagnosis for pneumonia patients. X-ray images provide visual indexes linked with COVID-19 Chest [6], and CT shows larger sensitivity to diagnose COVID-19 [7]. The chest imaging reports generate the peripheral airspace opacities and multilobar involvement. Diffuse airspace opacities or asymmetric patchy are also reported for COVID-19 [8]. As there are limited trained radiologists and the rate of suspected people increases, automatic approaches for early diagnosis are mandatory. AI/ML solutions are powerful tools to solve those issues.
Nowadays, the X-ray images related to COVID-19 are gathered as a tiny dataset that is more helpful for AI researchers for training the ML approach to execute the automatic COVID-19 detection from the images of X-ray [9 10]. Furthermore, these images are taken from the academic report on the consequences of CT and X-ray images of COVID-19 [11]. Moreover, a subset of images is used as the -ve samples from the ChexPert dataset for the COVID-19 diagnosis. Likewise, around five thousand X-ray images related to Chest are combined as the dataset [12 13], known as COVID-Xray-5 k, and it is categorized into three thousand testings and two thousand training samples.
The ML [14 15 16] structure is employed for predicting the COVID-19 by the Chest images of X-ray [17 18 19 20]. Different classical schemes are used for the classification of the medical image that includes 2 step procedure like hand-crafted recognition and feature extraction; End-to-end DL structures are used for the direct prediction of COVID-19 disease without any additional features from raw images [21 22 23]. In recent years, the DL (more specifically CNN) based models [24 25 26 27] are attained better performance in the classical AI models based on medical image analysis tasks and computer vision [28 29 30 31].The best possible environment that may be achieved for an aim under the present limitations is known as global optimization [54].The largest metropolitan area of the Chinese province of Hubei, Wuhan, reports the first official coronavirus case, as certified by WHO. Millions of verified cases have been reported worldwide, and it has already claimed thousands of lives [52]. According to studies, this family of viruses exhibits a considerable manifestation in radiographic pictures [53].
The following list of the model's main contributions: • Proposes an ensemble classifier that includes SVM, RF, CNN, and optimized NN for the final classification of COVID-19 chest images. • Presents the Self Adaptive Kill Herd Optimization (SAKHO) Method for determining the best weights for training the optimized NN model.
In this essay, section 2 presents an overview of COVID-19 detection. Section 3 provides an overview of the adopted COVID-19 detection model. Section 4 illustrates the pre-processing and suggested feature extraction method. Section 5covers optimization-assisted ensemble classification for the COVID-19 detection model. The weight optimization of a neural network using a self-improved krill swarm optimization technique is shown in Section 6. The outcome and discussion are described in Section 7.

Related works
In 2021, Shankar et al. [33] have introduced a new fusion method hand-crafted with DL features known as theFM-HCF-DLF approach for the COVID-19classification and diagnosis. Furthermore, the proposed FM-HCF-DLF approach comprised three major processes: "Gaussian filtering-based preprocessing, FM for feature extraction and classification." Moreover, the FM method has incorporated the handcrafted features fusion with the assistance of DL and LBP features and utilized the CNN-based Inception v3 schemes. The Adam optimizer used the backpropagation learning scheduler to improve the performance of the Inception v3 algorithm. The chest X-ray dataset evaluated the adopted FM-HCF-DLF method. The simulation results of the suggested model have, in the end, demonstrated improved performance with increased specificity, sensitivity, accuracy, precision, kappa value, and F score.
In 2020, Bejoy et al. [35] have determined the multi-CNN effectiveness for the automatic diagnosis of COVID-19 by mixing certain pre-trained CNNs from X-ray images. The adopted model has used the integration of features from multiple CNN with the Bayesnet classifier and CFS model for identifying . The proposed scheme was tested by two public datasets and attained better outcomes on both datasets. The simulation results have proven better effective during the detection of COVID-19in the pre-trained multi-CNN than the single CNN.
In 2020, Govardhan et al. [37] have introduced an alternative diagnostic tool and an advanced DL model for COVID-19 cases. The proposed method was introduced in 4 phases: "preprocessing, data augmentation, stage-I and stage-II deep network model." Moreover, the deep network wasexecuted in 2 phases that were implemented for differentiating the bacteria on chest X-ray images, COVID-19 with pneumonia from another virus-induced pneumonia,and healthy cases. The simulation outcomes of the proposed method have attained high classification accuracy, recall, and precision for detecting COVID-19.
In 2020, Suat et al. [38] determined a new ANN, Convolutional CapsNet, along with the capsule networks to identify the COVID-19 infection through chest X-ray images. To accomplish accurate and quick diagnostics with multi-class and binary classification, the adopted model was put into practice for COVID-19 disorders.The presented method has correspondingly attained better accuracy for multiple and binary classes. Further, the adopted method helped increase the diagnostic performance of COVID-19 disease. Further, the presented approach was believed to be an alternative scheme for diagnosing COVID-19 with a fast screening approach.
In 2020, Asif et al. [39] has implemented CoroNet, a Deep CNN scheme to diagnose the COVID-19 infection automatically. The presented approach was performed based on a trained end-to-end dataset while gathering the COVID-19 images, another chest pneumonia X-ray images from 2 various databases, and the Xception framework pretrained on the ImageNet dataset. The CoroNet was tested and trained on the dataset. The simulation outcomes have shown that the presented approach achieved better overall accuracy, recall rate, and precision for COVID-19 cases for 4-class cases. The adopted method has produced better classification accuracy for 3-class classification. Table 1 shows the reviews on COVID-19 diagnosis by the chest X-ray images.
In 2022, Wang et al. [32]deployed an enhanced multiple-way data augmentation. Second, a rank-based pooling module (NRAPM) was presented that used rank-based average pooling (RAP) specifically to prevent over-tapping. Third, a deep rank-based average pooling network (DRAP Net) based on NRAPM and motivated by the VGG network was proposed. Heatmaps were produced by Grad-CAM, which also provided an understandable analysis for our AI model. After

Overall description of adopted COVID-19 detection model
This study intended to introduce a COVID-19 detection method that includes three steps: "(i) preprocessing (ii) Feature extraction (iii) Classification."First, the source image is given as the source of preprocessing step, and it is performed by using the median filtering process. The preprocessed image is then used to extract deep features and texture characteristics.Here, the deep features are extracted by incep-tionv3. The features like proposed LVP and LBP are also extracted.
Moreover, the extracted features were fed asa source of the classification step;here, a proposed ensemble model is used to classify the image as diseased or not. The proposed ensemble model includes SVM, RF, Optimized NN, and CNN. The extracted characteristics were also used as individual inputs for each classifier, and the results from each classifier were averaged to produce the final result.SAKHO model ideally modifies the weight of NN to increase the classification's precision and accuracy. The broad structure of the study provided is shown in Fig. 1.

Preprocessing via median filtering
The median filtering approach enhances the image during the preprocessing stage.Here, the input image is smoothed and denoised using median filtering [40]. And then, the sound score or digital image sequence was restored through the (neighborhood) mask of the median value. The neighboring pixels are sorted and saved with the aggregated median value, which takes the place of the noisy value, depending on the gray levels.We can use linear or nonlinear filter methods to remove noise from an image that has been tainted by noise. In thefeatures of the image are high-frequency components in the frequency domain, which are readily confused with high-pitched noises. Consequently, the challenge is to maintain visual features while successfully filtering random disturbances crucial to the processing of picture filters. Nonlinear filter known as the median filter is commonly utilized in digital due to its effective edge-keeping abilities and capacity to reduce impulsive noise. The rank-order filter is the median filter. Depending on the size and shape of the filters, it can reduce noise. In addition, f(c, d) = med{h(c − u, d − v)u, v ∈ I } is the output of the median filtering [40], where,f(c, d), and h(c, d) related to output image and real image, accordingly, I shows 2D mask, M × M depicts the size of the mask (i.e.), M was an odd con-tains3 × 3,5 × 5, etc. The mask can also be cross-shaped, circular, square, or linear, among other shapes.
Lowering the noise performance:The median Filter, also considered a nonlinear filter, has a harder time processing images with noisy data. When using a median filter, the noise variance of a picture with a normal distribution and zero average noise is calculated as in Eq. (1).
In Eq. (1), M depicts size of median filter mask,σ 2 u depicts input noise power difference, F(M) and depicts density function of sound. The noise variability is represented in Eq. (2) when using the average Filter.
When comparing Eq. (1) with Eq. (2), the benefits of median filtering rely on distributions and mask size.Additionally, the outcomes of the median filtering provide low random noise, and it is higher than the average performance of the Filter. In the impulse noise, narrow pulses occur because the pulse is lower than the efficient median filter.Whenever the median and average filtering algorithms are combined, the average filtering performance is raised to resize the mask based on the noise density.

Feature Extraction: Extraction of deep and texture features
The feature extraction phase includes three processes as follows.
✓ Proposed LVP ✓ LBP ✓ Deep features by Inception V3 (i) Proposed LVP: Through computing the values between the adjacent pixels from various directions with varied distances and the reference pixel, it is established that the LVP [41] symbolizes the structure information and one-dimensional direction of the local text ure.In the existing LVP the local features are extracted by using the higher order derivatives. The mathematical representation of the LVP is determined in Eq. (3), Eq. (4), Eq. (5), and Eq. (6).
In Eq. (3), H D 4 () indicates the LVP at a nearby distanceD, and γ refers to the index angle. As per the proposed LVP, the mutual information μI is also computed as in Eq. (7).
In Eq. (7), (s 1 , r s2 ) indicates the pairs of elements of LVP. w ts1 , w ts2 denotes the weights, t 1 , t 2 refers to the tags and T i indicates the set of resources tagged witht i .
Color transformation: The distance between 2 features is calculated using cosine distance in Eq. (10).
In Eq. (10), G l indicates the query image feature, . denotes the dot product, G j specifies the feature library, and n depicts the total image in the dataset. The extracted proposed LVP feature is indicated asFE LVP .
(ii)LBP: The LBP [32] has computational simplicity and higher discriminative power. Additionally, the LBP operator labels each image pixel with decimal integers. The labeling process calculates every image pixel with its surrounding pixels by subtracting the mid-pixel value. Additionally, it encodes the negative values produced as 0, and the positive and 0 values as 1. Additionally, all the basic codes are spliced starting from the top-left and moving clockwise to create the binary number. This is known as the LBP codes.Those many local descriptions that make up the global description are constructed using the texture descriptor. Additionally, based on the capacity to distinguish between these texture items, the characteristics are retrieved. In Eq. (11), SH pl and SH cl indicates the mid pixelintensities and the imagemid pixel from relativepl, correspondingly. The pixel's LBP descriptor is displayed as LBP( • ) and NE Pl indicates the neighbor's count. FE LBP(pl,cl) -LBP descriptor function is expressed in Eq. (12).
(iii) Deep features by Inception v3:Five layers make up a CNN: convolutional, source layer, FC, output, and pooling. Additionally, the GoogleLeNet network is set up in Google and is meant to function like CNN.Further, the inception network model [33] is applied to improve a system's depth and limit the number of network attributes. As a result, it is frequently used in image classifications.
Convolution layer:It differs from NN in that bias and weight is unrelated to all of the subsequent layer's pixels.Nevertheless, the entire image is categorized into small areas following it using bias and weights. Moreover, the bias and weights are called kernels or filters and are convoluted with all the little areas of the input image, which provides a feature map. These filters are the easy 'features'discovered from this layer's input image. The size of the local region, count of filters, padding, and stride are known as the hyperparameters of this layer. Here, the hyperparameters endure the tuning for optimal outcomes based on the genre and size of an input image.
Pooling layer:This layer minimizes the parameter count and the image's physical dimensions.Additionally, a set function to an intake with no parameters was accomplished via the pooling layer. The max pooling, average pooling, and stochastic pooling are further forms of pooling layers.
FC layer: Additionally, the FC layer receives the compressed results of the last pooling layer as input. Moreover, it acts as a CNN where each neuron of the conventional layer is associated with the presentation layer. Consequently, the parameter count present in the convolution layer is higher.
Activation function: It is used in the dissimilar CNN framework. The nonlinear activation function provides an optimal result than the previous tangent or sigmoid functions. The nonlinear functions are meant to improve the training speed.
CNN learning model relies on the chain rule vector and calculus. Consider y ∈ RH as a scalar and x ∈ RG as a vector. While the partial derivative of y in terms of x which is a vector, y is a function of x and it is given in Eq. (13).
In Eq. (13), denotes the vector of the same size asx, and the ith element is represented as . Suppose x is a function ofz, and z ∈ RH B is the other vector. The partial derivative of X based on z is specified in Eq. (14).
Moreover, the L × B matrix present in the fractional derivative and access at the juncture of oth column and ith row i.e., ∂x i ∂z i . Further, y is a function of z in a chain-like argument. In addition, a function maps z tox, and other function maps x toy. Eq. (15) determines the chain rule. , as The loss or cost function is used to calculate the difference between the target ts and the prediction of a CNN, z HS z 1 →wg 1 , z 2 →, The predictive outcome is specified asargmax i z HS i . Further, the convolution model is defined in Eq. (16).
The Filter fh with size ( L × B × DL lc ) , and convolutional layer con- The possibility of all labels kl ∈ {1, ....K} is used for training the , in which y indicates the non-normalized log possibility. Further, the ground truth shares over labels qv(kl/z) are normalized as ∑ kl qv(kl/z) = 1. The loss lc is provided via the cross entropy and it is given in Eq. (17).
Moreover, the loss of cross-entropy is a differential value with respect to logit y kl and used as deep systems during gradient training as ∂lc ∂y kl = PT(kl) − qv(kl) bounded among − 1 and 1. In general, if the crossentropy is reduced, it shows the log possibility of a higher precise label. Further, the inception V3 is known as the collective labels autonomous of training case u(kl) with a flat parameterφ; the label shared qv(kl/z) = δ kl,x as given in Eq. (18). Else, these are inferred as cross-entropy and specified in Eq. (19).
Thus, the label-smoothing regularization is the same as the loss of a single cross-entropy during execution, L(qv, PT) and a pair of losses L(qv, PT) andL(u, PT). Further, the 2nd loss punishes the difference of the forecast label shared PT from prior u with φ (1− φ) relative weight. GoogLeNet's primary goal is to operate similarly to the Inception framework, which is why the GoogLeNet architecture is also known as the Inception network. This is because it consists of more GoogLeNet versions than any other, including Inception v1, v2, v3, v4, and Inception-ResNet.Therefore, the inception consists of 3 different sizes of maximum pooling and convolution. The network outcome in the preceding layer is known as the channels that are gathered after nonlinear fusion is performed once the convolution task is completed. Inception v3 preferred a network model organized via Keras that is advanced trained in Image Net. The Inception v3 network framework determined a convolution kernel splitting method to categorize the integrals of massive volume into lower convolutions than the Inceptions v1 and v2. The extracted deep features by Inception v3 were represented asFE v3 .
Finally, the overall extracted features FE are given in Eq. (20).

Svm
FE was the extracted feature which is provided as a source of an SVM. To performa simple regression model, SVM is defined [43]. To find the separating hyperplane of the SVM model, the saddle purpose, which effectively reduces the quadratic programming problems, is used to conduct the double issues of the Lagrange job. The SVM classifier assigns the decision boundary among all potential hyperplanes using the maximum margin. Further, ‖LP‖ it reduces the objective for maximizing theM, which was determined in Eq. (21). Where denotes the margin separating the hyperplane and the closest data point for both classes.
In Eq. (21), bs depicts scalar threshold number,O depicts source data count in SVM,R O depicts source data points, and LP expresses vector showing boundary. FK(R) portrays the attained optimal hyperplane of SVM as given in Eq. (22).
Here,R O is also said to be a support vector as a source data point R O with a non '0 ′ Lagrange multiplier (AS O ). It was not that important to calculate FK(R) by outer data points support vectors. Additionally, the SVM classifier's default settings offer the best possible data grouping. They brighten up area is crucial for analyzing the accuracy of the SVM ordering of the objects that were improperly categorized. Inadvertently positioned close to the dividing hyperplane were the ordered products. The supremacy within the separating strip is then employed with further tools. SVM result was depicted byCLS SVM .

Rf
The RF classifier receives the retrieved characteristics as input. Moreover, the RF [44] is an approach that combines multiple tree predictors and each tree depending on the value of a randomly selected vector between all trees in the forest in a similar manner. As the RF is coupled with one DT, the overriding difficulties are reduced, enhancing the quality of characterization. In the RF approach, the characterization of the calculation is more crucial. The RF algorithm has a few main limitations, such as the splitting basis, the excessive tree profundity, the degree of forest trees to take into account when looking for the optimal split, and a lot of other properties. The parting technique is the Gini debasement, which is provided in Eq. (23).
In Eq. (23), UJ ( OL hp ) represents the element subclass OL hp class in the tree nodeTR. Additionally, Eq. (24) expresses the splitting requirement for binary classification.
In Eq. (24), C 1 and C 2 depicts object total nodes to descendantsnodes of binary tree TR 1 and TR 2 , and C depicts object total in present node. The RF classifier's categorized results are indicated asCLS RF .

CNN model
The extracted features FE are given as input to the CNN [45] for diagnosing the COVID-19 by X-ray images ofchest. Three further layers, including pooling, fully connected, and convolution layers, are part of the CNN classifier. The convolution layer also includes a number of convolution kernels. Multiple kernels were used to analyze the entire feature map. Additionally,r th layers coupled to zl th feature map and position of feature map (e, xl) is displayed asSP r e,xl,zl , and this was shown in Eq. (25). And then, the zl th filter score was displayed in r th layer. Additionally, the bias term and the weight vector are denoted by the symbols BI r gk andWE r gk , accordingly. Source patch in zl th layer at location (e, xl) were displayed byIF r e,xl . The activation function, which forecasts the nonlinear characteristics of multi-layer networks, is how the nonlinearity is obtained.Keep in mind activation value The loss function in CNN is established in Eq. (28).(ϛ) was the condition of CNN are coupled to wanted IO source-outcome relation, and this was displayed as And then, CNN outcome, p th source data, and connected target score are displayed asOUT (p) ,U (p) andV (p) , accordingly.
The RF classifier's categorized results are indicated asCLS CNN .

Optimized NN
"NN is a series of algorithms that endeavours for recognizing the underlying relationships in a set of data through a process that mimics the way the human brain operates." The extracted features FE are subjected to the NN as its input [46] and are given in Eq. (29). Here, z extracted features are total.
The input, hidden, and output layers make up the NN framework. Here,ŷN displays output neuron total,PŶ and P ⌢ Y displayed actual andguessed output.
The optimized NN classifier's classified outcome is displayed asCLS NN . Thus, the overall classified output CLS is the average of classified outcomes such as SVM, RF, optimized NN, and CNN, which is given in Eq. (33).
Ensemble learning creates a new classifier that outperforms all of its constituent classifiers from various base classifiers. The algorithm employed, the hyper-parameters, the representation, or the training data may vary amongst these base classifiers. The classified outcome of each classifier is either 0 or 1. COVID positive is denoted as 0 and negative as 1. The output from all the four classifiers, such as SVM, RF, CNN, and NN,is averaged to get the final classification score. If a final score obtained is the decimal point, it is rounded off to the nearest integer ie. 0.5 and above is taken as 1, and below 0.5 is taken as 0. Based on this final score, the image is predicted as COVID Positive or Negative.

Objective function and solution Encoding
As previously stated, the suggested SAKHO approach allows for the best tuning of the weights of NN. The input solution for the suggested SAKHO model is shown in Fig. 2. In this case, the overall amount of weights in NN is shown as in Eq. (34), and the objective function is identified.

Proposed SAKHO algorithm
Although the traditional KHO [47] provides a more robust solution for solving complex optimization problems, the fundamental motions in the KH model are not improved and an optimal strategy of the early krill distribution is not selected. To tackle this disadvantage of existing KHO, the algorithm was improved, called the SAKHO approach.Generally, self-improvement is proved to be promising in solving many complex optimization issues [29 30 31 22 23]. In the existing KHO no essential strategy is chosen at the initial stage. The random process is not considered for the diffusion. For determining the parameters efficient strategy is not considered. To overcome all the drawbacks SAKHO algorithm are used. The convergence is improved in the proposed model. Further, the krill individual is based on the herding behavior of the KH algorithm. The distances reduced from the largest density of the herd and foods in each krill are regarded as the movement of krill.
Herding behavior of krill swarms: The best-studied species related to the marine animal is krill. The krill herd is also collected without parallel alignment while still living over distances of 10 to 100 m and during periods ranging from hours to days.
Lagrangian method of the krill herding: Moreover, the Predation eliminates the individuals.The average krill density is minimized as the krill swarm moves away from the food source. In the KH algorithm, it is assigned as the initialization process. The three main actions in a 2D surface dictate the time-dependent positioning of each individual krill. Movement simulated by another individual krill.
✓ Foraging activity ✓ Random diffusion Moreover, the KH approach has the searching ability in spaces with its arbitrary dimensionality. Consequently, the Lagrangian scheme is utilized in the m dimensional decision space.
In Eq. (35), R b denotes the foraging motion, S b specifies the physical diffusion of the b th individual krill, and A b indicates the motion induce via other krill individuals.
(i) Movement simulated by another individual krill: Further, the single krill tried to continue a larger density and moved owing to the mutual effects depending on the studied argument. The induced direction of movement was displayed asζ b , and it is determined from a repulsive swarm density, the target swarm density, and local swarm density. The individual krill movement is determined in Eq. (36).
Where, (37) In Eq. (16) (40) Where, O best and O worst refers to the single krill with best and the worst fitness values, O b indicates the fitness value or objective function of the b th krill individual; O a represents the fitness of a th (a = 1, 2, ...., NF) neighbor; Z indicates the neighbor location, and NF represents the neighbor total.
The sensing distance (ds) is used to determine the krill individual and find the neighbors. Moreover, various heuristic models compute the sensing distance for every krill individual as per Eq. (41).
In Eq. (41), ND indicates the count of the individual krill, and ds b denotes the sensing distance of the b th each krill's.
The impact of each krill having the best fitness on b th individual krill was determined in Eq. (42).
In Eq. (42), CJ best indicates the efficient coefficient of individual krill's to b th individual krill with greatest fitness. Moreover, the CJ best value is given in Eq. (43).
Eq. (43) shows random values between 0 and 1,intended to enhance exploration, IM max specifies the maximum count of iterations, and IM denotes the actual iteration number.
(ii) Foraging motion: It is examined fortwo major effective parameters, such as earlier knowledge regarding the food location and the food location. This motion of the i th krill individual is expressed in Eq. (44). (44) Where, Here, α food b portrays the food attractive, VG fl denotes the foraging speed, χ fl specifies the inertia weight of foraging movement among [0,1], and α best b indicates the effect of the most excellent fitness of the b th krill. The foraging speed of the measured value is 0.02 (ms − 1 ).
The center of the food is identified for each iteration using Eq. (46).
Consequently, for the b th krill individual, the food attraction is given in Eq. (47).
In Eq. (47), CJ food represents the food coefficient and it is specified in Eq. (48).
The best fitness effect of the b th individual krill is determined in Eq. (49).
In Eq. (49), O bbest indicates the best earlier appointment position of the b th krill individual.
(iii) Physical diffusion: It is measured as a random process. This motion is determined with respect to the random directional vector and highest diffusion speed, and it is given in Eq. (50).
In Eq. (50), θ denotes the random directional vector among − 1 and 1, and S max indicates the maximum diffusion speed. Moreover, depending on the time, it linearly decreased the random pace. and worked as the geometrical annealing schedule as per Eq. (51) Motion Process of the KH model: The position vector of an individual krill by various parameters efficacy of movement throughout t tot + Δt, and it is determined in Eq. (52).
Moreover, Δtp depends completely on the search space and it is expressed in Eq. (53).
In Eq. (53) NV indicates the total number of variables, CJ is a constant number between [0,2], UB b and LB a refers to the upper and lower bounds of the b th variables (b = 1, 2, ..., NV), correspondingly.
As per the proposed SAKHO method, the global search is performed using step size after exploration stage and it as given in Eq. (54).
, if nd > 10 In Eq. (54), nd denotes the dimension. Subsequently determines a probability valueprob, and if the probability is less than 0.5, then the update is done by Eq. (55) or Eq. (56). Then, The pseudo-code for the proposed SAKHO methodology is given in Algorithm 1.

Dataset description
Datasets were gathered from [36]. The dataset consists of COVID-19 X-ray samples and non-COVID samples. A dataset of 5,000 images with binary labels was created for the detection of COVID-19 in chest X-ray pictures. This dataset may be used by the scholarly community as a standard. The COVID-19 class labels are designated by aradiologist with board certification, and only those with a distinct signare employed as testing tools. Whereas 2000 images are considered for training samples and 3000 images are considered for testing.

Performance analysis
As shown in Figs. 4, 5, and 6, the performance analysis of the proposed Ensemble + SAKHO scheme is contrasted to the existing schemes, such as FM-HCF-DLF, DBN, FCM, LSTM, Ensemble + KHO, Ensemble + EHO, Ensemble + WOA, and Ensemble + BOA, by certain metrics. The Ensemble + SAKHO model also performs better in terms of positive metrics like sensitivity, accuracy, precision, and specificity than other current models for detecting COVID-19. Additionally, as shown in Fig. 4, the reliability of the chosen Ensemble + SAKHO approach for training examples 90 is 2.69 percent better than the reliability of training data 50. (a). For a model to operate effectively, texturing and deep features are used. There is no need to split the image independently when utilizing deep learning. The image will be automatically segmented using efficient features. The NN weights are fine-tuned to improve prediction accuracy using the SAKHO approach. The observed improvement provides the impact of the proposed SAKHO model on training the classifier in a superior manner.
The chosen ensemble + SAKHO model's negative metrics, such as FPR, FNR, FDR, and FOR, in comparison to other traditional schemes are shown in Fig. 5   for training data 70 in Fig. 5(c). Fig. 6 represents the other measures analysis, such as NPV, MCC, and FMS of the adopted Ensemble + SAKHO model and existing models. The graph demonstrates that for training data 80, the NPV of the adopted Ensemble + SAKHO scheme holds a higher value (89.2145). In contrast, the compared existing models, such as FM-HCF-DLF, DBN, FCM, LSTM, Ensemble + KHO, Ensemble + EHO, Ensemble + WOA, and Ensemble + BOA, each achieve lower values, as shown in Fig. 6.(a). As a result, the performance of the given Ensemble + SAKHO system has improved over other current models.

Overall performance analysis
The overall performance analysis of the presented Ensemble + SAKHO modelover other existing schemes for different training data to accuracy measuresare represented in Table 2 shows that the chosen Ensemble + SAKHO system has demonstrated superior detection performance for any training data compared to other traditional models. Which areFM-HCF-DLF, DBN, FCM, LSTM, ensemble + KHO, ensemble + EHO, ensemble + WOA, and ensemble + BOA, respectively. Similarly, the proposed Ensemble + SAKHO system gets a better accuracy score than other standard systems like FM-HCF-DLF, DBN, FCM, LSTM, Ensemble + KHO, Ensemble + EHO, Ensemble + WOA, Ensemble + BOA, SVM, RF, CNN and NN without optimization correspondingly for training data 60. Additionally, compared to the training data 50, the suggested ensemble + SAKHO system achieves the highest accuracy score (92.1375) for training data 90.An adopted ensemble + SAKHO model holds the highest value for training data 80 than other traditional models like FM-HCF-DLF, DBN, FCM, LSTM, Ensemble + KHO, Ensemble + EHO, Ensemble + WOA, Ensemble + BOA, Ensemble + BOA, SVM, RF, CNN and NN without optimization respectively in Table 2. Offers an ensemble classifier for the final prediction of COVID-19 chest pictures that combines SVM, RF, CNN, and optimal NN. The outcomes have summarized that the adopted Ensemble + SAKHOmodel performance is improved over conventional systems. Table 3 presents the statistical comparison of the chosen Ensemble + SAKHO system to the conventional system based on accuracy measures."The meta-heuristic algorithms are stochastic in nature; therefore, the algorithms are executed for several times to determine the objective of the work by evaluating different case scenarios." Moreover, the adop-tedEnsemble + under ideal circumstances, the SAKHO prototype has demonstrated greater performance. that was 10.48 %, 14.13 %, 14.858 %, 12.76 %, 12.88 %, 7.48 %, 20.74 % and 22.54 % better than standard systems like FM-HCF-DLF, DBN, FCM, LSTM.As a result, the suggested ensemble + SAKHO framework has been improved and successfully validated. Fig. 7 illustrates the convergence study of the proposed Ensemble + SAKHO method to various traditional models for different iterations ranging from 0 to 25. Additionally, the graphic illustrates how the cost function gradually decreases with more repetitions.For example, in Fig. 4, the performance of the proposed Ensemble + SAKHO model at the 25th iteration shows least cost function value (~10.2637) than the traditional models such as FM-HCF-DLF, DBN, FCM, LSTM, Ensemble + KHO, Ensemble + EHO, Ensemble + WOA, and Ensemble + BOA. The graph shows that "at first the chosen ensemble + SAKHO model obtains the worst value and at the final stage it obtains better solution converging to precise detection of COVID-19. Still, the adopted Ensemble + SAKHO method remains enhanced over other traditional

Analysis based on feature set:Existing vs Proposed
The analysis of the ensemble + proposed feature setover Ensemble + existing feature set forthe certain measure is represented in Table 4. Compared to other Ensemble + existing feature sets, the ensemble + suggested feature set has demonstrated a better ability to recognize objects, according to the table. The ensemble + suggested feature set achieves an accuracy value of 6.61 percent higher than the ensemble + existing feature set. Additionally, when contrasted to the Ensemble + current feature set, the ensemble + suggested feature set achieves the highest MCC values (0.92365). Compared to the Ensemble + current feature set in Table 4, the ensemble + suggested feature set has a lower FPR value and performs better. The outcomes have summarized that the ensemble + proposed feature set provided improved performance over the Ensemble + existing feature set.

Conclusion
This study introduces a COVID-19 detection model with three key phases. "(i) preprocessing (ii) Feature extraction (iii) Classification."The input image was initially used for the preprocessing step, and the deep and texture features were extracted from the preprocessed image. Particularly, it extracts the deep features by inceptionv3. Then, features like the proposed LVP and LBP were extracted from the preprocessed image. Moreover, the extracted features were subjected to the proposed ensemble model based classification phase, including SVM, CNN, Optimized NN, and RF. A new SAKHO method was used to optimize the weight of the NN to improve classification accuracy and precision. Finally, the effectiveness of the proposed scheme was compared to the performance of the conventional ways using a variety of measures,

Author Statement
Balasubramaniam S has made a substantial contribution to the concept or design of the article. Satheesh Kumar K drafted the article for important intellectual content and approved the version to be published. All authors approved the final manuscript as submitted and agree to be accountable for all aspects of the work.

CRediT authorship contribution statement
Balasubramaniam S: Conceptualization, Methodology, Software, Table 3 Obtained results are compared and conventional models' accuracy according to statistical analysis.