Covid-19 classification using sigmoid based hyper-parameter modified DNN for CT scans and chest X-rays.

Coronavirus disease (COVID-19) is an infectious disease caused by the SARS-CoV-2 virus. Diagnosis of Computed Tomography (CT), and Chest X-rays (CXR) contains the problem of overfitting, earlier diagnosis, and mode collapse. In this work, we predict the classification of the Corona in CT and CXR images. Initially, the images of the dataset are pre-processed using the function of an adaptive Gaussian filter for de-nosing the image. Once the image is pre-processed it goes to Sigmoid Based Hyper-Parameter Modified DNN(SHMDNN). The hyperparameter modification makes use of the optimization algorithm of adaptive grey wolf optimization (AGWO). Finally, classification takes place and classifies the CT and CXR images into 3 categories namely normal, Pneumonia, and COVID-19 images. Better accuracy of 99.9% is reached when compared to different DNN networks.

Introduction

The Covid-19 pandemic continues to affect the health and daily lives of the world’s people. The most important step in stopping Covid-19 is the effective detection and immediate isolation of infected patients. Patients with Covid-19 infection are abnormal in CT images that enable Covid-19 cases in clinical medicine to be detected. Furthermore, CT images may access the amount of infection that is useful for proper treatment and treatment. A lot of Covid 19 case detection methods were recently suggested, based on deeper learning [35], and some of them were very successful. The small number of cases and annotations remains, however, a major challenge to improve the accuracy of the classification of Covid-19. Moreover, given the low contrast between CT imagery, inaccurate and inaccurate information such as the border pixels and images of non-Covid-19 cases are difficult to process through deep-learning classification methods [19].

DNN (Deep Neural Network) and machine learning are reliable technologies that detect Covid-19 from X-ray images in chest seconds. The [5] PCR-Covid 19 standard detection test cannot be used anywhere in the world and it takes a great deal of sensitivity and time. But as the pandemic is increasing exponentially, it requires faster detection and deep learning as an alternative to clinical testing is technology such as machines. Using machinery and neural networks in medical and medical sciences has already brought about revolutionary changes in the past decade. The use of algorithms will save medical professionals valuable time [17].

Concerning COVID-19 remains a disastrous effect of infection in people who experience critical respiratory conditions on the health and well-being of the global population. The World Health Organization declared the outbreak as a “global public health emergency” on 30 January 2020. In the fight against COVID-19, effective and optimum tests for infected patients are crucial, enabling them to be given immediate treatment and quarantined to alleviate the spreading of infection [20].

In several countries, social solutions to prevent the spread of this disease, including global lockout, social distance, closure of schools, schools, universities, shopping centers, travel limitations, border closure, and other factors have been taken into consideration due to the high growth rate and fast transmission. These solutions have reduced the transmission rate and mortality of diseases [1]. While image gaining and test kits are relatively speed and stress-free, analyzing medical professionals in low-income countries can be challenging, costly, and time-consuming. Automatic diagnostic methods for the analysis of COVID-19 artificial intelligence-based images were studied to solve these problems [30]. To detect COVID-19, profound learning methods were proposed. They used the Dense Net method, the InceptionV3 method, and a new method, the New-Dense Net method, which is achieved by adding the convolution layer to the architecture of the Dense Net. These three methods were used with a dataset of 1130 X-ray images and a dataset of CT scanning, which includes 2482 CT scans [3, 9, 22, and].

In general, the most common way of detecting COVID-19 is to polymerize the chain reverse transcript in real-time (RT-PCR). The accuracy of RT-PCR is however low, 60%–70%. Even if there are negative results, radiological images of patients often show that symptoms can be detected [23]. In the detection of life-threatening diseases, CT and x-rays play an important part [42]. RT-PCR normally takes several hours, even one day. That is why CT scanning and X-ray were used to diagnose COVID-19 sensitively and quickly [25]. But COVID-19 findings are visible in the lung after 2 days [8] and after 10 days the highest result is observed [12, 24, 32, and].

Here we propose a new approach to optimizing DNN architectures for the classification of medical images. As a computer-aided tool for image-based clinical diagnosis, these approaches could soon play an important role [34]. Recently, many profound learning schemes have addressed the detection of infection with COVID-19 through x-rays. To help a radiologist to analyze a huge number of chest x-rays, the anomaly detection technique was proposed [40].CT images were used with deep learning to differentiate COVID-19 from other lung illnesses. Detection of infection with COVID-19 remains difficult because of the variation in size, position, and texture of infections with the high sensitivity and accuracy of CT pictures [11]. This paper’s primary contribution is:

The pre-processing steps use the method of adaptive Gaussian filter.

Classification using Sigmoid Based Hyper-Parameter Modified Deep Neural Network (SHMDNN).

Hyperparameter modification using AGWO Adaptive Grey Wolf Optimization.

Finally, the SHMDNN classifier classifies the Corona in CT and CXR images into 3 categories namely normal, Pneumonia, and COVID-19 image

The rest of the paper is described in Section 3 details the suggested method of the proposed system. The review of similar studies is included in Part 2 and Section 3 provides the approach proposed for SHMDNN. Section 4 analyses the experimental results and section 5 presents the conclusion.

Related works

Dilbag Singh et.al [36] Classification of lungs (COVID-19 + Ve) and not infected (COVID-19 + Ve) were presented for the patients as infected lungs. Nevertheless, the COVID-20 classification based on chest X-rays requires an expert in radiology and a significant amount of time value in COVID 19is rapidly increasing. The development of an automated testing procedure is therefore desirable to save valuable time for medical professionals. This paper contains the development and implementation of a deep Convolution Neural Network (CNN) approach. Furthermore, the hyperparameters of CNN are tuned with multi-objective adaptive development of differences.

Diaa Salama Abdelminaam et.al [2] provide a Deep neural network updated to detect false information. In our research, the doubted claims are divided into two categories: true and false. We compare the performance of different prediction algorithms. The six machine training techniques include decision-making trees and regression. of logistics and neighborhoods, forest randomness, support for vectors, and naïve bays (NB). Keras-Tuner optimizes deep learning technology parameters. Four datasets were used to extract basic datasets for a baseline learning model and word embedding function extracting methods for more depth neural network methods.

Amit Kumar Das et.al [15] Suggest a solution for detecting COVID-19 + ve X-ray pot patients. The proposed project included various state-of-the-art CNN models – DenseNet201, Resnet50V2, and InceptionV3. They were trained to produce independent projections. The models are combined with the new weighted average class value prediction system. The public X-ray case COVID+ve and -ve pictures were used in testing the solution’s efficiency. 538 COVID+V and 468 COVID photos were part of the training, test, and validation systems.

Kaoutar Ben Ahmed et.al [4] When the raw data was worked as closely as possible, the concept removed many confusing features. However, well-informed models can draw on source-specific confusers to the difference between COVID-19 and pneumonia to prevent new source information from being generalized. Our models could create a 1.00 AUC in data sources and a 0.38 AUC in the worst case. This shows that requires further assessment/development before large-scale clinical implementation.

Saleh Albahli et.al [6] there is an overwhelming need for COVID-19 and an intelligent system is needed for this in many countries. While the detection of coronavirus is not good, it is often misclassified because certain techniques are not good when only disease types can be identified and the rest ignored. This study is a deep study designed to differentiate between COVID-19 cases from other current chest diseases.

MichailMamalakis et.al [26] proposed a new pipeline for the deep transfer study of COVID diagnosis has now been developed for 19 patients, based on pneumonia and x-ray chest images. Tuberculosis In our model, both models were designed to add another layer to the neural blocks, ensuring superior performance over the model. The same strategy can also be useful in other applications in which two competing networks are complying with additional performance. Our proposed Network was tested for two classes (pneumonia versus healthy), three class problems (including COVID-19), and four-class problems (tuberculosis included).

Jinyu Zhao et.al [41] CT scans are developed as promising accurate, fast, and cost-effective tests and screening COVID-19. In this paper we create a publicly available COVID-CT dataset with 275 positive COVID-19 scans, to promote research and development through the examination of his/her CTs of profound learning methodologies that establish whether an individual is involved in COVID-19. On this dataset, we form a thorough and convolutionary Neural Network with an F1 of 0.85, which is promising but must still be improved.

Samritika Thakur et.al [37] research presented will use x-ray and computed (CT) tomographic to develop an in-depth knowledge strategy to automatically detect and identify the CNDC-19 disease (CNN). Two different classifications, namely binary and multi-class grades, are implemented with CNN. The binary model, of which Covid-19 is a source of 1917 photos, has been trained with a total of 3877 CT and x-ray images. The total accuracy of the binary classification was 99.64%, 99.58% recall (or sensitivity) 99%, 99.56% accuracy, 99.59% F1 and 100% ROC.

Xuehai He et.al [18] the proposed work requires many CTs to train precise and challenging diagnosis models. In this paper, we will discuss both these issues. We create a public Data Set containing hundreds of CT scans of COVID 19 and develop efficient profound learning methods which, while the number of CT scans is small, can achieve the high accuracy of COVID-19 diagnosis. In particular, we propose an approach to self-transition, which integrates contrastive auto-monitored learning with transfer education to learn strong, unbiased representations to reduce the risk of overfitting.

Muhammad TalhaNafees et.al [31] the proposal to assist radiologists and physicists to quickly detecting patients with COVID-19 offers a very simple, new, robust CNN model with fewer parameters for training. Patients can be also classified according to X-ray imagery in COVID-19, pneumonia, and normal. This extended set of data contains 4803 COVID-19 X-ray pictures of the chest of 686, 5000 normal samples, and 5.000 pneumonia samples available in public. The photographs are divided into 80% training and 20% validation. Training information is training. The CNN model is then tested in the validation data set.

Hasib-Al Rashid et.al [33] introduced CoughNet-V2, a multimodal, scalable DNN system to identify symptomatic COVID-19 cough. The framework was created to be applied to point-of-care edge devices to assist the doctors during the COVID-19 pre-screening step. The CoughNet-V2 framework was developed using a crowd-sourced multivariate data set that includes audio of participants’ coughs as well as other pertinent medical data. According to CoughNet-V2, multimodal integration of cough sounds and medical records enhances classification performance above any unimodal framework. Again for the binary classification task of clinical COVID-19 cough detection, the recommended CoughNet-V2 achieved an area-under-curve (AUC) of 88.9%.

The recent outbreak of COVID-19 impacts public health across the World. Although image gaining and testing kits are relatively fast and stress-free, automatic analysis of the options can be challenging, costly, and time-consuming for medical professionals in Low-income countries.

Another hand automatic diagnosis is Computed Tomography (CT), and Chest X-rays(CXR) to avoid the problem of overfitting, earlier diagnosis, and mode collapse and give the best performance results. Below Table 1 shows the comparison with existing methods.

Table 1

Comparison with existing methods

Comparison	Classification	Dataset	Accuracy	Advantages	Disadvantages
Dilbag Singh et.al [36]	DCNN deep Convolution Neural Network	chest X-ray dataset of COVID-19	98%	Significant Improvement in Specificity Values	Time complexity
Diaa Salama Abdelminaam et.al [2]	DNN	COVID-19 heAlthcare mIsinformatio, Disasters, PolitiFact, gossip Datasets	98.57%	Less time	Validation loss is quite high
Amit Kumar Das et.al [15]	CNN	open-source public datasets contain CXR images of COVID-19	91.62%	Reduced Equal Error Rate (EER)	Lower accuracy
Kaoutar Ben Ahmed et.al [4]	CNN	pneumonia/normal class dataset based on the pediatric dataset	97%	The average detection rate is high	Time complexity
Saleh Albahli et.al [6]	DNN	X-ray Images (frontal-view) of 32,717 unique patients.	87%	–	Low accuracy
MichailMamalakis et.al [26]	DNN	pediatric CXRs dataset to detect pneumonia IEEE COVID-19 CXRs dataset Tuberculosis CXRs from Shenzhen Hospital x-ray dataset	–	Reduced Equal Error Rate (EER) &| lesser processing time	Lack in process
Jinyu Zhao et.al [41]	AI	CT image dataset about COVID-19	–	–	Low accuracy
Samritika Thakur et.al [37]	CNN	X-rays and CTs	98.28%	A larger Dataset is used for Comparison	Lack in process
Xuehai He et.al [18]	CRNet architecture	COVID19-CT dataset	86%	–	Low accuracy
Muhammad TalhaNafees et.al [31]	CNN	Chest X-ray images along with 5000 normal and 5000 pneumonia samples.	92.29%	Accurate representation of graphs	Validation loss is quite high
Hasib-Al Rashid et.al [33]	DNN	CoughNet-V2 for COVID-19 signature detection in cough sound on the publicly available dataset, COUGHVID	–	Reduced Equal Error Rate (EER) &| lesser processing time	Lack in process

Proposed method

Earlier diagnosis of COVID-19 using CT and CXR images become a challenging task in the healthcare sector. To resolve these problems, this paper presents a sigmoid-based hyper-parameter modification on deep neural networks (SHMDNNs) technique for COVID-19 diagnosis and classification. In the pre-processing stage, the noise removal function enhances the feature of an image, disturbed by noise. In detail, the adaptive Gaussian function was utilized that performs the de-noising process in the images. Then, the proposed SHMDNN classifier classifies the Corona in CT and CXR images into 3 categories namely normal, Pneumonia, and COVID-19 image based on the pre-processed image. Here, the SHMDNN classifier is adapted with the sigmoid function, and to tune the hyperparameter modification involved in the DNN model, the AGWO (Adaptive Grey Wolf Optimizer) algorithm is utilized. Hyper-parameters: learning rate, batch size, momentum, and decrease in weight. The results will be analyzed to show the performance of the classification technology proposed using the existing technology. Figure 1 presents the block diagram of the proposed effective segmentation and classification technique.

Fig. 1

Block diagram of the proposed model

Preprocessing

Consider ΔS is the CT and CXR image database, ΔS∈ {S1, S2, S3, ....Sn} where ‘n’ is the number of images and the vector function. Initially, the input images are preprocessed using an adaptive Gaussian filtering function for noise removal. A Gaussian filter is a linear filter. Filters are used to increase where the underlying purpose is to estimate a noise-contained image of the original image by suppressing it. Equations define the Gaussian filter [20] (1),

Where (p, q) is the current pixel of the image.

Classification using sigmoid-based hyper-parameter modified DNN (SHMDNN)

A deep neural network (DNN) is an artificial, multi-lag, input-output network (ANN). Neural networks have different components, but they always include the same: neurons, synapses, biases, weights, and functions. They are different DNNs typically networks where data flow from the input level to the output layer. In the beginning, a map will be created of virtual neurons and random numeric values or weights assigned to each other. Weights and inputs are increased, resulting in between 0 and 1. If the network does not recognize a particular pattern, the weight is adjusted by an algorithm. A DNN is a type of machine learning system that uses numerous layers of nodes to extract high-level functions from input data. It entails translating data into a more abstract and creative form. Convolution, Sigmoid-based normalization, pooling, and a connection layer are only a few of the layers of the proposed SHMDNN, which solve the DNN problems. C-convolution, MP-max pooling, and FC-full connectivity are explained in the layer type. Table 2, containing three convolutionary layers, two max-pointing layers, a fully connected layer, and a softmax classification, gives a comprehensive illustration of DNNs with the input patch dimensions from 16 × 16 to 7 layers. After the convolutionary layers, the max-pooling was adopted. The first convolutionary layer C1 consists of a data set that is attached to all the patched images of 16 × 16. This layer produces a set of features of 5 × 5. The second layer is the kernel size pooling of 2 × 2. There were no overlapping fields receptive. The second level output was taken by the third layer as a size 5 × 5 input. The same convolutional operation was also used to obtain reduced feature maps in the fourth layer with a size of 2 × 2. The 5th layer takes the fourth layer output as the filter size 5 × 5 entry. The sixth layer was made up of 3 × 1 map size characteristics. At the top of the DNNs, the 6th fully connected layer was applied to detect the relationships between high-level features from past layers. The layers are subject to sigmoid-based changes in the hyperparameter. The last layer of convolution consisted of characteristic 1 × 1 maps. In the final level, one neuron activated by softmax regression produced a value that can be interpreted as the chance of normal, pneumonic, or COVID-19 pixels being centered on the patch. Algorithm 1 delivers the code of the proposed SHMDNN. Figure 2a and b illustrate the construction of the Sigmoid Based Hyper-Parameter Modified DNN (SHMDNN).

Table 2

Details of the proposed sigmoid-based hyper-parameter modified deep neural network (SHMDNN)

Patch Size		Layer1	Layer2	Layer3	Layer4	Layer5	Layer6	Layer7
16X16	Layer Type	C	MP	C	MP	C	FC	Softmax
	Filter Size	5 X 5	2X2	5 X 5	2X2	5X5	3X1	1X1

Fig. 2

a Proposed sigmoid based hyper-parameter modified deep neural network (SHMDNN). b Hyper-parameter optimization using deep neural network

Algorithm 1 Pseudo code of the proposed SHMDNN

The SHMDNN classifier finishes up the conclusion that depends on the weight and biases of the earlier layers in the structure design.

The convolution layer recognizes various input characteristics. A series of convolutionary kernels consist of this layer. The coded kernels divide the image into tiny pieces to extract patterns or maps. By multiplying their instances with the corresponding instances of the specific domain, kernels converge with pictures based on certain weights [10].By using algorithm 1 the weight initialization in the deep neural network and used below equation.

Where Wmeans the weight, B means the bias,n means the layer number, λ means the regularization parameter, LRmeans the learning rate, N means the total amount of training sets,m means momentum, tmeans the upgrading phase andC means the cost function.

Adaptive Grey wolf optimization (AGWO)

We proceed to the Adaptive GWO; there are two reasons to offer the GWO diagnostic algorithm for COVID-19. First, the optimization algorithm is very competitive. It applied to various fields of research including a selection of functions, economic problems in the dispatch of loads, and problems in flow planning. The AGWO algorithm also benefits from avoiding high local optimism, which prevents overlaps in feature selection problems this is a swarm intelligence technique in a deep neural network that copies the organization of control of wolves, which is notable for its group hunting. Boarding a pack is often more valuable to grey wolves. They require a rigid socially dominant progressive system, with an Alpha (α) who can be either male or female. Usually, the alpha bears the brunt of the leadership responsibilities. The pack is required to follow the commands of most wolves. The Betas (β) are the alpha’s subordinate wolves that assist him in basic leadership. The beta is the alpha’s advisor and the pack’s enforcer. When a wolf is neither a (nor), it is referred to as a wolf. Omega wolves are led by delta (δ) wolves, who report to alpha and beta wolves. The fittest solution has been termed the alpha (α) in the mathematical model for the Random Support-based AGWO. Beta (β) and delta (δ) are the names for the second and third best solutions, respectively. Α, β,δ, and lead the hunt here. To boost AGWO and perform optimization, wolves’ hunting style and social hierarchy of command are mathematically modeled. The hyperparameter modification using the Adaptive GWO method has a pseudo-code given in algorithm 2.

Algorithm 2 Pseudo Code of the AGWO

Initialize the AGWO parameter are search agents (Z), vectors , and the most extreme number of iterations [29] (Imax).

The estimations linearly decrease from 2 to 0 through the span of iterations andr1, r2 are random vectors in [0, 1]. The parameter is linearly updated in each cycle to go from [2-0] as indicated by the condition (6),

Wherek is the iteration number andImax is the total number of iterations taken into consideration in the optimization.

Based on the size of the pack, generate wolves at random.

Using the Random Support value as a criterion, evaluate each hunt agent’s fitness esteem (7)

Where is as characterized in (6) andk is the iteration number, are coefficient vectors, is the prey position, and is the grey wolf position.

Find the finest hunt mediator (Z), second-preeminent hunt negotiator (Z), and also the third finest hunt mediator (Z) utilize the circumstance (9),

Using condition, update the current hunt agent’s location (11)

For all hunts assess the fitness value.

Renew the assessment of, and.

If the iteration reaches a maximum, check for a halting condition; if so, offer the best estimate of the answer; otherwise, proceed to step 7.

The Adaptive grey wolf optimization algorithm outputs the Modified hyperparameter. Here, dimensionality lessening of the dataset by utilizing an AGWO algorithm that significantly decreases the computational cost and expands the classification accuracy of data. The SHMDNN classifier contains various kinds of layers below according to the subsequent,

Layer 1: Convolution layer: This layer finishes the convolution of the input data with the kernel by using a condition (12).

WhereZ represents reproduced segmented images, represents the filter, andM represents the number of components inZ& the output vectorC.

Layer 2: Sigmoid-based normalization layer

Sigmoid function:

A sigmoid function consists of a mathematical function with a typical S-shaped curve known as a sigmoid curve. The sigmoid function is shown in the following:

The input is (sig), and the output is (f). In the output of a sigmoid function, the neural network must constantly learn to resolve tasks in a more qualified manner or to apply a variety of methods to achieve a better outcome. It learns how to respond to a replacement situation when it receives new information from the system.

Normalization

The linear alteration of data to fit into a specific range is known as normalization. For data standardization, the Z-score normalization method is used, which transforms data linearly. By using Eq. (13) the Eq. (14) describes how to normalize Z-scores:

Here, Zis the normalized output, f is the sigmoid function value, μ &σsignifies the mean and STD of the output image. The convolution layer output image is normalized using the sigmoid function by using the Eq. (14). This layer leads to the sigmoid-based normalized image and the layer of pooling is given as an input. This layer brings about the support of value-based normalized images and is anticipated to contribute to the pooling layer.

Layer 3: Pooling layer: Another name for the layer is down-sampling. The bundling procedure decreases the size and the fitting strength of the outlet neurons in the convolution layer. The max-pooling algorithm selects only the highest value in each feature map, resulting in fewer output neurons. Pooling layers are often used after convolution layers to simplify the data within the output of the convolution layer.

Layer 4: Fully connected layer: The actuation work computes a probability distribution of the classes. By algorithm 1 the weight initialization is done here. Thus, the output layer uses the softmax function to search out a preceding layer outcome that matches the foremost normal, pneumonia, and COVID-19.

Wherey, which represents the resultant image. Here, the SHMDNN is adapted with the sigmoid function-based normalization to direct the over-fitting in layers and conclusions in the important classification of Corona in CT and CXR images into 3 categories namely normal, pneumonia, and COVID-19 images.

Results & discussion

The results of the experiments will show that the strategy we’ve provided outperforms traditional methods. The findings of the implementation are based on Matlab2018a software running on Intel Core TM i7 CPUs running at 1.6 GHz. Extensive experimental research was conducted to determine the modified hyper parameter chosen by AGWO that provides the highest potential accuracy when utilizing various classifiers.

Dataset

This study used CXR images of COVID-19, normal patients with pneumonia collected from publicly accessible repositories [16]. These repositories produced a sum of 2700 images, including 900 images of COVID-19. All pictures have been set to a resolution of 224x224x3 pixels. The image details are given in Table 3. Before further use, all 5 datasets had been combined with 5000 people (57% male, 32% female), 3500 infected and 1500 healthy controls, and age group 38 to 55 years). The fact that all 5 databases are open source and fully available to clinicians and research community and the general public has been the basis on which these databases are selected for the production of “Hybrid-COVID,” as well as meeting COVID 19 Diagnostic Criteria defined by the World Health Organisation (WHO) [20].

Table 3

Different types of dataset collection

Dataset	Images category	No. of images	Reference
Chest imaging	COVID-19	134	[13]
CT Kaggle	Normal	900	[27]
Covid- chest x-ray	COVID-19	646	[13]
KaggleCXR	Pneumonia	900	[14]
CT Online dataset	COVID-19	1252	[38]

This section presents the detailed data distribution used for the proposed SHMDNNs framework, to get a better understanding of how SHMDNNs make decisions. It authenticates whether it is making recognition decisions, based on significant information (data) or inaccurate information, i.e., biased decisions based on inappropriate data. Such situations are very problematic and difficult to track. A dataset of over 5000 COVID patients was used in this study. The data distribution was analyzed to train and test the X-ray and CT images. The distribution of the CT images for COVID-19 detection is shown in the first half of Table 4. Similarly, the distribution of X-ray images for COVID-19 detection is shown in the second half of Table 4. The training and testing images for all 3 categories (normal, pneumonia, and COVID-19) are shown separately. It can be seen from the table that almost 80% of the data was used for training and almost 20% of the data was used for testing. The evaluation of the training and testing performance of the Sigmoid-based Hyper Parameter Modified Deep Neural Network.

Table 4

Distribution of X-ray and CT images for different categories of disease

Images category	Number of Images (CT)
	Training	Testing
COVID-19	800	200
Normal	400	200
Pneumonia	500	200
Images category	Number of Images (X-ray)
	Training	Testing
COVID-19	1000	200
Normal	300	200
Pneumonia	800	200

Performance and evaluation

The presentation of performance evaluation of the proposed SHMDNNs with Recurrent Neural Networks (RNN) [21], Deep Belief Networks (DBNs) [7], DNNs [39], and Hybrid deep neural network HDNNs [39] classifiers to analytics [16] of results in performance measures such as accuracy, sensitivity, specificity, precision, F1-score and Error Rate shown in the equation in Table 5. The X-ray and CT images dataset are utilized to study the order of images into COVID-19, normal, and pneumonia using the proposed SHMDNNs classification.

Table 5

Performance measures calculation formula for COVID-19

Performance Measures	Formula
Accuracy	TN+TPTN+TP+FN+FP
Sensitivity	TPTP+FN
Specificity	TNTN+FP
Precision	TPTP+FP
Recall	TPTP+FN
F1-score	2TP2TP+FP+FN
Error rate	E_r=1N∑i=1NO_i−O^_i^2

Our results show Fig. 3 which shows the proposed SHMDNNs method has an accuracy slightly higher compared to RNN, DBNs, DNNs, and HDNNs amongst the COVID-19 dataset and testing for 10 to 90 images. The accuracy of the proposed SHMDNNs method is 99.09%, the HDNNs method is 94.50% compared to the DNN Method, which achieves 92.50%, DBN Method, which achieves 89.17%. The RNN had the lowliest accuracy with 89.17% of records correctly classified. The good classifiers noted from the above results are proposed HDNNs and DNN. It can be seen that in all cases, the RNN algorithm has shown to have the lowliest performance over our COVID-19 database.

Fig. 3

Comparison of accuracy with different DNN networks

Figure 4 shows the sensitivity of the proposed SHMDNNs method at 99.05%, HDN Ns method is 97.00% compared to the DNN Method, which achieves 83.00%, DBN Method, which achieves 89%. The RNN had the lowliest accuracy with 82.00% of records correctly classified. The good classifiers noted from the above results are proposed HDNNs and DNN. It can be seen that in all cases, the RNN algorithm has shown to have the lowliest performance over our COVID-19 database.

Fig. 4

Comparison of sensitivity with different DNN networks

Figure 5 clearly shows that the proposed SHMDNNs method has specificity greater than the HDNNs, DNN, DBNs, and RNN with rates of 99.32%. It can be seen that in all cases, the existing algorithms have shown to have the lowliest performance over our database.

Fig. 5

Comparison of specificity with different DNN networks

Figure 6 clearly shows that the proposed SHMDNNs method has precision greater than the HDNNs, DNN, DBNs, and RNN with rates of 96.00%. It can be seen that in all cases, the existing algorithms have shown to have the lowliest performance over our database.

Fig. 6

Comparison of precision with different DNN networks

Figure 7 clearly shows that the proposed SHMDNNs method has an F-Score greater than the HDNNs, DNN, DBNs, and RNN with rates of 98.00%. It can be seen that in all cases, the existing algorithms have shown to have the lowliest performance over our database.

Fig. 7

Comparison of F1-Score with different DNN networks

Figure 8 shows the error rate (ER) of the proposed SHMDNNs method ER is 6%. Without optimization, ER is 9.6%. The good classifiers noted from the above results are proposed with optimization. It can be seen that in all cases, the without optimization algorithm has shown to have the lowliest performance over our work.

Fig. 8

Comparison of Error Rate with different DNN networks

Table 6 shows the accuracy of the proposed SHMDNNs method with classes normal at 89.00%, Pneumonia at 90%, and Covid-19 at 99.9%. In existing HDNNs, DNN, DBN, and RNN methods with classes comparable to lowliest performance over our COVID-19 database.

Table 6

Performance measures accuracy calculation

Accuracy
Neural Network Architecture	Normal	Pneumonia Patient	Covid-19 Patient
RNN [21]	79%	78%	80%
DBN [7]	80%	82%	82.7%
DNN [39]	82%	86%	83%
Hybrid deep neural network [39]	80%	89%	95%
Proposed (SHMDNNs)	89%	90%	99.9%

Table 7 shows the sensitivity of the proposed SHMDNNs method with classes normal at 90.00%, Pneumonia at 92%, and Covid-19 at 99.5%. In existing HDNNs, DNN, DBN, and RNN methods with classes comparable to lowliest performance over our COVID-19 database.

Table 7

Performance measures sensitivity calculation

Sensitivity
Neural Network Architecture	Normal	Pneumonia Patient	Covid-19 Patient
RNN [21]	76%	77%	82%
DBNs [7]	80%	82.8%	83.7%
DNNs [39]	81%	86.5%	83.8%
Hybrid deep neural network [39]	89%	90%	97%
Proposed (SHMDNNs)	90%	92%	99.5%

An important aspect of ROC curves is their visual interpretation, as the curves display the trade-off between sensitivity (TPR-True Positive Rate) and specificity (FPR -False Positive Rate) for distinct solutions of AGWO. We analyzed ROC curves for the COVID-19 dataset (3 classes) as well as for Class 1- COVID-19, Class 2- Normal, and Class 3-Pneumonia). The simulated result is shown in Fig. 9 with the optimal number of classes. As class values increase, causing the class to overlap, their corresponding AUCC values decrease considerably. From this perspective, scenarios in which only low to moderate AUCC evaluations are observed for a given ground-truth solution, cannot be properly recovered despite AGWO algorithms.

Fig. 9

ROC curves of the AGWO (Class 1- COVID-19, Class 2- Normal, Class 3-Pneumonia)

The confusion matrix for each DNN network is presented in Fig. 10 and the accuracy of the performance matrix is computed. These comparisons show that AGWO-optimized DNN has the best accuracy. The proposed network can therefore be reliably used for COVID-19 diagnostics in real-time applications. Confusion matrices are generated based on the subsequent conditions.

Fig. 10

Confusion matrix of various DNN networks with the performance matrix accuracy calculation

TP: True Positive: The image accuracy values were positive and were predicted positive.

FP: False Positive: The image accuracy values were actually negative but falsely predicted as positive.

FN: False Negative: The image accuracy values were positive but falsely predicted as negative.

Comparative analysis

Table 8 lists the respective accuracy, sensitivity, precision, and specificity values of the test on different groups of X-ray and CT images, as well as a comparison of the proposed methods with related work. In comparative analysis first used the dataset to compare the proposed SHMDNN experimental outcomes with the [27-33],

Table 8

Comparison of the results of various DNN methods

Reference	Dataset	Method	Accuracy	Sensitivity	Specificity	Precision	F1 Score
[27]	COVID-19 Bac.Pneu* Vir.Pneu#	CNN	83.5	–	–	–	–
[14]	COVID-19	ResNet	–	96.6	70.7	–	–
[38]	COVID-19 Pneumonia Normal	VGG-19	93.48	–	–	–	–
[21]	COVID-19 (+) COVID-19(−)	ResNet-50 + SVM	95.38	–	–	–	–
[7]	COVID-19(+) No findings COVID-19(+)	DarkCovidNet	98.8	–	–	–	–
[39]	COVID-19	COVID-CAPS	95.7	90	95.8	–	–
[20]	COVID-19	COVID-Net	96.23	–	–	–	–
Proposed SHMDNN	COVID-19 Pneumonia Normal	SHMDNN	99.9	96	97.5	94	93

Conclusion

This paper presents SHMDNNs that are subject to a sigmoid-based hyper-parameter modification using AGWO on deep neural networks for the diagnosis of corvid-19, normal, and pneumonia patients from CT and CXR images. The proposed network consists of layers that insist on a deep neural network. The processing is done through a Gaussian filter then the filtered image goes under the classification stage. The acquired outcomes show that the hyperparameter modification usingAGWO performed well. The proposed SHMDNNs produced better performance metrics when compared with the existing works. With this work, more and more cases of COVID-19 are determined. In future work to increase the performance of COVID-19 classification using a modified deep learning method used to improve the classification.