Abstract
The COVID19 pandemic globally and significantly has affected the life and health of many communities. The early detection of infected patients is effective in fighting COVID19. Using radiology (XRay) images is, perhaps, the fastest way to diagnose the patients. Thereby, deep Convolutional Neural Networks (CNNs) can be considered as applicable tools to diagnose COVID19 positive cases. Due to the complicated architecture of a deep CNN, its realtime training and testing become a challenging problem. This paper proposes using the Extreme Learning Machine (ELM) instead of the last fully connected layer to address this deficiency. However, the parameters’ stochastic tuning of ELM’s supervised section causes the final model unreliability. Therefore, to cope with this problem and maintain network reliability, the sine–cosine algorithm was utilized to tune the ELM’s parameters. The designed network is then benchmarked on the COVIDXray5k dataset, and the results are verified by a comparative study with canonical deep CNN, ELM optimized by cuckoo search, ELM optimized by genetic algorithm, and ELM optimized by whale optimization algorithm. The proposed approach outperforms comparative benchmarks with a final accuracy of 98.83% on the COVIDXray5k dataset, leading to a relative error reduction of 2.33% compared to a canonical deep CNN. Even more critical, the designed network’s training time is only 0.9421 ms and the overall detection test time for 3100 images is 2.721 s.
Similar content being viewed by others
Explore related subjects
Find the latest articles, discoveries, and news in related topics.Avoid common mistakes on your manuscript.
1 Introduction
In recent decades, the detection and diagnosis of various diseases have been successfully investigated by scientists (Jiang (2017); Li 2020; Zhu et al. 2020a; b; Zou et al. 2019). However, the early diagnosis of coronavirus has become a challenge for scientists due to the limited treatments and vaccines (AlWaisy et al. 2020; Ashraf et al. 2020; Dansana 2020; Selvakumar and Lokesh 2021; Yousri et al. 2021). The polymerase chain reaction (PCR) test has been introduced as one of the primary methods for detecting COVID19 (Bwire et al. 2020). However, the PCR test is a laborious, timeconsuming, and complicated process with current kits in short supply (Wu et al. 2007). On the other hand, Xray images are extensively accessible (Hu et al. 2020; Jiang 2020; Li et al. 2020), and scans are comparatively lowcost (Pan 2020; Zenggang et al. 2019; Zuo et al. 2017).
Therefore, a method based on chest Xray imaging has become almost the most useful method to detect COVID19 positive cases (Alabool et al. 2020). However, this method suffers from the longtime needed by the radiologists to read and interpret Xray images (Eken 2020). Besides, due to the increasing prevalence of the COVID19 virus, the number of patients, who need an Xray image interpretation, is much higher than the number of radiologists leading to the radiologists overloaded, longtime diagnosis process, and a critical risk of other people’s infection. Thereby, the rapid and automated Xray image interpretation for accurately diagnosing the COVID19 positive cases is necessary. In this regard, ComputerAided Diagnostic (CAD) models have been recently utilized to help radiologists (AlWaisy et al. 2020; Dansana 2020; Alabool et al. 2020; AlQaness et al. 2020).
DeepLearning (DL) models have been widely utilized in various challenging image processing and classification tasks (He et al. 2020; Ma and Xu 2020; Yang et al. 2021) including the COVID19 positive cases’ early detection and diagnosis (Abudureheman and Nilupaer 2021). DeepCOVID (Minaee et al. 2020a) was almost the pioneer in COVID19 detection using DL models. In this research, four wellknown DEEP CNNs, including SqueezeNet, ResNet18, ResNet50, and DenseNet121 were proposed to identify COVID19 positive cases in the analyzed chest Xray images. Aside from the results, this reference provides a unique dataset of 5000 Chest Xrays (called COVIDXray5k) that radiologists have validated. This distinctive feature of the provided dataset motivates us to use it as a benchmark dataset.
Ozturk et al. (2020), an automated DarkNet model was used to perform a binary and a multiclass classification task. This model has designed to achieve up to 98% accuracy, but it used seventeen convolutional layers and numerous filtering on each layer leading to a model with high complexity. A particular deep CNN named CoroNet (Khan et al. 2020) was proposed to recognize COVID19 positive cases from chest Xray images automatically. CoroNet is based on Xception architecture pretrained on ImageNet dataset and trained endtoend on a dataset developed by gathering COVID19 and other chest pneumonia Xray images from two separate publicly accessible databases. Although the proposed model was fast and straightforward, the results were highly tolerable in accuracy and reliability. A customized deep CNN for detecting COVID19 positive cases, named COVIDNet, was proposed by Wang et al. (2020a). This model was utilized to divide the chest Xray image into normal and COVID19 classes. The performance of the COVIDNet model was evaluated using two publicly available datasets. It is noted that the highest accuracy rate of 92.4% was obtained by COVIDNet, which is not very interesting. COVIDXNet (Hemdan et al. 2020) is another DL model utilized to diagnose the COVID19 positive cases by chest Xray images’ analysis. This model has been evaluated on seven wellknown pretrained models (e.g., DenseNet201, VGG19, ResNetV2, Inception, Xception, MobileNet, and V2InceptionV3) using a small dataset of fifty Xray images. In this experiment, the highest accuracy rate of 91% was obtained using the DenseNet201. Reference (Mohammed 2020) proposed a novel model to select the best COVID19 detector using the TOPSIS and Entropy technique as well as 12 machine learning classifiers. The linear SVM classifier obtained the highest accuracy of 98.99%. Although the proposed represents a high classification accuracy, the model complexity was very high in time and space.
In another point of view, several deep CNNs were also utilized as feature descriptors to transfer the input image into lowerdimensional feature vectors (Kassani et al. 2020; Zhang et al. 2020a; Apostolopoulos and Mpesiana 2020; Abualigah et al. 2017). Afterward, these extracted feature vectors were fed into various classifiers to produce the final decision. Despite the reasonable classification accuracy (between 98 and 99%), these methods require manual parameter setting and matching feature extraction section with the classifier section. Also, the complexity of the final model is relatively high.
On the other hand, several methods have utilized preprocessing methods to improve the performance of classifiers. Heidari et al. (2021), Authors tried to use preprocessing methods to eliminate diaphragms, normalize Xray image contrasttonoise ratio, and produce three preprocessed images, which are then linked to a transfer learningbased deep CNN (i.e., VGG16) to categorize chest Xray images into three classes of COVID19, pneumonia, and normal cases. The classifier obtained the highest accuracy of 93.9%. A comparison study between VGG19, Inception_V2, and the decision tree model was performed in Dansana (2020) to develop a binary classifier. In this work, first, the input images’ noise level was eliminated using a feature detection kernel to produce compact feature maps. These feature maps were fed into the DL models as input. The best accuracy rate of 91% was obtained using VGG19 compared to 78%, and 60% were obtained by Inception_V2 and the decision tree method, in order. Heidari et al. (2020), after using a preprocessing model to detect and eliminate diaphragm areas showing on images, a histogram equalization algorithm and a bilateral filter are utilized to process the primary images to produce two sets of filtered images. Afterward, the primary image and the two filtered images are applied as inputs of three channels of the deep CNN to increase the model’s learning information. The designed model with two preprocessing stages generates a total accuracy of 94.5%, whereas without using two preprocessing steps, the designed model generates a lower classification accuracy of 88.0%. Although these methods increase the classifier’s accuracy, they will increase the overall complexity of the network.
Consequently, the necessity of designing an accurate (Liu et al. 2021; Yang and Sowmya 2015; Zhang et al. 2020b, c) and realtime detector (Ran et al. 2020; Wang 2020; Zuo et al. 2015) has become more prominent. Besides, this review on COVID19 detection systems shows that most of the existing deep learningbased systems have used deep CNNbased networks (Li et al. 2019a; Ma et al. 2019; Xu et al. 2020; Yang et al. 2020a,2021); thereby, we propose to employ the ability of deep CNN as a COVID 19 detector.
However, the aforementioned CNNbased methods are timeconsuming, at least throughout the training phase. Therefore, before the user obtains feedback from the training phase, training and testing time can take hours even if the detector works well in the determined case. Besides, selflearning Xray image detection, which trains progressively based on the user’s feedback, may not have an excellent user experience because it takes too long until the model converges while operating with it. In this case, the challenging point is having an appropriate model for Xray image detection, which is efficient in both processing time and accuracy.
For the sake of having a realtime COVID19 recognizer, this paper proposes using ELM (Huang et al. 2006) instead of a fully connected layer to provide a realtime training process. In the proposed approach, we combine automatic feature learning of deep CNNs with efficient ELMs to address the mentioned shortcomings, i.e., manual feature extraction and extended training time, respectively. Consequently, the first phase is the deep CNN’s training, which is considered an automatic feature extractor. In the second phase, a fully connected layer will be replaced by ELM for designing a realtime classifier.
It is proven that the ELM’s origin is based on Random Vector Functional Link (RVLF) (Pao et al. 1994; Wang et al. 2021), leading to the ultrafast learning and outstanding generalization capability (Zhang 2020; Niu 2020). Literature survey shows that ELM has been broadly utilized in many engineering applications (Li et al. 2019b; Liu 2020; Yang et al. 2020b). Although various kinds of ELMs are now accessible for image detection and classification tasks, it confronts serious issues such as the need for many hidden nodes for better generalization and determining the activation function type. Besides, ELM’s stochastic nature causes an additional uncertainty problem, particularly for highdimensional image processing problems (Xie et al. 2012; Chen et al. 2012).
The ELMbased models randomly select the input weights and hidden biases from which the output weights are calculated. During this procedure, ELMs try to minimize the training error and identify the smallest output weights’ norm. Due to the stochastic choice of the input weights and biases in ELM, the output matrix may not indicate full column rank, leading to the system’s illconditioned matrices that produce nonoptimal solutions (Xiong et al. 2016; Niu et al. 2020). Consequently, we apply a novel metaheuristic algorithm called SCA (Mirjalili 2016) to improve ELM conditioning and ensure optimal solutions.
For the rest of this research paper, the organization is as follows. In Sect. 2, some background resources are reviewed. Section 3 introduces the proposed scheme. Section 4 presents the simulation and discussion results, and finally, conclusions are presented in Sect. 5.
2 Background and materials
This section will represent the background knowledge, including the deep CNN, ELM, SCA, and COVIDXray5k dataset.
2.1 Deep convolution neural network
Generally, deep CNN is a conventional Multilayer perceptron (MLP) based on three concepts: connection weights sharing, local receive fields, and temporal/spatial subsampling (AlSaffar et al. 2017). These concepts can be arranged into two classes of layers, including subsampling layers and convolution layers. As shown in Fig. 1, the processing layers include three convolution layers C1, C3, and C5, located between layers S2 and S4, and final output layer F6. These subsampling and convolution layers are organized as feature maps. Neurons in the convolution layer are linked to a local receptive field in the prior layer. Consequently, neurons with identical feature maps (FMs) receive data from various input regions until the input is completely skimmed. However, the same weights are shared.
In the subsampling layer, the FMs are spatially by a factor of 2. As an illustration, in layer C3, the FM of size 10 × 10 is subsampled to conforming FM of size 5 × 5 in the next layer, S4. The classification process is the final layer (F6). Each FMs are the outcome of a convolution from the previous layer’s maps by their corresponding kernel and a linear filter in this structure. The weights \(w^{k}\) and adding bias bk generate the kth (FM) \({\text{FM}}_{ij}^{k}\) using the tanh function as Eq. (1).
By reducing the resolution of FMs, the subsampling layer leads to spatial invariance, in which each pooled FM refers to one FM of the prior layer. The subsampling function is defined as Eq. (2).
where \(\alpha_{i}^{n \times n}\) are the inputs,\(\beta\) and b are trainable scalar and bias, respectively, after various convolution and subsampling layers. The last layer is a fully connected structure that carries out the classification task. There is one neuron for each output class. Thereby, in the case of the COVID19 dataset, this layer contains two neurons for their classes.
2.2 Extreme learning machine
ELM is one of the most widely used singlehidden layer neural network (SLNN) learning algorithms (Huang et al. 2006). ELM first randomly sets the input layer’s weights and biases and then calculates the output layer’s weights using these random values. This algorithm has a faster learning rate and better performance than traditional NN algorithms. Figure 2 indicates a typical SLNN, in which n denotes the number of input layer neurons, L indicates the number of hidden layer neurons, and m shows the number of output layer neurons.
As indicated in Huang et al. (2006), the activation function can be shown as Eq. (3).
where w_{i} denotes the input weight, b_{i} shows the ith hidden neuron’s bias, x_{j} represents the output weight, and Z_{j}is the SLNN output. The matrix representation of Eq. (3) is shown in Eq. (4).
where \(Q = [Q_{1} ,Q_{2} ,...,Q_{L} ]^{{\text{T}}}\), \({\mathbf{Z}}^{T}\) is the transpose of matrix Z, H is a matrix named hidden layer output matrix, which is calculated in Eq. (5).
Minimizing the training error is the primary training goal of ELM. In the conventional ELM, input biases and weights must be stochastically chosen, and the activation function must be infinitely differentiable. In this regard, the training of ELM leads to obtaining the output weight (Q) by optimizing the leastsquares function indicated in Eq. (6), and the result can also be calculated as Eq. (7)
In this equation, H^{+} denotes the generalized Moore–Penrose inverse of the H matrix.
2.3 Sine–Cosine algorithm
Generally speaking, the optimization process in populationbased methods begins with a series of responses that are randomly selected. The output function continually evaluates these random responses. Finally, the result of the output function gets optimized by the intended optimization method. If the number of selected responses and the iterations are appropriately considered, the probability of getting the best answer is also increased (Khishe and Mosavi 2020a; Abualigah and Diabat 2021).
Despite the differences between existing algorithms for populationbased random optimization, in all of them, the optimization process is performed in two stages: exploration and exploitation (Mosavi et al. 2016b; Khishe and Mosavi 2020b; Khishe and Safari 2019). A randomized algorithm combines stochastic responses at a high rate in the search stage to find possible areas in search space. At the identification stage, slight changes are made to random responses, and outputs are recalculated. The method to calculate these outputs after applying changes to random responses is shown in Eqs. (8) and (9) (Mirjalili 2016).
In which \(X_{i}^{t}\) is the location of current response in ith dimension and tth iteration. Also, \(r_{1} ,r_{2} ,r_{3}\) are random numbers, p_{i} is the location of a destination in the ith dimension and \( \cdot \) represents absolute value. Equations (8) and (9) can be combined to generate Eq. (10).
In which r_{4} is a random number in a range of [0, 1]. As shown in Eq. (10), there are four main parameters \(r_{4} ,r_{3} ,r_{2} ,r_{1}\) in the algorithm. The parameter r_{1} shows the next location area (or direction of motion) that can be between the source and destination (or outside of it). The parameter r_{2} defines the amount of movement toward the destination or in the opposite direction. The parameter r_{3} determines the size of random weight to reach the destination (which may have a value as r_{3} > 3 or r_{3} < 3). Eventually, r_{4} changes equally between the components of the sinus and cosine as shown in Eq. (8). Figure 3 shows the effect of the sinus and cosine functions on Eqs. (8) and (9). This figure shows how the proposed equation defines the area between two responses in the search area (of course, this figure is plotted for the twodimensional space).
It should be noted, however, that Eqs. (8) and (9) can be extended to higher dimensions. The periodic form of the sinus and cosine functions allows a response to accumulating around another response. Therefore, identifying the defined space between the two responses is guaranteed. In order to find the destination (target) in the search area, the solution should search the space between similar responses (targets) comprehensively (Wang et al. 2020b). As shown in Fig. 4, this ability is achievable by changing the range of the sinus and cosine functions.
A conceptual model is shown in Fig. 5 to indicate the effectiveness of the sinus and cosine functions. This figure shows how the range of sine and cosine changes in order to update the location of a response.
If the parameter r_{2} in Eq. (10) is defined as a random number in the range [0, 2π], then the existing mechanism guarantees to explore the search area. An appropriate algorithm should balance the exploration and exploitation operations, identify possible search areas, and ultimately converge to a general optimum. To achieve a balance between the exploitation and exploration phases, the domain of the sinus and cosine functions in Eqs. (8), (9), and (10) varies by Eq. (11).
where t is the current step, T is the maximum number of steps, and a is also a fixed number. Figure 6 shows the reduction in the range of the sinus and cosine functions during iterations.
According to Figs. 3 and 4, when the sinus and cosine functions are in the range of [−2, −1) and (1, 2], the algorithm will explore the search area. On the contrary, when they are in the range of [−1, 1], the algorithm detects the search area. This figure shows that the algorithm starts the optimization process using a set of random answers. Then the algorithm reserves the best answers (solutions) that have been obtained so far. The reserved answers are set as targets, and the rest of the responses are updated according to these targets. Besides, the range of the sinus and cosine functions are updated to enhance the search space identification and increase the number of steps.
The optimization process by the algorithm ends when the number of steps exceeds the maximum defined by default. Of course, it should be noted that other conditions, such as the maximum number of function evaluations or overall optimization accuracy, can be considered as conditions to end the optimization process. By using the operators mentioned above, the proposed algorithm can solve optimization problems theoretically for the reasons given below.

The algorithm creates and optimizes a set of random answers for a particular problem. Therefore, its advantage compared to other algorithms that are based on one response is the high exploration ability and avoidance of trapping in local minima.

When the sinus and cosine functions have values greater than 1 or smaller than −1, different search space areas are explored to find the answer.

When the sinus and cosine functions have values between 1 and −1, the explored areas are likely to be part of the answer.

The algorithm alters slowly from exploration to exploitation mode based on changes in the range of the sinus and cosine functions.

The best optimum approximation is stored in a variable as the target (response) and maintained throughout the entire optimization process.

As responses constantly update their location around the best answer, they always tend to choose the best search area during the optimization process.

Since the proposed algorithm considers the problem as a black box, it can be easily used for wellformulated problems.
2.4 COVIDXray dataset
A dataset named COVIDXray5 k dataset, including 2084 training and 3100 test images, was utilized (Minaee et al. 2020a). In this dataset, considering radiologist advice, only anterior–posterior COVID19 Xray images are used because the lateral photos are not applicable for detection purposes. Expert radiologists evaluated those images, and those that did not have clear pieces of evidence of COVID19 were eliminated. In this way, 19 images out of the whole 203 images were removed, and 184 images remained, indicating clear pieces of evidence of COVID19. With this method, a group with a more clearly labeled dataset was introduced. Out of 184 photos, 100 images are considered for the test set, and 84 images are intended for the training set. For the sake of increasing the number of positive cases to 420, data augmentation is applied. Since the number of normal cases was small in the covidchestxraydataset (Wynants et al. 2020), the supplementary ChexPert dataset (Irvin 2019) was employed. This dataset includes 224,316 chest Xray images from 65,240 patients. Two thousand and 3000 nonCOVID images were chosen from this dataset for the training and test sets, respectively. The final number of images related to various classes is reported in Table 1. Figure 7 indicates six stochastic sample cases from the COVIDXray5 k dataset, including two positive and four normal samples.
3 Methodology
As previously stated, this paper uses the LetNet5 structure as a COVID19 positive cases detector. It consists of three convolutional layers, two pooling layers followed by a Fully Connected (FC) layer, which uses Gradient Descentbased Back Propagation (GDBP) algorithm for learning. Considering the aforementioned GDBP deficiencies, we propose to use a singlelayer ELM instead of FC layers to classify the extracted features, as shown in Fig. 8.
The convolutional layers’ weights are pretrained on a large dataset as a complete LetNet5 with a standard GDBP learning algorithm. After the pretraining phase, the FC layers are removed, and the remaining layers are frozen to exploit as a feature extractor. The features generated by the stubCNN will provide the ELM network’s input values. In the proposed structure, ELM has 120 hidden layer neurons and two output neurons. Noted that the sigmoid function is used as an activation function.
3.1 Stabilizing ELM using SCA
Despite the reduction of training time in ELMs compared to the standard FC layer, ELMs are not stable and reliable in realworld engineering problems due to the random determination of the input layer’s weights and biases. Thereby, we apply the SCA for tuning the input layer weights and biases of ELM to increase the network stabilization (SCAELM) and reliability while keeping the realtime operation. Generally, there are two main issues in tuning a deep network using a metaheuristic optimization algorithm. First, the structure’s parameters must be represented by the searching agents (candid solution) of the metaheuristic algorithm; next, the fitness function must be defined based on the considered problem’s interest.
The presentation of network parameters is a distinct phase in tuning a Deep Convolutional ELM using SCA (DCELMSCA) algorithm. Thereby, ELM’s input layer weights and biases should be determined to provide the best diagnosis accuracy. To sum up, SCA optimizes the input layer weights and biases of ELM, which are used to calculate the loss function as a fitness function. In fact, the values of weight and bias are used as searching agents in the SCA. Generally speaking, three schemes are used to present weights and biases of a DCELM as candid solutions of the metaheuristic algorithm: vectorbased, matrixbased, and binary state (Mosavi et al. 2017a, b, 2019). Because the SCA needs the parameters in a vectorbased model, in this paper, the candid solution is shown as Eq. (12) and Fig. 9.
where n is the number of the input nodes, W_{ij} indicates the connection weight between the ith feature node and the jth ELM’s input neuron, and b_{j} is the bias of the jth input neuron. As previously stated, the proposed architecture is a simple LeNet5 structure (LeCun 2015). In this section, two structures, namely in_6c_2p_12c_2p and in_8c_2p_16c_2p, are used where c and p, are convolution and pooling layers, respectively. The kernel size of all convolution layers is 5 × 5, and the scale of pooling is downsampled by a factor of 2.
3.2 Loss function
In the proposed metaheuristic method, the SCA algorithm trains DCELM to obtain the best accuracy and minimize evaluated classification error. This objective can be computed by the loss function of the metaheuristic searching agent or the mean square error (MSE) of the classification procedure. However, the loss function used in this method is as follows (Mosavi et al. 2016a):
where o shows the supposed output, u indicates the desired result, and N indicates the number of training samples. Two termination criteria include reaching maximum iteration or predefined loss function are utilized by the proposed SCA algorithm. Consequently, the pseudocode of DCELMSCA is shown in Fig. 10. Also, a schematic workflow explaining the proposed method is shown in Fig. 11.
4 Simulation results and discussion
As previously stated, the hybrid method’s primary target is to enhance the diagnosis rate of classic deep CNN by using the ELM and SCA learning algorithms. In the DCELMSCA simulation, the population is equal to 50, and the maximum iteration is equal to 10. The parameter of deep CNN, i.e., the learning rate \(\alpha\) and the batch size, are equal to 0.0001 and 12, respectively. Also, the number of epochs is considered between 1 and 10 for every evaluation. We downsample all input images to 31 × 31 before applying them to deep CNNs. The assessment was carried out in MATLABR2019a on a PC with Intel Core i74500u processor, 16 GB RAM, in Windows 10, with ten individual runtimes. The performance of DCELMSCA is compared with DCELM (Kölsch et al. 2017), DCELMGA (Sun et al. 2020), DCELMCS (Mohapatra et al. 2015), and DCELMWOA (Li et al. 2019c) on the COVIDXray5k dataset. The parameters of the SCA, GA, CS, and WOA are shown in Table 2.
4.1 Evaluation metrics
Various metrics can be remarkably used to measure classification models’ efficiency, such as sensitivity, classification accuracy, specificity, precision, Gmean, Norm, and F1score. Since the dataset is significantly imbalanced (100 COVID19 images, 3000 NonCOVID images), we utilize specificity (true negative rate) and sensitivity to correctly reporting the performance of designed models, as following equations (true positive rate).
where TP denotes the number of true positive cases, FN is the number of falsenegative cases, TN indicates the number of true negative cases, and FP represents the number of falsepositive cases.
4.2 Structure expected probability grades
As previously stated, as the importance of time complexity, we utilize two simple LetNet5 convolutional structures, i. e., in_6c_2p_12c_2p and in_8c_2p_16c_2p. The probability grade for each image is predicted by these structures, which indicates the possibility of the image being identified as COVID19. Comparing this likelihood with a threshold, we can extract a binary label indicating whether the specified image is COVID19 or not. A perfect structure must identify all COVID19 cases’ likelihood close to one and NonCovid cases close to zero.
Figures 12 and 13 indicate the distribution of Expected Probability Grades (EPG) for the images in the test dataset, by in_6c_2p_12c_2p and in_8c_2p_16c_2p models, respectively. Because the NonCovid category in covidchestxraydataset includes general cases and other kinds of infections, the distribution of EPG is presented for three categories, i.e., Covid19, NonCovid other infections, and NonCovid general cases. As shown in Figs. 12 and 13, the NonCovid images with other kinds of infections have slightly larger grades than the NonCovid general samples. It is logical since NonCovid other infection images are more complicated to recognize from COVID19 than general cases. Positive COVID19 cases are expected to have much higher probabilities than the NonCovid cases, which is certainly stimulating, as it indicates the structure is learning to recognize COVID19 from NonCovid samples. The confusion matrices for these two structures on COVIDXray5k are shown in Figs. 14 and 15.
Considering the calculated result, we choose the in_8c_2p_16c_2p structure as a benchmark structure named conventional deep CNN.
4.3 The comparison of specificity and sensitivity
Each structure EPG is indicating the possibility of the image being COVID19. These EPGs can be compared with a cutoff threshold to deduce whether the image is a positive COVID19 case or not. We use calculated labels to evaluate the specificity and sensitivity of each detector. Various specificity and sensitivity rates can be calculated based on the value of the cutoff threshold. The specificity and sensitivity rates based on conventional deep CNN, DCELM, DCELMGA, DCELMCS, DCELMWOA, and DCELMSCA models for various thresholds are represented in Table 3.
Given that the results are provided for ten individual runs, Table 3 shows the Average (Ave) and Standard deviation (Std) of the results. Besides, Wilcoxon’s ranksum test (Wilcoxon et al. 1970), a nonparametric statistical test, was carried out to investigate whether the results of the DCELMSCA differ from other compared models in a statistically significant way. It must be noted that a significance level of 5% was achieved in this case. In addition to AVE and STD, the ranksum’s p values are reported in Table 3. It is worth noting that the N/A in the tables of results shortened form of “Not Applicable,” which indicates that the relating algorithm cannot be compared with itself in Wilcoxon’s test. Values greater than 0.05 indicate that the two comparison algorithms are not significantly different from each other; it should be noted that these numbers have been marked with an underline.
The data presented in Table 3 shows that all benchmark networks obtain very encouraging outcomes, and the best performing structure (DCELMSCA) achieves a sensitivity rate of 100% and a specificity rate of 99.11%. In second and third place, DCELMCS and DCELMWOA get slightly better efficiency than other benchmark structures.
4.4 The Reliability analysis of imbalance dataset
Considering the limitation of the number of approved labeled positive COVID19 cases, we just have 100 positive COVID19 cases in the COVIDXray5k dataset. Therefore, the reported sensitivity and specificity rates in Table 3 may not be completely reliable. Theoretically, more numbers of positive COVID19 cases are needed to carry out a more reliable assessment of sensitivity rates. However, the 95% confidence interval of the obtained specificity and sensitivity rates can be evaluated to examine what is the feasible interval of calculated values for the current number of test cases in each category. We can calculate the accuracy rate’s confidence interval as Eq. (16) (Hosmer and Lemeshow 1992).
where p indicates the confidence interval’s significance level, i.e., the Gaussian distribution’s standard deviation, N represents the number of cases for each class, Accuracy · Rate is the evaluated accuracy, which is sensitivity and specificity in this example. The 95% confidence interval is utilized to lead to the corresponding value of 1.96 for p. Because a sensitive network is essential for the COVID19 detection problem, the particular threshold levels are selected, which corresponds to a sensitivity rate of 98% for each benchmark network, and their specificity rates are then examined. The comparison of the six model’s performance is presented in Table 4. The data presented in Table 4 show that the specificity rates’ confidence interval is about 1%. In comparison, it is equal to around 2.8% for sensitivity because there are 3000 images for the NonCovid class, whereas 100 images for the sensitivity rate in the test set.
As can be seen in Table 4, the specificity of canonical deep CNN was reduced when the ELM network was applied, i.e., the specificity of DCELM is lower than deep CNN. However, the specificity of DCELMSCA is higher than canonical deep CNN and DCELM because of applying the SCA algorithm to improve the whole network’s stability.
The comparison of various structures just based on their specificity and sensitivity rates does not represent enough information about the detector’s performance because various threshold levels cause different specificity and sensitivity rates. The precisionrecall curve is a good presentation that can be utilized to see the comprehensive comparison between these networks for all feasible cutoff threshold levels. This presentation indicates the precision rate as a function of recall rate. Precision is defined as the TPR divided by the TP [i.e., Eq. (14)], and the recall is the same as TNR [i.e., Eq. (15)]. Figure 16 shows the precisionrecall plot of these six benchmark models. The Receiver Operating Characteristic (ROC) plot is another appropriate tool representing the TPR as a function of FPR. Therefore, Fig. 16 also shows the ROC curve of these six benchmark structures. The ROC curves show that DCELMSCA significantly outperforms other DCELMbased networks as well as conventional deep CNN on the test dataset. However, it should be noted that the area under curve (AUC) of ROC curves may not right indicate the model efficiency since it can be very high for broadly imbalanced test sets like the COVIDXray5k dataset.
4.5 The analysis of time complexity
Measuring the time complexity is necessary for the sake of analyzing a realtime detector. In this regard, besides the benchmark networks, we implement the designed COVID19 detector using NVidia Tesla K20 as the GPU and an Intel Core i74500u processor as the CPU. The testing time is the time required to process the whole test set of 3100 images. As shown from Fig. 16, the DCELMSCA detector indicates outstanding COVID19 detection results compared with other benchmark models. For the sake of comparison, the proposed DCELMSCA provides over 99.11% correct COVID19 sample detection for less than a 0.89% false alarm detection rate, which shows the SCA algorithm’s capability to increase the performance of the deep CNN model.
Generally, the precisionrecall plot shows the tradeoff between recall and precision for various threshold levels. A high area under the precisionrecall curve represents both high precision and recall, where high precision indicates a low falsepositive rate, and highrecall indicates a low falsenegative rate. As can be observed from the curves in Fig. 16, DCELMSCA has a higher area under the precisionrecall curves. Therefore, it means a lower falsepositive and falsenegative rate than other benchmark detectors. The simulation results indicate that DCELMSCA represents the best accuracy for all epochs.
As shown from the ROC and precisionrecall curves, the area under curve (AUC) of DCELM (deep CNN with ELM) is reduced compared to conventional deep CNN. It means that deep CNN’s performance decreases when we replace the fully connected layer with ELM because the advantages of supervised learning are neglected. However, it is pronounced that other evolutionary deep CNNs have better performance compared to standard deep CNN. We benefit from the stochastic supervised nature of the evolutionary learning algorithm and the unsupervised nature of ELM. Consequently, the result detector’s performance is improved by combining the advantages of these hybrid supervisedunsupervised learning algorithms.
From another point of view, when considering the result of Table 5, it is apparent the training and testing time of DCELMs is remarkably lower than classic deep CNN. Notably, in GPU accelerated training, the proposed approach is more than 538 times faster than the current deep CNN. Considering the number of testing and training images in Table 1 and also the entire test and training processing time in Table 5, we can easily conclude that DCELMs require less than one millisecond per image for both training and testing, thus making DCELMs realtime in both phases. Because more than 90% of the processing time is related to the feature extraction part, using other deeplearning models can reduce the processing time even further. Note that the best results are highlighted in bold type.
4.6 Sensitivity analysis of designed model
This subsection evaluates the sensitivity analysis of three control parameters employed in the designed model. The first parameter is a, which controls the reduction rate in the range of the sinus and cosine functions during the execution of iterations and its contribution to the optimization process, and the second and third ones are related to the network structure, i.e., the number of layers and batches. The analysis indicates which parameters are sensitive to various inputs and which ones are robust. Considering the references (Chai et al. 2019, 2020), experiments were conducted by defining fourparameter levels, as represented in Table 6. Afterward, an orthogonal array can be generated to characterize various parameter combinations (as represented in Table 7). The designed model is trained for each parameter combination. The calculated MSEs for various experiments are also represented in Table 7. Considering the results from Table 7, the level trends of parameters are indicated in Fig. 17. As shown in this figure, the best performance is obtained if these three parameters are set as N_{L} = 5, a = 1, and N_{b} = 10.
4.7 The analysis of convergence behavior
For more clarification, this subsection describes the experimental analyses of SCA’s searching agents’ convergence behavior. So, SCA’s searching agents’ convergence behavior is evaluated using qualitative metrics, including average fitness history and dynamic trajectories. Figure 18 represents the qualitative metrics for SCA’s searching agents’ convergence behavior in the four categories of benchmark optimization functions (i.e., unimodal, multimodal, fixeddimension multimodal, and composition benchmark functions), which are described in Table 8. In Fig. 18, the first column indicates the twodimensional view of benchmark functions. The second column shows the convergence curve, which is the best solution that has been updated by now. It can be observed from the figures in this column that each group of the function represents a particular downward behavior. SCA can initially encircle the optimum point in unimodal functions and then improve the solutions as iterations pass.
Contrary, the SCA’s searching agents attempt to globally discover the search space even in the final iterations to obtain superior solutions for other benchmark functions. This explorative behavior causes SCA’s searching agents to the steplike convergence curves. In other words, the convergence curve indicates the performance of the best SCA’s searching agents in obtaining the optimum point, whereas it does not represent any idea about the performance of the entire SCA’s searching agents. For this reason, we utilize another metric to investigate the entire SCA’s searching agents’ performance in the optimization process named average fitness history. This metric’s general pattern is almost similar to the convergence curve, while it focuses more on the total behavior and its impact on the results, improving from the initial stochastic population.
The trajectory of SCA’s searching agents is another metric, which is represented in column four. This trajectory indicates the topological amendments from the start to the end of the optimization task. Having many dimensions in the search space, only the first dimension is selected of an agent to show its trajectory. As shown in this column, the searching agents’ trajectory has high frequency and magnitude in the beginning iterations, vanishing in the last iterations. These figures verify the exploration phase in the beginning iterations while changing to the exploitation phase in the final iterations cause searching agents to converge to the global optimum finally.
The last column shows the search history as the fourth metric, indicating how searching agents’ diversity causes SCA to reach global optimum among various local optima. These figures indicate a more population density around the unimodal functions’ optimum points, contrary to multimodal and composition functions, in which there are more scattered SCA’s searching agents in the search space.
4.8 Identifying the region of interest
From the viewpoint of data science experts, the best result could be indicated in terms of the confusion matrix, overall accuracy, precision, recall, ROC curve, etc. However, these optimal results might not be sufficient for the medical specialists and radiologists if the results cannot be interpreted. Identifying the Region of Interest (ROI) that leads to the network’s decision making will enhance the understanding of both medical specialists and data science experts.
In this section, the results provided by designed networks for the COVIDXray5k dataset were investigated. The class activation mapping (CAM) (Fu et al. 2019) results were displayed for the COVIDXray5k dataset to localize the areas suspicious of the COVID19 virus. The probability predicted by the deep CNN model for each image class gets mapped back to the last convolutional layer of the corresponding model that is particular to each class to emphasize the discriminative regions. The CAM for a determined image class is the outcome of the activation map of the Rectified Linear Unit (ReLU) layer following the last convolutional layer. It is identified by how much each activation mapping contributes to the final grade of that particular class. The novelty of CAM is the total average pooling layer applied after the last convolutional layer based on the spatial location to produce the connection weights. Thereby, it permits identifying the desired regions within an Xray image that differentiates the class specificity preceding the Softmax layer, which leads to better predictions. Demonstration using CAM for deep CNN models allows the medical specialists and radiology experts to localize the areas suspicious of the COVID19 virus, indicating Figs. 19 and 20.
Figures 19 and 20 indicate the results for COVID19 detection in Xray images. Figure 19 shows the outcomes for the case marked as ‘COVID19’ by the radiologist, and the DCELMSCA model predicts the same and indicates the discriminative area for its decision. Figure 20 shows the outcomes for a ‘normal’ case in Xray images, and different regions are emphasized by both comparing models for their prediction of the ‘normal’ subset. Now, medical specialists and radiology experts can choose the network architecture based on these decisions. This kind of CAD visualization would provide a useful second opinion to the medical specialists and radiology experts and also improve their understanding of deeplearning models.
5 Conclusion
In this paper, the SCA and ELM were proposed to design an accurate and reliable deep CNN model for COVID19 positive cases from Xray images. Numerical studies were carried out to evaluate the realtime capability of the proposed model. The 95% confidence interval of the obtained specificity and sensitivity rates was performed to confirm the proposed method’s reliability. According to the obtained results, we can conclude that the proposed model tends to be easier and more straightforward to implement compared to other benchmark models. Moreover, this design has the potential to be implemented in realtime COVID19 positive case detection. Consequently, we believe the proposed model and obtained numerical results are of practical interest to communities that are involved with deep neural networkbased detectors and classifiers. The concept of class activation map was also applied to detect the virus’s regions potentially infected. It was found to correlate with clinical results, as confirmed by experts. A few research directions can be proposed for future work with the DCELMSCA, such as underwater sonar target detection and classification. Also, changing SCA to tackle multiobjective optimization problems can be recommended as a potential contribution. The investigation of the chaotic maps’ effectiveness to improve the performance of the DCELMSCA can be another research direction. Although the results were promising, further study is needed on a larger dataset of COVID19 images to have a more comprehensive evaluation of accuracy rates.
Availability of data and materials
The resource images can be downloaded using the following link and references (Minaee et al. 2020b). https://github.com/ieee8023/covidchestxraydataset, 2020.
Code availability
The source code of the models can be available by request.
Change history
29 May 2023
This article has been retracted. Please see the Retraction Notice for more detail: https://doi.org/10.1007/s0050002308595x
References
Abualigah L, Diabat A (2021) Advances in sine cosine algorithm: a comprehensive survey. Artif Intell Rev 54:1–42. https://doi.org/10.1007/s10462020099093
Abualigah LM, Khader AT, AlBetar MA, Alomari OA (2017) Text feature selection with a robust weight scheme and dynamic dimension reduction to text document clustering. Expert Syst Appl 84:24–36
Abualigah L, Diabat A, Mirjalili S, Abd Elaziz M, Gandomi AH (2021) The arithmetic optimization algorithm. Comput Methods Appl Mech Eng 376:113609
Abudureheman A, Nilupaer A (2021) Optimization model design of crossborder ecommerce transportation path under the background of prevention and control of COVID19 pneumonia. Soft Comput 1–9. https://doi.org/10.1007/s00500021056856
Alabool H, Alarabiat D, Abualigah L et al (2020) Artificial intelligence techniques for containment COVID19 pandemic: a systematic review. https://doi.org/10.21203/rs.3.rs30432/v1
AlQaness MA, Ewees AA, Fan H, Abualigah L, Abd Elaziz M (2020) Marine predators algorithm for forecasting confirmed cases of COVID19 in Italy, USA, Iran and Korea. Int J Environ Res Public Health 17(10):3520
AlSaffar AAM, Tao H, Talab MA (2017) Review of deep convolution neural network in image classification. In: 2017 international conference on radar, antenna, microwave, electronics, and telecommunications (ICRAMET). IEEE, pp 26–31
AlWaisy AS et al (2020) COVIDCheXNet: hybrid deep learning framework for identifying COVID19 virus in chest Xrays images. Soft Comput 1–16. https://doi.org/10.1007/s00500020054243
Apostolopoulos ID, Mpesiana TA (2020) Covid19: automatic detection from xray images utilizing transfer learning with convolutional neural networks. Phys Eng Sci Med 43(2):635–640
Ashraf S, Abdullah S, Almagrabi AO (2020) A new emergency response of spherical intelligent fuzzy decision process to diagnose of COVID19. Soft Comput 1–17. https://doi.org/10.1007/s00500020055708
Bwire GM, Majigo MV, Njiro BJ, Mawazo A (2020) Detection profile of SARSCoV2 using RTPCR in different types of clinical specimens: a systematic review and metaanalysis. J Med Virol. https://doi.org/10.1002/jmv.26349
Chai R, Tsourdos A, Savvaris A, Chai S, Xia Y, Chen CP (2019) SixDOF spacecraft optimal trajectory planning and realtime attitude control: a deep neural networkbased approach. IEEE Trans Neural Netw Learn Syst 31(11):5005–5013
Chai R, Tsourdos A, Savvaris A, Chai S, Xia Y, Chen CLP (2020) Design and implementation of deep neural networkbased control for automatic parking maneuver process. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2020.3042120
Chen X, Liu W, Lai J, Li Z, Lu C (2012) Face recognition via local preserving average neighborhood margin maximization and extreme learning machine. Soft Comput 16(9):1515–1523
Dansana D et al (2020) Early diagnosis of COVID19affected patients based on Xray and computed tomography images using deep learning algorithm. Soft Comput 1–9. https://doi.org/10.1007/s0050002005275y
Eken S (2020) A topicbased hierarchical publish/subscribe messaging middleware for COVID19 detection in Xray image and its metadata. Soft Comput 1–11. https://doi.org/10.1007/s00500020053875
Fu K, Dai W, Zhang Y, Wang Z, Yan M, Sun X (2019) Multicam: Multiple class activation mapping for aircraft recognition in remote sensing images. Remote Sens 11(5):544
He S, Guo F, Zou Q (2020) MRMD2. 0: a python tool for machine learning with feature ranking and reduction. Curr Bioinform 15(10):1213–1221
Heidari M, Mirniaharikandehei S, Khuzani AZ, Danala G, Qiu Y, Zheng B (2020) Improving the performance of CNN to predict the likelihood of COVID19 using chest Xray images with preprocessing algorithms. Int J Med Inform 144:104284
Heidari M, Mirniaharikandehei S, Khuzani AZ, Danala G, Qiu Y, Zheng B (2021) Detecting COVID19 infected pneumonia from xray images using a deep learning model with image preprocessing algorithm. In: Medical imaging 2021: computeraided diagnosis, vol 11597. International Society for Optics and Photonics, p 115970V
Hemdan EED, Shouman MA, Karar ME (2020) Covidxnet: a framework of deep learning classifiers to diagnose covid19 in xray images. arXiv preprint arXiv:2003.11055
Hosmer DW, Lemeshow S (1992) Confidence interval estimation of interaction. Epidemiology 3(5):452–456. https://doi.org/10.1097/0000164819920900000012
Hu Y, Chen Q, Feng S, Zuo C (2020) Microscopic fringe projection profilometry: a review. Opt Lasers Eng 106192. https://doi.org/10.1016/j.optlaseng.2020.106192
Huang GB, Zhu QY, Siew CK (2006) Extreme learning machine: theory and applications. Neurocomputing 70(1–3):489–501
Irvin J et al (2019) Chexpert: a large chest radiograph dataset with uncertainty labels and expert comparison. Proc AAAI Conf Artif Intell 33:590–597
Jiang Q et al (2017) Alzheimer’s disease variants with the genomewide significance are significantly enriched in immune pathways and active in immune cells. Mol Neurobiol 54(1):594–600
Jiang D et al (2020) Bioenergetic crosstalk between mesenchymal stem cells and various ocular cells through the intercellular trafficking of mitochondria. Theranostics 10(16):7260
Kassani SH, Kassasni PH, Wesolowski MJ, Schneider KA, Deters R (2020) Automatic detection of coronavirus disease (covid19) in xray and ct images: a machine learningbased approach. arXiv preprint arXiv:2004.10641
Khan AI, Shah JL, Bhat MM (2020) CoroNet: a deep neural network for detection and diagnosis of COVID19 from chest xray images. Comput Methods Progr Biomed 196:105581
Khishe M, Mosavi M (2020b) Classification of underwater acoustical dataset using neural network trained by Chimp Optimization Algorithm. Appl Acoust 157:107005
Khishe M, Mosavi MR (2020a) Chimp optimization algorithm. Expert Syst Appl 149:113338
Khishe M, Safari A (2019) Classification of sonar targets using an MLP neural network trained by dragonfly algorithm. Wirel Pers Commun 108(4):2241–2260
Kölsch A, Afzal MZ, Ebbecke M, Liwicki M (2017) Realtime document image classification using deep CNN and extreme learning machines. In: 2017 14th IAPR international conference on document analysis and recognition (ICDAR), vol 1. IEEE, pp 1318–1323
LeCun Y (2015) LeNet5, convolutional neural networks. URL: http://yann.lecun.com/exdb/lenet 20(5):14
Li LL, Sun J, Tseng ML, Li ZG (2019c) Extreme learning machine optimized by whale optimization algorithm using insulated gate bipolar transistor module aging degree evaluation. Expert Syst Appl 127:58–67
Li T, Xu M, Zhu C, Yang R, Wang Z, Guan Z (2019a) A deep learning approach for multiframe inloop filter of HEVC. IEEE Trans Image Process 28(11):5663–5678
Li G, Chen B, Qi X, Zhang L (2019b) Circular convolution parallel extreme learning machine for modeling boiler efficiency for a 300 MW CFBB. Soft Comput 23(15):6567–6577
Li A et al (2020) A tutorial on interference exploitation via symbollevel precoding: Overview, stateoftheart and future directions. IEEE Commun Surv Tutor 22(2):796–839
Li BH, Liu Y, Zhang AM, Wang WH, Wan S (2020) A survey on blocking technology of entity resolution. J Comput Sci Technol 35(4):769–793
Liu Y et al (2020) Development of 340GHz transceiver front end based on GaAs monolithic integration technology for THz active imaging array. Appl Sci 10(21):7924
Liu S, Yu W, Chan FT, Niu B (2021) A variable weightbased hybrid approach for multiattribute group decision making under intervalvalued intuitionistic fuzzy sets. Int J Intell Syst 36(2):1015–1052
Ma HJ, Xu LX (2020) Decentralized adaptive faulttolerant control for a class of strong interconnected nonlinear systems via graph theory. IEEE Trans Autom Control. https://doi.org/10.1109/TAC.2020.3014292
Ma HJ, Xu LX, Yang GH (2019) Multiple environment integral reinforcement learningbased faulttolerant control for affine nonlinear systems. IEEE Trans Cybern
Minaee S, Kafieh R, Sonka M, Yazdani S, Soufi GJ (2020a) Deepcovid: Predicting covid19 from chest xray images using deep transfer learning. Med Image Anal 65:101794
Minaee S, Kafieh R, Sonka M, Yazdani S, Soufi GJ (2020b) Deepcovid: predicting covid19 from chest xray images using deep transfer learning. arXiv preprint arXiv:2004.09363
Mirjalili S (2016) SCA: a sine cosine algorithm for solving optimization problems. KnowlBased Syst 96:120–133
Mohammed MA et al (2020) Benchmarking methodology for selection of optimal COVID19 diagnostic model based on entropy and TOPSIS methods. IEEE Access 8:99115–99131
Mohapatra P, Chakravarty S, Dash PK (2015) An improved cuckoo search based extreme learning machine for medical data classification. Swarm Evol Comput 24:25–49
Mosavi M, Kaveh M, Khishe M (2016a) Sonar data set classification using MLP neural network trained by nonlinear migration rates BBO. In: The 4th Iranian conference on engineering electromagnetic (ICEEM 2016), pp 1–5
Mosavi M, Kaveh M, Khishe M, Aghababaee M (2016b) Design and implementation a sonar data set classifier by using MLP NN trained by improved biogeographybased optimization. In: Proceedings of the 2nd national conference on marine technology, pp 1–6
Mosavi MR, Khishe M, Akbarisani M (2017) Neural network trained by biogeographybased optimizer with chaos for sonar data set classification. Wirel Pers Commun 95(4):4623–4642
Mosavi M, Khishe M, Hatam Khani Y, Shabani M (2017) Training radial basis function neural network using stochastic fractal search algorithm to classify sonar dataset. Iran J Electr Electron Eng 13(1):100–111
Mosavi MR, Khishe M, Naseri MJ, Parvizi GR, Mehdi A (2019) Multilayer perceptron neural network utilizing adaptive bestmass gravitational search algorithm to classify sonar dataset. Arch Acoust 44(1):137–151
Niu Z, Li D, Ji D, Liu Y, Feng Y, Zhou T, Zhang Y, Fan (2020) A mechanical reliability study of 3 dB waveguide hybrid couplers in the submillimeter and terahertz band. J Zhejiang Univ Sci C 1(1)
Niu Z et al (2020) The research on 220GHz multicarrier highspeed communication system. China Commun 17(3):131–139
Ozturk T, Talo M, Yildirim EA, Baloglu UB, Yildirim O, Acharya UR (2020) Automated detection of COVID19 cases using deep neural networks with Xray images. Comput Biol Med 121:103792
Pan D et al (2020) COCO enhances the efficiency of photoreceptor precursor differentiation in early human embryonic stem cellderived retinal organoids. Stem Cell Res Ther 11(1):1–12
Pao YH, Park GH, Sobajic DJ (1994) Learning and generalization characteristics of the random vector functionallink net. Neurocomputing 6(2):163–180
Ran W, Liu S, Zhang Z (2020) A pollingbased dynamic orderpicking system considering priority orders. Complexity 2020:1–15. https://doi.org/10.1016/j.optlaseng.2020.106192
Selvakumar K, Lokesh S (2021) The prediction of the lifetime of the new coronavirus in the USA using mathematical models.Soft Comput 1–20. https://doi.org/10.1007/s00500021056432
Sun Y, Xue B, Zhang M, Yen GG, Lv J (2020) Automatically designing CNN architectures using the genetic algorithm for image classification. IEEE Trans Cybern 50(9):3840–3854. https://doi.org/10.1109/TCYB.2020.2983860
Wang S et al (2020) Neurostructural correlates of hope: dispositional hope mediates the impact of the SMA gray matter volume on subjective wellbeing in late adolescence. Soc Cogn Affect Neurosci 15(4):395–404. https://doi.org/10.1093/scan/nsaa046
Wang L, Lin ZQ, Wong A (2020a) Covidnet: a tailored deep convolutional neural network design for detection of covid19 cases from chest xray images. Sci Rep 10(1):1–12
Wang Y, Yuan L, Khishe M, Moridi A, Mohammadzade F (2020b) Training RBF NN using sinecosine algorithm for sonar target classification. Arch Acoust 45(4):753–764. https://doi.org/10.24425/aoa.2020.135281
Wang B, Zhang B, Zou F, Xia Y (2021) A kind of improved quantum key distribution scheme. Optik
Wilcoxon F, Katti S, Wilcox RA (1970) Critical values and probability levels for the Wilcoxon rank sum test and the Wilcoxon signed rank test. Sel Tables Math Stat 1:171–259
Wu LC, Horng JT, Huang HY, Lin FM, Huang HD, Tsai MF (2007) Primer design for multiplex PCR using a genetic algorithm. Soft Comput 11(9):855–863
Wynants L et al (2020) Prediction models for diagnosis and prognosis of covid19: systematic review and critical appraisal. BMJ 369:1–16
Xie SJ, Yang J, Gong H, Yoon S, Park DS (2012) Intelligent fingerprint quality analysis using online sequential extreme learning machine. Soft Comput 16(9):1555–1568
Xiong L, Zhang H, Li Y, Liu Z (2016) “Improved stability and H∞ performance for neutral systems with uncertain Markovian jump. Nonlinear Anal Hybrid Syst 19:13–25
Xu S, Wang J, Shou W, Ngo T, Sadick AM, Wang X (2020) Computer vision techniques in construction: a critical review. Arch Comput Methods Eng 1–15
Yang S et al (2021) BiCoSS: toward largescale cognition brain with multigranular neuromorphic architecture. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2020.3045492
Yang M, Sowmya A (2015) An underwater color image quality evaluation metric. IEEE Trans Image Process 24(12):6062–6071
Yang J, Li S, Wang Z, Dong H, Wang J, Tang S (2020) using deep learning to detect defects in manufacturing: a comprehensive survey and current challenges. Materials 13(24):5755
Yang Y, Hou M, Sun H, Zhang T, Weng F, Luo J (2020) Neural network algorithm based on Legendre improved extreme learning machine for solving elliptic partial differential equations. Soft Comput 24(2):1083–1096
Yang S, Gao T, Wang J, Deng B, Lansdell B, LinaresBarranco B (2021) Efficient spikedriven learning with dendritic eventbased processing. Front Neurosci 15:97
Yousri D, Abd Elaziz M, Abualigah L, Oliva D, AlQaness MA, Ewees AA (2021) COVID19 Xray images classification based on enhanced fractionalorder cuckoo search optimizer using heavytailed distributions. Appl Soft Comput 101:107052
Zenggang X, Zhiwen T, Xiaowen C, XueMin Z, Kaibin Z, Conghuan Y (2019) Research on image retrieval algorithm based on combination of color and shape features. J Signal Process Syst 93:1–8
Zhang J, Sun J, Chen Q, Zuo C (2020) Resolution analysis in a lensfree onchip digital holographic microscope. IEEE Trans Comput Imaging 6:697–710
Zhang J, Chen Q, Sun J, Tian L, Zuo C (2020) On a universal solution to the transportofintensity equation. Opt Lett 45(13):3649–3652
Zhang B et al (2020) Fourhundred gigahertz broadband multibranch waveguide coupler. IET Microw Antennas Propag 14(11):1175–1179
Zhang J, Xie Y, Li Y, Shen C, Xia Y (2020) Covid19 screening on chest xray images using deep learning based anomaly detection. arXiv preprint arXiv:2003.12338
Zhu S, Wang X, Zheng Z, Zhao XE, Bai Y, Liu H (2020a) Synchronous measuring of triptolide changes in rat brain and blood and its application to a comparative pharmacokinetic study in normal and Alzheimer’s disease rats. J Pharm Biomed Anal 185:113263
Zhu S, Zheng Z, Peng H, Sun J, Zhao XE, Liu H (2020b) Quadruplex stable isotope derivatization strategy for the determination of panaxadiol and panaxatriol in foodstuffs and medicinal materials using ultra high performance liquid chromatography tandem mass spectrometry. J Chromatogr A 1616:460794
Zou Q, Xing P, Wei L, Liu B (2019) Gene2vec: gene subsequence embedding for prediction of mammalian N6methyladenosine sites from mRNA. RNA 25(2):205–218
Zuo C, Chen Q, Tian L, Waller L, Asundi A (2015) Transport of intensity phase retrieval and computational imaging for partially coherent fields: the phase space perspective. Opt Lasers Eng 71:20–32
Zuo C, Sun J, Li J, Zhang J, Asundi A, Chen Q (2017) Highresolution transportofintensity quantitative phase microscopy with annular illumination. Sci Rep 7(1):1–22
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Communicated by Victor Hugo C. de Albuquerque.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This article has been retracted. Please see the retraction notice for more detail: https://doi.org/10.1007/s0050002308595x
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author selfarchiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Wu, C., Khishe, M., Mohammadi, M. et al. RETRACTED ARTICLE: Evolving deep convolutional neutral network by hybrid sine–cosine and extreme learning machine for realtime COVID19 diagnosis from Xray images. Soft Comput 27, 3307–3326 (2023). https://doi.org/10.1007/s00500021058396
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500021058396