In December 2019, Wuhan City (Hubei, China) had an outbreak with the evolution of new coronavirus. This is a virus transmitted from person to person causing COVID-19. It was reported that this virus evolved because to zoonotic transmission and with a detailed study of its biological properties, a survey concluded that it belongs to the family of coronaviridae and is named as 2019-nCoV (novel coronavirus). This novel coronavirus is a single-stranded RNA genome with a strong capsid. A person infected with 2019-nCoV eventually develops mild symptoms such as sore throat, dry cough, and fever. If 2019-nCoV host the human body for longer periods, it can cause severe respiratory illness and, in the worst case, can lead to death. Four main stages 1 are considered to analyse the severity of the virus in the human body. The first stage lies from zero to four days, i.e. the asymptomatic stage from the 1 These observations were reported with clinical experimentation [2] . day of infection. The second stage is progressive stage, it lies from the five to eight days where one might develop mild symptoms. Stage three is considered as a peak stage ranging from 9th -13th day. The final stage is an absorption stage where a load of virus exponentially increases [1] . Observing the extremity, during the end of January W.H.O declared the situation as a public emergency due to the rapid spread of this virus. Further, 2019-nCoV was properly amended as SARS-CoV-2 beta-coronavirus [7] (by Coronavirus Virus Study Group(CVSG)) due to its potential characteristics to affect the human respiratory tract with high similarities with the genomic structure of SARS-CoV [8] [9] .
The upsurge of COVID-19 led to its declaration as a pandemic. Due to its rapid growth scientists are striving to provide proper vaccination and medication. COVID-19 erupted progressively by increasing mortality rate in various regions of the world [3] . Many preventive measures such as social Figure 1 : An upsurge in no. of cases & death rate from January to July is depicted. An exponential increment in death rate & infected people increased to a factor of ≈ 10 5 during a span of 6 months.
distancing, proper sanitization and face-cover have been in practice. Even then people are encountered with the virus causing fatal deaths. According to Chinese N.H.C (National Health Commission), there was 2.1% & 0.2% mortality rate in and outside of China (as of February 4th, 2020). With a high mortality rate, the propulsion of virus spread worldwide havoc. This led to worldwide panic with unavailability of proper medication. In recent survey, there were contradictory studies stating asymptomatic spread of the virus and under certain circumstances they can be erroneous if the person is having direct contact with the patient infected with COVID-19 or the symptoms which are self-reported [5] [6] . To avail proper information about a patient's health, precise and proper diagnostic-tests are required. The diagnostic tests are performed either by collecting samples from the individual patient for testing in a laboratory or point-care-testing is performed [4] . Manual testing consumes time with a lot of human effort and it is unfit in a pandemic. To overcome such problems, in this urgency, AI-based computerized techniques are adapted for faster & feasible outcomes using the deeplearning approach [51] . The radiologists examined patients' Chest X-ray (CXR) and Computed-Tomography (CT) images to assess the severity of infection in the lungs [2] . These examinations led to aid people to depict infection under various scans under different lesions of Chest. With these observations, a lot of computer scientists developed machinevision models to combat COVID-19 by diagnosing either with CXR or CT images. In this research, a stacked-ensemble is proposed for the classification of patients' CXR images as Pneumonic, COVID-19 infected or uninfected.
There are several works proposed in automated detection, classification and segmentation for COVID-19 diagnosis from CXR and CT images imparting deep learning [52] . These works include lung lesion segmentation and classification of CXR or CT images by extracting a generic feature-vector representing higher dimensional features with great precision. F. Deng-ping et al., (2020) [18] proposed a segmentation network, Inf-Net, for segmentation of patients infected with COVID-19 using Transverse C.T images. The network architecture has Res2Net as a backbone. Their model Inf-Net attains a dice score of 0.682 and also, a Semi-Inf-Net model which in turn attains highest dice score of 0.739. Fengshi et al., (2020) [23] classified C.T images containing pneumonia and COVID-19 using Random-Forest by attaining an accuracy score of 0.87 and with high sensitivity of 0.907 on 5 fold cross-validation. L. [15] tailored a deep network using the concept of Identity mapping (residual connections) by classifying them as Normal, Pneumonic & COVID-19 infected Chest-X Ray images and named it as CovidNet. They attained an overall accuracy score of 93.3% over sequential training for very few epochs. Zhenyu Tang et al., (2020) [17] considered COVID-19 infected patients' CXR images to classify the severity of the patient. The severity classification is trained using Random Forest and attained an accuracy score of 87.5% by 3-fold cross-validation. Xiaocong et al., (2020) [16] developed a U-Net architecture constructing intermediate Residual connections (U-Net+ResNext) for segmentation & detection of 110 axial C.T images of patients infected with COVID-19. This model attained an accuracy score of 79% without augmentation and 89% with the use of augmentation. Yugin et al., (2020) [13] implemented 2 different approaches, global patch matching and local patch matching for the purpose of segmentation & classification. Their method used ResNet-18 as the backbone to classify variant lung infections (4-Classes) similar to that of COVID-19 and attained the highest accuracy score of 88.9% & specificity of 0.946 on randomly cropped patches using local-approach.
Rahimzadeh et al., (2020) [10] constructed an 8-phase training concatenating Xception and ResNet-50 architectures. In each phase, samples were trained using a proper stratification in-order to overcome class imbalance for 100 epochs. This model attained an overall accuracy score of 91.4%by cross-validating on 5-folds. Tulin et al., (2020) [11] proposed a Dark-CovidNet model for binary and triclass classification of CXR images infected with COVID-19. This model was trained by constructing a deep neural architecture with a series of convolutional layers and maxpooling layers by attaining accuracy scores of 98.3% (binary classification) and 87.2% (Tri-class classification) on 5-fold cross-validation. Ioannis et al., (2020) [12] applied transfer learning using diverse pre-trained architectures on two different datasets for the classification of CXR images consisting of COVID-19. Their transfer learning methodology attained an accuracy score of 98.75% using VGG-19 pre-trained weights for binary classification and accuracy of 94.7% using MobileNet-V2 for classification of CXR images consisting of 3-classes. M. Farooq et al., (2020) [14] developed a model using ResNet-50 as the backbone and performed training CXR images consisting of COVID-19 in three different stages. In each stage, the model is fine-tuned on decreasing learning schedules and attained an accuracy of 96.23% on data with four non-identical classes of CXR images. E. Hemdian et al., (2020) [19] implemented models by sharing weights from pre-trained models and attained the highest accuracy score of 90% by training over 50 epochs. L. [20] proposed a network named 'CovNet' by training a deepmodel with ResNet-50 as a backbone for sharing weights and attained an accuracy of 96%. Charmaine et al., (2020) [21] considered Transverse-section of CT sample images as the dataset for training the model where ResNet-18 pertains as the backbone. This classifies CT images consisting of COVID-19 by extracting lung lesions with location-attention procedure with an accuracy score of 86.7%. A. Iqbal et at., (2020) [22] designed CoroNet-architecture with Xception as an underlying weight-sharing model. This model achieved an accuracy score of 99% (binary classification), 95% for three non-identical classes (one class belongs to and 89.6% for four variant classes with constructing a 4-fold cross-validation framework.
Most of the existing literature for classification & segmentation were proposed on deep neural-networks with their versatile nature of the weight-sharing mechanism and high per-formance. Despite this most of the proposed deep-networks for COVID-19 classification had drawbacks.
• As mentioned, most of the models were trained for a longer training schedules and this eventually causes overwhelmed understanding of training samples (overfitting). • The data is chosen to have identical class distributions during training but in real-world scenarios, classimbalance is commonly seen. • Individual pixels play a significant role in understanding entities inside an image and extracting features without losing information is challenging. • Inappropriate generalizations can mislead diagnostic performance by misclassifying the samples.
In this research, we address these drawbacks and proposed a novel stacked-ensemble neural network for classifying existence of COVID-19 in a given CXR image by vanquishing the problem of longer training schedules, proper pixelresolution and generalization constraints.
The complete data is collected from the mentioned repository 2 . The total dataset consists of 3 non-identical classes of CXR images either infected with COVID-19, viral-Pneumonia or having a healthy profile. The COVID-19 class consists of 219 CXR images. Whereas, viral-pneumonia and normal class contain 1345, 1341 CXR images. The dataset of whole comprises of 2905 CXR images. The CXR images in the database are visually depicted in Fig. 2 . This database was developed from major research contributed institutes such as Italian Society of Medical and Interventional Radiology and also from variant standard publications. The collected data curated with appropriate labels and used for the purpose of research. Now, it is attempted to divide the complete dataset (D total ) into 2 divisions: The first division comprises of training samples (D train ) i.e. samples that are to be fed into a neural network for learning. The next division consists of testing samples (D test ) and obliges to generalize model. The training and testing divisions are partitioned into 80% − 20% by maintaining consistency in class labels at each partition (But, overall class imbalance is present throughout the training data) . To assess partition consistency, D total is randomly divided into train-test divisions multiple times (5 times) and newly shuffled samples are examined. During the examination, it is found that each randomly shuffled sample maintained utmost consistency in stratifying class labels. All these partitioned samples are gradually evaluated to assess the performance of the model and aided network with careful generalization. Figure 3 : The above figure illustrates the complete methodology from data collection to that of classification. Initially, various samples are considered and are pre-processed to a certain resolution (224x224x3). These pre-processed images are further fed into various deep-networks designed on variant paradigms for extracting features to certain latent dimensions. Then, assessments for extracted feature-vectors are done and among them, two best performing models are chosen to form a stacked ensemble. This ensemble is evaluated by classifying input to a tri-class and a binary class where COVID-19 class in given more importance. This network was proposed to compete Inception Network by addressing flaws and eventually diminishing them. The simultaneous mapping of spatial and cross-channel correlations guides for proper learning with small receptive fields and improves perceptive ability. The depth-wise separable convolutional layers enhance the learning by detailed feature extraction. These networks are computationally less expensive and have high performance compared to Inception Network [37] . connections(including residual connections) which enhances network capability of extracting detailed features and vanquishes degradation. The sequential dense block and transition blocks provide a collection of knowledge and a bottleneck receptive field of 3x3 out-turns computational efficiency. The fine-tuning of larger weights improved generalization in deeper networks ranging its depth from 121-201 layers [38] . α ← 2 * α 0 ; β ← β o + 10; ← 100 * 0 ; 15: opt ← Ad( ); This demonstrated learning paradigm for convolution-cells by learning from distinct classification tasks. This network is designed by stacking normal cell & reduction cell by stacking depth-wise providing an appropriate search space by decoupling sophisticated architectural design. This adaptability of Nas-Nets tends to perform well even to mobile applications. The computational cost is reduced to a greater extent and performance was varied by enhancing the depth [40] . The divided training samples, D train , are inserted into each model to capture latent feature-vectors 3 . Now, a feedforward neural network is built to classify these extracted feature vectors. So, individual models are trained using Algorithm: 1 and access the performance of each network. The extracted feature-vector is of three dimensions with varying shape based on the model. These latent representations are classified by attaching a dense layer consisting of 256 neurons followed by dropout [41] and batch-normalization [42] layers for the purpose of regularization. The final layer consists of softmax activations layer with c neurons (where, c: no. of classes). The choice for dropout percentage is carefully tuned to 30%. The assessment for generalization is obtained for individual models.
During construction of the model architecture, ReLU [43] is chosen as non-linearity for all the layers except the final layer, where in that case feed is forwarded by softmax. Initializations for most of the layers are chosen to be glorot [44] but, for only dropout layer, glorot normalization constraint is considered for initializations. These initializations with appropriate activations led to extract intricate features at deeper layers.
The performance of each model is evaluated, employing standard classification metrics used for a bio-medical problem statement [45] . The chosen metrics are accuracy score, Precision (PPV) & Sensitivity (recall). Accuracy score is a typical classification metric determining robustness of classification but, in the presence of class-imbalance, models tend to attain acceptable accuracy score deteriorating performance by misclassifying the samples in a class with low in number. To be well informed, individual class scores are calculated and tabulated (Table: 2).
The above table concludes that both the VGG-Nets outperform existing models on test samples (D test with an error rate of 4.7-4.9 % . Res-Net models (comprising 50, 101layers) competed Vgg-Nets with a close error of 14.3-18%. This stunning outcome of Vgg-Nets with lowest error values deemed us to analyse it performance to farther extent. To understand Vgg-Nets, analysing invariances is considered to be a crucial part. Hence visualization of individual layer activation-maps is found to be necessary [46] . Visualizing features gives intuition of network's ability to perceive and projections of pixels at each layer. The visualizations of individual activation-maps for a layer illustrate the visual perception for captured features (including shape, size, orientation etc.) during the process of training with updated weights. Now, these visualizations assist in analysing spatial structures of latent feature-vectors.
In presence of huge activation maps at each layer of a deepnetwork, complete visualization for the individual layers can be sophisticated to comprehend. feature-vectors are adapted to depict the model robustness by visualizing first, intermediate and final layers 4 .
Additionally, t-sne visualizations [55] are adapted to observe underling distribution pattern for the data(D) and the a feed forward dense network with 2 parameters one is input and other is no of hidden neurons: f (x, n) = W.x + b(W:weight matrix;b:bias; n:no.of neurons determining shape of W,b) Act(.) Activation function softmax: Act(x i ) = e x i Σ i .e x i parameters involved are described 5 .Further, to analyse these feature-vectors a histogram plot is outlined (Fig. x) to inspect amount of information.
In this research, we propose stacked-ensemble by considering Vgg-Nets as our individual networks as they manifest 5 The parameters involved are, angle ← 0.6; iterations ← 2 * 10 3 ; perplexity ← 10 2 ; distance = Euclidean; initializations = P CA; method = Barneshut. Approximately 8.23 minutes was consumed for visualizing each input 
Dense ← f (stack, 16) rich features with significant performance in classification . Ensembling two Vgg-Nets performs well by reducing generalization error to substantial amount. The performance of joint networks is always higher compared to that of a single Network[47] [48] . The error attained by Vgg-Nets can be further decreased by coupling them to aggregate learning capacity. Eventually, generalization increases combining these two networks. So, Our present ensemble model construction using Vgg-Nets is described in Algorithm: 2 using Tensorflow 6 [49] . As mentioned, the VGG-16 and VGG-19 network's final activations are captured and are stacked by aggregating them along their vertical dimensions( As mentioned at step:6 in Algorithm.2). This stacked vector is fed into a series of fully connected layers with ReLU as activa- 6 Tensorflow (Version 1.15) is chosen as the execution platform for constructing deep architectures provided by a hardware acceleration using Nvidia-1660 Ti GPU and a CPU with Intel i7-8700 VOLUME 4, 2016 tion. Finally, the feed is forwarded with softmax as activation to predict whether the given CXR input has COVID-19(either in binary or tri-class classification).
The idea of generalization-error attained by stacking various deep learning models is theoretically analysed and mathematically evaluated. Here we considered our network to be a function that predicts for a certain input x, where our true function is T i (x) and approximated function is
Where, r i is generalization error ∀ i = 1, 2
Where, Z i is the individual estimated error for the model.
So,the average error settled from the networks estimating individually is, 
Estimated error resided by stacking these ensembles,
Substituting equation (1) in Z stack ,
If individual network do not persist any correlation among themselves stacking an ensemble halves the original generalization of the individual networks. But, in most of the real world scenario correlation in generalization do exist which intern can increase error to a an estimated amount. So, we consider r ij = 0
This constant 'e' is additional error caused due to the covariances obtained in the perception of individual networks. Now this intuition drives to evaluate the predictive capacity of the designed stacked-ensemble model both on binary and tri-class classification.
In this section, the complete training process and results obtained preferring Algorithm-1 are described.A detailed explanation is obtained by explaining computational reason in using it. In most of the recent research, models are trained for higher values of iterations (epochs). Larger iterations can mislead predictions by over-fitting i.e. model properly fits on training samples but declines its performance on test samples [10] [11] [13] . Some of the researchers consider a relatively low resolution for training and this low-pixel density results is dropping the quality of an image [22] [12] [14] . For a bio-medical problem quality of input is a considered to be crucial as low-quality images capture poor features and cannot be apt for real-world situations. A generic model is the one which even sustains the problem of class-imbalance. Most of the designed models are trained to stratify their training set [10] [12][13] [22] which can be bothering in actuality. Most importantly, generalization is crucial in determining the robustness of the model. The ensemble model is designed is resilient to class imbalance as the number of COVID-19 samples fed into the networks are few (≈ 7 − 8%) compared to that of healthy and viral-pneumonia samples. The ensemble model constructed acquires input with a resolution of 224x224 with 3 channel variants (RGB) CXR images. The designed training algorithm is a generic training algorithm which aids training process by acquiring faster convergence and with low-computations (Iterations). During the process of training, at each iteration, the batch size is increased and moderately learning rate is increased for a balanced criterion. This conception was perceived from Smith et al., (2017) [53] . As noise during training can be reduced by properly choosing the parameters which are batches fed into network, learning rate of the optimizer and momentum assigned for a faster search.
The noise due to training is theoretically represented as, (assuming momentum is constant). Conceptualizing the noise constraint, a training algorithm is developed. Just by decaying learning rate can decrease the noise but the computational time for training increases gradually. Lowering batch size can also reduce noise but it leads to lowering the generalizing capacity of the model. To overcome these problems by attaining faster convergence with better generalizations, the algorithm is developed by increasing batch size during the specified iteration and cautiously increasing the learning rate. Firstly the algorithm is iterated for 16278 steps which is considered as iteration 1, where the learning rate is set to 10 −4 by sending 15 samples as a batch at a time. In the next iteration (iteration 2), the batch size is increased by a factor of 50% and the learning rate is increased by 10 times.
To maintain a consistent trade-off between generalization and faster convergence batch size is increased by a factor of 150% and the learning rate is tuned as of previous. During experimentation, it is found that the proposed training procedure led to a faster convergence by training on few steps (≈ 20 epochs). Appropriate training with fine-tuning the ensemble was critical to attaining insightful outcomes. As mentioned training and testing, samples were randomly shuffled into different patterns at a fixed size (i.e. 80-20). Test for generalization is done at each level i.e. each shuffled sample is trained on the given ensemble by maintaining stratification. During shuffling, different accuracy score is obtained for each shuffle different samples are constructed by maintaining stratification in the available data. At a certain shuffling pattern, highest accuracy score of 97.4% is obtained for 3 class classification and for binary classification an accuracy score of 99.48% is obtained for most of the shuffle pattern. It is observed that the use of dropout and batchnormalization layers sustainably increased training process and improved models performance significantly. Adam optimizer aided for faster convergence by tweaking learning rate at a consistent frequency. To assess the predictive capacity of ensemble confusion matrices are obtained for both the classes to represent individual class performance. For the binary classification problem, misclassification of COVID-19 samples as Non-COVID-19 was 3 by attaining a sensitivity of 100% and specificity of 99.44%. Then for 3 class classification ensemble model, the highest accuracy score of 97.4% is obtained and an average score of 96.16±0.9%(aggregating all the shuffles). These results reveal utmost consistency for both the classification problems. Finally, the novelty of the developed stacked-ensembles is evaluated by comparing the performance with existing literature (Table ) .
In our research, A stacked-ensemble is proposed using Vgg-Nets for binary and tri-class classification of CXR images infected with COVID-19 with state-of-the-art performance. The least classification error of 2.6% and highest sensitivity, PPV of 100%, 97.5% are attained for COVID-19 class. In the case of binary classification, the least error of 0.52% is obtained. These on par outcomes determine the robustness of the ensemble model. The proposed model vanquishes the pitfalls of the existing model by visually understanding the extracted feature pattern and to provide a great deal of generalization with variant shuffles. Even with a great deal of success, some of the challenges are yet to compete with a vigilant observance. These challenges include training of multiple neural networks to the ensemble model, which consumes dual effort by training individual models as well as the ensemble. As observed noise in data might affect testing performance by attaining distinct accuracy scores during the variant shuffling of data with little inconsistency in the predictions. Further, crossvalidating deep neural networks with divergent folds are significant but due to computational constraints, the train-test scheme is chosen. Finally, overcoming these loopholes and developing a versatile model which is capable of identifying the severity by analysing the evolving pattern of the virus in the lungs periodically from CXR images is considered as a challenge for the future work.