
\subsection{Dataset}



We employ a large-scale of chest X-ray dataset \textit{COVIDx}~\cite{wang2020covid} to validate the proposed model. It is comprised of 18,543 chest radiography images across 13,725 cases. Example chest X-ray images belonging to normal, pneumonia, and COVID-19 classes from COVIDx dataset  are shown in Figure~\ref{ExampleImagesCOVIDX}. When we examine these examples, we can differentiate these images in terms of features shown within areas marked by the blue circle since we can observe some lighter areas indicating COVID-19 infected regions in the blue circle.

Additionally, when examining the class distribution between training and testing data, we noticed that class distribution of the training set is significantly different from that of testing set. Hence we rebuild the data by splitting the dataset into training and testing datasets that share similar class distributions, where 70\% and 30\% of data are used for training and testing datasets, respectively. The detailed information of the rebuilt dataset is shown in Table~\ref{tab1_sd} for sample distribution. 
 
\begin{table}[h!]
	\caption{Sample distribution in different classes for training and testing datasets}
        \begin{center}
                \begin{tabular}{|l|cccc|}
                \hline \textbf{Dataset} & \textbf{Normal} & \textbf{Pneumonia} & \textbf{COVID-19} & \textbf{Total} \\ \hline
                           Training		&  6,195	& 6,708	& 75  	&  12,978	 \\       
                           Testing		&  2,656	& 2,876	& 33		&   5,565	\\
                           Total		&  8,851	& 9,584	& 108	&   18,543	\\
                   \hline        
                \end{tabular}
       \end{center}
       \label{tab1_sd} 
\end{table}

We can observe that the sample distribution is extremely unbalanced regarding the number of samples of COVID-19 class. This poses a great challenge for obtaining a classifier with high performance.We overcome this challenge by the weighted cross entropy loss in the proposed model that is to assign more weight to the minority class (COVID-19 class) during the training, where the details are presented in section two. 

\subsection{Experimental settings}
In this experiment, our proposed model performed  COVID-19 classification. The key hyper parameters for training the proposed model are: 
Minibatch size: 256,
Number of epoch: 50,
Optimizer: Adam optimizer,
and Initial Learning rate: 0.1.
They are determined by trial and error. Moreover, the details of the model architecture is illustrated in Table~\ref{Table1_NetworkArchitecture}, where the residual block is the standard one~\cite{he2016deep}. Specifically, the output of the proposed model contains two parts: image class $\phi{(z^{sup})}$  and a new representation $z^{unsup}$. We employ COVID-Net\footnote{https://github.com/lindawangg/COVID-Net}~\cite{wang2020covid} as a baseline supervised model to present the state-of-the-art performance of COVID-19 image classification for comparison. Furthermore, we compared the proposed model with SRC-MT~\cite{liu2020semi} that is the state-of-the-art of semi-supervised learning since it outperformed $\Pi$ model~\cite{laine2016temporal} and mean teacher model~\cite{tarvainen2017mean}  in the area of medical image classification.

\begin{table}[h!]
	\caption{The proposed network architecture.}
	\begin{center}
	\begin{tabular}{ll}
		\hline
		\textbf{Name} & \textbf{Description}  \\ \hline
		Input &  Medical Images \\ \hline
		Shared ResNet &  one convolutional layer, 2 residual block,  \\
		&  batch normalization,  one pooling layer \\
	\hline
		Supervised ResNet &  one convolutional layer, 2 residual block,  \\
		&  batch normalization,  one pooling layer \\ \hline
		Unsupervised ResNet &  one convolutional layer, 2 residual block,  \\
		&  batch normalization,  one pooling layer \\ \hline
		Output & image class $\phi{(z^{sup})}$  and \\ 
		  &  a new representation $z^{unsup}$\\ \hline
	\end{tabular}
	\end{center}
	\label{Table1_NetworkArchitecture}
\end{table}


\subsection{Evaluation metric}



We applied different evaluation metrics to evaluate the performance of our proposed model. Since our task is a multi-class classification problem, we use accuracy, macro-average Precision (MacroP), macro-average Recall (MacroR), and macro-average Fscore (MacroF)~\cite{van2013macro, zhu2017learning, borgli2020hyperkvasir}. Accuracy is calculated by dividing the number of medical images identified correctly over the total number of testing medical images. 

\begin{equation}
	Accuracy = \frac{N_{correct}}{N_{total}}.
\end{equation}

Macro-average~\cite{yang2001study} is to calculate the metrics such as Precision, Recall and F-scores independently for each image class and then utilize the average of these metrics.  It is to evaluate the whole performance of classifying image classes.  
\begin{equation}
	MacroF = \frac{1}{C} \sum_{c=1}^{C} Fscore_c.
\end{equation}
\begin{equation}
	MacroP= \frac{1}{C} \sum_{c=1}^{C} Precision_c.
\end{equation}
\begin{equation}
	MacroR= \frac{1}{C} \sum_{c=1}^{C} Recall_c.
\end{equation}
where $C$ denotes the total number of image classes and $Fscore_c$, $Precision_c$, $Recall_c$ are $Fscore$, $Precision$, $Recall$ values in the $c^{th}$ image class which are defined by

\begin{equation}
	Fscore = \frac{2 \times Precision \times Recall}{Precision + Recall}.
\end{equation}

where $Precision$ defines the capability of a model to represent only correct image classes and $Recall$ computes the aptness to refer all corresponding correct image classes:

\begin{equation}
	Precision = \frac{TP}{TP+FP}.
\end{equation}

\begin{equation}
	Recall = \frac{TP}{TP+FN}.
\end{equation}
whereas ${TP}$ (True Positive) counts total number of medical images matched the annotated images. ${FP}$ (False Positive) measures the number of recognized classes does not match  the annotated images. ${FN}$ (False Negative) counts the number of medical images that does  not match  the predicted medical images. 
The ideal case of learning from imbalanced datasets such as \textit{COVIDx} is to improve the recall without hurting the precision. However, recall and precision goals are often conflicting, since when increasing the true positive (TP) for the minority class (True), the number of false positives (FP) can also be increased; this will reduce the precision~\cite{chawla2009data}. In addition, we employ confusion matrix to check the detailed performance for each class, especially on COVID-19 class.



\subsection{Experimental results}
\begin{table*}[ht!]
	\caption{ Comparison on supervised baseline performance.  ResNet is trained on different ratios (\%) of labeled X-ray images.  Weighted ResNet is built by assigning more weight to COVID-19 class during training for overcoming the challenge of data imbalance. }
       
        \begin{center}
                \begin{tabular}{|l|cccc|}
                \hline \textbf{DL} & \textbf{Accuracy (\%)} & \textbf{MacroP (\%)} & \textbf{MacroR  (\%)} & \textbf{MacroF  (\%)} \\ \hline 
                		  COVID-Net (100\%)	&  93.98		& 72.70 		& 96.05		&  77.33 	\\ 
		  \textbf{ResNet (100\%)}		&   \textbf{94.68}	& \textbf{90.52}		& \textbf{78.87}		& \textbf{83.04}	\\
		  \hline 
                	           ResNet (5\%)			&  87.59 		& 58.23 		& 58.50 		&  58.30  	\\
                 	   ResNet (7\%)			&  89.27 		& 59.51 		& 59.91 		&  59.68  	\\
			   ResNet (9\%)			&  90.10 		& 60.05  		& 60.44 		&  60.24  	 \\
			   \hline 			   
			   Weighted ResNet (5\%)		&  86.45 		& 57.63 		& 57.95 		&  57.78  	\\
                 	   Weighted ResNet (7\%)		&  88.70 		& 59.15 		& 59.54 		&  59.31  \\
			   Weighted ResNet (9\%)		&  89.36 		& 66.16  		& 60.46  		&  60.78   \\
                    	  
			  
			    \hline
	   		       
                     \hline
                      
                \end{tabular}
       \end{center}
         \label{tab3_covid-19}
\end{table*}


\newcommand{\photo}[1]
{
    \includegraphics[width=5.5cm]{#1}
}

\begin{figure*}[h!]
 \begin{center}
\begin{tabular}{cc}
	\photo{Figure/result/baseline/covid-net/COVID-NETbaseline.pdf} &  \photo{Figure/result/baseline/ResNet.pdf} \\
	(a) COVID-Net (100\%) &  (b) ResNet (100\%)  \\	
\end{tabular}
 \end{center}
 \caption{Comparison of confusion matrix generated by COVID-Net (100\%) and ResNet (100\%).}
 \label{Fig_covid-net}
\end{figure*}


We evaluated the proposed model performance in four steps. The first step is to examine the performance of supervised learning baselines, which is to prove if ResNet is a reasonable supervised model for COVID-19 image classification. A competitive supervised baseline is useful to compare the proposed semi-supervised model in order to present the effectiveness of the proposed model. Furthermore, we will check whether fewer labeled data will lead to lower performance. The second step is to comparing the proposed model with  state-of-the-art semi-supervised learning. The third step is to examine whether the hyper-parameter setting will affect the performance of the proposed model significantly. Finally, we will discuss why the proposed model cannot classify certain COVID-19 cases.

\subsubsection{Supervised learning for COVID-19 classification}

\begin{figure*}[h!]
 \begin{center}
\begin{tabular}{ccc}
	\photo{Figure/result/baseline/ResNet05.pdf} &  \photo{Figure/result/baseline/ResNet07.pdf} &  \photo{Figure/result/baseline/ResNet09.pdf}\\
	(a) ResNet (5\%) &  (b) ResNet (7\%)  &  (c) ResNet (9\%) \\
	\photo{Figure/result/weighted/ResNet05.pdf} &  \photo{Figure/result/weighted/ResNet07.pdf} &  \photo{Figure/result/weighted/ResNet09.pdf}\\
	(d) Weighted ResNet (5\%) &  (e) Weighted ResNet (7\%)  &  (f) Weighted ResNet (9\%) \\
	
\end{tabular}
 \end{center}
 \caption{Comparison of confusion matrix generated by different ResNets training on different ratios of labeled data. Weighted ResNet is built by assigning more weight to COVID-19 class during training for overcome the challenge of data imbalance.}
 \label{Fig3_covid-19}
\end{figure*}

Table~\ref{tab3_covid-19} presents the comparison of supervised baselines built with ResNet. We observed that ResNet (100\%) can outperformed COVID-Net (100\%) when comparing accuracy, macro-average precision, and macro-average Fscore. It means that ResNet is a competitive supervised baseline for COVID-19 image classification. Additionally, for learning on fewer labeled data, we only focus on the cases of 5\%, 7\%, and 9\% labeled data since the labeled data will be very scarce in medical domain~\cite{litjens2017survey} during the early stage of a global pandemic such as COVID-19 outbreak.  We observed that the classification accuracy can be improved by increasing the labeled data to train ResNet. Meanwhile, the performance such as accuracy and MacroF is reduced significantly when comparing with ResNet (100\%), which demonstrates that more labeled data is imperative for building high-performance supervised models. Moreover, we observed that weighted ResNet cannot improve the performance since we might assign inappropriate weight to different classes.

On the other side, we compare their confusion matrix to examine the performance details in Fig.~\ref{Fig_covid-net}. It indicates that ResNet (100\%) can be a promising supervised baseline model when compared to COVID-Net in terms of the accuracies on the normal and pneumonia classes. For the COVID-19 class, ResNet is lower than COVID-Net since COVID-Net employed transfer learning to enhance performance. 

To check the performance for each class when learning on fewer labeled data, we present the detailed performance with confusion matrix shown in Fig.~\ref{Fig3_covid-19}. When we use low ratios of labeled training data to train models, ResNet cannot recognize COVID-19 images effectively, which is duo to insufficient COVID-19 labeled samples. In the training sets of these cases, only few of images are for the COVID-19 class. For example, in the case of ResNet (5\%), we only have three images for COVID-19 class in the training data, which means most of training images are for the classes of Normal and Pneumonia. Learning on this data will lead to classification bias. Weighted ResNet was no sufficient to enhance the performance, which means even more weight assigned to COVID-19 class is not enough to overcome the lack of labeled samples to learn distinguish features to differentiate COVID-19 patients from Non-COVID-19 patients on X-ray images with supervised learning.

\subsubsection{Comparing the proposed model with state-of-the-art semi-supervised learning}

\begin{table*}[h!]
	\caption{\label{tab1_ml} Comparing performance between SRC-MT and Our model (Semi-supervised ResNet (SSResNet)).}
       
        \begin{center}
                \begin{tabular}{|l|cccc|}
                                 \hline \textbf{Semi-supervised Model} & \textbf{Accuracy (\%)} & \textbf{MacroP (\%)} & \textbf{MacroR  (\%)} & \textbf{MacroF  (\%)} \\ \hline 
                 	   SRC-MT (5\%)		&  90.67 		& 61.08 		& 60.75 		&  60.59  	\\
                 	   SRC-MT (7\%)		&  89.82 		& 89.92 		& 74.13 		&  78.95  	\\
			   SRC-MT (9\%)		&  92.79 		& 93.61  		& 79.15  		&  84.15  \\
\hline 			   

                    \hline \textbf{Our model} & \textbf{Accuracy (\%)} & \textbf{MacroP (\%)} & \textbf{MacroR  (\%)} & \textbf{MacroF  (\%)} \\ \hline
                    	   SSResNet (5\%)	&  84.95 		& 61.18 		& 66.76 		&  62.41  	\\
	   		   SSResNet (7\%)	&  84.21 		& 63.67 		& 67.85 		&  62.83  \\
			   SSResNet (9\%)	&  81.79 		& 59.34 		& 70.99 		&  59.19  	\\	   	\hline  
                \end{tabular}
       \end{center}
         \label{tab4_covid-19}
\end{table*}
\begin{figure*}[h!]
	\begin{center}
	\begin{tabular}{ccc}
	\photo{Figure/result/semisupervised/Densenet52.png} &  \photo{Figure/result/semisupervised/Densenet72.png} &  \photo{Figure/result/semisupervised/Densenet92.png}\\
	(a) SRC-MT (5\%) &  (b) SRC-MT (7\%)  &  (c) SRC-MT (9\%) \\	
	\photo{Figure/result/semisupervised/ResNet05022.pdf} &  \photo{Figure/result/semisupervised/ResNet07052.pdf} &  \photo{Figure/result/semisupervised/ResNet09102.pdf}\\
	(d) SSResNet (5\%) &  (e) SSResNet (7\%)  &  (f) SSResNet (9\%) \\	
	\end{tabular}
 	\end{center}
 \caption{Comparison of confusion matrix generated with SRC-MT and SSResNets  trained on different ratios of labeled data. }
 \label{Fig4_covid-19}
\end{figure*}


In this section, we will examine if the proposed model is able to effectively identify COVID-19 samples by training on very limited amount of annotated images. Table~\ref{tab4_covid-19} presents the comparison of classification performance between SRC-MT and the proposed model (SSResNet). Overall accuracies of SRC-MT are better than those of the proposed model. However, when only 5\% labeled samples were used for training, MacroF of our proposed model is higher than that of SRC-MT, which indicates that the proposed model is more effective in detecting COVID-19 samples. can detect COVID-19 samples with higher performance. It means  that compared to SRC-MT, the unsupervised path could enhance the data representation for improving COVID-19 classification more effectively. 

In addition, we examine detailed performance of each class with confusion metrics shown in  Fig.~\ref{Fig4_covid-19}. We observed that the accuracy of recognizing COVID-19 by the proposed model is higher than that of SMC-TC, which means SSResNets can learn more effective features from unlabeled data to recognize COVID-19 samples. Furthermore, with the increased ratios of labeled data, the accuracies of recognizing COVID-19 is enhanced significantly. It means that the unsupervised path can enhance the representations of images to improve the classification. In other words, unlabeled data contributed to increasing the COVID-19 classification performance significantly by enhancing the image representations with the unsupervised path of the SSResNet.  





\begin{table*}[h!]
	\caption{\label{tab_label_weight} Comparing performance with different class weights. $c_{1}$, $c_{2}$, and $c_{3}$  are the weights of Normal class, Pneumonia class, and COVID-19 class, respectively.} 
        \begin{center}
                \begin{tabular}{|c|cccc|}
                    \hline  &  & 5\% Labeled Data &  & \\ 
                    \hline \textbf{Class Weight} & \textbf{Accuracy} & \textbf{MacroP} & \textbf{MacroR} & \textbf{MacroF}\\ \hline
                    	   $c_{1}$ = 1, $c_{2}$ = 1, $c_{3}$ = 2			&  84.95 		& 61.18 		& 66.76 		&  62.41  	\\
                            $c_{1}$ = 1, $c_{2}$ = 1, $c_{3}$ = 5			&  78.82 		& 58.18 		& 67.38 		&  56.79  	\\  
                            $c_{1}$ = 1, $c_{2}$ = 1, $c_{3}$ = 10			&  66.78 		& 57.24 		& 66.70 		&  50.77  	\\                   \hline
                    \hline  &  & 7\% Labeled Data &  & \\
                    \hline \textbf{Class Weight} & \textbf{Accuracy} & \textbf{MacroP} & \textbf{MacroR} & \textbf{MacroF}\\ \hline
                    	   $c_{1}$ = 1, $c_{2}$ = 1, $c_{3}$ = 2			&  85.90 		& 65.75 		& 64.62		&  64.84  \\
                            $c_{1}$ = 1, $c_{2}$ = 1, $c_{3}$ = 5			&  84.21 		& 63.67 		& 67.85 		&  62.83  	\\ 
                            $c_{1}$ = 1, $c_{2}$ = 1, $c_{3}$ = 10			&  79.31 		& 58.57 		& 67.71 		&  59.39 	\\
                      \hline
                     \hline  &  & 9\% Labeled Data &  & \\ 
                      \hline \textbf{Class Weight} & \textbf{Accuracy} & \textbf{MacroP} & \textbf{MacroR} & \textbf{MacroF}\\ \hline
                    	   $c_{1}$ = 1, $c_{2} = $1, $c_{3}$ = 2			&  87.28 		& 70.32 		& 62.93 		&  64.65  	\\
                            $c_{1}$ = 1, $c_{2}$ = 1, $c_{3}$ = 5			&  84.69 		& 60.91 		& 66.79 		&  61.86  	\\   
                            $c_{1}$ = 1, $c_{2}$ = 1, $c_{3}$ = 10			&  81.79		& 59.34 		& 70.99 		&  59.19  	\\             \hline
                    
                \end{tabular}
       \end{center}
         \label{tab_batch_size}
\end{table*}

\begin{figure*}[t] 
	\centering

	\subfigure[Normal]{
		\label{Fig-01-1}
		\includegraphics[height=1.85in]{./Figure/result/error/covid2normal.jpeg}} 
	\hspace{0.02in}
	\subfigure[COVID-19]{
		\label{Fig-01-2}
		\includegraphics[height=1.85in]{./Figure/result/error/covid19.jpg}}
	\hspace{0.02in}
	\subfigure[Pneumonia]{
		\label{Fig-01-3}
		\includegraphics[height=1.85in]{./Figure/result/error/covid2pneumonia.jpeg}}
	\hspace{0.02in}
	\caption{COVID-19 samples classified into Normal, COVID-19, and Pneumonia classes, are shown in (a), (b), and (c) respectively.  The blue circles locate the infected regions of COVID-19. }
	\label{ExampleError}
\end{figure*} 



\subsubsection{Hyper-parameter setting}

In addition to examining the performance comparison between the proposed models and baselines, we have to figure out whether the proposed model is sensitive to the hyper-parameters.  There are various hyper-parameters involved in the learning procedure of the proposed model. Here, we choose class weight to check since different weights would lead to different performance of recognizing COVID-19 samples. Table~\ref{tab_label_weight} shows the comparison results for different weights of three classes. We observe that different weights will result in significant differences of the performance when examining  the values of accuracy. On the other hand, compared to accuracy and MacroP,  MacroR and MacroF are less sensitive to the weight of COVID-19 class. Generally, we have to delicately select the weight for COVID-19 class  to obtain the optimal performance.





\subsubsection{Error Analysis}

Fig.~\ref{ExampleError} presents three COVID-19 samples that are classified into Normal, COVID-19, and Pneumonia classes, respectively. X-ray images of COVID-19 patients shows various features for different stages of COVID-19 patients\footnote{https://www.uclahealth.org\/radiology\/covid-19-chest-x-ray-guideline}. At the early stage of COVID-19 patients, X-ray images cannot present significant features (Fig.~\ref{ExampleError} (a)) that can be used to differentiate COVID-19 and Non COVID-19 patients, which leads to the incorrect classification result for the sample. It is consistent with the expectation that X-ray images are not ideal evidences to support diagnosis of COVID-19 for the patients at the early stage. 

However, with development of COVID-19, X-ray images are able to present obvious features such as multifocal lung airspace opacities, nodules  and consolidation (Fig.~\ref{ExampleError} (b)), which contributes to the correct classification result. Unfortunately, if the patients are at the late stage of COVID-19, X-ray images presents lobar diffused consolidation (See Fig.~\ref{ExampleError} (c)) that is similar to features of pneumonia. These features will be confusing to the proposed model and lead to the incorrect result  for the sample shown in Fig.~\ref{ExampleError} (c). In summary, in terms of samples shown in Fig.~\ref{ExampleError}, the proposed model will be effective for the patients who are in the development of COVID-19 rather than those at the early stage or late stage of such disease.




\section{Introduction}
\begin{figure*} []
	\begin{center}
		\includegraphics[width=0.75\linewidth]{Figure/semisupervisedresnet.pdf}
		\caption{Framework of the proposed semi-supervised learning. Input $x$ is the medical image. Labels such as $y$ are available only for the labeled inputs. Shared ResNet will evaluate the input to obtain the low-level representations as inputs to supervised ResNet and unsupervised ResNet, where these three ResNets are built with residual blocks and  $N$, $M$, and $K$ are numbers of residual blocks for these three ResNets. Then $z^{sup}$ and $z^{unsup}$ are outputs from the supervised ResNet and the unsupervised ResNet, respectively. Moreover, $z^{sup}$ and $y$ will be applied to calculate a weighted cross entropy loss $l^{WCEL}$ whereas $z^{sup}$ and $z^{unsup}$ are used to calculate a mean squared error loss $l^{MSEL}$, where $w$ the weight to different classes of samples. We jointly optimize the combined losses, where $\lambda$ is the weight for unsupervised loss. $\oplus$ is the short-cut connection in the residue operation.}
		\label{Fig1:semisupervisedresnet}
	\end{center}
\end{figure*}

Coronavirus disease 2019 (COVID-19) outbreak has led to the heavy losses of the world's economy and life. To reduce the spread of COVID-19 and the death rate, it is essential to detect the disease at the early stage with effective and timely screening/testing and place COVID-19 infected patients in quarantine immediately~\cite{NYtimes,CDCguide}. Artificial intelligence (AI), an emerging technology for medical imaging processing, has actively contributed to the fight against COVID-19~\cite{bullock2020mapping}. Compared to the traditional imaging workflow that heavily relies on human interpretation, AI enables more safe, accurate and efficient imaging solutions. 

Recent AI-empowered applications in COVID-19 detection include the dedicated imaging platform, the lung and infection region segmentation, as well as the clinical assessment and diagnosis~\cite{shi2020review, gozes2020rapid, zheng2020deep}. Moreover, commercial products integrate AI to combat COVID-19 and demonstrate the capability of the AI technology~\cite{shi2020review}. All of these examples show the tremendous enthusiasm cast by the public for AI-empowered progress in the medical imaging field, especially during the ongoing COVID-19 pandemic. 

Regarding the COVD-19 research based on AI, COVID-19 image classification  becomes more and more attractive, which is to separate COVID-19 patients from non-COVID-19 subjects using the features extracted from medical images. Specially, supervised deep learning such as convolutional neural networks (CNN) has been very popular in this research area. For example, Wang \textit{et al.} proposed a 2D CNN supervised model to analyze delineated region patches to accomplish classification between COVID-19 and typical viral pneumonia~\cite{wang2020deep}. Similarly, Xu \textit{et al.} utilized candidate infection regions to complete COVID-19 classification via supervised ResNet-18~\cite{butt2020deep}. 

In addition, as a powerful deep learning model for medical image analysis, UNet~\cite{ronneberger2015u} was employed for COVID-19 image classification and segmentation. For example, Zheng \textit{et al.} employed UNet to obtain lung segmentation and predicted the probability of COVID-19 with 3D CNN on segmentation features~\cite{zheng2020deep}. Jin \textit{et al.}  proposed a UNet++ based segmentation model for locating lesions and built a ResNet-50 based classification model for COVID-19 diagnosis~\cite{jin2020ai}. Chen \textit{et al.} implemented COVID-19 classification with the patterns of segmented lesions extracted by supervised UNet++~\cite{zhou2018unet++, chen2020deep}. Moreover, they employed a 2D Deeplab model for the lung segmentation and a 2D ResNet-152 model for lung-mask slice based identification of positive COVID-19 cases~\cite{jin2020development}. Although supervised deep learning presents impressive performance on COVID-19 image classification, it requires a large amount of annotated medical images to train models, which is not practical with respect to limited data resources related to COVID-19, due to huge costs of labeling medical images, and labeling noise~\cite{litjens2017survey}.

To reduce the efforts on labeling medical images for COVID-19 image classification, we build a two-path semi-supervised deep learning model that is able to learn on both labeled and unlabeled medical images, based on residual neural networks (ResNet)~\cite{he2016deep}. ResNet is an artificial neural network developed by mimicking pyramidal cells in the cerebral cortex. It is to introduce a so-called ``identity shortcut connection" that skips one or more layers since stacking layers should not degrade the network performance. With ResNet, we implement a two-path semi-supervised learning model that is composed of three components, namely, shared ResNet, supervised ResNet, and unsupervised ResNet.  

Framework of the proposed model is shown in Fig.~\ref{Fig1:semisupervisedresnet}. One path is composed of a shared ResNet and a supervised ResNet while the other path consists of the shared ResNet and an unsupervised ResNet. All data (labeled and unlabeled data) will be evaluated to calculate the unsupervised loss that is the mean squared error loss (MSEL), while only labeled data will be used to calculate the supervised loss that is the cross entropy loss (CEL). Specifically, we design a weighted cross entropy loss (WCEL) that assigns more weight to the COVID-19 class for addressing the data imbalance. Reducing MSEL is to enhance the image representation while decreasing WCEL is to enhance classification performance. We validate the proposed model on a large-scale of X-ray image dataset \textit{COVIDx} and experimental results demonstrate the proposed model can accomplish COVID-19 image classification with promising performance even when trained on the extremely limited amount of labeled X-ray images.

The contributions in this study are below.

\begin{itemize}
\item We propose a semi-supervised deep learning model with ResNet through jointly training a supervised ResNet and an unsupervised ResNet. We observed  that the proposed model can learn on both unlabeled images and labeled images jointly for COVID-19 image classification with high performance.

\item The proposed model is validated on a large-scale COVID-19 image dataset. Experimental results indicate the proposed model is able to effectively recognize COVID-19 images by learning on very few labeled medical images, for example, less than 10\% samples in the training data, which meets the requirement of  few available labeled data from the medical domain for real applications~\cite{litjens2017survey}, especially for the cases at the early stage of such global pandemic.
\end{itemize}










\section{Introduction}
\label{sec1}
\input{Introduction}

\section{Proposed Methodology}
\label{sec2}
\input{Method}


\section{Experiment}
\label{sec3}
\input{Experiment}

\section{Related Work}
\label{sec4}
\input{Relatedwork}


\section{Conclusion and Future Work}
\label{sec5}
\input{Conclusion}


\appendices


\section*{Acknowledgment}
\label{acknowledgement}
This research work is supported in part by the Texas A\&M Chancellor's Research Initiative (CRI), the U.S. National Science Foundation (NSF) award 1464387 and 1736196, and by the U.S. Office of the Under Secretary of Defense for Research and  Engineering (OUSD(R\&E)) under agreement number FA8750-15-2-0119. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the U.S. National Science Foundation (NSF) or the U.S. Office of the Under Secretary of Defense for Research and Engineering (OUSD(R\&E)) or the U.S. Government. In addition, Y. Zhao, in the nursing program of Houston Community College, helped complete the error analysis of COVID-19 classification by using her medical imaging expertise.

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