# Investigating the Performance of FixMatch for COVID-19 Detection in Chest X-rays
## 3 Materials and Methods  
### The FixMatch Algorithm  
The FixMatch algorithm proposed by [PERSON] et al. [11] in 2021 is a semi-supervised learning algorithm that makes use of the consistency regularization and pseudo-labeling techniques commonly employed as part of semi-supervised learning [9]. Consistency regularization exploits the argument that realistic perturbations of input data points should not significantly change the predictions of a model in the label space [50]. This technique is based on the manifold and smoothness assumptions required to be met by algorithms in order to effectively train in a semi-supervised manner [51]. Pseudo-labeling is the process by which the model is trained on labeled data before the unlabeled data are passed through it in order to generate predictions. These predictions are then treated as true labels to further \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Authors** & **Year** & **Dataset** & **No. of Data Points** & **Model** & **Best Results** \\ \hline [PERSON] et al. [46] & 2020 & Private dataset & \begin{tabular}{c} COVID-19: 102 \\ Pneumonia: 102 \\ Normal: 102 \\ \end{tabular} & \begin{tabular}{c} MixMatch + \\ wide-Resnet \\ \end{tabular} & Accuracy: 96.6\% \\ \hline [PERSON] et al. [47] & 2021 & Private dataset & \begin{tabular}{c} COVID-19: 102 \\ Pneumonia: 102 \\ Normal: 102 \\ \end{tabular} & \begin{tabular}{c} MixMatch + \\ DenseNet121 \\ \end{tabular} & Accuracy: 91.3\% \\ \hline [PERSON] et al. [44] & 2021 & COVID + BIMCV + MIDRCRICORD & \begin{tabular}{c} COVID-19: 3795 \\ Pneumonia: 6045 \\ Normal: 8851 \\ \end{tabular} & \begin{tabular}{c} CNN for pseudo \\ label generation + \\ CNN for classification \\ \end{tabular} & 40\% labeled sample with F1 score of 93\% \\ \[PERSON] et al. [49] & 2021 & \begin{tabular}{c} COVIDGR, \\ C19-Cohen \\ \end{tabular} & \begin{tabular}{c} COVID-19: 426 \\ Normal: 426 \\ C19-Cohen \\ \end{tabular} & \begin{tabular}{c} COVIDGR: 100\% \\ fraction: AUC of 97\% \\ pairs + wide ResNet50 \\ \end{tabular} & \begin{tabular}{c} COVIDGR: 100\% \\ fraction: AUC of 97\% \\ C19-Cohen: 10\% \\ fraction: AUC of 91.5\% \\ \end{tabular} \\ \hline [PERSON] et al. [48] & 2021 & Private dataset & \begin{tabular}{c} COVID-19: 576 \\ Normal: 1583 \\ Pneumonia: 4273 \\ \end{tabular} & \
\begin{tabular}{c} Auto Encoder + CNN \\ with ImageNet weights \\ \end{tabular} &
\begin{tabular}{c} Accuracy: 99.8\% on \\ second dataset \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of work using semi-supervised deep learning for COVID-19 classification through X-rays. train the model in a supervised manner [52]. FixMatch leveraged these two techniques by a process where an artificial label is first produced by using a weakly augmented image before the model is trained to predict this label when a strongly augmented version of the same image is input to it. A loss term is then computed which consists of a supervised terms and an unsupervised term. The supervised and unsupervised loss terms can be seen in Equations (1) and (2), respectively, where \(p_{b}\) is the predicted distribution for the labeled sample, \(x_{b}\) is the true distribution (label), \(B\) is the labeled batch size, \(\mu B\) is the unlabeled batch size, \(q_{b}\) is the pseudo-label generated from the weakly augmented image and \(q\theta\) is the predictions on the strongly augmented image. \[\mathcal{L}_{s}=\frac{1}{B}\sum_{b=1}^{B}CE(p_{b},x_{b}) \tag{1}\]  
\[\mathcal{L}_{u}=\frac{1}{\mu B}\sum_{b=1}^{\mu_{B}}1(\max(q_{b})\geq\ \tau)\ CE(q_{b},q\theta\ (y\mid A(u))) \tag{2}\]  
This procedure is relatively simple compared to many of the prevailing state-of-the-art semi-supervised learning techniques. However, FixMatch achieved the state-of-the-art when compared with prevalent semi-supervised algorithms such as MeanTeacher [53], MixMatch [45], Unsupervised Data Augmentation [54] and ReMixMatch [55] on common benchmarking datasets such as CIFAR10, CIFAR100 [56] and SVHN [57].