# Survey on Recent Trends in Medical Image Classification Using Semi-Supervised Learning
## 4 Survey Results
### Adversarial Methods  
Uncertainty-Guided Virtual Adversarial Training With Batch Nuclear-Norm Optimization [56]: This method incorporates batch-nuclear norm (BNN) optimization [57] to prevent overfitting to the labeled data and to improve the diversity and discriminability of the model. As proposed by [PERSON] et al. [57], the nuclear-norm \(\parallel P(\theta)\parallel_{*}\) of the \(m\times n\) prediction matrix \(P(\theta)\) is calculated as follows:  
\[\parallel P(\theta)\parallel_{*}=\sum\
olimits_{i=1}^{min(m,n)}\sigma_{i}(P( \theta)) \tag{12}\]  
where \(\sigma_{i}(P(\theta))\) represents the \(i\)th largest singular value of \(P(\theta)\). As mentioned previously, the goal of incorporating BNN optimization is to improve generalization and avoid overfitting the labeled data. This is achieved by minimizing the BNN of the labeled data and maximizing the BNN of the unlabeled data batch. Thus, the labeled BNN loss \(L_{IBNN}\) and unlabeled BNN loss \(L_{uBNN}\) are defined as follows:  
\[L_{lBNN}=\frac{1}{B_{l}}\parallel P_{l}(\theta)\parallel_{*} \tag{13}\]  
\[L_{uBNN}=-\frac{1}{B_{u}}\parallel P_{u}(\theta)\parallel_{*} \tag{14}\]  
\(B_{l}\) and \(B_{u}\) represent the size of the labeled and unlabeled datasets, while \(\parallel P_{l}(\theta)\parallel_{*}\) and \(\parallel P_{u}(\theta)\parallel_{*}\) represent the nuclear norm of the labeled and unlabeled prediction matrices, \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Type** & **Dataset Used** & **Best Results** \\ \hline SRC-MT [19] & Consistency-based & Chest X-ray14 and ISIC2018 & X-ray14: AUC 79.23 \\  & & ISIC2018 & ISIC2018: AUC 93.58, \\  & & F1 60.68 \\ NoT [52] & Consistency-based & Chest X-ray14, RSNA & X-ray14: AUC 79.49 \\  & & Brain CT, Knee MRNet & RSNA: AUC 93.31 \\  & & & MRNet: AUC 91.49 \\ S\({}^{2}\)MTS\({}^{2}\)[55] & Consistency-based & Chest X-ray14, ISIC2018, & X-ray14: AUC 82.51 \\  & & CheXpert & ISIC2018: AUC 94.71, \\  & & CheXpert & F1 62.67 \\  & & & CheXpert: AUC 71.58 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of consistency-based methods. respectively. In addition to BNN, the model incorporates uncertainty guidance during VAT loss computation to filter out unlabeled samples close to the decision boundary. The uncertainty \(U^{i}\) is calculated for each unlabeled sample \(x^{i}_{u}\) in a batch, and predictions with high uncertainty are filtered out to ensure that only reliable targets are used for learning. \(U^{i}\) is calculated as follows:  
\[U^{i}=-\sum_{j=1}^{c}p_{u}^{ij}log\Big{(}p_{u}^{ij}\Big{)}.i\in 1\dots B_{u} \tag{15}\]  
with \(p_{u}^{ij}\) representing the predicted probability of \(x^{i}_{u}\) for the \(j\)th class and C denoting the number of classes. Thus the model is trained using the following losses: the cross-entropy loss of the supervised model (\(L_{cls}\)), the VAT loss calculated from labeled data (\(L_{lvat}\)), the uncertainty-guided VAT loss computed from the unlabeled data (\(\widetilde{L}_{uvat}\)), and the BNN losses \(L_{lBNN}\) and \(L_{uBNN}\). The overall loss for the labeled data is the combination of all losses calculated over the labeled data:  
\[L_{l}=L_{cls}+\lambda_{vat}L_{lvat}+\lambda_{lBNN}L_{lBNN} \tag{16}\]  
Similarly, the unlabeled loss can be calculated as follows:  
\[L_{u}=\lambda_{vat}\widetilde{L}_{uvat}+\lambda_{uBNN}L_{uBNN} \tag{17}\]  
wherein \(\lambda_{vat}\), \(\lambda_{lBNN}\) and \(\lambda_{uBNN}\) are weighting coefficients. The overall objective function is the addition of the supervised and unsupervised losses \(L_{l}+L_{u}\). The model was tested on the ISIC2018 and Chest X-ray14 datasets as well as an in-house collected hip X-ray dataset composed of 26,075 X-ray images labeled into four categories. The ISIC2018 and hip X-ray images were resized into \(224\times 224\) images. DenseNet121 [23], pre-trained on ImageNet, was used as the backbone network for both datasets. The X-ray14 dataset was resized into \(256\times 256\) images with DenseNet169 [23] as the backbone network.