# Survey on Recent Trends in Medical Image Classification Using Semi-Supervised Learning
## 4 Survey Results
### Graph-Based Methods  
GraphXNET: GraphXNET is a semi-supervised graph-based framework that performs a classification task with an extremely small number of labeled samples and a large number of unlabeled samples. The function used in this model is \(\Delta_{1}(u)=\left|WD^{-1}u\right|\), based on the normalized graph p-Laplacian with p = 1. The algorithm is as follows: for each class \(k\), the model assumes that there exists a set of labeled nodes \(\mathcal{I}_{k}\subset\{1\cdots l\}\). For each class \(k\), a variable \(u^{k}\) is chosen that has values in all nodes of the graph. Assume the total number of classes is \(L\). For all unlabeled nodes \(i>l\), the \(L\) chosen variables are coupled with the following constraint: \(\sum_{k=1}^{L}u_{i}^{k}=0,\forall i>l\). Using a small positive number \(\epsilon\), the following constraint is applied:  
\[\left\{ \begin{array}{ll}u_{i}^{k}\geq\epsilon&\text{ if }i\in\mathcal{I}_{k} \\ u_{i}^{k^{\prime}}\leq-\epsilon&\text{ if }i\in\mathcal{I}_{k}\text{ and }k^{\prime}\
eq k \end{array} \right. \tag{24}\]  
The goal of the model is then to minimize the normalized ratios \(\sum_{k}\frac{\Delta_{1}(u^{k})}{|u^{k}|}\). This model was evaluated using the ChestX-ray14 dataset. The results of the classification task were compared to two previously existing state-of-the-art deep learning methods for X-ray classification proposed by [PERSON] et al. [68] and [PERSON] et al. [69]. For both methods, 70% of the data was labeled, whereas, for the GraphXNET method, only 20% was labeled. The metric used for comparison was the average of the AUC score over all 14 classes. GraphXNET achieved the highest average score (0.78) despite using a much lower number of labeled samples. Additionally, when tested with three different, random partitions of data, GraphXNET proved to be more stable to variations in the data partition. Graph-Embedded Random Forest [70]: This method makes the standard random forest algorithm more reliable when dealing with a low number of labeled samples. With the traditional method, insufficient training data leads to a limited depth, an inaccurate prediction model for leaf nodes, and a sub-optimal splitting strategy [71]. In the graph-based model, [PERSON] et al. [70] improved the splitting strategy by replacing the information gain algorithm with a graph-embedded entropy. The goal is to utilize the local structure of unlabeled data to achieve higher reliability when using a small number of labeled data while maintaining the advantages of the random forest, such as low computational burden and robustness towards overfitting. The loss function is a sum of the supervised loss \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Type** & **Dataset Used** & **Best Results** \\ \hline \multirow{4}{*}{Uncertainty-guided VAT with BNN [56]} & \multirow{4}{*}{Adversarial (VAT-based)} & Chest X-ray14, ISIC2018 & X-ray14: 80.69 AUC \\  & & & Skin Lesion Analysis, Hip & F1 69.67 \\  & & & X-ray & Hip X-ray: AUC 92.43, \\  & & & F1 72.39 \\ \hline \multirow{2}{*}{SSAC [58]} & \multirow{2}{*}{Adversarial (GAN-based)} & LIDC-IDRI and Tianchi & \multirow{2}{*}{AUC 92.82, Accuracy 90.58} \\  & & Lung Nodule dataset & \\  & & combined & \\ \hline \multirow{2}{*}{Bi-Modality Image Synthesis [62]} & \multirow{2}{*}{Adversarial (GAN-based)} & Locally collected dataset & \multirow{2}{*}{Accuracy 93} \\  & & and PROSTATEx & \\ \cline{1-1}  & & combined & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of adversarial methods. and a graph Laplacian regularization term. First, a graph \(G=(V,\ E,\ W)\) is constructed using labeled and unlabeled data. The nodes represent the training samples and \(W\) is the symmetric weight matrix, calculated as follows:  
\[W_{ij}= \begin{cases}exp\left(-\frac{\|x_{i}-x_{j}\|_{2}^{2}}{\sigma^{2}}\right) \text{ if }\big{(}x_{i},x_{j}\big{)}\text{ are neighbors}\\ 0\quad\quad\text{ if }\big{(}x_{i},x_{j}\big{)}\text{ are not neighbors}\end{cases}