# Survey on Recent Trends in Medical Image Classification Using Semi-Supervised Learning
## 2 Background
### Adversarial Methods  
We will discuss two commonly used methods called Virtual Adversarial Training (VAT) and Generative Adversarial Network (GAN) methods in this category. Adversarial training methods involve the presence of \"adversarial attacks,\" which cause various errors in prediction [28]. These attacks are small perturbations to the input data applied in the direction where the model's label assignment is most sensitive [29]. In VAT, adversarial attacks are generated and incorporated into the training of the model in order to increase its robustness. The aim of this method is to achieve high smoothness at each data point in order to prevent small perturbations from causing classification errors. The loss function used is the local distributional smoothness (LDS) loss, a measure of the local distributional smoothness which indicates the robustness of the model against local perturbation around each input data point. The LDS is calculated as follows:  
\[LDS(x_{*},\theta):=D\big{[}p(y|x_{*},\hat{\theta}),p(y|x_{*}+r_{vudv},\theta) \big{]} \tag{2}\]  
wherein \(x_{*}\) is a labeled or unlabeled data point and \(D[p,p^{\prime}]\) is a function that evaluates the divergence between the distributions \(p\) and \(p^{\prime}\). \(p(y|x_{*},\hat{\theta})\) is an approximation of the true distribution of the output label calculated based on probabilistically generated \"virtual\" labels. Thus, the goal is to minimize the divergence between the distribution of \(x_{*}\) and itstransformed version \(x_{*}+\tau_{vadv}\), making the model more robust to adversarial perturbations. The full objective function of VAT is as follows:  
\[\ell(\mathcal{D}_{l},\theta)+\alpha\mathcal{R}_{vadv}(\mathcal{D}_{l},\mathcal{ D}_{ul},\theta) \tag{3}\]  
wherein \(\ell(\mathcal{D}_{l},\theta)\) is the negative log-likelihood of the labeled dataset, and \(\alpha\) is the regularization coefficient which controls the relative balance between \(\ell(\mathcal{D}_{l},\theta)\) and \(\mathcal{R}_{vadv}\). \(\mathcal{R}_{vadv}\) is the regularization term which is defined as the average of the loss \(LDS(x,\theta)\) over all input data points. In GAN-based methods, the adversary is a generator network whose role is to create fake images that fit the distribution of the real data as closely as possible. This generator competes against a discriminator network whose role is to distinguish the fake data from the real data. As the two networks compete, they both gradually improve. The optimal state of the model is reached when the generator has learned to create perfectly realistic samples which the discriminator cannot distinguish from the real data [30]. This ability to synthesize samples with high levels of realism can be used to solve the issue of scarcity of labeled data. Additionally, the classifier training can also be embedded directly into the GAN framework for improved generalization and robustness [4]. Generative Adversarial Nets (GANs) [31] are deep neural network architectures involving two networks; a generator model (G) and a discriminator model (D). The name \"adversarial\" comes from the fact that G and D are pitted against each other; G generates samples while D learns to distinguish between the samples generated by G and samples from the real data. The competition between the two networks leads to both networks improving over time, with G generating more realistic images increasingly until they are undistinguishable from the real samples. Deep Convolutional Generative Adversarial Networks (DCGAN) [32] is a type of GAN that uses Convolutional Neural Networks (CNN) in its generator in order to create a higher quality generator model and achieve stable training across different datasets.