## 4 Proposed Methodology
### Modified Conditional Generative Adversarial Network (MCGAN)  
A generative adversarial network (GAN)is a deep learning technique that mimics the game theory concept of two-human zero-sum games and is utilized to handle large-scale real-time complex information. This technique is used to oversample the available data by balancing minority and majority classes [27]. GAN incorporated two neural networks, namely generator (g) and discriminator (X). Let g be used to analyze the distribution of actual input samples \(S=\{s_{1},s_{2},\ldots,s_{n}\}\) and create a new set of data samples, and X be considered as a binary classifier utilized to specify whether the \(s\) is original or engendered data \((z)\). The classified outcome reverts to g and D to eradicate the weight loss. The process repeats until D has successfully classified original and engendered data samples. Thelearning method is a mini-max game to obtain a Nash equilibrium among \(\mathfrak{g}\) and \(\mathfrak{D}\). The optimization function for GAN is represented as  
\[\min_{\mathfrak{g}}\max_{\mathfrak{D}}V(\mathfrak{g},\ \mathfrak{D})=\mathbb{E}_{s \sim p(s)}\Big{[}\log\mathfrak{D}(s)\big{]}+\mathbb{E}_{z\sim p(z)}[\ \log(1-\mathfrak{D}(\mathfrak{g}(z))] \tag{2}\]  
where \(p(s)\) specifies the dispersal of actual data instances, the method \(\mathfrak{g}(z)\) implies the noise information (\(z\)) to the search space, and \(\mathfrak{D}(s)\) denotes the probability that instance \(s\) is actual data. Moreover, the \(\mathfrak{D}(s)\) samples must have more data than \(\mathfrak{D}(\mathfrak{g}(z))\) to differentiate the actual and generated data. The traditional GAN technique has the drawback of mode-collapse occurrence; the outcome leads to only one class instead of giving importance to the entire distribution. This problem may occur when the actual sample distribution is multi-modal. To handle the above issue, we proposed the conditional generative adversarial network (CGAN) that is a modified technique of the GAN Model, in which the categorical data and noise information are clubbed together with the actual samples as the input to the \(\mathfrak{g}\) and \(\mathfrak{D}\) with loss strategy. CGAN is effective in learning together with the existing distribution samples. \[\min_{\mathfrak{g}}\max_{\mathfrak{D}}V(\mathfrak{g},\ \mathfrak{D})=\mathbb{E}_{s \sim p(s)}\Big{[}\log\mathfrak{D}(s|x)\big{]}+\mathbb{E}_{z\sim p(z)}[\ \log(1-\mathfrak{D}(\mathfrak{g}(z|x))] \tag{3}\]  
where \(x\) denotes the class details and the other parameters as specified in Equation (1). The working process of CGAN is presented in Figure 1. Generally, GAN and CGAN create a set of instances and minimize the class disparity issues. Nevertheless, their practice of the Jensen Shannon distributer involves overlay between the scattering of actual and produced cases, which is unreal or unacceptable. The \(\mathfrak{D}\) is trained to be optimal; hence, it may lead to the prototypical downfall and wipe out gradient issues [28]. In this work, we modified CGAN by merging the Lipschitz boundary and Wasserstein distance to handle the above issues. These incorporated techniques address the \(\mathfrak{D}\), \(z\) vector and mapping labels to \(\mathfrak{g}\). Here, we utilize \(\mathfrak{D}\) to determine the actual and created instances \(s\). If \(\mathfrak{D}\) fails to distinguish the genuine and generated \(s\), then we fine-tune the \(\mathfrak{g}\) and train the \(\mathfrak{D}\) and vice versa. We replicate the process until the loss rate is minimized at about 0.5. The proposed model can create the data of a quantified pattern to balance the imbalance  
Figure 1: The architecture of conditional generative adversarial network. dataset by eradicating the waning gradients that affect the \(\mathfrak{D}\) in the training process. The fitness function of MCGAN is presented below.