## 3 Proposed Methodology
### Generative Adversarial Network  
The implicit GAN model reported in [17] failed to estimate the probability density of the randomly sampled input data. With the complexity of sampling in multi-dimensional data, the GAN failed to generate the synthetic sample for a subset of data. The contingent GAN model resolved the issue by including the conditional constrained \(\chi\) on the input abstraction layer of the generator network and its discriminator part.  
\[G_{min}D_{max}f(G,D)=\zeta_{r\sim p(r)}[logD(r|\chi)]+\zeta_{\tau\sim p(\tau)}[ log(1-D(G(r|\chi))] \tag{1}\]  
The mapping \(f:\{\tau,\chi\}\to r\) transforms the GAN from an unsupervised to a partially supervised network. The objective function in Equation (1) defines the conditional GANs (CGAN), with the real sample denoted by variable \(r\) and the synthetic by variable \(\chi\). The \(f\) denotes the CGAN, with \(p(r)\) as the probability of the real sample, and \(p(\tau)\) denotes the probability of the random noisy input sample. The symbol \(\zeta\) with subscript \(r\sim p(r)\) denotes the expected value of the random real samples \(r\), while \(\zeta_{\tau\sim p(\tau)}\) denotes the expected value of the synthetic samples \(\tau\). The variables \(G\) and \(D\) represent the generator and the discriminator, respectively.  
In the conditional GANs, the generator part produces the synthetic samples as much similar to the original content, whereas the discriminator part has to differentiate in the original and synthetic samples. The issue of pattern collapse has been resolved by employ  
Figure 3: Data Preprocessing.  
ing the pixel-to-pixel sample selection in the conditional GANs. The objective function of the pixel-to-pixel conditional GAN \(g\) is given in Equation (2).  
\[g(G,D)=\zeta_{r,\chi}[logD(r|\chi)]+\zeta_{r,\tau}[log(1-D(x,G(r|\tau)))] \tag{2}\]  
where the symbol \(g\) denotes the pix2 pix conditional GAN model. The loss function of the proposed multi-face GANs consisting of pixel-to-pixel conditional GAN depending on the hybrid raw feature is represented with Equations (3) and (4).  
\[L(g)=\zeta_{v,r,\chi}[||\chi-g(v,\tau)||] \tag{3}\]  
\[L^{*}=argG_{min}D_{max}L_{g}(G,D)+\lambda L(g) \tag{4}\]  
whereas the symbol \(v\) denotes the input raw feature vector. The variable \(\lambda\) works as an adjustment parameter in Equation (4); when the \(\lambda\) is zero, then the loss function of the pix2 pix CGAN turns to a conditional GAN model.  
The proposed multi-face contingent pixel-to-pixel version of the GAN model is presented in Figure 4.  
The pixel-to-pixel considers the feature values individually in the raw feature set. The raw feature is divided into N \(\times\) 1 and patch, and the discriminator judges the patch instead of the whole feature vector for authenticity. The N dimension equals 128, which provided a higher recognition in the proposed model. The classification method of LeNet-5 [39] is employed, and the features extracted are classified with the fully connected layer to reduce the complexity of the computational procedures. The network parameters are trained separately to optimize the classification performance of the network.