## 3 Proposed Methodology
### Feature Representation for Expression Classification
Suppose a dropout probability of 0.5 is used; in this case, roughly half of the activation in each layer is deleted for every training sample, thus preventing hidden units from relying on other hidden units present. * _Optimisation:_ The proposed FERS problem has been solved by stochastic optimization methods to optimize our CNN models. In this study, we used the popular first-order gradient-based Adam optimizer of the stochastic objective function. The popular optimization methods used for solving FERS problems are Adagard, SGD, RMSProp, SGD with momentum, AggMo, Demon, Demon CM, DFA, and Adadelta optimization methods. They use their stochastic mini-bath method. This method estimates the learning rate based on lower-order momentum. Adam [61] uses only the first two moments of gradient \(\widetilde{v}_{t}\) and the learning rate or steps size \(\eta\). The weight updates for the Adam optimizer are mathematically calculated as \(w_{t}=w_{t-1}-\eta\frac{\hat{v}_{t}}{\sqrt{\widetilde{v}_{t}}-\epsilon}\), where \(\epsilon\) is a smaller number. The primary advantages of using the Adam optimizer are that it works well and is suitable for problem-solving for large training data sets. Adam can handle non-stationary objective functions as in RMSProp while overcoming the sparse gradient issue drawbacks that appear in RMSProp. Adam is favorable compared to other stochastic optimizers. The implementation of Adam is straightforward and computationally efficient with less memory required. The proposed CNN architectures are based on several blocks as discussed in the previous section. Here, an input image \(\mathcal{F}_{n_{H}\times n_{W}}\) is convolved with a set of kernels of size \(t\times t\). These convolution layers are called feature maps. The feature maps are stacked to provide multiple filters on the input. We used \(3\times 3\) sized filters with a stride of 1 for each convolution layer. The activation function for each convolution layer was ReLU. The computational complexity of the CNN models was reduced by using \(d\times d\) pooling layers, which reduces the output size from one layer to the next in the hidden network layers. To select maximum elements, we used \(2\times 2\) max-pooling operations to preserve the important features [62]. Hence, these layers reduce the size of the input image by half. To feed the pooled output from the stacked featured map to the final layer, the maps were flattened into one column. The final layers of the CNN had two fully connected layers with \(M\) number of nodes each. Fully connected layers also used the ReLU activation function. These two layers were regularized by using the dropout layers with the regularization technique. Finally, the Softmax layer was employed, followed by two fully connected layers, and the number of nodes of this layer was equal to the number of expression classes. During the feature representation of images using deep learning approaches, it was observed that the CNN models obtained better representation when patterns were analyzed from the multi-resolution of images. Additionally, increasing some layers in the architecture while increasing the resolution of the images results in more deeply analyzing some hidden patterns in the feature maps. Inspired by these observations, we applied multi-resolution of the facial images with varying layers in different CNN architectures. During feature representations, we considered facial images with three different resolutions such  
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