## 3 Proposed Methodology
### Feature Representation for Expression Classification
Here, \(n^{\prime}\) is calculated by \(n^{\prime}=\frac{n-t+2\times\mathcal{P}}{\mathcal{S}}+1\), where \(\mathcal{S}\) is the stride that governs how many numbers of cells will be moved by the filter to the right and down, from the top-left corner to the bottom-right corner, in the input image to calculate the next cell in the result. Additionally, \(\mathcal{P}\) is the padding that shrinks the height and width of the volumes. Mathematically, the formulation of the convolution operation is denoted as follows [51]: for input feature vector \(\mathrm{F}=\mathbf{f}(v)\) and a filter vector \(\mathrm{W}=\mathbf{w}(v)\), the convolution operation is obtained as \(\mathbf{F}\star\mathbf{W}=\sum_{u\in\mathbf{U}}\mathbf{f}(u)\mathbf{w}(v-u)= \langle\mathbf{f}(u),\mathbf{w}(v-u)\rangle\), where the operator \(\star\) denotes the convolution operation and \(\langle\cdot,\cdot\rangle\) represents the sliding vector inner product between the input feature \(\mathbf{f}(u)\) and the flipped kernel \(\mathbf{w}(v-u)\). It measures the similarity between the two vectors. The primary benefits of the convolution operation are: (i) parameter or weight sharing, as a feature detector is used in one part and transfers into other parts of the image; (ii) the fact that it reduces the number of effective parameters and image translation; and (iii) the sparsity of connections, i.e., the hidden layers' input and output dependencies. * _Max-pooling:-_ A pooling operation is a mathematical operation that performs pixel-wise average or median operations to reduce the input image size by half its size. The effective advantages of using pooling operations concern a means of removing noise, correcting images, and overcoming incidental occlusions [52]. The pooling layer is used to reduce the size of the representation to speed up the process as well as to make some of the features it detects more robust. There are different types of pooling operations, such as average pooling, fractional max-pooling, and max-pooling. Max-pooling is a commonly used pooling operation that is used in most CNN models. Max-pooling calculates the maximum value for patches of a feature map and uses it to create a down-sampled feature map. It is usually used after a convolutional layer. The primary benefits of max-pooling are as follows: (i) it is a translation invariance, i.e., it translates the image by a small amount that does not significantly affect the values of most pooled outputs; (ii) has reduced computational costs; (iii) has faster matching; and (iv) has improved accuracy. * _Fully Connected Layers:_- It has been stated that fully connected layers and convolutional layers are distinct, but it has been observed that fully connected layers are a special case of convolutional layers [53]. In our proposed CNN model, we used two fully connected layers denoted as \(\mathcal{FC}_{1}\) and \(\mathcal{FC}_{2}\). Here, \(n_{2}\) neurons in \(\mathcal{FC}_{2}\) have full connections to all activation \(n_{1}\) in \(\mathcal{FC}_{1}\). The activation function can be computed with a matrix multiplication followed by a bias offset. Let \(x\in\mathbf{R}^{n_{1}\times 1}\) represent the single output vector of layer \(\mathcal{FC}_{1}\) and let \(\mathbf{W}\in\mathbf{R}^{n_{1}\times n_{2}}\) denote the weight matrix of the \(\mathcal{FC}_{2}\). Suppose \(w_{i}\) is the weight vector of the corresponding \(i_{th}\) neuron of the column vector of \(\mathbf{W}\) in layer \(\mathcal{FC}_{2}\)[54]. Then, the output of \(\mathcal{FC}_{2}\) is obtained by \(\mathbf{W}^{T}\times x\). The output of fully connected layers is independent of the input image size. Fully connected layers of a CNN architecture will reduce the full image size, compute the single vector of class scores, and produce a resulting vector of size \([1\times 1\times\mathcal{C}_{i}]\). * _Dense Layers:_- The dense layer is a type of fully connected connection layer in deep neural networks [55]. In a dense layer, all input layers are connected to the output layers by a weight.