## 2 Related Works
### Models  
Face identification and facial expression recognition are highly researched areas, and new models with state-of-the-art (SOTA) performance are constantly being developed. However, the focus of our study is not to create a new face identification or facial expression recognition model with the highest performance but to compare the impact of different facial areas. To achieve this, we utilized an existing high-performance model for face identification and facial expression recognition. Face identification can be divided into two categories: close-set and open-set [17]. Close-set recognition involves recognizing people within a specific group, whereas open-set recognition involves matching people not in the training set. Learning proceeds to solve this problem by embedding facial images into a discriminative feature space using methods such as triplet loss. A typical example is FaceNet [18], released by Google in 2015, which uses triplet loss for learning. Instead of considering the absolute distance, the triplet loss learns the difference in the relative distance. It learns by minimizing the distance between images with the same ID as the center image and maximizing the distance between images with different IDs. This study has the disadvantage of using large amounts of private data and numerous computer sources; therefore, the results are not reproducible. VGGFace [19], released in 2015, achieves similar performance with less data than FaceNet and achieves 99% accuracy; it has also made its dataset public. Subsequent studies on face identification focused on datasets, preprocessing methods, and loss functions. ArcFace [20], releasedin 2018, is a representative example of a study focusing on loss functions. It locates the feature-embedding values derived from the image data in a spherical surface space and minimizes the spherical angle of the data for the same person. This approach prevents the model from converging toward its origin and still exhibits state-of-the-art performance in face verification. The equation for calculating the ArcFace loss is shown in Equation (1). \(W_{y_{i}}\) represents the representative vector of the correct answer class and \(W_{j\
eq y_{i}}\) represents the representative vector of the non-correct class. \[\mathrm{L}_{arcface}=-\frac{1}{N}\sum_{i=1}^{N}log\frac{e^{\mathrm{s}(\cos \left(\theta_{y_{i}}+m\right))}}{e^{\mathrm{s}(\cos\left(\theta_{y_{i}}+m \right))}+\sum_{j=1,j\
eq y_{i}}^{n}e^{\mathrm{s}\cos\theta_{j}}} \tag{1}\]  
Equation (1) can be explained using Figure 1, where we assume that there is a representative vector \(W_{y_{i}}\) for the correct answer class, a representative vector \(W_{j\
eq y_{i}}\) for the non-correct answer class, and an image-embedding vector \(X_{i}\) that is being processed. The distance between the image and the correct answer is denoted as \(\theta_{y_{i},\,i}\), whereas the distance from the incorrect vector is denoted as \(\theta_{j,\,i}\). ArcFace aims to minimize the distance \(\theta_{y_{i},\,i}\) between the image-embedding and the correct answer classes while simultaneously maximizing the distance \(\theta_{j,\,i}\) between the image-embedding and the incorrect answer classes. This is done by introducing a margin m, such that learning is performed in a way that \(\theta_{j,\,i}\) is larger than \(\theta_{y_{i},\,i}+m\). This approach ensures that the intra-class distances are kept very small, whereas the inter-class distances are increased, thereby improving the overall performance of the model. Therefore, our study applied the ArcFace model to ResNet50 [21] to obtain the face identification results. The overall architecture of face identification is shown in Figure 2. Figure 2a shows an example of the same person's image; in contrast, Figure 2b shows an example of a different person's images. The model attempts to update its weights to minimize angle \(\theta_{1}\) and maximize angle \(\theta_{2}\).