# A Multi-Input Fusion Model for Privacy and Semantic Preservation in Facial Image Datasets
## 5 Experimentation and Results
### Privacy Preservation Evaluation  
We established a dataset consisting of original, surrogate, and de-identified images for training the model. By including a surrogate and four de-identified images in the dataset, we aimed to improve the model's ability to conceal facial privacy. Considering the protection performance of the model, in this training process, we set \(\alpha\) in Equation (19) to 0. During training, we experimented with different values of \(\beta\) to minimize the loss, after which we checked the maintenance quality loss to choose the most suitable percentage of \(\beta\). The graph depicted in Figure 4 illustrates the change in the loss rate with different values of \(\beta\). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Brief Description** & **Range** \\
**Name** & & **of Value** \\ \hline \(k\) & \begin{tabular}{c} Allocate the relative weight to be given to the image coordinates and \\ their corresponding centroid image coordinate \\ \end{tabular} & [0, 1] \\ \(t\) & \begin{tabular}{c} Control the proportional weight of the image region and the \\ corresponding centroid image region to synthesize a surrogate image \\ Commitment loss in \(\mathbb{L}_{m_{1}}\), ensuring that the encoder is dedicated to \\ the embedding \\ \(\beta_{m_{2}}\) \\ \end{tabular} & [0, 1] \\ \(\alpha\) & \begin{tabular}{c} Commitment loss in \(\mathbb{L}_{m_{2}}\), making sure the encoder commits to \\ the embedding \\ \end{tabular} & [0.1, 2] \\ \(\beta\) & \
\begin{tabular}{c} Determine the appropriate balance between the weight assigned to the \\ loss of service and the loss of image fusion \\ \end{tabular} & [0, 1] \\ \(\beta\) &
\begin{tabular}{c} Control the proportional weight of original images and surrogate images \\ \end{tabular} & [0, 1] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Model parameters and settings. Figure 4: The changing trend of the loss rate when \(\alpha=0\). As Figure 4 depicts, when \(\beta\) is about 0.2, the effort of the model is much better, and after 50 rounds, the loss rate is reduced to 0.09 which is less than other proportions. This represented a significant reduction of at least 2.4% compared to the initial loss rate. To verify the effect of privacy preservation of our method, we conducted re-identification experiments that evaluate the risk of successfully identifying the subject contained in the input dataset utilizing de-identified facial images in the generated dataset. Drawing on the k-anonymity theory, we consider that when the generated image \(I\) is more similar to other original images in the same cluster compared to its original image, \(I\) meets the criteria. Specifically, if the cosine similarity between \(I\) and its corresponding original image is larger than the smallest value of similarity calculated between \(I\) and other authentic images in the same cluster, the privacy of the image is protected. Let \(N_{protected}\) be the number of privacy-protected images generated and \(N_{total}\) represent the total number of images in the dataset. The privacy protection rate, denoted as \"RP\", is calculated according to Equation (20). As the proportion of the surrogate image increases, generated images have a much greater chance of not being identified from the original cluster. We measured the percentage rate for privacy-preserved images, respectively. \[RP=\frac{N_{protected}}{N_{total}} \tag{20}\]  
As indicated in Figure 5, overall, there was a significant upward trend, which indicates that the effect of the model on image privacy protection improves. The highest percentage is up to 84% when the proportion of surrogate images is 80%. It can be concluded that the identity of images is obviously concealed after our method, achieving privacy protection. To preserve the privacy of facial images in the dataset, we utilized models with various values of \(\beta\). Initially, we employed the model with a relatively small value of \(\beta\) for protection.