## 4 Results and Discussion
### Image and Semantic Classification Detection Results  
The purpose of the image and semantic classification detection experiment was to assess the performance of the proposed method in the context of privacy-preserving machine learning for image-related tasks, particularly in terms of both classification and object detection accuracy. The experiment was designed to compare the effectiveness of different privacy-preserving techniques, including MPC, HE, DP, FL, and the proposed method. The key metrics used for evaluation include precision, recall, F1 score, accuracy, and mAP at thresholds of 50% (mAP@50) and 75% (mAP@75). These metrics are particularly important for image classification and object detection tasks, as they provide a comprehensive view of both the accuracy and robustness of the model in handling different types of image data. Through this experiment, the aim was to demonstrate that the proposed method could achieve a high level of privacy protection while maintaining or even improving classification and detection performance compared to traditional methods. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Model** & **Precision** & **Recall** & **F1 Score** & **Accuracy** & **Computation Complexity** \\ \hline Multi-party Secure Computation & 0.83 & 0.78 & 0.80 & 0.80 & 12.83 \\ Homomorphic Encryption & 0.86 & 0.82 & 0.84 & 0.84 & 83.14 \\ Differential Privacy & 0.89 & 0.86 & 0.87 & 0.88 & 4.71 \\ Federated Learning & 0.92 & 0.89 & 0.90 & 0.91 & 31.65 \\ Proposed Method & 0.95 & 0.91 & 0.93 & 0.93 & 3.28 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Financial fraud detection results. From the results presented in Table 4, it is clear that the proposed method outperforms all the other models in terms of precision, recall, F1 score, accuracy, and mAP. The precision of 0.93, recall of 0.90, and F1 score of 0.91 indicate the method's high ability to both correctly identify positive instances and minimize false positives, making it highly effective for detecting relevant objects in image data. In terms of accuracy, the proposed method achieves 0.91, surpassing the other models. Additionally, the mAP@50 and mAP@75 values of 0.91 and 0.90, respectively, highlight the model's strong performance in object detection, especially in challenging detection scenarios where the object-to-background ratio is low or when the objects are obscured. When compared with the baseline models, such as MPC, HE, and DP, the proposed method consistently provides superior results. For example, MPC, with a precision of 0.84, recall of 0.80, and F1 score of 0.82, performs relatively well but still lags behind in terms of both accuracy and mAP. HE offers better performance than MPC, with a precision of 0.86, recall of 0.82, and F1 score of 0.84, but still falls short of the proposed method. The DP method, which applies noise to the data to preserve privacy, achieves a precision of 0.89, recall of 0.86, and F1 score of 0.87, but still faces a trade-off between privacy and accuracy. FL, with its decentralized training approach, yields the best results among the baseline methods with a precision of 0.91, recall of 0.88, and F1 score of 0.89, but it still does not reach the performance level of the proposed approach. The superior performance of the proposed method can be attributed to its ability to balance privacy protection and model utility. The method integrates symmetric projection space extraction and adversarial training, enabling it to obfuscate sensitive information in the data while retaining the essential features for classification and detection. Mathematically, the symmetric projection space ensures that the data are projected into a low-dimensional space in such a way that the critical features necessary for training are preserved, while unnecessary information is discarded. The adversarial training framework further strengthens the model's ability to generate privacy-preserving data while optimizing the generator's ability to produce realistic data and the discriminator's ability to detect generated data.