## 4 Results and Discussion  
### Financial Fraud Detection Results  
The purpose of the financial fraud detection experiment was to evaluate the effectiveness of the proposed method compared to several existing privacy-preserving techniques in terms of key performance metrics, including precision, recall, F1 score, and accuracy. Financial fraud detection tasks often deal with highly imbalanced data, where fraudulent transactions are much fewer than legitimate transactions. This makes the use of a model capable of distinguishing between these classes crucial. Additionally, the integration of privacy-preserving techniques is essential to ensure that sensitive financial data, such as credit card transactions, are protected while maintaining the model's performance. The experiment aimed to validate whether the proposed method could not only provide strong privacy protection but also improve or maintain high classification accuracy compared to other existing methods. The results presented in Table 3 reflect the performance of various models, including MPC, HE, DP, FL, and the proposed method. From the results, it is clear that the proposed method surpasses all other models in terms of precision, recall, F1 score, and accuracy. With a precision of 0.95, recall of 0.91, and F1 score of 0.93, the method demonstrates its capability to achieve both accurate detection and a low rate of false positives, making it particularly efficient in identifying fraudulent activities. Comparatively, baseline methods such as MPC, HE, DP, and FL show inferior performance across all metrics. For example, MPC, with a precision of 0.83 and recall of 0.78, achieves an F1 score of 0.80, indicating challenges in balancing privacy preservation with detection accuracy. HE, despite offering strong privacy guarantees, achieves slightly better results but remains behind the proposed method, with an F1 score of 0.84 derived from a precision of 0.86 and recall of 0.82. DP, which applies noise to obscure individual information, achieves a precision of 0.89, recall of 0.86, and F1 score of 0.87, but struggles with a clear trade-off between privacy and performance. FL, which enables training on decentralized data while ensuring privacy, achieves a precision of 0.92, recall of 0.89, and F1 score of 0.90, demonstrating its ability to preserve privacy while maintaining relatively high performance. The proposed method, however, likely benefits from its capability to effectively balance the trade-off between privacy and model utility. By integrating symmetric projection space extraction with adversarial training, the framework obfuscates sensitive information while retaining critical features needed for fraud detection. From a mathematical standpoint, the approach employs adversarial learning, optimizing the generator (responsible for creating obfuscated data) and the discriminator (tasked with distinguishing real from generated data) in a game-theoretic manner. This ensures that the obfuscated data remain of sufficient quality for decision-making processes without compromising sensitive details. Moreover, the incorporation of symmetric projection space ensures robust privacy protection with minimal information loss during dimensionality reduction. This synergy of advanced techniques contributes to the method's exceptional performance in both privacy preservation and model accuracy within the context of financial fraud detection. The proposed method's strong performance, particularly in recall, precision, and F1 score, is largely due to its ability to handle imbalanced datasets effectively while ensuring robust privacy protection. Unlike traditional methods such as DP, which degrade performance by adding noise, the proposed approach achieves a fine balance between privacy and utility through its innovative design, thereby improving fraud detection without compromising model integrity. The F1 score underscores the method's balanced effectiveness in achieving high precision and recall, especially in scenarios with imbalanced data.