## 3 Materials and Method
### Proposed Method
#### 3.3.1 Data Obfuscation Strategy Based on Probability Density and Information Entropy  
This study proposes a data obfuscation strategy based on probability density and information entropy to address the trade-off between data privacy protection and analytical performance. By coordinating the probability density extraction module and the information entropy fusion module, the strategy achieves the targeted obfuscation of data, balancing privacy protection and task performance, as shown in Figure 3. Figure 3 illustrates the architecture of the proposed data obfuscation strategy, which is composed of three main layers: the Training Management Layer, the Privacy Evaluation Layer, and the Feature Processing Layer. The Training Management Layer oversees the optimization process by iteratively adjusting the parameters based on the loss function, ensuring a balance between privacy protection and task performance. The Privacy Evaluation Layer integrates a privacy discriminator and sensitive information detector, which dynamically assess the risk of privacy leakage and provide feedback to guide the obfuscation intensity. The Feature Processing Layer consists of the Encoder Network, Attribute Suppression Module, and Decoder Network, which work collaboratively to extract features, suppress sensitive attributes, and reconstruct data, retaining core utility while obfuscating sensitive information. These components interact seamlessly to provide a comprehensive solution for data obfuscation. In its implementation, the probability density extraction module first models the distribution features of the raw data. The raw data \(X=\{x_{1},x_{2},\ldots,x_{n}\}\) are fed into a kernel density estimator to compute its probability density function (PDF). The kernel density estimation is given by  
\[\hat{f}(x)=\frac{1}{nh}\sum_{i=1}^{n}K\bigg{(}\frac{x-x_{i}}{h}\bigg{)}, \tag{12}\]  
Figure 3: Architecture of the data obfuscation strategy proposed in this paper. Figure 2: Overview of the proposed method. where \(K(\cdot)\) is a Gaussian kernel function and \(h\) is the bandwidth parameter. The distribution features generated by kernel density estimation are further processed by a deep neural network. The network consists of three convolutional layers (each with kernel size \(3\times 3\), 64 channels, and ReLU activation), followed by two fully connected layers with 128 and 64 nodes, respectively. The final output is a high-dimensional distribution feature vector representing the data's distribution pattern in the feature space. The probability density feature vector is then fed into the information entropy fusion module. This module dynamically adjusts the obfuscation intensity using information entropy, \(H(X)\), a key metric for measuring data uncertainty, defined as  
\[H(X)=-\sum_{i}P(x_{i})\log P(x_{i}), \tag{13}\]  
where \(P(x_{i})\) represents the probability of data point \(x_{i}\). Information entropy is computed based on the distribution features generated by the probability density extraction module, with the intensity of obfuscation adjusted based on these entropy values. For data points with higher information entropy (indicating higher sensitivity), stronger obfuscation is applied. Conversely, data points with lower entropy (indicating lower sensitivity) are subject to milder obfuscation. The dynamic adjustment of the obfuscation intensity allows the model to target data regions that are more sensitive to perturbations, applying stronger obfuscation where privacy is more critical while minimizing the impact on less sensitive regions. The obfuscation process is implemented using the following formula:  
\[M(x)=\alpha\cdot G(x)+\beta\cdot T(x), \tag{14}\]  
where \(G(x)\) represents Gaussian noise-based obfuscation, \(T(x)\) represents gradient perturbation-based obfuscation, and \(\alpha\) and \(\beta\) are dynamically generated weights based on information entropy, satisfying \(\alpha+\beta=1\).