## 3 The Proposed Model
### Feature Extraction and Embedding
#### 3.1.3 Price Feature Extraction and Embedding
Due to variations in pricing strategies among different brands, some brands are positioned in the high-end market with relatively higher prices, while others target the mass market with a focus on high cost-performance, resulting in relatively lower prices. Additionally, certain brands may cater to multiple market segments, leading to significant price fluctuations. By extracting these features, it is possible to effectively capture the pricing strategy characteristics across different brands. (6) User Brand Preference Price Features  
For the historical purchase or outfit records of user \(u\), we further extract price preference features at the brand level. These features include the mean and standard deviation of the user's prices for brand \(b\):  
\[\mu_{\text{user-brand}}(u,b)=\frac{1}{N_{b}}{\sum_{i=1}^{N_{b}}P_{\text{user -brand}}^{(i)}}\]  
\[\sigma_{\text{user-brand}}(u,b)=\sqrt{\frac{1}{N_{b}}{\sum_{i=1}^{N_{b}}\left( P_{\text{user-brand}}^{(i)}-\mu_{\text{user-brand}}(u,b)\right)^{2}}}\]where \(\mu_{\text{user-brand}}(u,b)\) and \(\sigma_{\text{user-brand}}(u,b)\) represent the mean and standard deviation of prices for user \(u\) under brand \(b\), respectively, \(P_{\text{user-brand}}^{(i)}\) denotes the price of the \(i\)-th clothing item purchased or matched by user \(u\) under brand \(b\), and \(N_{b}\) is the number of historical records of user \(u\) for brand \(b\). By statistically analyzing the user's historical behavior in selecting clothing items across different brands, the recommendation system can infer the user's price tolerance for various brands, thereby enhancing the personalization of the recommendation results [34; 35]. Discretization of Price Features  
To enhance the model's ability to handle continuous variables, all continuous price features undergo discretization. Specifically, an equal-frequency binning method is employed to divide each continuous feature into 10 groups, which are then transformed into a sparse feature matrix using one-hot encoding. The implementation process is as follows:  
Assume that the continuous price feature \(P_{\text{price}}\) is discretized into \(K\) intervals, each representing a discrete category \(\{C_{1},C_{2},\dots,C_{K}\}\). If the price feature value \(P_{\text{price}}\) of a data-point falls into the j-th interval, the discretized category label for that data point is \(C_{j}\). For each discretized category label \(C_{j}\), its corresponding one-hot encoding is represented as a \(K\)-dimensional vector. Given \(N\) samples, the feature vector after discretization is expressed as:  
\[E_{3}= \begin{bmatrix}x_{1}^{T}\\ x_{2}^{T}\\ \vdots\\ x_{N}^{T}\end{bmatrix}  \tag{1}\]  
where \(x_{i}\) denotes the one-hot encoded vector for the \(i\)-th sample, with a dimensionality of \(K\). Through this method, a sparse matrix \(E_{3}\) is obtained, where each row corresponds to the one-hot encoding of the discretized price feature for a sample. After one-hot encoding transformation, each price feature is represented as a sparse vector, with a non-zero value (1) only at the position corresponding to its interval and zeros elsewhere. This approach helps reduce the nonlinear complexity of the model when processing continuous features and facilitates efficient matrix computations by the computer.