## 3 Methodology
### Intelligent Recognition Algorithm  
(1) K-means  
K-means is a clustering method based on an iterative algorithm. Due to its high computational efficiency and fast processing speed, K-means is widely used in clustering  
Figure 4: Schematic diagram of t-SNE algorithm. Figure 5: Schematic diagram of UMAP algorithm. and data vectorization tasks [52]. In the process of clustering using K-means, suppose that \(N\) data points and \(p\) feature parameters are involved, and we want to classify the data points into \(k\) clusters. The clustering process is as follows:  
(1) Select \(k\) initial cluster centers as the starting point of clustering. (2) For each data point, calculate its distance from each of the \(k\) cluster centers, and assign the data point to the cluster \(C(l)\) that has the closest distance to it. If the cluster assignment of a data point changes, the center point of each cluster is recalculated. Through such an iterative process, K-means is able to gradually adjust the positions of the cluster centers until a certain stable state is reached. This partitions the data points into \(k\) different clusters, where the data points within each cluster are highly similar and the data points between different clusters are less similar. \[d\left(x_{i},x_{j}\right)=\left[\sum_{r=1}^{p}\left|x_{ir}-x_{j}\right|^{2} \right]^{\frac{1}{2}} \tag{5}\]  
\[C(l)=arg\underset{1\leq l\leq K}{min}d(x_{i},v_{i}),i=1,2\cdots,N \tag{6}\]  
\(d\left(x_{i},x_{j}\right)\) is the Euclidean distance selected for this clustering. \(x_{i}\) is the \(i\)-th data point. \(x_{ir}\) is the \(r\)-th feature parameter for the \(i\)-th data point. \(C_{l}\) is the set of data points contained in class \(l\). \(v_{i}\) is the center of gravity of class \(i\). (3) By using this method, the sample can be repeatedly selected and the iterative calculation can be carried out until the preset number of iterations is met or the calculation result becomes stable, thereby terminating the calculation process (Figure 6). (2) CatBoost  
Gradient Boosting Decision Tree (GBDT) is an ensemble learning algorithm that iteratively trains multiple weak classifiers. By leveraging the residual information from the preceding model, it optimizes the new model in each iteration to gradually enhance overall prediction performance. Grounded in the core concept of gradient descent, GBDT fits a new model along the negative gradient direction of the loss function. This approach exhibits strong nonlinear modeling capabilities and has been widely applied to classification and  
Figure 6: Schematic of the K-means algorithm. regression tasks. Nevertheless, traditional GBDT faces certain limitations when handling categorical features, feature interactions, and gradient estimation, which may lead to overfitting or performance degradation. CatBoost is an improved algorithm based on the Gradient Boosted Decision Tree (GBDT) framework, which enhances the model performance by optimizing the feature processing and gradient estimation mechanism [53]. The core innovation of CatBoost is reflected in the following three aspects:  
(1) Categorical feature coding  
For mixed datasets (including numeric and categorical features), CatBoost adopts an ordered target coding strategy. First, the samples are randomly permuted to generate multiple sets of sequences, and then the target statistics of the same class samples are calculated dynamically based on the permutation order. Specifically, for the class feature \(k\) of sample \(x_{i}\), its encoding value is as follows:  
\[\hat{x}_{k}=\frac{\sum_{j=1}^{p-1}\left[x_{\sigma_{j},k}=x_{\sigma_{p},k} \right]Y_{\sigma_{j}}+aP}{\sum_{j=1}^{p-1}\left[x_{\sigma_{j},k}=x_{\sigma_{p}, k}\right]+a} \tag{7}\]  
(2) High-order feature interactions  
The algorithm automatically generates feature combinations during tree construction: only original features are used in the first split level, and all features on the current path are dynamically combined in subsequent splits.