## 3 Results and Discussion  
### Analysis of Warning Level Classification  
To achieve the optimal dimensionality reduction, Maximum Likelihood Estimation (MLE) was employed as the criterion for determining intrinsic dimensionality. Compared to other estimation methods, MLE demonstrated superior convergence properties and asymptotically approaches unbiased estimation in theory. The MLE results indicated that compressing the sample variables to two dimensions preserved the essential data characteristics. Through this approach, the data was embedded into a two-dimensional space, ensuring intuitive data visualization. Furthermore, to evaluate the dimensionality reduction performance of t-SNE, both PCA and SNE methods were applied to the original data using identical procedures. The visualization results in two dimensions of data related to coal spontaneous combustion under different dimensionality reduction methods are shown in Figure 3. PCA, as a linear dimensionality reduction method, resulted in significant data stacking in two-dimensional space and failed to effectively compress the data. In contrast, both SNE and t-SNE methods successfully mapped nonlinear data from high-dimensional space to low-dimensional space with better preservation of the data structure. The PCA projection shows significant overlap between data points and lacks clear boundaries between different regions, indicating its limitation in capturing nonlinear relationships. The SNE method demonstrates better separation of data points but still exhibits some clustering inconsistencies at region boundaries. The t-SNE projection achieves the most distinct separation of data points with clear boundaries between different regions, suggesting its superior ability to preserve both local and global data structures. These visualization results demonstrate that t-SNE is more effective at capturing the intrinsic nonlinear relationships in coal spontaneous combustion data compared to traditional dimensionality reduction methods. The k-means clustering algorithm was employed to classify the warning levels for coal spontaneous combustion. The first crucial step was determining the optimal number of clusters (k) for partitioning the combustion data, as both excessive and insufficient cluster numbers would compromise the warning system's effectiveness. Therefore, the range of \(k\) values was set between 2 and 7, and the clustering performance was evaluated using silhouette coefficients for each k value, as illustrated in Figure 4. The analysis revealed that the clustering performance improved with increasing k values. Overall, t-SNE demonstrated superior clustering effectiveness, achieving a peak silhouette coefficient of 0.95 when k = 6, indicating both optimal cluster separation and cohesion. Based on the maximum silhouette coefficient values, the coal spontaneous combustion warning levels were classified into seven levels using PCA, while both the t-SNE and SNE methods yielded six distinct levels. Subsequently, iterative clustering was performed for each method independently, with the iteration process illustrated in Figure 5.  
Figure 3: Two-dimensional visualization results of coal spontaneous combustion data: (**a**) Principal Component Analysis (PCA) projection; (**b**) Stochastic Neighbor Embedding (SNE) projection; and (**c**) t-distributed Stochastic Neighbor Embedding (t-SNE) projection. The convergence patterns of the loss functions reveal the important characteristics of each method. PCA shows rapid initial convergence but stabilizes at a relatively high loss value, indicating potential information loss during the dimensionality reduction. SNE exhibits moderate convergence speed with intermediate loss values, suggesting a balance between data compression and information preservation. The t-SNE method, while showing slightly slower initial convergence, achieves the lowest final loss value, demonstrating its superior ability to maintain data relationships during the dimensionality reduction.