## 3 Results and Discussion
### Analysis of Warning Level Classification
The stabilization of all three methods after 15 iterations indicates that further iterations would not significantly improve the clustering results, confirming the optimization process's effectiveness. After 15 iterations, the loss functions for all methods stabilized, indicating that the models had achieved their optimal performance. Further iterations would not yield substantial improvements in the clustering results. The final clustering outcomes after the iteration convergence are presented in Figure 6.  
Figure 4: Silhouette coefficients under different dimension reduction methods. Figure 5: Loss function value of iteration process. After dimensionality reduction and clustering, the coal spontaneous combustion data was partitioned into six clusters (Clusters 1-6), though these clusters were not inherently ordered. To interpret the significance of each cluster, we analyzed the corresponding coal combustion temperatures and assessed the cluster risk levels based on temperature variations, thereby establishing the warning levels. PCA clustering yielded seven clusters, with the temperature frequency distributions shown in Figure 7. As shown in Figure 7, Clusters 5 and 1 predominantly span 30-120 \({}^{\circ}\)C, and Clusters 3 and 6 concentrate within 90-160 \({}^{\circ}\)C, while Clusters 7, 2, and 4 mainly distribute across 140-180 \({}^{\circ}\)C. Figure 7 further illustrates that Cluster 5 appears the earliest with the highest frequency, disappearing at 130 \({}^{\circ}\)C, indicating the lowest risk. Cluster 1 follows, with an increasing frequency until disappearing at 170 \({}^{\circ}\)C. Cluster 4 appears the latest, and is predominantly distributed between 170-180 \({}^{\circ}\)C, representing the highest risk, followed by Cluster 2. However, PCA's seven-level classification resulted in some clusters containing insufficient data points, making the risk level determination through the peak analysis unreliable. SNE clustering results, illustrated in Figure 8, reveal several limitations in classification effectiveness. The overall frequency distributions show relatively low and inconsistent  
Figure 6: Clustering visualization results using different dimensionality reduction methods: (**a**) PCA clustering results with 7 clusters and center points; (**b**) SNE clustering results with 6 clusters and center points; and (**c**) t-SNE clustering results with 6 clusters and center points. Figure 7: Classification of coal spontaneous combustion warning levels with PCA. patterns across different clusters, suggesting suboptimal data separation. Figure 8 demonstrates a particularly problematic aspect where Cluster 5 spans across the entire temperature range (30-180 \({}^{\circ}\)C), violating the physical principle of progressive risk development in coal spontaneous combustion. This unrealistic distribution indicates that SNE fails to capture the underlying temperature-dependent relationships between indicator gases. Moreover, the highly concentrated nature of SNE-reduced data manifests in significant cluster overlap, particularly in the middle temperature ranges (90-150 \({}^{\circ}\)C), where multiple clusters share substantial common regions. This overlap creates ambiguity in risk level determination, as similar gas concentration patterns are assigned to different clusters without clear physical justification. The lack of distinct boundaries between the adjacent clusters and the absence of clear temporal progression in the cluster appearances make it challenging to establish reliable temperature thresholds for different risk levels. These limitations stem from SNE's tendency to compress data points too closely in the reduced dimensional space, potentially losing important structural information about the relationships between different risk levels. Unlike t-SNE, which maintains both local and global data structures, SNE's focus on preserving local structures results in less interpretable clustering outcomes for coal spontaneous combustion warning level classification.