## 4 Results and Application  
### Experiment Results  
The model training process after training the model with more than 500 epochs is presented in Figure 5. With the continuous iteration of the network, the mean square error of the model gradually decreases and eventually approaches the global optimum. Initially, as the number of epochs increased, the loss decreased rapidly. After 30 epochs, the decrease slowed down and gradually stabilized. The loss value eventually stabilized around 0.05.  
To evaluate the performance of the proposed UMAP-CNN, based on the labeled seismic waveform classification dataset, we compared it with other widely used manifold learning methods, namely t-SNE, LLE and Isometric Mapping (Isomap). These experiments  
Figure 5: Training loss over 500 epochs.  
adopt the default parameters in the cited documents to make the results more consistent for comparison.  
Figure 6 shows the processing efficiency of four dimensionality reduction algorithms across different dataset sizes. LLE maintains a consistently low execution time across all dataset sizes, but it consumes a lot of computation time and memory for matrix operations. UMAP-CNN, while slightly less efficient than LLE, still offers a competitive runtime. In contrast, t-SNE and Isomap demonstrate a steep increase in runtime as the dataset size increases, culminating in over 80 s for the largest dataset evaluated, which suggests these two methods may not be the most appropriate choice for large-scale data processing tasks due to their computational intensity.  
By comparing the ROC curves of the four models (Figure 7), the AUC value of the UMAP-CNN model reaches the optimal value (0.96), followed by the t-SNE model (0.93), Isomap model (0.86), and LLE model (0.64). An AUC value equal to 0.5 indicates a random classification performance, and an AUC value equal to 1 indicates a perfect classification performance, showing that the performance of the UMAP-CNN is better than that of the t-SNE, Isomap, and LLE.  
UMAP-CNN and other manifold learning methods were employed to generate two-dimensional representations of seismic data. In Figure 8, panels A through D present the two-dimensional projections obtained using four dimensionality reduction methods: UMAP (A), t-SNE (B), LLE (C), and Isomap (D). A visual inspection of these projections indicates that UMAP-CNN and t-SNE outperform the other methods in terms of cluster separability and structural preservation. UMAP-CNN demonstrates an effective capacity to capture the intrinsic geometry of the data, striking a balance between maintaining both local and global structures. While t-SNE also provides clear cluster separation, it exhibits some overlap among adjacent clusters, suggesting a stronger emphasis on preserving local rather than global relationships. In contrast, LLE and Isomap show limited effectiveness in distinguishing distinct clusters, particularly when applied to datasets characterized by high complexity or variability.  
Figure 6: Runtime performance of four methods.  
For the quantitative assessment, the overall accuracy (OA) of all classes, the average accuracy (AA) of each class, and the Kappa score are calculated. As illustrated in detail in Table 1, the results reveal the good performance of UMAP-CNN compared to the other techniques. Clearly, UMAP-CNN provides a higher feature extraction capability in classification.  
Figure 8: Two-dimensional embedding distribution map of different methods: (**A**) UMAP-CNN; (**B**) t-SNE; (**C**) LLE; (**D**) Isomap.  
Figure 7: ROC curves of four methods.