## 3 Results and Discussion
### Supervised Learning: Classification  
At a test size of 0.20, with k-means method k = 5, then f = 4, the accuracies of Logistic Regression and Random Forest are 0.61 and 0.67, respectively. However, using XGBoost  
Figure 6: \(\Delta r_{eb}\) vs. interval time of (**a**) 90-sample dataset; (**b**) 48-sample dataset; (**c**) 90-sample dataset with bit, bit/\(\sqrt{2}\), and bit/\(\sqrt{2}\) groups specified. Figure 7: d\(\Delta r_{eb}\)/dt vs. energy of (**a**) 90-sample dataset; (**b**) 48-sample dataset. increased the accuracy to 0.78. Therefore, this study adopts XGBoost as the algorithm to analyze the experimental data obtained. Figure 7(a) presents the comparative performance of three classification algorithms--Logistic Regression, Random Forest, and XGBoost--in response to diverse test sizes. The algorithms were configured as follows: Logistic Regression was allotted a maximum of 1000 iterations for convergence, Random Forest employed an ensemble of 100 decision trees (n_estimators = 100), and XGBoost utilized the default value of 100 estimators. The x-axis unveils the spectrum of test sizes, spanning from 0.20 to 0.40, while the y-axis illustrates the corresponding accuracy scores. Notably, Logistic Regression consistently exhibits the lowest accuracy among the three models. At a test size of 0.30, a notable crossover occurred where Random Forest surpassed XGBoost, becoming the model with the highest accuracy. The highest accuracy among the three models occurs for the XGBoost algorithm, with an accuracy of 0.74 at a test size of 0.25. For Random Forest, the accuracy varies between 0.56 and 0.67, indicating a consistent performance across different test sizes. XGBoost consistently demonstrates competitive performance, with accuracies ranging from 0.53 to 0.74, showcasing its effectiveness under different test size conditions. XGBoost displays a general decreasing trend in accuracy as the test size increases, suggesting a potential sensitivity to data size. On the other hand, Random Forest maintains a relatively stable trend, indicating robustness to variations in test size. Figure 7(b) illustrates the performance of three classification algorithms using the percentile method. Similar to Figure 7(a), Logistic Regression consistently exhibits the lowest accuracy among the three models. This indicates its limited effectiveness in accurately categorizing samples based on the provided features. Notably, at a test size of 0.20, XGBoost demonstrates the highest accuracy with an impressive 0.78. As the test size increases, Logistic Regression shows a gradual decline in accuracy, suggesting potential sensitivity to data size. Random Forest maintains a relatively stable trend in accuracy across the entire range of test sizes, performing between 0.56 and 0.67. This indicates its robustness to variations in test size. Meanwhile, XGBoost starts strong, with a high accuracy of 0.78 at a test size of 0.20. However, it experiences a slight decrease as the test size increases, hinting at a potential sensitivity to data size. Nevertheless, even at the largest test size of 0.40, XGBoost maintains a competitive accuracy of 0.67. XGBoost consistently outperforms Random Forest. Figure 7(c) presents the performance of three classification algorithms utilizing a forced partition into five clusters. Consistent with previous observations in Figure 7(b), XGBoost consistently outperforms Random Forest across the entire range of test sizes. It is noteworthy that the accuracies obtained in Figure 7(c) are notably lower compared to those in Figure 7(a),b. Despite these lower accuracies, the relative performance of the models remains consistent, underscoring the effectiveness of XGBoost in this dataset. Logistic Regression consistently yields lower accuracy compared to the other models. At a test size of 0.20, XGBoost exhibits the highest accuracy, reaching 0.61.