## 4 Experiment Setup
### Analysis of Experimental Results of Regression Datasets with Different Feature Numbers
The MAE curve of the RFHFS algorithm reach the first peak at k = 6, reach the second peak at k = 12, and then continue to decline. The RMSE curve of RFHFS reaches the maximum at k = 6 and then decreases slowly until it rapidly decreases to the minimum at k = 30. The MAE curve of CSFFS is similar to the RMSE curve, reaching the maximum value at k = 6 and then decreasing slowly. Similarly, the MAE curve of the FSNT algorithm is similar to the RMSE curve. When k = 6, it drops to the lowest point, then rises to the highest point at k = 9, and then drops again. Finally, when k = 15, the three algorithms CSFFS, RFHFS, and FSNT descend to similar MAE and RMSE values. Since the feature selection algorithm used for both the Student-por dataset and the Student-mat dataset selects the same features, and the explained variance ratio of the Student-mat dataset has been previously presented, there is no need to reiterate the explained variance ratio for the Student-por dataset. As shown in Figure 8, Turning to the variance ratio of the Superconductivity dataset, the x-axis represents the number of selected features (k), while the y-axis represents the variance ratio obtained through the interpretation of each feature selection method. CSFFS, XGBFS, RFHFS, and FSNT all demonstrate an increase in variance ratio as the number of features increases. Among them, the RFHFS algorithm consistently yields the lowest variance ratio throughout the entire process, with the XGBFS algorithm also lagging behind the other two algorithms. Conversely, the CSFFS algorithm achieves the highest variance ratio. When the feature selection algorithm employs 81 features and k = 30, the explanatory variance ratio ranges between 0.7 and 0.8, indicating that it retains the most information. Similarly, when k = 30, the explanatory variance ratio of the FSNT algorithm surpasses 0.7, positioning it as the second-best method for information retention. Figure 6: Performance of different feature selection methods using different algorithms for Online News Popularity datasets. (**a**) MAE; (**b**) RMSE. Regarding the variance ratio of the Online News Popularity dataset, CSFFS, XGBFS, RFHFS, and FSNT exhibit an increase in variance ratio as the number of features increases. Throughout the entire process, the RFHFS algorithm consistently produces the lowest variance ratio, with the XGBFS algorithm also significantly trailing the other two algorithms. On the other hand, both the CSFFS and FSNT algorithms consistently maintain the same explanatory variance ratio, significantly surpassing the other algorithms. When the feature selection algorithm incorporates 61 features and k = 30, the explanatory variance ratio for both algorithms exceeds 0.8, meaning that, even with only 50% of the feature number used, more than 80% of the information is retained. Overall, CSFFS, XGBFS, RFHFS, and FSNT exhibit distinct advantages in the classification results across different datasets, with RFHFS showing a slightly inferior performance. However, the CSFFS algorithm solely relies on selecting features based on high correlation according to the chi-square value, without considering feature differences or redundancy. Consequently, it performs worse compared to other feature selection algorithms based on information theory, such as XGBFS, RFHFS, and FSNT. When evaluating the three datasets using the two criteria of Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE),  
Figure 8: Explanatory variance ratio of different feature selection methods on different datasets. (**a**) Superconductivity dataset variance; (**b**) Online News Popularity dataset variance. Figure 7: Performance of different feature selection methods using different algorithms for Student-por datasets. (**a**) MAE; (**b**) RMSE. along with considering the explained variance ratio, the classification accuracy of the FSNT method surpasses that of CSFFS, XGBFS, and RFHFS. This demonstrates that the FSNT method can obtain a feature subset with enhanced regression capabilities.