## 4 Experiment Setup
### Analysis of Experimental Results of Regression Datasets with Different Feature Numbers  
Figure 5 illustrates the average regression accuracy obtained by four feature selection algorithms (CSFFS, XGBFS, RFHFS, and FSNT) and ten regression algorithms (multiple linear regression, elastic net regression, random forest, extra trees, SVM, gradient boosted, decision tree regression, AdaBoost regression, Gaussian process regression, and MLP regression) used on the Superconductivity dataset. The x-axis represents the number of selected features (K), while the \(y\)-axis represents the average MAE and average RMSE achieved by each feature selection method. The black horizontal line represents the Baseline. The FSNT algorithm and the other three feature selection algorithms were compared using feature subsets ranging from 6 features to 30 features. On the Superconductivity dataset, the MAE and RMSE curves of XGBFS, RFHFS, and FSNT algorithms exhibit alternating increases with the number of selected features, whereas the MAE and RMSE curves of the CSFFS method initially rise and then decline, reaching their peak at k = 12, followed by a decrease with the increasing number of features. However, the final MAE and RMSE values for CSFFS are still larger than those of other methods. Regarding the MAE value, the XGBFS, RFHFS, and FSNT algorithms show slight increases as the number of features increases. When k \(\leq\) 18, the three methods exhibit minimal differences compared to the MAE value of the Baseline and display horizontal oscillation. At k = 24, the maximum MAE value for the three algorithms surpasses the Baseline, after which it decreases. Finally, when k = 30, the three methods converge to the MAE value of the Baseline. Concerning the RMSE value, XGBFS, RFHFS, and FSNT algorithms demonstrate an alternating oscillation pattern below the horizontal line of the benchmark as the number of selected features increases. At k = 24, the RMSE value reaches its peak before decreasing. Only the RFHFS algorithm eventually matches the RMSE value of the Baseline, while the FSNT algorithm slightly surpasses RFHFS and XGBFS slightly surpasses FSNT. As shown in Figure 6, on the Online News Popularity dataset, the MAE and RMSE values of the RFHFS and FSNT algorithms exhibit curves that remain below the curve obtained by the Baseline throughout the entire process. Additionally, at k = 18, these curves reach their lowest point before gradually increasing and returning to the horizontal line corresponding to the absence of feature selection at k = 30. In contrast, the MAE curve of the XGBFS algorithm oscillates around the horizontal line, reaching its peak at k = 18 and subsequently decreasing. Moreover, for k \(\leq\) 12, its RMSE curve is lower than the curves of the other three algorithms, after which it gradually rises. At k = 18, it surpasses the RMSE  
Figure 5: Performance of different feature selection methods using different algorithms for Superconductivity datasets. (**a**) MAE; (**b**) RMSE. curve of the RFHFS and FSNT algorithms, and, from k \(\geq\) 24 onwards, the three curves converge. The CSFFS algorithm displays significant variation in its MAE and RMSE curves, continually rising until k \(\leq\) 24. Notably, between k = 18 and k = 24, the curves experience a sharp increase, reach their maximum, and then decline. Finally, at k = 30, they return to the horizontal line representing the Baseline. As shown in Figure 7, the FSNT algorithm and the other three feature selection algorithms involved in the comparison range from selecting 3 features to selecting 15 features. On the Student-por dataset, with the increase in feature selection number, the MAE and RMSE curves of the CSFFS, XGBFS, RFHFS, and FSNT feature selection algorithms show an alternating oscillation state, and the whole process is above the horizontal line. The MAE and RMSE curves of the XGBFS algorithm are generally below the curves of the other three algorithms, rising to the maximum MAE and RMSE at k = 9, and then falling to near the horizontal line.