## 4 Experiment Setup
### Evaluation Metrics  
To validate the effectiveness of the FSNT method, it is crucial to employ the information obtained through different feature reduction techniques as input for prediction models. The performance improvement observed in prediction tasks after feature selection serves as evidence of the method's effectiveness. Consequently, ten popular regression machine learning algorithms are utilized, namely: multiple linear regression [33], elastic net regression [34], random forest [35], extra trees [36], SVM [37], gradient boosted [38], decision tree regressor [39], AdaBoost regressor [40], Gaussian process regressor [41], and MLP regressor [42]. For classification tasks, eight machine learning algorithms are employed: KNN [43], SVM, decision tree, random forest, Gaussian naive Bayes [44], neural network [45], logistic algorithm [46], and AdaBoost [47]. To evaluate the regression performance, the following indicators are used:  
* Mean absolute error (MAE) This indicator is the expected value of absolute error loss \[\text{MAE}\left(y,\hat{y}\right)=\frac{1}{n}\sum_{i=1}^{n}\left|y_{i}-\hat{y}_ {i}\right|\] (21)  
Root of square error or root of mean square error (RMSE), this indicator corresponds to the expectation of square (quadratic) error. \[\text{RMSE}\left(y,\hat{y}\right)=\sqrt{\frac{1}{n}\sum_{i=1}^{n}\left\|y_{i}- \hat{y}_{i}\right\|_{2}^{2}} \tag{22}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Name** & **Sample Size** & **Number of Features** & **Classification Category** \\ \hline Student-mat & 649 & 33 & 5 \\ Student Archive & 4424 & 36 & 3 \\ TCGA Info with Grade & 839 & 23 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Classified experimental datasets. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Name** & **Sample Size** & **Number of Features** \\ \hline Student-par & 649 & 33 \\ Superconductivity & 21,263 & 81 \\ Online News Popularity & 39,797 & 61 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Regression experimental datasets. In order to evaluate the classification performance, the following indicators are used. In a binary classification problem where instances are classified into positive or negative classes, the classification process can result in the following four scenarios: (1) when an instance belongs to the positive class and is correctly predicted as positive, it is considered a true positive (_TP_); (2) if an instance is positive but is incorrectly predicted as negative, it is a false negative (_FN_); (3) if an instance is negative but is erroneously predicted as positive, it is a false positive (_FP_); (4) when an instance belongs to the negative class and is accurately predicted as negative, it is a true negative (_TN_). _Accuracy_ is defined as the ratio of the number of samples correctly classified by the classifier to the total number of samples in a given test dataset. \[Accuracy=\frac{TP+TN}{TP+TN+FP+FN} \tag{23}\]  
_Precision_ is the ratio of the number of positive cases correctly classified to the number of instances classified as positive cases. It measures the accuracy of the algorithm. \[Precision=\frac{TP}{TP+FP} \tag{24}\]  
To assess the strengths and weaknesses of various algorithms, the concept of the \(F1\) score is introduced, which combines precision and recall to provide an overall evaluation; it integrates the outcomes of micro-average precision and micro-average recall, where 1 represents the optimal model output, while 0 represents the poorest model output:  
\[F_{1}=2\times\frac{Precision\times Recall}{Precision+Recall} \tag{25}\]  
In order to effectively measure the precision value for multiple classification targets, the micro-average precision is employed as the methodology. Firstly, the cumulative number of true positive (_TP_) and false positive (_FP_) predictions across all categories is computed.