## 3 Results  
Four metrics were used to evaluate model performance: _ACC_, _PD_, _Pfu_, and _Pmd_. These metrics are defined as:  
\[ACC=\frac{T_{P}+T_{N}}{T_{P}+T_{N}+F_{P}+F_{N}}*100 \tag{5}\]  
\[PD=\frac{T_{P}}{T_{P}+F_{N}}*100 \tag{6}\]  
\[Pfa=\frac{F_{P}}{T_{F}+F_{N}}*100 \tag{7}\]  
\[Pmd=\frac{F_{N}}{T_{N}+F_{P}}*100 \tag{8}\]  
where \(T_{P}\) defines the number of accurately predicted malicious samples, \(T_{N}\) denotes the number of predicted normal samples, \(F_{P}\) is the number of falsely predicted malicious samples, and \(F_{N}\) is the number of falsely predicted normal samples. This work applied a 10-fold cross-validation method to train 80% of the given data and test 20% of the remaining data. Table 3 summarizes the hyperparameter settings for the evaluated models with the best parameter values according to the Bayesian optimization technique. The regularized learning parameters determine the level of bias each model can tolerate with respect to an optimal value. We selected the degree of a correct classification parameter, such as \(C\) in SVM; a penalty parameter, alpha, in ANN; a complexity parameter, such as _ccp_alpha_, in RF and CART; a stable value of _var_smothing_ in GNB; and a regularization strength parameter, \(C\), in LR as the regularized learning parameters that play significant roles in model learning. The results are illustrated in Figures 3-8. Figure 3 depicts the detection model's performance using the different values of the regularized learning parameter, \(r\). A significant improvement for each model can be observed when using specific values. For instance, SVM reaches the highest performance at \(r=8\) with an _ACC_ of 96.2%, a _PD_ of 96.2%, a _Pmd_ of 4.9%, and a _Pfa_ of 6.2%. For \(r\) values higher than 8, this classifier's performance stagnates. The ANN classifier reaches its maximum performance at \(r=5\) with an _ACC_ of 99.34%, a _PD_ of 99.4%, a _Pmd_ of 0.6%, and a _Pfa_ of 1.7%. This classifier also stagnates at values higher than \(r=5\). Other classifiers performe similarly in terms of the regularized learning parameters, excluding the GNB classifier. Figure 4: Impact of hyperparameter fine-tuning on model performance. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Classifier** & **Regularized Learning Parameter** & **Optimal Hyperparameters Values** \\ \hline SVM & C & C = 8, degree = 1, gamma = 1.717, kernel = “poly” \\ ANN & alpha & activation =!identity”, solver =!bfgs”, alpha = 0.173 alpha = 0.173 alpha = 738, max\_depth = 112, min\_samples\_split = 5, ccp\_alpha = 10 \\ GNB & var\_smoothing & var\_smoothing = 5 \\  & & max\_depth = 32.0, Criterion =!gini’, splitter =!best’, ccp\_alpha = 5, \\  & & max\_features =!log2’ \\ LR & C & max\_iter = 10, penalty =!2’, C = 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Hyperparameter settings. Figure 3: Impact of regularization learning parameters on model performance. The GNB classifier reaches its highest performance at \(r\) = 5 with an _ACC_ of 91.2%, a _PD_ of 86.16%, a _Pmd_ of 13.84%, and a _Pfa_ of 2.23%. The _ACC_ of this classifier decreases slightly in the range of 0 to 0.1; however, it reaches a constant value of 84.9%. Other metrics, including _PD_, _Pfa_, and _Pmd_, follow similar trends. The RF classifier reaches a maximum _ACC_ of 99.43% at \(r\) = 5 and a maximum _PD_ of 99.6% at \(r\) = 0. This classifier also reaches a minimum _Pmd_ of 1.8% at \(r\) = 5 and a minimum _Pfa_ of 1.01% at \(r\) = 0.9. This classifier's performance remains constant with higher r values. The CART classifier also reaches its maximum with an _ACC_ of 99.9% at \(r\) = 10, a maximum _PD_ of 99.98% at \(r\) = 0.9, a minimum with a _Pmd_ of 0.02% at \(r\) = 10, and a _Pfa_ of 1.005 at \(r\) = 0.9. This classifier's performance remains constant at higher r values. The LR classifier reaches a maximum _ACC_ of 91.2% at \(r\) = 10 and a maximum _PD_ of 86.19% at \(r\) = 5, while reaching a minimum _Pmd_ of 13.84% and a _Pfa_ of 3% at \(r\) = 8.