## 5 Results and Discussion
### Performance Metrics  
When assessing the performance of multi-class classification models using the one-vs-rest (OvR) approach, accuracy, precision, recall, and F1-Score are important metrics. These metrics evaluate how well the model reduces false positive predictions and correctly identifies true positives for each class [28]. Moreover, micro, macro, and weighted averages offer a complete view of the overall performance, taking into account factors such as class distribution. A complexity matrix is used as part of the model performance assessment process. It has four distinct variables: True Positive \((TP)\), True Negative \((TN)\), False Positive \((FP)\), and False Negative \((FN)\). The accuracy of a prediction model is determined using the formula presented in Equation (6).  
\[Accuracy\ (\%)=(TP+TN)/(TP+TN+FP+FN) \tag{6}\]  
Precision measures the classifier's ability to correctly predict relevant data (Equation (7)). At the same time, Recall assesses the proportion of relevant data identified by the classifier (Equation (8)). The \(F1_{score}\) is a metric employed to evaluate the model's performance and is calculated by taking the harmonic mean of \(Precision\) and \(Recall\) (Equation (9)).  
\[Precision(P)=TP/(TP+FP) \tag{7}\]  
\[Recall(R)=TP/(TP+FN) \tag{8}\]  
\[F1_{Score}=2\times(Precision\times Recall)/(Precision+Recall) \tag{9}\]  
The accuracy rate produces high values when the class distribution is similar, while the \(F1_{Score}\) is better when unbalanced classes exist. The accuracy rate is used when \(TP\) and \(TN\) are more important, and \(F1_{Score}\) is used when \(FP\) and \(FN\) are more important. When a high Recall value is obtained, the model has low sensitivity. Therefore, most predicted labels need to be more classified than training labels. On the other hand, if the Sensitivity is high and the Recall is low, most predicted tags are correctly classified. Therefore, if high Precision and Recall values are obtained, all model results are labeled correctly [29].  
Micro- and macro-averaged metrics, including Micro-Precision, Micro-Recall, and Micro-F-measure, assess the overall performance of a classification model by considering the total value of \(TP\), \(FP\), and \(FN\) across all classes in a multi-class dataset. Micro- and macro-averaged \(F1_{Score}\) are calculated as follows:  
\[\text{Precision}_{\text{Micro}}=\frac{\sum_{c}TP_{c}}{\sum_{c}TP_{c}+\sum_{c}FP _{c}} \tag{10}\]  
\[\text{Recall}_{\text{Micro}}=\frac{\sum_{c}TP_{c}}{\sum_{c}TP_{c}+\sum_{c} FN_{c}} \tag{11}\]  
\[\text{F1}_{\text{Micro}}=\frac{2.\text{Precision}_{\text{Micro}}\times \text{Recall}_{\text{Micro}}}{\text{Precision}_{\text{Micro}}+\text{Recall}_{ \text{Micro}}} \tag{12}\]  
\[\text{F1}_{\text{Macro}}=\frac{1}{c}\sum_{i=1}^{c}F1_{Score_{i}} \tag{13}\]  
\[\text{F1}_{\text{Weighted}}=\frac{\sum_{i=1}^{c}w_{i}F1_{Score_{i}}}{\sum_{i= 1}^{c}w_{i}} \tag{14}\]  
where \(c\) is the class label and \(w_{i}\) is the support of class \(i\) (i.e., the number of samples in the class).  
The Receiver Operating Characteristics (ROC) and AUC are metrics used to evaluate the performance of classification models. The ROC curve plots the True Positive Rate (TPR) against the False Positive Rate (FPR) at various thresholds, illustrating the model's ability to distinguish between classes. The AUC, or the Area Under the Curve, represents the ROC curve as a single numerical value, summarizing the classifier's overall performance. Higher AUC values indicate a better balance between TPR and FPR, reflecting stronger classification capabilities [30].