## 9 Evaluation Methods and Results  
This section provides the results of the performance and efficiency of the proposed models, which were examined using a series of experiments and various evaluation parameters via GridSearchCV. We incorporated five-fold cross-validation and averaged the results. In this work, machine learning and ensemble algorithms were constructed, namely SVM, Multinomial NB, LR, DT, AdaBoost, XGBoost, and Bagging classifier. This study performed the analysis using the standard assessment and evaluation metrics, including accuracy, the area under the receiver operating characteristic curve (AUC) curve, Precision, Recall, precision-recall curve, and the F1-score. Accuracy (A) is defined as the proportion of the total number of correct predictions. It can be calculated as the ratio of correctly classified instances to the total number of instances and can be computed as given in Equation (2). \[Accuracy=\frac{(TP+TN)}{(TP+TN+FP+FN))} \tag{2}\]  
Precision (P) is the measure of the exactness of the model results. It is the ratio of the number of examples correctly labeled as positive to the total number of positively classified examples. It is given in Equation (3). \[Precision=\frac{TP}{(TP+FP)} \tag{3}\]  
Recall (R) is the overall coverage of the model. It measures the completeness of the classifier results. Recall shows how many of the total instances are correctly classified as cyberbullying instances. It can be identified as in Equation (4). \[Recall=\frac{TP}{(TP+FN)} \tag{4}\]  
F1 score is the weighted average of precision and recall. It is a harmonic mean of precision and recall. Usually, the F1 score is more beneficial than accuracy when even the minor class distribution imbalance occurs. Mathematically, it can be computed as given in Equation (5). \[F1 Score=2\times\frac{(Precision\times Recall)}{(Precision+Recall)} \tag{5}\]  
The results for mean accuracy scores (including standard deviation) of algorithms based on extracted feature vectors are depicted in Table 5.  
All of the significant results are highlighted in bold. It can be observed that the SVM model outperforms with the highest accuracy score of 83% on tfidf and unigrams and combined N-grams, i.e., unigrams and trigrams followed by the LR model. LR produces an accuracy of 80% on tfidf and unigrams closely followed by combined Ngrams with 79% accuracy level. Voting-based ensemble models Adaboost, XGboost, and bagging are unique in this study and we have validated the prediction of tweet labels by achieving the optimal accuracy level of 70%, 79%, and 78%, respectively. These levels were reached typically over tfidf and unigrams, and a combination of unigrams and bigrams. The performance evaluation of models based on precision (P), recall (R), and F-score (F1), including standard deviation, is presented in Table 6. Table 6 shows the mean results of each technique for the highest accuracy levels and feature parameters. Considering the F1-score (for both cyberbullying and non-cyberbullying scenarios), SVM, LR, and multinomial naive Bayes and among ensemble techniques, XGboost and bagging were the best-performing algorithms. We use the precision-recall (PR) curve as the visual representation for all the experimentations as presented in Figure 12. For each potential cut-off, the connection between precision (positive predictive value) and recall (sensitivity) is defined by a precision-recall curve. It illustrates the trade-off between recall and precision for various thresholds. Among the machine learning methods, over a cyberbullying class, SVM with the combination of unigrams and TFIDF feature set depicts the best precision-recall area.