## 4 Experimental Setup and Results
### Performance Metrics  
The effectiveness of the proposed models was evaluated using various established criteria, including precision, recall, accuracy, and weighted F1 score. Accuracy (Acc) quantifies the proportion of correctly classified instances within the total dataset, providing an overall assessment of model performance in slogan detection and classification. The F1 score, being the harmonic mean of precision and recall, balances these two metrics, offering a comprehensive measure of the model's efficacy in accurately classifying unseen slogans, particularly in scenarios with imbalanced or skewed data distributions. Recall (R) represents the proportion of actual slogans correctly identified by the model, indicating its sensitivity to true positives. Precision (P) denotes the ratio of correctly identified slogans to the total instances predicted as slogans, elucidating the model's reliability in minimizing false positives. Additionally, the evaluation encompassed metrics such as G-mean (GM), Normalized Mutual Information (NMI), and Matthews Correlation Coefficient (MCC). These metrics include True Negative (Tn), False Negative (Fn), True Positive (Tp), and False Positive (Fp), contributing to precision and recall calculations. These metrics are widely recognized for assessing a model's performance. Notably, the weighted F1 score, which represents a weighted average of F1 scores for individual classes, was calculated considering class size. This approach ensures a fair evaluation of the model's performance in multi-class classification tasks where class sizes vary. Consequently, F1 is regarded as the primary metric, while Acc, P, and R are considered secondary metrics in determining the model's efficacy.  
\[\text{Recall}=\frac{(\text{TP})}{(\text{TP}+\text{FN})} \tag{11}\]  
\[\text{Precision}=\frac{(\text{TP})}{(\text{TP}+\text{FP})} \tag{12}\]  
\[\text{F1}=2*\frac{(\text{Precision}\,\times\,\text{Recall})}{(\text{Precision}\, +\,\text{Recall})} \tag{13}\]  
\[\text{Accuracy}=\frac{(\text{TP}+\text{TN})}{(\text{TP}+\text{TN}+\text{FP} +\text{FN})} \tag{14}\]  
G-mean is a valuable metric for assessing a model's accuracy as it considers both precision and recall, providing a comprehensive evaluation of the model's performance, as follows:  
\[GM=\sqrt{\text{Pr}\,e\times\text{Re}\,c} \tag{15}\]  
MCC serves as a significant indicator of a binary classifier's performance. It measures the correlation between predicted and true classes, quantified by the Pearson correlation coefficient. In the MCC scale, a value of 1 signifies an ideal prediction, 0 indicates performance equivalent to random guessing, and \(-1\) represents the poorest prediction scenario, as follows:  
\[MCC=\frac{(Tp\times Tn)-(Tp\times Fn)}{\sqrt{(Tp+Fp)(Tn+Fn)(Tn+Fp)(Tp+Fn)}} \tag{16}\]  
In statistics, a mutual information measure quantifies the mutual information between two variables, normalized by their respective entropies. This metric finds frequent application in evaluating model performance in the fields of machine learning and information retrieval, as follows:  
\[NMI_{(X,Y)}=\frac{2I_{(X,Y)}}{\text{max}(H_{(X)},H_{(Y)})} \tag{17}\]  
where \(I_{(X,Y)}\) represents the mutual information between variables X and Y, and \(H_{(X)}\), \(H_{(Y)}\) denote the entropies of X and Y, respectively.