## 6 Experiments
### Evaluation Metrics  
The standard metrics widely used for evaluating the performance of classification models include _precision (P)_, _recall (R)_, _F1-score (F1)_, and _accuracy_. Given the built emotion recognition model and the set of emotion classes \(M\), we can compute the evaluation metrics to evaluate the model's performance with respect to each emotion label \(m\) as outlined below:  
\[Accuracy_{m}=\frac{TP_{m}+TN_{m}}{TP_{m}+TN_{m}+FP_{m}+FN_{m}}\]  
\[Precision_{m}=P_{m}=\frac{TP_{m}}{TP_{m}+FP_{m}}\]  
\[Recall_{m}=R_{m}=\frac{TP_{m}}{TP_{m}+FN_{m}}\]  
where \(TP_{m}\) represents the true positives, signifying the number of examples in the dataset correctly identified by the model as emotion \(m\), while \(TN_{m}\) represents the true negatives, denoting the number of examples correctly identified by the model as _not_ belonging to emotion \(m\). On the other hand, \(FP_{m}\) denotes the false positives, indicating the number of examples incorrectly labeled by the model as emotion \(m\), and \(FN_{m}\) represents the false negatives, signifying the number of examples erroneously labeled by the model as _not_ belonging to emotion \(m\).  
The F1-score is a balanced performance metric that calculates the harmonic mean of precision and recall. The equation of the F1-score is:  
\[F1\text{-}score_{m}=F1_{m}=2*\frac{P_{m}*R_{m}}{P_{m}+R_{m}}\]  
To evaluate the overall performance of the models we developed in our experiments and to compare their performance with state-of-the-art methods from the literature, we must assess the model's performance across multiple metrics. These metrics include accuracy, as well as the macro average, micro average, and weighted average of three key metrics: precision, recall, and F1-score. This is conducted as follows:  
\[Accuracy=\frac{\sum_{m=1}^{M}TP_{m}+\sum_{m=1}^{M}TN_{m}}{\sum_{m=1}^{M}TP_{ m}+\sum_{m=1}^{M}TN_{m}+\sum_{m=1}^{M}FP_{+}\sum_{m=1}^{M}FN_{m}}\]  
The macro average for the _precision_, _recall_, and _F1-score_ metrics are determined by computing the average of these metrics for each emotion class separately, assigning equal importance to each class. This method treats every emotion class equally, regardless of its frequency, and the calculations are carried out using the following formulas:  
\[P_{macro}=\frac{\sum_{m=1}^{M}P_{m}}{|M|}\]  
\[R_{macro}=\frac{\sum_{m=1}^{M}R_{m}}{|M|}\]  
\[F1_{macro}=2*\frac{P_{macro}*R_{macro}}{P_{macro}+R_{macro}}\]  
where \(|M|\) denotes the total number of emotion classes present in the dataset.  
The micro average focuses on the overall performance across all classes, with a significant emphasis on dominant classes, assigning them greater weight. The calculations for the micro average are determined by the following formulas:  
\[P_{micro}=\frac{\sum_{m=1}^{C}TP_{m}}{\sum_{m=1}^{M}TP_{m}+\sum_{m=1}^{M}FP_{m}}\]  
\[R_{micro}=\frac{\sum_{m=1}^{M}TP_{m}}{\sum_{m=1}^{M}TP_{m}+\sum_{m=1}^{M}FN_{m}}\]  
\[F1_{micro}=2*\frac{P_{micro}*R_{micro}}{P_{micro}+R_{micro}}\]  
The weighted average considers the proportion of each emotion class when computing the metric averages. It strikes a balance between micro and macro averaging, taking into account both the overall performance and the significance of each class. These calculations are determined using the following formulas:  
\[P_{weighted}=\frac{\sum_{m=1}^{M}P_{m}*|m|}{\sum_{m=1}^{M}|m|}\]  
\[R_{weighted}=\frac{\sum_{m=1}^{M}R_{m}*|m|}{\sum_{m=1}^{M}|m|}\]  
\[F1_{weighted}=\frac{\sum_{m=1}^{M}F1_{m}*|m|}{\sum_{m=1}^{M}|m|}\]  
where \(|m|\) represents the total number of examples in the dataset belonging to the emotion class \(m\) and \(\sum_{m=1}^{M}|m|\) denotes the summation of the total examples for each emotion class in the dataset, which is equal to the dataset's overall size.