## 3 Analysis of Emotions and Classification Results
### Classification Results  
Some classification experiments were carried out for the tasks described in Section 2.1. In the TV Debates dataset, 1266 chunks were selected and distributed into the three categories mentioned above (CALM, ANN, and ENT), and for the Empathic VA, 4023 samples were selected and divided into four categories (CALM, HAPPY, ANN, and PUZZ). When using the dimensional model, previous studies showed that trying to predict a specific value in 3D space (as a regression problem) leads to very poor results [2,15] due to the scarcity of data and the tendency toward neutrality. To solve this problem, a discretization of each dimension was carried out and the regression problem was converted into a classification one. The discrete levels were selected according to the distributions of the annotated data in Figure 6, with orange lines as selected frontiers for the TV Debates dataset and green lines selected for the Empathic VA dataset. According to the top row displayed in Figure 6, arousal can be approximated by a log-normal distribution with a longer tail towards higher values of excitement. Thus, we decided to discern between only two values: neutral and excited. The thresholds (0.25 for TV Debates and 0.075 for Empathic VA) were selected to keep the classes as balanced as possible without distorting the limits imposed by the density function form. In the case of valence, three categories were kept because of their similarity to a Gaussian distribution. The decisions related to these thresholds also avoided the imbalance problem. In the TV Debates set, since many of the samples are neutral, the values outside the limits [0.4, 0.6] were considered negative or positive samples respectively. The Empathic VA corpus was slightly more positive, and as a consequence, the limits were shifted towards the more positive values 0.45 and 0.8, respectively. Finally, the dominance distribution was similar to a Gaussian distribution. However, it shifted towards dominant values; intimidated samples were almost absent. Consequently, only two categories were considered: dominant and neutral. The cutoff limit between neutral samples and dominant ones was set to 0.75 for the TV Debates dataset and to 0.65 for the Empathic VA dataset, which was the less dominant corpus. Once the aforementioned discretization was applied, the distribution of samples in the different classes remained, as Table 7 shows. The classification results for the TV Debates and Empathic VA datasets are given in Table 8. The experiments were carried out by considering the categorical and VAD models in an independent way. In both series, the spectrogram represented the speech signal. Different evaluation metrics were given to provide better insight into the capabilities of the neural network in predicting: the accuracy (ACC), precision (P), recall (R), and \(F1\)-score (\(F1\)). Since we dealt with a multi-class classification problem, weighted and macro averages were considered. Macro \(F1\) is the average of the \(F1\)-scores for all classes; thus, it penalizes \begin{table}
\begin{tabular}{c c c c} \hline \hline  & & **TV Debates** & **Empathic VA** \\ \hline \multirow{2}{*}{arousal} & neutral & 3068 & 2498 \\  & excited & 1050 & 2027 \\ \hline \multirow{3}{*}{valence} & negative & 682 & 520 \\  & neutral & 2239 & 2811 \\  & positive & 1197 & 1194 \\ \hline \multirow{2}{*}{dominance} & neutral & 3039 & 2946 \\  & dominant & 1079 & 1579 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Final categories for each dimension of the VAD model with the number of samples they contain in each of the corpora. imbalanced datasets, which was the case in this work. It was computed as shown in Equation (1):  
\[F1=\frac{\sum\limits_{i=1}^{N_{c}}F1^{i}}{N_{c}} \tag{1}\]  
where \(N_{c}\) is the number of classes and \(F1^{i}\) is the \(F1\)-score computed assuming that the \(i\)-th class is the positive one and that the negative one is composed by the remaining classes.