## 4 Results
### Phone Embedding Analysis  
To investigate the contribution of each phone to the estimated impression across subjects, the \(GRU_{phones}\) neural network introduced in Section 3.2 was trained using the Adamax optimizer and mean square error as the loss function with a batch size of 32 for 100 epochs. Two copies of the model were trained, one for valence and other for arousal, to estimate the change in arousal and valence caused by a given string of phones. The output dimension of the embedding layer was chosen after trials with many different values; the best results were obtained with an output dimension of 64. Thus, the resulting embedding matrices for valence and arousal are of \(64\times 71\) dimension. However, since the  
Figure 12: Comparison between the actual impression and the impression predicted by \(MLP_{profile+prosody}\) for (**top left**) training data, (**top right**) validation data, and (**bottom**) test data. \begin{table}
\begin{tabular}{c c} \hline \hline
**Emotion Label** & **Number of Samples** \\ \hline Disgust & 118 \\ Angry & 113 \\ Happy & 78 \\ Surprised & 54 \\ Fearful & 46 \\ Sad & 43 \\ Calm & 38 \\ Neutral & 27 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of the sentiment analysis of volunteer’s speeches. each phone has a position in a high-dimension hyperspace, it is not possible to visualize their proximity graphically. To facilitate the analysis of the contribution of each phone, we used the k-means clustering method in order to group the phones accordingly to their proximity for both embedding matrices. In order to select the best number of clusters, we used the silhouette score analysis method [57] in order to determine the optimal number of clusters. The optimal number of clusters was 35 for valence and 26 for the arousal embedding matrices. The number of phones in the largest cluster was 5, and most phones were grouped with distant phones or alone in their own cluster. From the clusters of the embedding spaces for valence and arousal, we were able to obtain Figures 13a,b, 14 and 15, which allows us to visualize which vowels and consonants phones belong to the same clusters, since such phones are colored with the same color. The red-colored phones were not selected by the gibberish speech generation algorithm, since the algorithm randomly picked phones. However, since many phones were absent in [PERSON]'s gibberish speech, clustering might not be the best method to analyze which phones have a similar emotional impact on listeners, so we calculated the distance between the phones in the embedding space both for valence and arousal and for valence. Considering vowels and consonants separately, we obtained that for valence, the following phones that are close in their articulation loci are also the closest neighbors in the embedding space: [a]-[e], [a]-[e], [a]-[e], [i]-[u], [p]-[m], [d]-[t], [k]-[g] and [\(\xi\)]-[l]. If we consider all phones together, we have all combinations of vowels and consonants, but none with close articulation in the human mouth. We have performed the same analysis for the arousal embedding space, and fewer pairs have a close articulation locus in the human mouth were obtained than for valence. The following pairs were identified: [e]-[e], [o]-[e], [o]-[o], [z]-[f], [3]-[r] and [x]-[\(\chi\)]. Such results show that while some phones are close in the learned embedding space for valence, it is not possible to claim that similar phones, except for a few exceptions, are close in the embedding space, in the context of non-Yulean gibberish speech. Figure 13: Embedding values for vowels of the IPA for valence and arousal estimation. IPA symbols in red were absent in the generated utterances. Other symbols were colored according to the index of the cluster they belong to, as shown in the rightmost color bar; (**a**) Embedding values of vowel for valence change estimation; (**b**) embedding values of vowel for arousal change estimation.