# Synthesis of Non-Linguistic Utterances for Sound Design Support Using a Genetic Algorithm
## 3 GA Generated Sounds Valence and Arousal Evaluation Experiment
### Clustering and Statistical Analysis  
K-means clustering analysis was carried out to determine meaningful groupings of valence and arousal values for the 80 sounds used in the experiment. Firstly, the average values from all subjects for valence and arousal were normalized to be between 0 and 1, so that they could be compared to the predicted values from the random forest model which  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Variable** & **ICC** & **F** & **df1** & **df2** & \(p\)**-Value** & **CI95\%** \\ \hline Valence & 0.83 & 5.74 & 79 & 1027 & \(1.61\times 10^{-42}\) & 0.76–0.88 \\ Arousal & 0.75 & 3.97 & 79 & 1027 & \(6.80\times 10^{-25}\) & 0.66–0.82 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of ICC, F statistics, degrees of freedom, \(p\)-values, and confidence intervals.  
\begin{table}
\begin{tabular}{l c} \hline \hline
**Distribution** & **Shapiro-Wilk** & \(p\)**-Value** \\ \hline Valence Ratings & not normal & 0.0385 \\ Arousal Ratings & normal & 0.0655 \\ Valence Inferences & not normal & 0.0001 \\ Arousal Inferences & normal & 0.9308 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Distributions of valence and arousal ratings and inferences.  
were themselves normalized between 0 and 1. Next, for each sound, the absolute difference between the normalized average valence and the predicted valence from the random forest model was computed. The same was done for arousal. This value was subtracted from 1 to obtain the inverse error value to use as sample weights in the K-means analysis.  
The weight \(W_{i}\) is given by the equation:  
\[W_{i}=1-|P_{i}-A_{i}|,\quad\text{for }i=1,2,\dots,N \tag{4}\]  
K-means was then carried out for k values between 2 and 8 using sample weights of both the inverse error of valence and inverse error of arousal, respectively, and the best result, such that it was significant when either the valence inverse errors or arousal inverse errors were used as sample weights, was found using k = 5. ANOVA was performed using the clusters produced and resulted in statistically significant differences between the clusters. The clusters are shown in Figure 5(a),b for inverse valence error and inverse arousal error, respectively. Note that the values of valence and arousal shown in these cluster plots (used as x and y values for each sound) are from the average human ratings, rather than the inferences from the random forest model. These two cluster plots are nearly identical to each other. ANOVA box plots shown in Figure 6(a),b for inverse valence error and inverse arousal error, respectively, indicate the distributions of data within each cluster. A summary of the statistical results is shown in Table 3.  
Figure 6: Kmeans clusters for GA sounds with k = 5 clusters. (**a**) Weighted by inverse valence error, (**b**) weighted by inverse arousal error.  
Figure 7: ANOVA box-plots for GA sounds with k = 5 clusters. (**a**) Weighted by inverse valence error, (**b**) weighted by inverse arousal error.  
Following this, the clusters were labeled according to their valence and arousal ranges using [PERSON]'s Circumplex model of emotions to determine an appropriate emotion label, as shown in Table 4. The distribution of each cluster was checked first, as only normally distributed clusters can be considered meaningful for [PERSON]'s test for Honest Significant Difference, which was carried out to better understand the differences between individual clusters/emotions. The results are shown in Table 5, where the cells with ones show which normally distributed clusters differ significantly from each other.