## 6 Results
### Picture Clustering Based on Dominant Discrete Emotions  
In the second segment of the experiment, we investigated how basic emotion ratings are associated with well-defined regions in dimensional emotion space. As previously explained, we identified the optimal number of homogeneous clusters of dimensional emotions in the NAPS dataset [39]. Using the Monte-Carlo simulation stabilized \(k\)-means algorithm with \(p=2000\) iterations in range \(k=2\)-\(7\), we found that for \(k=4\) the stability error  
Figure 6: Correlations between 6 emotion norms (happiness, fear, sadness, surprise, anger, disgust) in the NAPS BE dataset: (**a**) Pearson correlation coefficient matrix (\(r\)); (**b**) [PERSON]’s rank matrix (\(r_{s}\)). Figure 7: Correlations among 6 emotion norms (happiness, fear, sadness, surprise, anger, disgust) and 2 emotion dimensions (valence, arousal) in the NAPS BE dataset: (**a**) Pearson correlation coefficient matrix (\(r\)); (**b**) [PERSON]’s rank matrix (\(r_{s}\)). is only 0.29% of the total number of the NAPS data points. These findings have provided us with the examination of their relationship with basic emotions. As the NAPS BE dataset is more complex than the NAPS in terms of the number of data dimensions, to visualize the cluster analysis results, only statistically significant correlations of discrete and dimensional ratings were considered. Silhouette coefficients graphs for the corresponding pairs of discrete and homogeneous clusters in dimensional emotion space are shown in Figure 8. It can be noticed that the silhouette method shows that the evaluation is consistently low when there are more than 8 distributions. This shows that the range \(k=2\)-7 is sufficient for mapping NAPS BE data points to the clusters in the NAPS database. Figure 8: Silhouette plots in interval \(k=2\)–19 for: (**a**) pairs of emotion norms {happiness, sadness}, {happiness, anger}, {sadness, anger}, {fear, surprise}; (**b**) tuples of emotion norms and emotion dimensions {happiness, valence}, {sadness, valence}, {fear, arousal}, {surprise, arousal}, {anger, valence}. Additional analyzes showed that the decrease in the average value of the silhouette coefficient for \(k>4\) was less significant than the increase in the number of clusters. Therefore, for the final results of stable partitioning of isolated correlation examples from the NAPS BE database into the NAPS database, the division of dimension scores into \(k=4\) clusters were chosen. The additional fact supports this choice that NAPS BE is almost three times smaller than the NAPS database, which is reflected in the lower point density. Furthermore, the choice of \(k=4\) is supported by a selection of the smallest number of homogeneous clusters, i.e., those with the lowest scatter of all data points in the dataset, as reported in [39]. The scatter plots in Figure 9 show k-means clustering results in dimensional space with \(p=2000\) iterations using the approach stabilized by Monte-Carlo simulation [39]. The results were obtained for \(k=4\) individual clusters and matched with the following pairs of discrete and dimensional emotion data dimensions: {happiness, sadness}, {fear, surprise}, {happiness, valence}, and {surprise, arousal}. These emotion tuples provide the most robust transformations of values between the two emotion models. The Monte-Carlo stabilized \(k\)-means method proved to be highly reliable. The stability error was measured to be only 0.29% of the total number of the NAPS database data points for the chosen number of data clusters \(k=4\) and \(p=2000\) iterations. The results are consistent with the expected relationship between dimensional emotions and semantic picture annotations in the NAPS database. In previously reported research, the optimal number of centroids in the dimensional space related to the description of stimuli was estimated using the minimum cumulative error rule [62]. Although the exact value of clusters was not determined, it was found that the optimal number is definitely in the open interval of \(k=2\)-16.