## 3 Results
### The Reference Mapping Accuracies for the SYNE-ANEW and NAWL-NAWL Datasets  
The mapping matrix derived from literature and reported as in Equation (1) was used as a reference model for the model proposed in this study. The results of mapping using the known matrix for the two datasets: SYNE-ANEW and NAWL-NAWL are provided in Tables 6 and 7, consecutively. The absolute measures for the dataset show small differences between the dimensions. A relatively high mean distance is obtained for joined dimensions, which is partially explained by cumulating errors from all dimensions, as the metric PAD\({}_{\text{ABS}}\) is calculated based on the geometrical distance in 3D space. It seems that setting a proper threshold is crucial and has an enormous influence on the resulting metrics (precision-accuracy trade-off). For a high precision (10% of the scale), accuracy results are around 25% for valence, 24% for arousal, and 23% for dominance. With lower precision requirements, the accuracies increase (46% for valence, 48% for arousal, and 45% for dominance). Setting the accuracy threshold based on standard deviation per word increases accuracies above 55% for the dimensions of arousal and dominance. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Dimension**} & \multicolumn{3}{c}{**Distance-Based Metrics**} & \multicolumn{6}{c}{**Threshold-Based Accuracy Metrics**} \\ \cline{2-9}  & **MAE/PAD\({}_{\text{ABS}}\)** & **RMSE** & **R\({}^{2}\)** & **M\({}_{10}\)/PAD\({}_{10}\)** & **M\({}_{20}\)/PAD\({}_{20}\)** & **M\({}_{\text{SD}}\)/PAD\({}_{\text{SD}}\)** & **DD\({}_{10}\)** & **DD\({}_{20}\)** \\ \hline P & 0.262 & 0.321 & \(-\)0.153 & 25.8\% & 45.7\% & 46.8\% & & \\ A & 0.242 & 0.293 & \(-\)1.229 & 23.9\% & 48.3\% & 68.9\% & & \\ D & 0.252 & 0.308 & \(-\)0.778 & 22.8\% & 44.6\% & 56.2\% & & \\ PAD & 0.487 & & & 1.5\% & 14.6\% & 25.8\% & 5.2\% & 32.2\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Accuracy metrics for reference mapping matrix applied on the SYNE-ANEW dataset. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Dimension**} & \multicolumn{3}{c}{**Distance-Based Metrics**} & \multicolumn{6}{c}{**Threshold-Based Accuracy Metrics**} \\ \cline{2-9}  & **MAE/PAD\({}_{\text{ABS}}\)** & **RMSE** & **R\({}^{2}\)** & **M\({}_{10}\)/PAD\({}_{10}\)** & **M\({}_{20}\)/PAD\({}_{20}\)** & **M\({}_{\text{SD}}\)/PAD\({}_{\text{SD}}\)** & **DD\({}_{10}\)** & **DD\({}_{20}\)** \\ \hline P & 0.157 & 0.177 & 0.327 & 27.2\% & 67.9\% & 59.8\% & & \\
**A** & 0.136 & 0.178 & \(-\)0.088 & 49.5\% & 75.9\% & 88.9\% & & \\
**D\({}^{\star}\)** & na & na & na & na & na & na & \\
**PA\({}^{\star}\)** & 0.235 & & & 6.7\% & 46.1\% & 59.9\% & 32.0\% & 80.8\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Accuracy metrics for reference mapping matrix applied on NAWL-NAWL dataset. The joined dimensions accuracies are lower than for separate dimensions, which could have been expected. If for one dimension mapping is precise, it might not be for the other one and, as a result, the errors cumulate over dimensions. Therefore, we have only 1.5% accuracy for an expected precision of 10% of the scale, 14.6% accuracy for 20% precision and 25.8% for SD-based precision. For the second dataset, the mapping accuracies are higher for all precision thresholds. This might be a result of the set size and quality (the set is derived from one lexicon purposefully annotated twice); however, one must notice the lack of _Surprise_ and _Dominance_ dimensions among the annotation labels. Please note, that due to the latter limitation, the results between the two sets are comparable for the single-dimension metrics, but incomparable for joint-dimensions metrics. Accuracies are still dependent on the set precision threshold. As precision and accuracy are interchangeable, one might go further in proposing new thresholds. Perhaps, the acceptable precision should be set case-by-case, as this might depend on the context of the emotion recognition.