## 4 Summary of Results and Discussion  
The mapping technique using the linear transformation based on a coefficient matrix was evaluated in this study. The results may be summarized in the following statements. Obtaining both accurate and precise mapping results is a challenge. The results confirm standard observations of precision-accuracy conflict. The mapping model provided is better than a reference model, but still might be insufficient for high precision requirements. The summary of results is provided in Table 11.  
In the SYNE-ANEW dataset, the accuracy results are better for the proposed mapping than for the reference mapping. The same applies to the NAWL-NAWL results. In the latter, the results in cross-validation are even better than for the ANEW-MEHR dataset. Interpretation of cross-set evaluation results is limited because the dataset (and obtained matrices) differed in dimension count (for one of the datasets surprise and dominance was missing). The proposed mapping matrices might be applied in the comparison and fusion of emotion recognition results; however, the required precision must be taken into account. Acceptable precision should be set based on the emotion recognition goals and application context, and especially on the significance of I type and II type error. Using standard deviation as a threshold for precision is one of the promising directions. The proposed method and metrics for accuracy proved useful and allowed the mapping technique to be evaluated. Please note, that the proposed metrics are: \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{3}{c}{**Threshold-Based Accuracy Metrics**} \\ \cline{2-10}  & **MAE/PAD\({}_{\textbf{ABS}}\)** & **RMSE** & **R\({}^{2}\)** & **M\({}_{\textbf{10}}\)/PAD\({}_{\textbf{10}}\)** & **M\({}_{\textbf{20}}\)/PAD\({}_{\textbf{20}}\)** & **M\({}_{\textbf{SD}}\)/PAD\({}_{\textbf{SD}}\)** & **DD\({}_{\textbf{10}}\)** & **DD\({}_{\textbf{20}}\)** \\ \hline
**P** & 0.093 & 0.109 & 0.744 & 56.5\% & 95.8\% & 87.3\% & - & - \\
**A** & 0.116 & 0.144 & 0.282 & 50.8\% & 84.4\% & 92.6\% & - & - \\
**D** & na & na & na & na & na & - & - \\
**PA \({}^{\star}\)** & 0.162 & & & 29.9\% & 81.1\% & 81.5\% & 43.3\% & 93.1\% \\ \hline \hline \end{tabular} Note. \({}^{\star}\) dominance dimension is not available for the set.  
\end{table} 
Table 10: Accuracy metrics for the mapping obtained from SYNE_ANEW applied on the NAWL-NAWL dataset (cross-set results). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Model** & **Dataset/Analysis** & **PAD\({}_{\textbf{ABS}}\)** & **PAD\({}_{\textbf{10}}\)** & **PAD\({}_{\textbf{20}}\)** & **PAD\({}_{\textbf{SD}}\)** & **DD\({}_{\textbf{10}}\)** & **DD\({}_{\textbf{20}}\)** \\ \hline PAD & ANEW-MEHR simple pairing & 0.172 & 33.9\% & 79.5\% & 91.1\% & 56.2\% & 95.5\% \\ PAD & SYNE-ANEW reference mapping & 0.487 & 1.5\% & 14.6\% & 25.8\% & 5.2\% & 32.2\% \\ PAD & SYNE-ANEW proposed mapping cross-validation & 0.239 & 17.8\% & 54.9\% & 59.9\% & 32.0\% & 80.8\% \\
**PA** & NAWL-NAWL reference mapping & 0.235 & 6.7\% & 46.1\% & 59.9\% & 32.0\% & 80.8\% \\
**PA** & NAML-NAWL proposed mapping cross-validation & 0.090 & 70.5\% & 97.6\% & 98.4\% & 83.7\% & 99.8\% \\
**PA** & Cross-set mapping evaluation on NAWL-NAWL dataset & 0.162 & 29.9\% & 81.1\% & 81.5\% & 43.3\% & 93.1\% \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Mapping accuracy metrics for ANEW-MEHR dataset. * dataset-independent: might be applied to any dataset constructed
* scale-independent: due to setting precision thresholds as percent of the scale or SD-based
* model-dependent: they have been proposed specifically for the pleasure-arousal dominance model; however, they might be adapted to any dimensional emotion representation model
* ambiguity-robust: valid for metrics based on the standard deviation threshold: \(M_{SD}\), PAD\({}_{SD}\)  
The author acknowledges that this study is not free from some limitations.