## 3 Emotion Recognition with Selected Statistical PPG Features
### Feature Extraction Based on the Selection of Statistical Features
#### 3.2.3 Selection of Statistical Features  
As mentioned before, we obtained 19 statistical features for emotion recognition (six features for the time domain and 13 features for the frequency domain). In this work, we developed a feature selection method for emotion recognition using these 19 features. In fact, not all the statistical features were associated with emotion, and the valence and the arousal were not affected by these features. Features that were not related to emotion could interfere with the learning of emotion recognition.  
\begin{table}
\begin{tabular}{c c l} \hline \hline
**Domain** & **Feature** & **Description** \\ \hline \multirow{6}{*}{Frequency PPG signal} & VLFa & area of VLF \\  & LFa & area of VLF \\  & HFa & area of VLF \\  & TOTALa & total area of all band \\ \cline{2-3}  & VLFh & highest power in VLF \\  & LFh & highest power in LF \\  & HFh & highest power in HF \\ \cline{2-3}  & VLFp & VLFa/TOTALa \\  & LFp & LFa/TOTALa \\ \cline{2-3}  & LFn & normalized area of LF LFLa/(LFa+HFa) \\  & HFn & normalized area of HF HFa/(LFa+HFa) \\  & LFHF & ratio of LFa and HFa \\ \hline \hline \end{tabular}
\end{table}
Table 2: Description of frequency domain features.  
Figure 6: PSD obtained from the PPG signal for high valence and low valence.  
Therefore, it was essential to consider the relation to the parameters. Consequently, we selected several features by using [PERSON]'s correlation, which measured the linear correlation between two variables. Before applying [PERSON]'s correlation, we set all feature values between zero and one. The formula of [PERSON]'s correlation is presented in (1), and the correlation coefficient had a value between \(+1\) and \(-1\), where \(1/-1\) denotes a positive/negative linear correlation and zero no correlation between the parameters. In this equation, \(\bar{x}\) and \(\bar{y}\) are the mean value of \(x\) and \(y\), respectively. In general, if the absolute value of R is between 0.1 and 0.3, it has a weak linear correlation, and if the absolute value of R is between 0.3 and 0.7, it has a distinct linear correlation.  
\[R_{xy}=\frac{\sum_{i=1}^{n}(x_{i}-\overline{x})(y_{i}-\overline{y})}{\sqrt{ \sum_{i=1}^{n}(x_{i}-\overline{x})^{2}(y_{i}-\overline{y})^{2}}} \tag{1}\]  
Figure 7 shows the result of [PERSON]'s correlation between emotions and statistical features. The first and the second columns represent the valence and the arousal, respectively, and the first and second rows correspond to the correlation between emotions (valence and arousal) and statistical features. Each coefficient value indicates how much it affects the valence and the arousal. To fuse the features in the neural network, it is essential to unify the number of features when training. Therefore, we decided to use 10 statistical features, which were one half of all the features with large coefficient values; we set each threshold for the valence and the arousal on the basis of the correlation coefficient.  
Table 3 describes the selected features and the correlation threshold. In Figure 7, valence correlations were stronger than those of arousal, and we set a higher threshold for valence. As the correlation coefficients of valence and arousal were different, the selected features were also different. In both the valence and the arousal cases, three time domain features and seven frequency domain features were selected on the basis of the correlation coefficients. As a result, 10 features were selected for both valence and arousal each, which were used for emotion classification.  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Emotion** & **Threshold** & **Features (10)** \\ \hline Valence & \(R\geq 0.2\) & meanNN, medianNN, NN50, VLFa, LFa, \\  & HFa, TOTALa, VLFp, LFp, HFp \\ \hline Arousal & \(R\geq 0.13\) & meanNN, SDNN, RMSSD, LFa, HFa, VLFp, \\  & LFp, HFp, LFn, LFHF \\ \hline \hline \end{tabular}
\end{table}
Table 3: Selected statistical features.  
Figure 7: [PERSON]’s correlation result between emotion and features.