# Estimation of Mental Distress from Photoplethysmography
## 3 Results  
Table 2 shows mean and standard deviation of the features under study. All characteristics calculated are shown, regardless of their statistical significance Only 4 out of 14 parameters show statistical differences when PRV is analyzed; and, all of them correspond to the time domain. More precisely, standard deviation (_SDNN_), dynamic range (_DRNN_) and standard error (_SENN_) of PRV series, as well as standard deviation of PRV derivative (_SDSD_), show statistical significance. In this regard, _DRNN_ achieves the highest discriminatory power. It is worth noting that all significant parameters report an increasing temporal value when participants are elicited with stressing stimuli. In order to estimate a reliable and robust power classification for each single parameter, a stratified 10-fold cross-validation is run five times. Figure 3 shows the ROC curves at a random iteration, together with the sensitivity (Se), specificity (Sp) and area under curve (AUC) for the four parameters that reported statistical significance. Additionally, average values of Se, Sp and accuracy (Ac), for both training and test subsets iterations, are shown in Table 3.  
The single classification results are in agreement with the discriminatory power obtained previously. _DRNN_ achieves the highest accuracy, correctly classifying 72.06% conditions. The rest of markers reach poorer performances, ranging from 66.18 to 67.65%. It is worth noting that features report a higher capability in discriminating true negatives, i.e., calmness than discriminating stress. In this regard, _SDNN_ and _DRNN_ achieve specificity values 76.47 and 82.35%, respectively. Additionally, a series of tree-based classification models are calculated in order to study the potential relations among the different parameters. It is worth noting that all the parameters calculated are included in this analysis, regardless if they show statistical relevance, as there might exist underlying complementaries not revealed yet. Figure 4 shows the structure and the parameters composing the tree-based discriminant model more frequently obtained among the different iterations. As can be observed, the model is formed exclusively of temporal PRV parameters. Thus, the _SDNN_ parameter is chosen as the most relevant in the model and a threshold of 0.5250 serves to divide the sample into two subgroups, calmness and stress. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Physiological** & **Feature** & **Calmness** & **Distress** & \\
**Analysis** & **Acronym** & **Mean \(\pm\) Std** & **Mean \(\pm\) Std** & \(\rho\) \\ \hline Temporal & _MNN_ & 0.7941\(\pm\) 0.1021 & 0.7765\(\pm\) 0.1064 & 0.4890 \\ Temporal & _SDNN_ & 0.0596 \(\pm\) 0.0243 & 0.1064 \(\pm\) 0.0527 & 0.0046 \\ Temporal & _DRNN_ & 0.2652 \(\pm\) 0.1025 & 0.4522 \(\pm\) 0.2453 & \(1.15\times 10^{-4}\) \\ Temporal & _SENN_ & 0.0634 \(\pm\) 0.0294 & 0.0934 \(\pm\) 0.0500 & 0.0036 \\ Temporal & _SDFD_ & 0.0589 \(\pm\) 0.0361 & 0.1039 \(\pm\) 0.0723 & 0.0018 \\ Temporal & _RMSFD_ & 0.0853 \(\pm\) 0.0570 & 0.1140 \(\pm\) 0.0712 & 0.075 \\ Temporal & _PNN50_ & 0.9997 \(\pm\) 0.0018 & 0.9986 \(\pm\) 0.0039 & 0.1495 \\ \hline Morphological & _HRNN_ & 5.2802 \(\pm\) 1.4449 & 5.6542 \(\pm\) 1.8026 & 0.3487 \\ Morphological & _TINN_ & 0.3606 \(\pm\) 0.1960 & 0.4894 \(\pm\) 0.2373 & 0.053 \\ Morphological & _SKNN_ & \(-\)0.1009 \(\pm\) 1.2990 & \(-\)0.1335 \(\pm\) 1.0867 & 0.9107 \\ Morphological & _KINN_ & 5.9136 \(\pm\)6.8703 & 4.9149 \(\pm\) 3.9008 & 0.4637 \\ \hline Frequency & _LF_ & 0.0032 \(\pm\) 7.5112 \(\times\) 10\({}^{-4}\) & 0.0031 \(\pm\) 8.5693 \(\times\) 10\({}^{-4}\) & 0.5710 \\ Frequency & _HF_ & 0.0073 \(\pm\) 0.0017 & 0.0071 \(\pm\) 0.0019 & 0.5711 \\ Frequency & _NHF_ & 0.4401 \(\pm\) 1.7377\(\times\)10\({}^{-4}\) & 0.4401 \(\pm\) 1.7022 \(\times\) 10\({}^{-4}\) & 0.9107 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results obtained. Mean and std values for emotional states of calm and distress and statistical significance (\(\rho\)), for all parameters are presented.