## 4 Discussion
### Machine Learning Performance  
We explored the machine learning classification for baseline and pain states and different pain intensity levels. We addressed the challenge of using a relatively small dataset and minimized the risk of overfitting by implementing a classifier with repeatednested CV. In the PFI analysis for baseline versus painful states, SCR, SCL, and RESP were the most influential features, with SCR showing notably higher importance. Employing these three features yielded an F1 score of 0.83, indicating that even a minimal physiological set could reliably detect emotional pain. This high performance aligns with our findings, which demonstrate strong sympathetic involvement (as shown by SCR and SCL) during emotional pain. Moreover, these results demonstrate an accuracy comparable to that of the baseline versus high-pain classification reported in previous studies based on physical pain (Table 1). Regarding the classification of pain intensity levels, we evaluated physiological signals alone and in combination with the subjective ratings of valence and arousal. For the 6 vs. 7 binary classification, combining PTT, SCR, and valence yielded the highest F1 score (0.733). The accuracy for classifying intensity levels 6 and 7 was approximately 0.70, even when only the three highest-ranked physiological features were used. This value surpasses the \(\sim\)0.61 accuracy obtained solely with valence and arousal. This demonstrates the pivotal role of physiological measures in differentiating closely spaced pain intensities and suggests that a subset of physiological signals can lead to effective pain intensity classification. The PFI rankings revealed that PTT and SCR were consistently informative, further corroborating our statistical findings. However, only 17 participants classified pain intensity level as 5, and this posed significant challenges. Therefore, the classification results involving level 5 should be interpreted cautiously due to the small sample size. Despite using SMOTE, performance varied substantially, reflecting the inherent difficulty of modeling under-sampled classes. Notably, for well-separated intensities (5 vs. 7), subjective ratings alone could achieve relatively high accuracy, but more nuanced classifications (such as 5 vs. 6 or 6 vs. 7) benefited greatly from the inclusion of physiological features. These findings imply that self-ratings and physiological indicators each have distinct advantages, with subjective measures capturing broad emotional distinctions and physiological signals offering finer granularity when differentiating closely spaced intensity levels. The classification results for differentiating pain intensity levels using physiological signals achieved an accuracy of 0.7, indicating feasibility, but falling short of the over 0.8 accuracy observed in the baseline versus the painful state classification. Previous studies on physical pain have reported higher accuracies, even with multiclass problems, but these studies typically relied on distinct stimuli for each intensity level (Table 1) [11; 12]. In contrast, our study focuses on classifying individually perceived intensities under a single standardized stimulus, which is a more challenging task. Therefore, our classification accuracy is expected to be lower than that observed in studies with varied stimuli. In addition, even in physical pain research, distinguishing very low-intensity stimuli from the baseline is difficult, with five-class classification results of approximately 40% (Table 1) [7; 9]. Given this context, our near-0.7 performance using selected physiological signals highlights that the perceived intensity can be classified from such signals, presenting a promising finding for further research into emotionally induced pain. Overall, the machine learning results suggest that integrating physiological signals with self-reported states yielded the most robust models for classifying perceived pain intensity.