## 4 Discussion
First, it is the first to classify the severity of pain using infrared thermography and ML, providing a non-invasive and objective method for pain evaluation. Second, the study used nonlinear feature extraction techniques to capture the complex relationship between the patient's characteristics and pain severity. Third, the study integrated several clinical characteristics, including sex, age, duration of pain, and nonlinear features, to increase the accuracy of pain severity classification. However, there are also several limitations to the current study. First, the sample size was relatively small, which may limit the generalizability of the findings. The small number of patients was insufficient to apply ML. Future studies involving more patients are warranted. To ensure generalization performance, data from two other hospitals were used, and verification was performed by applying the calibration method. Second, the study did not consider clinical outcomes with a model net benefit. Although the model's accuracy was evaluated using several indicators, such as an F1 score, balanced accuracy, sensitivity, and specificity, and we also performed model calibration to overcome the overfitting issue, it was insufficient to verify the analysis of the net benefit of the clinical outcomes of the proposed model. The modeling of variables confined to linear regression analysis may not be suitable for examining the benefits of nonlinear analysis and models by observing the net benefit with or without the specific variable. However, in recent years, mathematical methods and prior studies have been presented to overcome these shortcomings [20; 21; 22], and the authors will have to conduct additional analyses in future studies considering the net benefit of the model to evaluate its clinical usefulness. Third, the study used patient-reported pain as a label, which is subjective and may vary between individuals. The variation between individuals' subjective reports was minimized through the use of two classifications: severe-to-intractable pain and mild-to-moderate pain. Future studies should consider objective measures of pain severity, such as functional MRI, to improve the accuracy of pain classification. The proposed method may have potential for application to other types of pain, such as cancer pain or chronic headaches, but future studies are needed to investigate its generalizability across different pain types. Additionally, future research should investigate the predictive power of the proposed method to improve pain management and treatment outcomes. Another potential use of the proposed method is in evaluating the efficacy of pain interventions, such as medication, physical therapy, or surgery. Future studies should investigate the use of the proposed method to monitor the effectiveness of pain treatments and optimize treatment plans. Furthermore, the proposed method may be integrated with other pain-assessment tools, such as self-report questionnaires, to improve pain-assessment accuracy. Future studies should investigate the use of the proposed method in combination with other pain-assessment tools to improve the accuracy and reliability of pain assessment. Finally, the proposed method may have potential for use in real-time pain-monitoring systems, such as hand-held thermography devices with mobile apps. Future studies should investigate the feasibility and effectiveness of implementing the proposed method in real-time pain-monitoring systems to provide patients with continuous pain-monitoring and self-management tools. Overall, the proposed method shows promise for improving pain assessment and management, but further research is needed to fully explore its potential applications and limitations.