## 3 Results
### Machine Learning Analysis for Pressure Estimation
#### 3.2.2 Analysis of Correlation Between Consolidated Temperature and Pressure Prediction
high error metrics (e.g., RMSE values of 57.8543 and 55.4159, respectively) and negative R\({}^{2}\) values (\(-1.9084\) and \(-1.7926\)), further underscoring the inadequacy of using consolidated temperature data to predict the pressure metrics at the fifth metatarasus. The Least Angle Regression model once again produced extreme results, with errors of the same magnitude as those observed in the previous table, highlighting its unsuitability for this task. Overall, these results suggest that the consolidated temperature data from multiple anatomical points are not sufficient to predict the pressure metrics accurately at specific locations on the foot. The negative R\({}^{2}\) values across all the models indicate that the regression models failed to capture any meaningful relationship between the temperature data and the pressure metrics. The consistently high errors in metrics such as MAE, MSE, RMSE, RMSLE, and MAPE further reinforce this conclusion, suggesting that alternative data sources or additional features may be required to enhance the accuracy of the pressure prediction models. The results of this analysis suggest that consolidating thermal data from multiple anatomical points did not improve the accuracy of the pressure predictions at individual anatomical points, as demonstrated by the regression metrics for the lateral midfoot targeting peak plantar pressure (Table 7). The weak correlation between the consolidated temperature data and the pressure metrics is evident from the consistently negative R\({}^{2}\) values and the high errors observed across the various models. For example, the Extra Trees Regressor, which is generally a strong performer in regression tasks, yielded an MAE of 21.6342 and an RMSE of 24.3457, accompanied by a significantly negative R\({}^{2}\) value of \(-4.1466\). Similarly, the Elastic Net and Extreme Gradient Boosting models also exhibited poor performances, with negative R\({}^{2}\) values of \(-4.509\) and \(-4.8219\), respectively, and relatively high error metrics (e.g., RMSE values of 26.9775 and 26.2291, respectively). These results indicate that the models were unable to effectively capture the relationship between the consolidated temperature data and the pressure at the lateral midfoot, leading to inaccurate predictions. Additionally, the Passive Aggressive Regressor, which had one of the lowest RMSE values at 20.8999, still exhibited a negative R\({}^{2}\) value of \(-5.027\), further confirming the lack of a meaningful relationship between the temperature data and the pressure metrics. The consistently high MAE, MSE, RMSE, and RMSLE values across all the models, coupled with the negative R\({}^{2}\) values, suggest that the temperature data from different anatomical points may not be directly related to the pressure at a specific location, at least with the models and features used in this study. The results for other models, such as the Decision Tree Regressor and Linear Regression, are even more striking, with highly negative R\({}^{2}\) values (\(-8.7018\) and \(-16.3879\), respectively) and large errors (e.g., RMSE values of 31.3636 and 33.3176, respectively). These metrics highlight the complexity of accurately predicting the pressure distribution in the feet based on thermal data alone. In all the models tested, negative \(R^{2}\) values were consistently observed, as shown in Tables 1-7. A negative \(R^{2}\) value indicates that the model's predictive power is worse than simply predicting the mean of the data. This suggests that the temperature data alone do not contribute effectively to predicting the plantar pressure at the anatomical points analyzed. These results corroborate the findings of the correlation analysis, where weak or no significant correlations were detected between the temperature and pressure data. Therefore, the poor predictive accuracy of the models, as indicated by the negative \(R^{2}\) values, is consistent with the inherent lack of a strong relationship between the two modalities.