## 3 Results
### Machine Learning Analysis for Pressure Estimation
#### 3.2.1 Pressure Estimation at Individual Anatomical Points  
As part of the first set of experiments, a dataset was constructed where the target regression values were each of the three pressure metrics. The features were derived from the thermal time series data. The temperature measurements, representing a time series, were recorded at specific intervals--30 s, 90 s, 120 s, and 180 s--at various anatomical points on the feet. The pressure values were consolidated into three metrics: peak pressure, average peak pressure, and average pressure for each anatomical point. The analysis of the machine learning models revealed a lack of a significant correlation between the thermal time series data and the predicted pressure values. This outcome was consistent across all the anatomical points and pressure metrics, as indicated by the negative R\({}^{2}\) values. The performance metrics for the regression models, including MAE, MSE, RMSE, RMSLE, and MAPE, exhibited high error rates and negative R\({}^{2}\) values, suggesting that the models struggled to accurately estimate the pressure values based on thermal data alone. These findings indicate that thermal data, when used in isolation, may not provide a reliable basis for pressure estimation. Due to the extensive volume of results, only the outcomes for three anatomical points are presented as examples. Table 2 provides the metrics for a regressor estimating the average peak pressure at the hallux, Table 3 presents the metrics for the average peak plantar pressure estimation at the third metatarsus, and Table 4 displays the metrics for peak plantar pressure estimation at the heel. As shown in these tables, large errors were obtained, suggesting the difficulty of predicting pressure values solely from thermal time series data. These results raise questions about the suitability of using thermal data alone for pressure estimation. Further investigation is necessary to identify additional features or data sources that may enhance the accuracy of pressure prediction models. The results indicate significant challenges in predicting pressure values using thermal time series data alone, as evidenced by the high error rates and negative R\({}^{2}\) values across most of the models. For the hallux, as shown in Table 2, the Extra Trees Regressor had the best performance among the models, but even this model yielded a negative R\({}^{2}\) value (\(-0.4872\)) and substantial errors (MAE = 23.7315; RMSE = 27.1971), indicating poor predictive accuracy. Other models, such as the K Neighbors Regressor and Random Forest Regressor, demonstrated even higher errors and more negative R\({}^{2}\) values, further underscoring the difficulty of estimating pressure from thermal data in this region. In the third metatarsus (Table 3), the models performed similarly poorly. The Light Gradient Boosting Machine and Dummy Regressor produced the same results, with a negative R\({}^{2}\) value of \(-0.7524\) and considerable errors (MAE = 59.1336; RMSE = 69.5438). The Least Angle Regression model performed particularly poorly, with extreme errors (MAE = 1358.865; RMSE = 1583.866) and a highly negative R\({}^{2}\) value of \(-1376.8\), suggesting that this model is entirely unsuitable for this task.