## 3 Results
### Correlation Between Plantar Pressure and Temperature Data
#### 3.1.1 Calculation of Correlation Coefficients  
The relationship between pressure and temperature was assessed by computing both Pearson and Spearman correlation coefficients for each combination of temperature  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Model** & **Type** & **Default Hyperparameters** \\ \hline Logistic Regression & Classification & C = 1.0, penalty = l2, solver = lbfgs, max\_iter = 100 \\ \hline Random Forest Classifier & Classification & n\_estimators = 100, criterion = gini, max\_depth = None, min\_samples\_split = 2, min\_samples\_leaf = 1 \\ \hline K-Nearest Neighbors & Classification & n\_neighbors = 5, weights = uniform, algorithm = auto \\ \hline Support Vector Machine (SVC) & Classification & C = 1.0, kernel = rbf, gamma = scale \\ \hline Gradient Boosting Classifier & Classification & n\_estimators = 100, learning\_rate = 0.1, max\_depth = 3, min\_samples\_split = 2, min\_samples\_leaf = 1 \\ \hline Extra Trees Classifier & Classification & n\_estimators = 100, criterion = gini, max\_depth = None, min\_samples\_split = 2, min\_samples\_leaf = 1 \\ \hline Naive Bayes & Classification & No tunable parameters \\ \hline XGBost Classifier & Classification & n\_estimators = 100, learning\_rate = 0.1, max\_depth = 6, min\_child\_weight = 1, subsample = 1.0, colsample\_bytes = 1.0 \\ \hline LightGBM Classifier & Classification & n\_estimators = 100, learning\_rate = 0.1, max\_depth = \(-\)1, num\_leaves = 31 \\ \hline Decision Tree Classifier & Classification & criterion = gini, max\_depth = None, min\_samples\_split = 2, min\_samples\_leaf = 1 \\ \hline AdaBoost Classifier & Classification & n\_estimators = 50, learning\_rate = 1.0 \\ \hline Ridge Classifier & Classification & alpha = 1.0 \\ \hline Random Forest Regressor & Regression & n\_estimators = 100, criterion = mse, max\_depth = None, min\_samples\_split = 2, min\_samples\_leaf = 1 \\ \hline Gradient Boosting Regressor & Regression & n\_estimators = 100, learning\_rate = 0.1, max\_depth = 3, min\_samples\_split = 2, min\_samples\_leaf = 1 \\ \hline Extra Trees Regressor & Regression & n\_estimators = 100, criterion = mse, max\_depth = None, min\_samples\_leaf = 1 \\ \hline XGBost Regressor & Regression & n\_estimators = 100, learning\_rate = 0.1, max\_depth = 6, min\_child\_weight = 1, subsample = 1.0, colsample\_bytes = 1.0 \\ \hline LightGBM Regressor & Regression & n\_estimators = 100, learning\_rate = 0.1, max\_depth = \(-\)1, num\_leaves = 31 \\ \hline Decision Tree Regressor & Regression & criterion = mse, max\_depth = None, min\_samples\_split = 2, min\_samples\_leaf = 1 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Default hyperparameters for classification and regression models.  
and plantar pressure features. The Pearson correlation coefficient measures the linear relationship between two continuous variables, while the Spearman correlation coefficient captures potential non-linear relationships by assessing the monotonic association between ranked data. The formulas used for these calculations are as follows:  
* **Pearson correlation:** \[r=\frac{\sum(X_{i}-\bar{X})(Y_{i}-\bar{Y})}{\sqrt{\sum(X_{i}-\bar{X})^{2}\sum(Y_{ i}-\bar{Y})^{2}}}\] where \(X_{i}\) and \(Y_{i}\) represent the data points for temperature and pressure, respectively, and \(\bar{X}\) and \(\bar{Y}\) are their respective means.
* **Spearman correlation:** \[\rho=1-\frac{6\sum d_{i}^{2}}{n(n^{2}-1)}\] where \(d_{i}\) is the difference between the ranks of the corresponding values and \(n\) is the number of observations. Both correlation coefficients were computed for each anatomical point, such as the first metatarsal (1 stM), fifth metatarsal (5 thM), hallux, heel, and the lateral and medial midfoot (LatM and MedMF), in combination with various temperature measurements.