# Ensemble Learning for Skeleton-Based Body Mass Index Classification
## 6 Results
### Results of Leave-One-Person-Out Cross-Validation

Table 10: Leave-one-person-out cross-validation results of the five benchmark methods when the undersampling technique is used. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**Class**} & \multirow{2}{*}{**TPR**} & \multirow{2}{*}{**PPV**} & \multirow{2}{*}{\(\mathbf{F_{1}}\)} & \multicolumn{4}{c}{**Macro-Average**} & \multirow{2}{*}{**Accuracy**} \\ \cline{5-8} \cline{7-9}  & & & & & **TPR** & **PPV** & \(\mathbf{F_{1}}\) \\ \hline \multirow{4}{*}{C-SVM} & Underweight & 0.1667 & 0.1163 & 0.1370 & & & & \\  & Normal weight & 0.6821 & 0.6896 & 0.6858 & 0.3981 & 0.3904 & 0.3926 & 0.5560 \\  & Overweight & 0.3455 & 0.3654 & 0.3551 & & & & \\ \hline \multirow{4}{*}{nu-SVM} & Underweight & 0.0333 & 0.0303 & 0.0317 & & & & \\  & Normal weight & 0.7255 & 0.6881 & 0.7063 & 0.3620 & 0.3662 & 0.3633 & 0.5719 \\  & Overweight & 0.3273 & 0.3803 & 0.3518 & & & & \\ \hline \multirow{4}{*}{\(k\)-NN [28]} & Underweight & 0.3000 & 0.2000 & 0.2400 & & & & \\  & Normal weight & 0.6223 & 0.7316 & 0.6725 & 0.4852 & 0.4536 & 0.4627 & 0.5790 \\  & Overweight & 0.5333 & 0.4293 & 0.4757 & & & & \\ \hline \multirow{4}{*}{NB} & Underweight & 0.0333 & 0.0227 & 0.0270 & & & & \\  & Normal weight & 0.6304 & 0.6610 & 0.6453 & 0.3404 & 0.3450 & 0.3422 & 0.5187 \\  & Overweight & 0.3576 & 0.3512 & 0.3544 & & & & \\ \hline \multirow{4}{*}{DT} & Underweight & 0.0769 & 0.1000 & 0.0870 & & & & \\  & Normal weight & 0.6474 & 0.6386 & 0.6430 & 0.3387 & 0.3411 & 0.3394 & 0.5062 \\ \cline{1-1}  & Overweight & 0.2919 & 0.2848 & 0.2883 & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Leave-one-person-out cross-validation results of the five benchmark methods when SMOTE is used. To find the optimal number of \(k\)-NN classifiers in the proposed ensemble model, we evaluated the performance of the ensemble models with different numbers of \(k\)-NN classifiers. Table 13 lists the performance metrics for each model. From this table, it can be seen that the best performance was achieved when the ensemble model consisted of 15 \(k\)-NN\({}_{q}\) models (\(q\in\{1,2,\cdots,14,15\}\)). Based on these results, we selected an ensemble model consisting of 15 \(k\)-NN models for additional testing. Table 14 lists the macro-average values of TPR, PPV and \(F_{1}\) scores, as well as the accuracy of each method over leave-one-person-out cross-validation. As shown in the table, for all evaluation metrics, the proposed method outperforms the other methods, achieving a BMI classification accuracy of 73%. In the proposed method, anthropometric features calculated over long/mid/short-term periods were used for the training of the ensemble model. In addition, the use of such features in the training phase could reduce the adverse effects of a variance in extracted features. As a result, the model could be trained effectively and achieved the best performance among the methods. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{4}{c}{**Macro-Average**} & \multirow{2}{*}{**Accuracy**} \\ \cline{2-2} \cline{4-5}  & **TPR** & **PPV** & & \(F_{1}\) \\ \hline C-SVM & 0.3981 & 0.3904 & 0.3926 & 0.5560 \\ nu-SVM & 0.3620 & 0.3662 & 0.3633 & 0.5719 \\ \(k\)-NN [28] & 0.4852 & 0.4536 & 0.4627 & 0.5690 \\ NB & 0.3404 & 0.3450 & 0.3422 & 0.5187 \\ DT & 0.3387 & 0.3411 & 0.3394 & 0.5062 \\ Proposed & 0.6422 & 0.5878 & 0.6058 & 0.7300 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Leave-one-person-out cross-validation performance comparisons between the proposed ensemble model and five benchmark methods.