# Ensemble Learning for Skeleton-Based Body Mass Index Classification
## 6 Results
### Results of Five-Fold Cross-Validation
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**Class**} & \multicolumn{3}{c}{**Fold \#1**} & \multicolumn{3}{c}{**Fold \#2**} & \multicolumn{3}{c}{**Fold \#3**} & \multicolumn{3}{c}{**Fold \#4**} & \multicolumn{3}{c}{**Fold \#5**} \\ \cline{3-14}  & & **TPR** & **PPV** & **\(F_{1}\)** & **TPR** & **PPV** & **\(F_{1}\)** & **TPR** & **PPV** & **\(F_{1}\)** & **TPR** & **PPV** & **\(F_{1}\)** & **TPR** & **PPV** & **\(F_{1}\)** \\ \hline \multirow{3}{*}{C-SVM} & 1 & 0.50 & 0.75 & 0.60 & 0.67 & 1.00 & 0.80 & 0.67 & 1.00 & 0.80 & 0.83 & 1.00 & 0.91 & 1.00 & 0.75 & 0.86 \\  & 2 & 0.97 & 0.85 & 0.90 & 0.96 & 0.93 & 0.95 & 1.00 & 0.95 & 0.97 & 0.97 & 0.99 & 0.98 & 0.99 & 0.92 & 0.95 \\  & 3 & 0.66 & 0.91 & 0.76 & 0.91 & 0.91 & 0.91 & 0.91 & 0.97 & 0.94 & 1.00 & 0.94 & 0.97 & 0.75 & 0.96 & 0.84 \\ \hline \multirow{3}{*}{nu-SVM} & 1 & 0.50 & 0.75 & 0.60 & 0.67 & 1.00 & 0.80 & 0.67 & 1.00 & 0.80 & 0.83 & 1.00 & 0.91 & 1.00 & 0.75 & 0.86 \\  & 2 & 0.96 & 0.85 & 0.90 & 0.95 & 0.92 & 0.93 & 1.00 & 0.95 & 0.97 & 0.97 & 0.99 & 0.98 & 0.99 & 0.94 & 0.96 \\  & 3 & 0.69 & 0.88 & 0.77 & 0.88 & 0.88 & 0.88 & 0.91 & 0.97 & 0.94 & 1.00 & 0.94 & 0.97 & 0.78 & 0.96 & 0.86 \\ \hline \multirow{3}{*}{\(k\)-NN [28]} & 1 & 0.83 & 0.50 & 0.63 & 1.00 & 0.86 & 0.92 & 0.83 & 0.71 & 0.77 & 1.00 & 0.75 & 0.86 & 1.00 & 0.55 & 0.76 \\  & 2 & 0.90 & 0.93 & 0.92 & 0.97 & 0.97 & 0.97 & 0.96 & 1.00 & 0.98 & 0.93 & 1.00 & 0.96 & 0.92 & 0.97 & 0.94 \\  & 3 & 0.78 & 0.83 & 0.81 & 0.91 & 0.94 & 0.92 & 1.00 & 0.94 & 0.97 & 1.00 & 0.91 & 0.96 & 0.88 & 0.90 & 0.89 \\ \hline \multirow{3}{*}{NB} & 1 & 0.33 & 0.13 & 0.19 & 0.17 & 0.13 & 0.14 & 0.50 & 0.38 & 0.43 & 0.33 & 0.29 & 0.31 & 0.67 & 0.27 & 0.38 \\  & 2 & 0.68 & 0.79 & 0.74 & 0.78 & 0.79 & 0.79 & 0.78 & 0.83 & 0.80 & 0.73 & 0.87 & 0.79 & 0.64 & 0.87 & 0.74 \\  & 3 & 0.53 & 0.52 & 0.52 & 0.63 & 0.65 & 0.63 & 0.63 & 0.59 & 0.61 & 0.78 & 0.58 & 0.67 & 0.66 & 0.50 & 0.57 \\ \hline \multirow{3}{*}{DT} & 1 & 0.17 & 0.10 & 0.13 & 0.50 & 0.20 & 0.29 & 0.50 & 0.43 & 0.46 & 0.50 & 0.43 & 0.46 & 0.67 & 0.31 & 0.42 \\  & 2 & 0.71 & 0.71 & 0.71 & 0.73 & 0.79 & 0.76 & 0.77 & 0.77 & 0.82 & 0.90 & 0.86 & 0.70 & 0.78 & 0.74 \\ \cline{1-1}  & 3 & 0.38 & 0.43 & 0.40 & 0.53 & 0.59 & 0.56 & 0.47 & 0.48 & 0.48 & 0.75 & 0.65 & 0.70 & 0.53 & 0.52 & 0.52 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Five-fold cross-validation results of the five benchmark methods when the synthetic minority oversampling technique (SMOTE) is used. \begin{table}
\begin{tabular}{l c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{3}{c}{**Macro-Average**} & \multirow{2}{*}{**Accuracy**} \\ \cline{2-3} \cline{5-6}  & **TPR** & **PPV** & **\(F_{1}\)** & **Accuracy** \\ \hline C-SVM + undersampling & 0.6863 & 0.7096 & 0.6604 & 0.7135 \\ C-SVM + SMOTE & 0.8517 & 0.9215 & 0.8760 & 0.9261 \\ \hline nu-SVM + undersampling & 0.6812 & 0.7069 & 0.6783 & 0.7459 \\ nu-SVM + SMOTE & 0.8520 & 0.9178 & 0.8752 & 0.9243 \\ \hline \(k\)-NN + undersampling [28] & 0.6906 & 0.5074 & 0.5035 & 0.5459 \\ \(k\)-NN + SMOTE & 0.9276 & 0.8512 & 0.8798 & 0.9297 \\ \hline NB + undersampling & 0.4760 & 0.4106 & 0.3537 & 0.4054 \\ NB + SMOTE & 0.5890 & 0.5444 & 0.5536 & 0.6829 \\ \hline DT + undersampling & 0.4681 & 0.3945 & 0.3640 & 0.4198 \\ DT + SMOTE & 0.5810 & 0.5385 & 0.5493 & 0.6685 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Average performance comparisons of five benchmark methods over five-fold cross validation. To verify the benefits of using the anthropometric features calculated for various different periods in the BMI classification task, we analyzed the standard deviations of the anthropometric features. For explanation, let \(AF(r)\) be \(AF\) for the \(r\)th skeleton sequence in the dataset. Here, according to the definition of \(AF\) in (6), the dimension of \(AF(r)\) is 20. In addition, let \(AF(r)[u]\), \(u\in\{1,2,\cdots,19,20\}\), be the \(u\)th element of \(AF(r)\).