# Ensemble Learning for Skeleton-Based Body Mass Index Classification
## 6 Results
### Results of Leave-One-Person-Out Cross-Validation  
Figure 8 shows the leave-one-person-out cross-validation process used in this work. As shown in the figure, in each validation round, the skeleton sequences for one person were used to test the classifier, and the sequences for the remaining 111 people were used for training. In each validation round, the predicted results (i.e., predicted BMI classes) for the testing skeleton sequences were obtained. After all 112 validations rounds were completed, we calculated a confusion matrix using all \begin{table}
\begin{tabular}{l c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{3}{c}{**Macro-Average**} & \multirow{2}{*}{**Accuracy**} \\ \cline{2-2} \cline{4-5}  & TPR & PPV & \(\mathbf{F_{1}}\) & \\ \hline C-SVM & 0.8517 & 0.9215 & 0.8760 & 0.9261 \\ nu-SVM & 0.8520 & 0.9178 & 0.8752 & 0.9243 \\ \(k\)-NN [28] & 0.9276 & 0.8512 & 0.8798 & 0.9297 \\ NB & 0.5890 & 0.5444 & 0.5536 & 0.6829 \\ DT & 0.5810 & 0.5385 & 0.5493 & 0.6685 \\ Proposed & 0.9862 & 0.9603 & 0.9721 & 0.9820 \\ \hline \hline \end{tabular}
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Table 9: Five-fold cross-validation performance comparisons between the proposed ensemble model and five benchmark methods. predicted results. Based on the confusion matrix, we calculated the TPR, PPV and \(F_{1}\) values over the three classes in order to evaluate the performance of the classifier. Table 10 shows the leave-one-person-out cross-validation results of the five benchmark methods when the undersampling technique was used. On the other hand, Table 11 shows the leave-one-person-out cross-validation results when SMOTE was used. By using (12) to (14),  
Figure 8: Leave-one-person-out cross-validation process to evaluate the performance of each method. Figure 7: Standard deviations of 20 anthropometric features for long/mid/short-term periods. we computed the macro-average values of these metrics over the three classes. In addition, we calculated the classification accuracy of each benchmark method. The performance evaluation results for the five benchmark methods are summarized in Table 12. From the table, it is seen that SMOTE improves the macro-average of the TPR, PPV and \(F_{1}\) of each benchmark method, compared with the results where the undersampling technique was used. In addition, the BMI classification accuracy of each method also improved when SMOTE was used. These results demonstrate that SMOTE is more effective at overcoming the class imbalance problem in the dataset used in [28] than the undersampling technique. \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 & 0.2667 & 0.0563 & 0.0930 & & & \\  & Normal weight & 0.4130 & 0.7273 & 0.5269 & 0.3397 & 0.3493 & 0.3057 & 0.3837 \\  & Overweight & 0.3394 & 0.2642 & 0.2971 & & & & \\ \hline \multirow{4}{*}{nu-SVM} & Underweight & 0.2667 & 0.0533 & 0.0889 & & & & \\  & Normal weight & 0.4022 & 0.7184 & 0.5157 & 0.3361 & 0.3474 & 0.3019 & 0.3766 \\  & Overweight & 0.3394 & 0.2705 & 0.3011 & & & & \\ \hline \multirow{4}{*}{\(k\)-NN [28]} & Underweight & 0.2000 & 0.0405 & 0.0674 & & & & \\  & Normal weight & 0.3342 & 0.6150 & 0.4331 & 0.3054 & 0.3162 & 0.2774 & 0.3410 \\  & Overweight & 0.3818 & 0.2930 & 0.3316 & & & & \\ \hline \multirow{4}{*}{NB} & Underweight & 0.1000 & 0.0211 & 0.0349 & & & & \\  & Normal weight & 0.3696 & 0.5913 & 0.4548 & 0.2616 & 0.2949 & 0.2606 & 0.3393 \\  & Overweight & 0.3152 & 0.2723 & 0.2921 & & & & \\ \hline \multirow{4}{*}{DT} & Underweight & 0.2000 & 0.0405 & 0.0674 & & & & \\  & Normal weight & 0.3342 & 0.6150 & 0.4331 & 0.3054 & 0.3162 & 0.2774 & 0.3410 \\ \cline{1-1}  & Overweight & 0.3818 & 0.2930 & 0.3316 & & & & \\ \hline \hline \end{tabular}
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