## 3 Case Study and Results
### Result of the Feature Selection  
Figure 7 shows the result of estimating the body height using the XGBoost (the top subplot) and the RF (the bottom subplot). In either subplot, each tick on the x-axis is labeled with a feature name, corresponding to a feature in the datasets. Only 60 features out of the total 117 are presented on the x-axis for the simplicity of the presentation. As seen, the feature importance and the MSE are on the first and the second y-axis, respectively. The red dotted-line represents the value of feature importance for current feature shown on the x-axis. As seen, the red dotted line is monotonically decreasing, which means the features become less important along the x-axis. In other words, the feature importance is ranked in a descending order along the x-axis. For instance, the most important feature for the body height estimation using the XGBoost (the top subplot) is the \"side upper torso length right\", while the most important feature for the body height estimation using the RF (the bottom subplot) is the \"high waist height\".  
More importantly, the blue dotted-line in each subplot represents the MSE when the more important features plus the current feature are taken as the input to the ML methods. For instance, in the top subplot, the value of the blue dot corresponding to the \"side upper torso length right\" shows the MSE when only the \"side upper torso length right\" is the input to XGBoost. The value of the blue dot corresponding to the \"croth length, rear\" shows the MSE when the \"side upper torso length right\", the \"neck height\" plus the \"croth length, rear\" are the input to XGBoost. Generally speaking, the trend of the blue-dotted line is downward since the more features that are considered as input to the ML method, the better accuracy the estimation will be. However, the marginal effect for the MSE improvement decreases as shown in Figure 7. Therefore, a vertical line is plotted in both subplots at the 20 th feature since the improvement is negligible when more than 20 features are used as the input.  
It is worth mentioning that the stability of the ML models to changes in the number of features needs to be considered. Here, the feature selection is well aligned with the findings in [37], which indicates that the ML model is robust to the inclusion of enough variables of moderate to low importance. In the proposed framework, we select the top 20 body features based on their importance, as shown in Figure 7. As seen, the vast majority of those features are of moderate to low importance. Therefore, the proposed ML models are stable when the top 20 body features are selected. In the latter part of this paper, we focus on analysis of the accuracy of the proposed ML models.  
Figure 8 shows the top 20 most important features for the XGBoost (the top subplot) and for the RL (the bottom subplot). The frequency on the y-axis of each subplot represents the occurrences when this feature lies within the top 20 features in predicting all 116 other features. For example, the top feature for the XGBoost is the \"arm length to neck right\" with a frequency of over 105. This indicates that this feature is among the top 20 features for predicting all the other 116 features. As seen in Figure 8, the most important body feature for the XGBoost is the \"Arm length to neck right\" with a 105 frequency. However,  
the most important body feature for the RF is the \"weight\" with a 36 frequency. The feature selection is applied based on the results in Figure 8. The top 20 body features with the highest frequency are selected for each ML model, the performance of which will be tested and analyzed next.  
Figure 7: Illustration of the relationship between feature importance and MSE.