# A Boundary Zone Method for the Generation of Multivariate Representative Humanoids
## 4 Evaluation Results  
The results of the MAP and outlier analyses are summarized in Table 2 for the RHs generated by the existing (SM, RM, and CM) and proposed (BZM) methods with the selected 1988 U.S. Army anthropometric data for \(\kappa\pm\delta=90\%\pm 1\%\). Various groups of RHs were formed by increasing the number of factors or principal components from two to six in the existing methods and by repeating the K-mean cluster analysis with \(n=10\) in the proposed method. The MAP analysis results identified that the BZM was most preferred in terms of precise accommodation and the RM was most preferred in terms of the number of RHs. The BZM generated RH groups that accommodated precisely (90.6 \(\pm\) 0.7%) the designated \(\kappa=90\%\) of the target population, while the RM tended to generate over-accommodating RH groups and both the SM and CM tended to generate under-accommodating RH groups. Next, the minimum number of RHs satisfying the designated \(\kappa\) was nine (MAP = 93%) for \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Generation Method**} & \multicolumn{2}{c}{**Number of**} & \multicolumn{2}{c}{**Percentage of**} & \multicolumn{2}{c}{**Multivariate**} & \multirow{2}{*}{**Outlier**} & \multicolumn{2}{c}{**Normalized Outlier Magnitude (\%)**} \\  & **Factors/Principal** & **Variance** & & & & **Accommodation** & **Percentage (\%)** & **Mean** & **SD** & **Max** \\ \hline \multirow{4}{*}{SM} & 2 & 72 & 5 & 18 & 0 & - & - & - \\  & 3 & 83 & 9 & 43 & 0 & - & - & - \\  & 4 & 90 & 17 & 60 & 0 & - & - & - \\  & 5 & 94 & 33 & 69 & 0 & - & - & - \\  & 6 & 96 & 65 & 72 & 1.5 & 0.3 & - & 0.3 \\ \hline \multirow{4}{*}{RM} & 2 & 72 & 5 & 62 & 0 & - & - & - \\  & 3 & 83 & 9 & 93 & 11.1 & 4.7 & 6.0 & 9.0 \\  & 4 & 90 & 17 & 98 & 35.3 & 2.5 & 3.1 & 11.1 \\  & 5 & 94 & 33 & 99 & 45.5 & 4.1 & 4.7 & 20.1 \\  & 6 & 96 & 65 & 99 & 26.2 & 4.5 & 4.9 & 24.8 \\ \hline \multirow{4}{*}{CM} & 2 & 72 & 9 & 62 & 0 & - & - & - \\  & 3 & 83 & 19 & 81 & 0 & - & - & - \\ \cline{1-1}  & 4 & 90 & 33 & 84 & 12.1 & 2.7 & 3.7 & 8.2 \\ \cline{1-1}  & 5 & 94 & 51 & 87 & 25.5 & 2.0 & 2.9 & 8.7 \\ \cline{1-1}  & 6 & 96 & 73 & 92 & 15.1 & 2.2 & 2.6 & 9.0 \\ \hline BZM \({}^{*}\) & - & - & \(44\pm 2\) & \(90.6\pm 0.7\) & 0 & - & - & - \\ \hline \hline \end{tabular} \({}^{*}\) Number of repeated trials = 10.  
\end{table} 
Table 2: Performance comparison of multivariate representative humanoid generation methods (SM, square method; RM, rectangular method; CM, circular method; BZM, boundary zone method). the RM, 41 for the BZM (MAP = 91%), and 73 for the CM (MAP = 92%)--note that the SM could not generate any RH group satisfying the designated \(\kappa\). However, this preference for the RM in terms of the number of RHs was limited due to existence of outliers in the corresponding generated RH groups. The outlier analysis results showed that the BZM was most preferred, followed by the SM, CM, and RM in terms of outlier percentage and normalized outlier magnitude. Figure 6 illustrates that the minimum values of forearm-to-forearm breadth (FFB) and abdominal extension depth (AED) of the 33 RHs generated by the RM were 27.2 cm and 12.3 cm, respectively, which were smaller than their corresponding minima (37.3 cm for FFB and 15.3 cm for AED) of the target population. Of the existing methods, the RM generated improper RHs with the largest values of outlier percentage and normalized outlier magnitude, followed by the CM and then the SM. On the contrary, the BZM did not include any outliers in its generated RHs. An in-depth analysis identified that the RHs of the BZM properly represented the body size diversity of the target population, while the RHs of the existing generation methods failed to do so, especially for ADs with a similar factor loading pattern.