## 3 Result and Discussion
### Improvement of Prediction Performance by Data Augmentation
#### 3.2.2 With Bone Density  
Previous analyses have shown that differences between potential artificial and cadaveric bones can affect the analysis results. Therefore, the analysis was conducted by introducing the bone density of the clinical data, which is foundational information, as a feature of the teaching data. Each fold was the same as that in the analysis without bone \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Analysis Data**} & \multirow{2}{*}{**Fold**} & \multicolumn{2}{c}{**Number of Explanatory**} & \multirow{2}{*}{**Determination Coefficient**} & \multirow{2}{*}{**MSE**} \\  & & **Variables** & & \\ \hline \multirow{4}{*}{Without bone density} & 1 & & 0.629 & 0.233 \\  & 2 & 0.869 & 0.125 \\  & 3 & & 0.591 & 0.268 \\  & Average & & 0.697 & 0.208 \\ \hline \multirow{4}{*}{With bone density} & 1 & & 0.972 & 0.0355 \\  & 2 & 0.885 & 0.104 \\ \cline{1-1}  & 3 & & 0.718 & 0.169 \\ \cline{1-1}  & Average & & 0.858 & 0.103 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental results of the three-fold validation of machine learning performance with and without the introduction of bone density. Figure 6: Analysis results of a three-fold cross validation using a mixed dataset of artificial and cadaveric bones without bone density: (**a**) relationship between measured and predicted insertion torques; (**b**) Bland–Altman plot. density, as shown in Figure 6. The evaluation results are shown in Figure 7. The highest prediction accuracy was obtained in this analysis, as shown in Figure 7a. A three-fold average coefficient of determination \(R^{2}\) = 0.858 and MSE of 0.103 was obtained, which is comparable to the prediction accuracy of the simulated bone in a previous study [10]. The Bland-Altman plot shown in Figure 7b indicates that the proportional error that appeared before the introduction of bone density, as shown in Figure 6b, disappeared, resulting in a prediction with less error. In addition, 96% of all predictions (46 of 48) were within the 95% confidence interval, and 100% of the cadaver bone predictions were within the confidence interval of the analysis method. The width of this confidence interval of 1.7 Nm (\(-\)0.91 to 0.79 Nm) was the best among the data processing. Moreover, it was a dramatic improvement over the 8.9 Nm (\(-\)5.1 to 3.8 Nm) obtained with the log approximation of one explanatory variable for only artificial bone in the previous study [10]. Table 3 presents the explanatory variables used in this study. Newly introduced bone density was employed as the explanatory variable with the highest priority, and the highest performance was obtained with SVR using eight variables, which is the largest number to date. However, the peak frequency (1000-5000 Hz), which was previously the most important variable, was given the sixth highest priority by LASSO. Figure 8 shows the performance changes in the (a) coefficient of determination and (b) MSE when introducing SVR for the explanatory variables prioritized by LASSO. In this study, the coefficient of determination, which is the index for optimizing SVR, showed approximately the same value for up to ten variables. However, the MSE showed the lowest value among the six variables when the peak frequency (1000-5000 Hz) was introduced. From these results, it was possible to verify the SVR optimization index. In future work, further performance improvements can be recognized by examining the percentage of cadaveric bone data that should be included in the training data and SVR optimization index. Furthermore, it is possible to introduce explanatory variable selection through sequential selection, without using LASSO. However, in this study, a prediction accuracy in cadaver bones was achieved that was comparable to that of simulated bones by using a uniquely simple selection of explanatory variables by LASSO and SVR optimization, consistent with the coefficient of determination.