## 3 Results
### Single Layer Perceptron  
The ML model improved the accuracy for the prediction of the BMD (R\({}^{2}\) = 0.580, \(p\) < 0.001) (Figure 5). It demonstrated significative accuracy when used with a nominal dependent variable, i.e., the clinical condition  
The accuracy for training and test is reported in Table 4 and illustrated with a box-plot for the pseudoprobability of the predicted groups (Figure 6). Figure 4: Box plot illustrating the adjusted predicted values of the linear regression model grouped by clinical population. Figure 5: Cluster scatterplot of the adjusted predicted values obtained using the single-layer perceptron with the BMD. The cost function graph helps visualize how the sample is sufficient for the task, and the risk of overfitting is minimal (Figure 7). The following table (Table 5) reports the normalized importance for each feature in the building of the model. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{4}{c}{**SLP**} \\ \hline \multirow{3}{*}{**Sample**} & \multicolumn{4}{c}{**Predicted**} \\ \cline{2-6}  & \multicolumn{2}{c}{**Normal**} & **Osteopenic** & **Osteoporotic** & **Correct** \\ \hline \multirow{3}{*}{Training} & normal & 21 & 0 & 0 & 100.0\% \\ \cline{2-6}  & osteogenic & 1 & 10 & 0 & 90.9\% \\ \cline{2-6}  & osteoporotic & 1 & 0 & 5 & 83.3\% \\ \cline{2-6}  & global perc. & 60.5\% & 26.3\% & 13.2\% & 94.7\% \\ \hline \multirow{3}{*}{Test} & normal & 2 & 0 & 0 & 100.0\% \\ \cline{2-6}  & osteogenic & 0 & 5 & 0 & 100.0\% \\ \cline{2-6}  & osteoporotic & 0 & 0 & 1 & 100.0\% \\ \cline{2-6}  & global perc. & 25.0\% & 62.5\% & 12.5\% & 100.0\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The accuracy of the single-layer perceptron to predict the clinical condition, in the training and test cohorts. Figure 6: Box plot for the pseudoprobability of the predicted groups. Dots: values beyond 2 SD; *: outliers. Figure 7: Gain function in subsequent training epochs. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Feature** & **T1** & **T2** & **T2 FS** & **Shape** & **\%** \\ \hline CONVENTIONAL\_min & 38.3\% & 36.8\% & 68.2\% & \begin{tabular}{c} SHAPE\_Volume (mL) \\ \end{tabular} & 31.2\% \\ \hline CONVENTIONAL\_mean & 32.9\% & 40.4\% & 29.3\% & \begin{tabular}{c} SHAPE\_Volume (vx) \\ \end{tabular} & 43.7\% \\ \hline CONVENTIONAL\_std & 46.8\% & 27.7\% & 28.6\% & \begin{tabular}{c} SHAPE\_Sphericity \\ \end{tabular} & 31.5\% \\ \hline CONVENTIONAL\_max & 28.0\% & 23.4\% & 43.7\% & \
\begin{tabular}{c} SHAPE\_Surface (mm\({}^{2}\)) \\ \end{tabular} & 52.5\% \\ \hline CONVENTIONAL\_Q1 & 27.9\% & 24.9\% & 40.0\% &
\begin{tabular}{c} SHAPE\_Compacity \\ \end{tabular} & 23.1\% \\ \hline CONVENTIONAL\_Q2 & 35.3\% & 30.9\% & 42.8\% & \\ \hline CONVENTIONAL\_Q3 & 35.9\% & 35.2\% & 31.0\% & \\ \hline CONVENTIONAL\_Skewness & 43.3\% & 65.7\% & 69.5\% & \\ \hline CONVENTIONAL\_Kurtosis & 38.6\% & 58.8\% & 27.2\% & \\ \hline CONVENTIONAL\_ExcessKurtosis & 56.0\% & 52.9\% & 41.2\% & \\ \hline CONVENTIONAL\_peakSphere0.5 mL:discretized & 34.1\% & 26.5\% & 27.1\% & \\ volume sought & & & & \\ \hline CONVENTIONAL\_peakSphere0.5 mL(value only for PET or NM) & 23.8\% & 35.7\% & 54.4\% & \\ \hline CONVENTIONAL\_peakSphere1 mL:discretized & 28.9\% & 16.2\% & 46.8\% & \\ volume sought & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Normalized importance for each feature in the single-layer perceptron. Conditional formatting helps highlight the most important feature on each sequence. The background color of the cells is in a scale from green to red, to highlight the most (green) and least (red) important features.