## 3 Results
### Model Selection
#### 3.2.2 Clustering  
See Table 7 for a summary of cluster model performance. A single cluster yielded the most optimal model of one PGs: intra-PTV dose falloff. Therefore, a single value was defined for all patient for this PG and feature datasets were not essential in generation of the predicted weight. Silhouette and SSE values suggest clusters had high degrees of dispersion within clusters and/or low variance between clusters. However, comparable to regression, validation MSE values were overall more desirable. PCA feature types were selected for 3 out of 6 PG.  
\begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Planning** & **Regression** & \multicolumn{2}{c}{**Features**} & \multicolumn{2}{c}{**Training**} & **Validation** \\
**Goal** & **Equation** & & & **Av adj R\({}^{2}\)** & **MSE** & **MSE** \\ \hline \multirow{2}{*}{\begin{tabular}{l} Rectum D\({}_{\text{mean}}\) \\ \end{tabular} } & 3 features & Volume of the external (cm\({}^{3}\)) & 0.835 & 368 & 7025 \\  & quadratic & \begin{tabular}{l} Rectum VI\({}_{\text{PTV48}}\) (cm\({}^{3}\)) \\ Slope between OV\({}_{\text{rectum,PTV48}}\) and OV\({}_{\text{rectum,PTV48}}\) \\ \end{tabular} & & & & \\ \hline \multirow{2}{*}{\begin{tabular}{l} Bladder \\ D\({}_{\text{mean}}\) \\ \end{tabular} } & 5 features & Volume of the rectum (cm\({}^{3}\)) & 0.858 & 24.5 & 271 \\  & linear & \begin{tabular}{l} OV\({}_{\text{rectum,PTV48}}\) (cm\({}^{3}\)) \\ Total OAR VIFPTV60 (cm\({}^{3}\)) \\ Distance from centre of PTV48 to the centre of rectum (cm) \\ Ratio between PTV48 and rectum volume \\ \end{tabular} & & & & \\ \hline \multirow{2}{*}{\begin{tabular}{l} PTV \\ Conformality linear \\ \end{tabular} } & 5 features & Volume of the PTV48 (cm\({}^{3}\)) & 0.907 & 1441 & 19,442 \\  & \begin{tabular}{l} Distance from centre of PTV48 to the centre of rectum (cm) \\ Slope between OV\({}_{\text{rectum,PTV48}}\) and OV\({}_{\text{rectum,PTV48}}\) \\ Ratio between bladder and rectum volume \\ Ratio between PTV48 and bladder volume \\ \end{tabular} & & & & \\ \hline \multirow{2}{*}{\begin{tabular}{l} Rectum D\({}_{\text{max}}\) \\ \end{tabular} } & 4 features & Volume of the rectum (cm\({}^{3}\)) & 0.997 & 0.125 & 5.82 \\  & quadratic & Distance from centre of PTV48 to the centre of PTV60 (cm) & & & \\  & Ratio between bladder and rectum volume \\ \hline \multirow{2}{*}{\begin{tabular}{l} PTV Dose \\ Falloff \\ \end{tabular} } & 4 features & Volume of the PTV48 (cm\({}^{3}\)) & 0.998 & 2.62 & 495 \\  & quadratic & \begin{tabular}{l} Rectum VIFPTV48 (cm\({}^{3}\)) \\ Distance from centre of bladder to the centre of rectum (cm) \\ Distance from centre of PTV48 to the centre of rectum (cm) \\ \end{tabular} & & & & \\ \hline \multirow{2}{*}{\
\begin{tabular}{l} Bladder \\ D\({}_{\text{max}}\) \\ \end{tabular} } & 4 features & OV\({}_{\text{rectum,PTV60}}\) (cm\({}^{3}\)) & 0.999 & 0.309 & 69.3 \\  & quadratic &
\begin{tabular}{l} Total OAR VIFPTV48 (cm\({}^{3}\)) \\ Distance from centre of bladder to the centre of rectum (cm) \\ Slope between OV\({}_{\text{bladder,PTV48}}\) \\ \end{tabular} & & & & \\ \hline \end{tabular}
\end{table}
Table 6: Summary of PGAP-ML\({}_{\text{reg}}\) model formations defined during the automated leave-one out process.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Planning** & **Number** & **Feature** & **SSE** & **Silhouette** & **MSE** & **Validation** \\
**Goal** & **of Clusters** & **Type** & **Average** & **MSE** & **MSE** \\ \hline \multirow{2}{*}{
\begin{tabular}{l} Rectum D\({}_{\text{mean}}\) \\ Bladder D\({}_{\text{mean}}\) \\ PTV Conformality \\ \end{tabular} } & 2 & Raw & 416 & 0.173 & 698 & 1273 \\  & 11 & Raw & 123 & 0.058 & 9.89 & 298 \\  & 9 & PCA & 562 & 0.162 & 2320 & 4037 \\  & 7 & PCA & 802 & 0.182 & 0.592 & 6.42 \\  & 1 & n/a & 540 & n/a & 10.8 & 133 \\  & 12 & PCA & 416 & 0.128 & 0.791 & 37.9 \\ \hline \hline \end{tabular}
\end{table}
Table 7: A summary of final PGAP-ML\({}_{\text{clus}}\) models defined using the training dataset.