## 5 Results
### Classification Results
As it was described in the first optimization phase, due to the high number of coefficients, PCA is used to keep around 95% of the features variance, significantly reducing the final dimension of the number of input features to the SVM classifier. The confusion matrices of the different configurations analyzed for the first and third Pareto front solutions are presented in Figure 13 (for W, C1 and W+C1 sources used for VOIs selection). The results obtained using an independent cohort of MRI subjects for the testing phase have yielded promising results, taking into account that the problem is complex because it has five different classes, with an imbalance between them. For the first Pareto Front solution using both whole matter and gray matter, the accuracy obtained in the confusion table is 97%, requiring 466 VOIs. Analyzing the third Pareto solution, focusing on the gray matter, using 86 VOIs reaches 95.9 % precision. Note that the brain regions used in whole matter may be different from those used in gray matter. Table 6 shows the locations of the 73 and 86 VOIs selected by the third solution of Pareto Front, for whole and gray matter, respectively. Graphically, Figures 14 and 15 show the location in three-dimensional space of these VOIs in the brain. In the left part of the figures, the spatial location of the selected VOIs is shown. On the right side, and in order to facilitate its location in slices, three slices of the brain and the location of the VOIs are presented. It is relevant to make a comparison of the PD disease classification results presented in the bibliography, with those obtained in the present methodology (although it should be noted that the number of classes in this paper is higher than those commonly presented in publications). Table 7 presents a summary of relevant contributions that, based on MRI images, have used machine learning and artificial intelligent techniques for the automatic classification of PD. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Solution (PF)** & **Source** & **\#VOIs** & **\#Features** & **\#PCA** & **Accuracy** & **Conf.Matrix** \\ \hline \multirow{3}{*}{1} & W & 231 & 6930 & 511 & 70.8 & Figure 13a \\  & C1 & 235 & 7050 & 464 & 96.2 & Figure 13c \\  & W+C1 & 466 & 13,980 & 535 & 97.0 & \\ \hline \multirow{3}{*}{2} & W & 133 & 3990 & 419 & 63.8 & \\  & C1 & 132 & 3960 & 416 & 95.9 & \\  & W+C1 & 265 & 7950 & 498 & 96.2 & \\ \hline \multirow{3}{*}{3} & W & 73 & 2190 & 339 & 60.8 & Figure 13b \\  & C1 & 86 & 2580 & 380 & 95.9 & Figure 13d \\  & W+C1 & 159 & 4770 & 448 & 96 & \\ \hline \multirow{3}{*}{4} & W & 6 & 180 & 32 & 48.0 & \\  & C1 & 21 & 630 & 224 & 93.7 & \\  & WC1 & 27 & 810 & 232 & 93.5 & \\ \hline \multirow{3}{*}{5} & W & 4 & 120 & 37 & 49.86 & \\  & C1 & 22 & 660 & 221 & 92.9 & \\  & WC1 & 26 & 780 & 230 & 93.18 & \\ \hline \multirow{3}{*}{7} & W & 4 & 120 & 3 & 49.0 & \\  & C1 & 11 & 330 & 136 & 88.8 & \\ \cline{1-1}  & WC1 & 15 & 450 & 138 & 90.5 & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Test results for several solutions of the Pareto front. Details of the number of VOIs, number of features and components of the PCA for W,C1 and W+C1 sources. Figure 14: Selected brain regions from the third Pareto solution (whole matter source, W). Figure 13: Confusion matrices obtained in the testing phase, for the first (**left**) and third (**right**) solution of the Pareto Front, using W and C1 sources.