## 5 Results
### Classification Results  
Once the optimization process had ended, it is important to analyze the non-dominated solutions obtained from the Pareto front, observing their complexity and the accuracy obtained (Table 4). The first subject of the Pareto front is the individual who achieves the best accuracy. However, it is also the most complex and contains the most VOIs. This solution has 466 VOIs, taking into account both whole and gray sources (W + C1 sources). As can be seen from Table 4, for Pareto front solutions with a higher number of VOIs, the precision is high (It is above 98%, bearing in mind that it is a measure of accuracy obtained with training data during the first optimization phase), the ratio of the number of VOIs being similar for both gray matter and whole matter. As the number of selected VOIs is smaller, the precision decreases and most of the VOIs selected by MOE are in the volumetric information of the brain belonging to the gray matter. This statement can be corroborated thanks to Figure 11, which shows the Pareto Genome, that is, the selected VOIs of the brain are represented on the x-axis (both for gray matter and for whole matter), and the y-axis represents the precision of the MOE solution with these selected VOIs. For solutions with low complexity, most of the sources are in the gray matter part. Remember that the brain is divided into 12 \(\times\) 12 \(\times\) 12 partitions, with VOIs from 1 to 1728 coming from whole matter and from 1729 to 3456 from gray matter images. Figure 12 shows the complexity (measured as the number of VOIs), together with the error obtained for the classification in the training stage, for all the solution populations of the MOE (zoomed to 700 VOIs solutions). The last generation solutions (filled blue circles) and Pareto front solutions (filled red circles) are also included in the figure. It should be noted that the results presented in Table 4 come from the VOI optimization phase (Figure 1), and therefore, the precision results are related to the training phase. These solutions have been obtained using the MOE algorithm, within which there is an evaluation stage of the solutions selected, using an SVM classifier. This SVM classifier uses 550 training MR images. \begin{table}
\begin{tabular}{c c c c c} \hline
**Pareto Solution** & **Accuracy (\%)** & **Total VOIs** & **W-VOIs** & **C1-VOIs** \\ \hline
1 & 99.73 & 466 & 231 & 235 \\
2 & 99.18 & 265 & 133 & 132 \\
3 & 98.91 & 159 & 73 & 86 \\
4 & 98.09 & 27 & 6 & 21 \\
5 & 97.54 & 26 & 4 & 22 \\
6 & 97.27 & 18 & 6 & 12 \\
7 & 96.18 & 15 & 4 & 11 \\
8 & 95.64 & 11 & 4 & 7 \\
9 & 94.00 & 7 & 0 & 7 \\
10 & 85.55 & 6 & 0 & 6 \\ \hline \end{tabular}
\end{table} 
Table 4: Pareto front for VOI optimization. Training phase. To analyze the robustness of the proposed methodology, it is necessary to carry out the second phase, consisting of performing the classification with test data, using the solutions proposed in the Pareto front. The Pareto front solutions obtained in the first optimization phase (VOI selection) were tested on the test images, where 367 new MRI images are classified with an SVM, the coefficients of the selected VOIs being the input of the classifier. It is relevant to emphasize that the MRIs used during the first phase (optimization phase for VOI selection) are different and independent from the MRIs used in the testing phase. Carrying out the test phase guarantees the solidity and robustness of the results presented by the proposed methodology. Different Pareto front solutions and configurations regarding the selection of the VOIs selected (gray matter, whole matter or both) were tested, showing in Table 5 some of the most relevant results. Figure 11: Pareto front genome, where the VOIs that are most relevant to obtain a high accuracy in the classifier, are highlighted. Figure 12: Evolution of all populations of individuals of the MOE algorithm (including the last generation and the Pareto front).