## 3 Methodology
### Feature Extraction from Both Types of ROIs  
Once the mask is generated from both ROI_CL and ROI_AAL, they are processed further for ROI analysis where each mask fuses with every image of each patient to generate only the important voxels. This voxel is higher in dimensions and is difficult to use as a feature. Consequently, the feature dimensionality is reduced with their intensity values averaged to obtain a mean intensity value. For each participant's MRI, voxels that are within the ROI are averaged to obtain a single representative value. The larger the ROI area, the higher is this value as we have used the weighted mean as in Equation (2), which becomes biased in the highly activated non-binary ROI. Although the ROI selection is a general and typical process, it can be a pivotal factor for obtaining good results. An efficient \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**ADNI Test Condition** & **AAL Region** & **Number of Voxels** & **Mean T** & **SD of T** & **Cluster Number** \\ \hline \multirow{8}{*}{CN \textgreater{} AD (FWE \(p<0.001\))} & Insula\_L & 508 & 3.5646 & 0.333 & 1 \\ \cline{2-5}  & Amygdala\_L & 256 & 7.602 & 0.6846 & 1 \\ \cline{2-5}  & Olfactory\_L & 107 & 4.3285 & 0.9015 & 1 \\ \cline{2-5}  & Amygdala\_R & 329 & 6.5708 & 0.9011 & 2 \\ \cline{2-5}  & ParaHippocampal\_R & 138 & 6.9469 & 0.5042 & 2 \\ \cline{2-5}  & Hippocampus\_R & 60 & 7.6221 & 0.3329 & 2 \\ \cline{2-5}  & Thalamus\_R & 1020 & 5.2492 & 0.6611 & 3 \\ \cline{2-5}  & Thalamus\_L & 981 & 4.4001 & 0.4153 & 3 \\ \cline{2-5}  & Hippocampus\_L & 13 & 6.2737 & 0.3692 & 4 \\ \cline{2-5}  & Temporal\_Inf\_L & 1148 & 4.6223 & 0.6231 & 5 \\ \cline{2-5}  & Fusiform\_L & 490 & 3.9798 & 0.684 & 5 \\ \cline{2-5}  & Temporal\_Inf\_R & 440 & 4.3544 & 0.6455 & 6 \\ \cline{2-5}  & Temporal\_Mid\_R & 238 & 4.7228 & 0.6999 & 6 \\ \hline \multirow{4}{*}{CN \textgreater{} MCI (FWE \(p<0.001\))} & Hippocampus\_L & 53 & 5.5327 & 0.1259 & 1 \\ \cline{2-5}  & Amygdala\_L & 20 & 5.4556 & 0.1059 & 1 \\ \cline{2-5}  & Hippocampus\_R & 25 & 5.4315 & 0.0893 & 2 \\ \cline{2-5}  & Amygdala\_R & 24 & 5.5113 & 0.1407 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Result of ROI analysis for ADNI test condition. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**GARD Test Condition** & **AAL Region** & **Number of Voxels** & **Mean T** & **SD of T** & **Cluster Number** \\ \hline \multirow{8}{*}{NC \textgreater{} AD (FWE \(p<0.001\))} & Hippocampus\_L & 247 & 6.192 & 0.3964 & 1 \\ \cline{2-5}  & ParaHippocampal\_L & 212 & 6.4757 & 0.6251 & 1 \\ \cline{2-5}  & Amygdala\_L & 208 & 6.0849 & 0.2441 & 1 \\ \cline{2-5}  & Fusiform\_L & 103 & 6.4647 & 0.5286 & 1 \\ \cline{2-5}  & Temporal\_Pole\_Sup\_L & 90 & 6.2633 & 0.2723 & 1 \\ \cline{2-5}  & ParaHippocampal\_R & 179 & 6.4194 & 0.4744 & 2 \\ \cline{2-5}  & Hippocampus\_R & 145 & 6.7702 & 0.5669 & 2 \\ \cline{2-5}  & Amygdala\_R & 29 & 5.8039 & 0.0179 & 4 \\ \hline \multirow{4}{*}{NC \textgreater{} MCI (no FWE \(p<0.001\))} & Hippocampus\_L & 82 & 3.5717 & 0.2273 & 1 \\ \cline{2-5}  & Hippocampus\_R & 53 & 3.5466 & 0.2281 & 2 \\ \cline{1-1} \cline{2-5}  & Thalamus\_R & 19 & 3.4174 & 0.1511 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Result of ROI analysis for GARD test condition. SPM extension tool, MARSeille Boite A Region d'Interet (MarsBaR) [35] was used for this feature extraction process:  
\[x^{\prime}=\frac{\sum_{i=1}^{n}x_{i}\times w_{i}}{\sum_{i=1}^{n}w_{i}} \tag{2}\]  
Here, \(x_{i}\) represents the voxel intensity value for n voxels lying inside the ROI and \(w_{i}\) is the weight of the voxel. Here, \(w_{i}\) will have high values representing high confidence for voxels within the ROI, and \(w_{i}\) values are nearly zero representing low confidence in outlier voxels.