# Explainable MRI-Based Ensemble Learnable Architecture for Alzheimer's Disease Detection
## 4 Results and Discussion
### Performance Analysis Using the Confusion Matrix
#### 4.1.1 Analysis of misclassifications and hard voting performance  
In reference to Table 3, several critical observations warrant discussion regarding the classification performance metrics of the evaluated deep learning architectures. The ViT architecture demonstrates superior performance with remarkably low misclassification rates (0.17-0.65%) across all diagnostic transition boundaries, suggesting enhanced feature representation capabilities for neurological status differentiation. A substantial performance gradient is evident between the highest-performing models (ViT, CNN) and the remaining architectures. Specifically, the error rates increase by approximately 3-fold from CNN_model3 (1.52-1.59%) to the next-tier models DenseNet3 and MobileNet3 (4.18-5.62%), suggesting significant differences in their ability to capture relevant diagnostic features. The ResNet implementation exhibits notable asymmetry in its error distribution pattern, with acceptable performance at the cognitively normal to mild cognitive impairment (CN-MCI) boundary (6.92%), but significantly compromised classification at the MCI to Alzheimer's disease (MCI-AD) boundary (22.70%). This suggests differential sensitivity to feature characteristics across the cognitive decline spectrum. The EfficientNet implementation demonstrates concerning performance metrics with 50% error rates universally, indicating potential implementation issues or sub-optimal hyperparameter selection. Further investigation into training protocols and architectural modifications is warranted. Importantly, the symmetrical distribution of false positive and false negative rates within each model at specific diagnostic boundaries suggests appropriately calibrated classification thresholds, a critical factor for potential clinical deployment considerations. The hard voting ensemble (0.967 accuracy) effectively mitigated these misclassifications across all categories, as demonstrated in the confusion matrix (Figure 6). For the CN class, hard voting achieved 97.9% accuracy, with 16 instances misclassified as MCI and 2 as AD. In the MCI class, the accuracy reached 98.7%, with 7 samples misclassified as CN and 5 as AD. The AD class showed a slightly lower accuracy of 93.9%, where 11 cases were misclassified as CN and 15 as MCI. Despite including lower-performing models, hard voting neutralized extreme misclassification patterns by leveraging complementary strengths of different architectures, while not achieving the highest absolute accuracy (Figure 7), this approach provided more balanced and clinically reliable classification, substantially reducing systematic misclassification risks. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Model** & **CN\(\rightarrow\)MCI (FP)** & **MCI\(\rightarrow\)AD (FP)** & **MCI\(\rightarrow\)CN (FN)** & **AD\(\rightarrow\)MCI (FN)** \\ \hline ViT3 & 0.17\% & 0.65\% & 0.17\% & 0.65\% \\ CNN\_model3 & 1.52\% & 1.59\% & 1.52\% & 1.59\% \\ DenseNet3 & 5.25\% & 4.69\% & 5.25\% & 4.69\% \\ MobileNet3 & 5.62\% & 4.18\% & 5.62\% & 4.18\% \\ VGG19\_3 & 7.84\% & 8.08\% & 7.84\% & 8.08\% \\ ResNet3 & 6.92\% & 22.70\% & 6.92\% & 22.70\% \\ EfficientNet3 & 50.00\% & 50.00\% & 50.00\% & 50.00\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: False positive and false negative rates by model. 4.1.2. Analysis of misclassifications and stacking performance  
Table 4 provides a comprehensive overview of all misclassification patterns. The most frequent error type is misclassifying class 2 (severe abnormalities) as class 0 (normal), which accounts for 44.44% of all errors. This represents the highest clinical risk as it could lead to missed diagnoses of severe conditions. ResNet demonstrated superior performance on these critical errors with 75% accuracy, while most other models struggled. The table categorizes each error by type and indicates its clinical impact. Table 5 breaks down how each individual model performed across different error categories.