## 3 Methodology  
The early diagnosis of Alzheimer's disease (AD) can be formulated as a mathematical problem involving the identification of reliable biomarkers and the development of accurate diagnostic models. Let X be the set of potential biomarkers, including neuroimaging data, genetic markers, and biomarker measurements. Let Y be the set of diagnostic outcomes, with Y = \(\{0,1\}\) representing healthy individuals and individuals with AD, respectively. Let D be the dataset consisting of N samples, where each sample \(d_{i}=(x_{i},y_{i})\) represents the biomarker measurements and corresponding diagnostic outcome for the \(i_{th}\) individual. The goal is to learn a mapping function f : X \(\rightarrow\) Y that accurately predicts the diagnostic outcome based on the biomarker measurements. Our proposed architecture includes two steps: the training of individual deep convolutional classifiers and ensembling them. As an end-to-end method, deep learning relies on a large amount of labelled data to obtain features from graphs. Medical data on Alzheimer's disease, in particular, are scarce. In order to meet the requirements of the deep network, we adopt the transfer learning method, which can not only reduce the amount of calculation in the model, but can also greatly improve model performance. The last layer of the fully connected network can be altered and omitted depending on the categorising of our classes, namely, cognitively normal and mild cognitive impairment. Hence, the final fully connected layer for this purpose would have only 2 neuron units instead of 1000 employed in the models for the ILSVRC challenge. The proposed research work model architecture combines features from 8 models.  
Features from all models are retrieved in this case, and the final layers are then modified as necessary. Before adding the final 2 units, dropouts are also added. The final layer computes the classification probability of each output type using the Softmax function:  
\[\sigma\Big{(}\overset{\rightarrow}{z}\Big{)}_{i}=\frac{e^{z_{i}}}{\sum_{j=1}^ {K}e^{z_{j}}}, \tag{1}\]  
where \(\sigma\) corresponds to Softmax function, \(\overset{\rightarrow}{z}\) is the input vector, \(e^{z_{i}}\) and \(e^{z_{j}}\) denote the standard exponential function applied to the input and output vectors, while \(K\) represents the number of classes within the multi-class classifier.  
Consequently, the accuracy of individual models was improved. Secondly, 8 individual architectures after training individually on dementia images and saving the model predictions and ensembling using different weights for each model's predictions are employed. This proposed ensemble of classifiers ensures that each architecture can operate independently.  
By integrating the ensembled learners, it often outperforms a single algorithm by determining the average to obtain a higher accuracy, as it is less sensitive to noise, outliers, or changes in sampling [45]. The majority of the labels predicted by each particular result of feature representation for a subject constitute the expected label. The projected label for a certain subject is the label that indicates the highest likelihood of these findings for the subject if there is a scenario in which a subject cannot be categorised when we combine two results of a single feature representation.