# A Practical Multiclass Classification Network for the Diagnosis of Alzheimer's Disease
## 3 The Proposed Methodology
### The Proposed Practical Multiclass Classification Network for Alzheimer's Disease  
In this section, we explain the framework of the practical multiclass classification network to classify various stages of Alzheimer's disease based on the MRI data. A comprehensive pre-processing pipeline was designed to extract the 2D images from the 3D MRI volumes for the proposed network to detect AD at the earliest possible stage (pre-dementia). Because of the complexity of the pattern, it is difficult to discriminate between the patterns with quantitative analysis and even radiological scans at the early stages of AD. To detect changes in the biomarkers, the pre-processed data (i.e., 2D slices extracted from the MRI volumes) were fed to the network. The network learned to classify changes in the information to distinguish EMCI, LMCI, NC, and AD. The proposed learning-based framework limits the complexities of diagnosing and monitoring disease at an early stage. Figure 3: Overview of the capturing process. (**a**) The scans, (**b**) pre-processed 3D images of axial, sagittal, and coronal views, and (**c**) processed axial, sagittal, and coronal views. Convolutional layers extract the features and initialize the process in deep learning-based frameworks. The images in the data were multiplied with the convolutional kernel following the window. The formula for the height and width of the convolution output after the convolution filter is expressed below. \[C_{o}=\frac{I_{h}-R_{h}+2P}{S}+1 \tag{1}\]  
\[C_{o}=\frac{I_{w}-R_{w}+2P}{S}+1 \tag{2}\]  
where \(I_{h}\), and \(I_{w}\), show the image height and width, with \(R_{h}\) and \(R_{h}\) representing the kernel height and width along with filter size with the padding \(P\) and stride \(S\). The proposed convolutional neural network takes the pre-processed data with a size of 224, beside a kernel size of 3, stride of 1, and padding of 1. After that, we applied batch normalization to normalize the data. To bring non-linearity, a rectified linear unit (ReLU) was applied, and next to it, a max-pooling was applied with a kernel size of 2 to adjust the output shape. It reduced the height and width of the convolutional output following a factor of 2. The shape of the convolutional layer output was next adjusted with a stack of convolutional layers and a ReLU layer (\(3\times 3\), Conv+ReLU). Finally, a fully connected layer was applied with the input features following the convolutional layer output. It resulted in the general output features following the output class. This output, when fed to the fully connected layer, reshaped the desired matrix, providing the final output. The output classes in PMCAD-Net were 4 when we utilized the Adam optimizer and backpropagation in the proposed framework. The learning rate was 0.0001 for 100 epochs in the presence of categorical cross-entropy loss. It is critical to improve the model's performance in terms of accuracy. The performance and accuracy of the model are improved by the loss function, which also depicts the model's deviation from the correct predictions. In general practice, logistic regression following linear classification algorithms and convolutional neural networks are utilized for classification problems. These tasks involve the prediction of one or more input variables with class labels for the classification models. Where binary class classification has only two labels, multiclass classification has more than two labels. Thus, the loss function also varies from binary class to multiclass problems. The proposed PMCAD-Net can predict more than two class labels for a given pre-processed ADNI data sample. Thus, we utilized the categorical cross-entropy loss function for the available classes, including NC, EMCI, LMCI, and AD. The cross-entropy for this data can be categorically described by assigning the probability values as variables.