# Computer-Aided Diagnosis of Alzheimer's Disease via Deep Learning Models and Radiomics Method
## 4 Convolution Neural Network Assisting Diagnose
### Construction of Convolution Neural Network
#### 4.1.1 Convolution Neural Network Structure  
The first convolutional neural network designed in this paper was based on the classical convolutional neural network model LeNet-5 [18]. This CNN model had 10 layers, and Figure 13 shows the CNN model structure.  
The first layer is the input layer. The input image is divided into three stages. Each stage consists the convolution layer and the down-sampling layer. The convolution kernel is \(9*9\), and the down-sampling layer is sampled by \(2*2\) region. Each stage has the same structure and relative operation. The first stage output is six pieces of \(60*60\) feature graphs. The second stage output is 12 pieces of \(26*26\) feature graphs. The third stage finally forms 18 pieces of \(9*9\) feature graphs after down-sampling, and each of graphs has a corresponding bias term. The eighth layer is a convolution layer, which contains 120 feature graphs. Each element in the feature graph relates to the feature graph of the previous layer. After \(9*9\) convolution kernel operation, the size of the feature graph in  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **SE** & **TE** & **MG** & **MI** & **CERF** & **PSNR** \\ \hline Traditional Wavelet Fusion & 6.7249 & 4.8320 & 2.8021 & 0.3543 & 1.3224 & 26.5542 \\ Improved Wavelet Fusion & 8.3019 & 4.9741 & 3.4290 & 0.3117 & 1.2041 & 32.0910 \\ \(p\)-value & \textless{}0.001 & 0.011 & \textless{}0.001 & 0.005 & \textless{}0.001 & 0.017 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Objective evaluation results of fusion algorithm.  
Figure 12: Network training diagram.  
Figure 13: Convolution neural network mode.  
this layer is \(1*1\), which constitutes the full connection between the fifth and sixth layers. The ninth full connected layer contains 84 neurons.  
The final output layer consists of the Euclidean Radial Basis Function (RBF) unit, and each represents a category. In this project [PERSON]'s disease diagnosis is a two-classification problem that is ill or not, so the output layer has two units.  
Before CNN training, parameter initialization is needed. Parameter initialization is very important in the gradient descent algorithm. If the error surface is relatively flat, it will lead to a very slow convergence rate. In general, more initialization weights are distributed as follows:  
\[W\sim U\Bigg{[}-\frac{\sqrt{6}}{\sqrt{P^{(l)}+P^{(l-1)}}}\frac{\sqrt{6}}{\sqrt {P^{(l)}+P^{(l-1)}}}\Bigg{]} \tag{14}\]  
This is the representation of Xavier initialization, where \(P^{(l)}\) means the number of pixels in layer \(l\), and each parameter will have the value from the interval specified by \(U\).  
CNN model training uses the back propagation (BP) algorithm. The main content of the algorithm is divided into forward propagation and back propagation. First, the training data is input into the CNN-10 model, and then the gradient of the weight and bias and inverse calculation error is calculated by the convolution filtering, the down sampling and the activation function, and the weight and bias are updated.