## 4 Quantitative Methods for the Detection of AD
### Neural Networks
CNNs also use non-linearities between layers to model non-linear relations within the data. CNNs may also contain one or more fully connected layers that are usually found at the end of the network architecture. The input to these layers is the flattened feature maps computed from the final convolutional/pooling layer. A loss function is used in conjunction with these final layers to compute any errors that exist between the network's prediction and the ground-truth label (in the case of supervised learning) [136]. These errors are interpretable as losses that are to be minimized in the network's training (learning) phase. The softmax function is, again, a very popular choice of loss function. Figure 7 gives a representation of a simple CNN architecture containing convolutional, pooling, and fully connected layers. In contrast to a network's hyperparameters, which are set by the user, the learnable parameters are those that are modified in response to the error computed at the loss layer, often as the difference between the network prediction and a known label. The loss is minimized by use of gradient descent [136; 137; 139]. CNNs are, however, not the only type of deep neural network, but rather the most well-known, especially in the neuroimaging research community. The recurrent neural network (RNN) model inputs vary over time or even space and are rapidly becoming more common in neuroimaging literature [140]. Generative adversarial networks (GANs) are a type of generative model that learns the distribution of training images and has been utilized for PET-based AD image classification [141]. The common theme in GANs and RNNs is using convolutional operations upon an input image and backpropagation by gradient descent to learn filter weights, reduce the dimensionality of an image, often with the point of producing a classification label [139; 140]. CNNs have been widely applied for the detection and diagnosis of AD from neuroimaging studies. [PERSON] et al., used an ensemble of RNNs to classify AD vs. HC subjects with 91.2% accuracy, 91.4% sensitivity, 91% specificity, and AUC = 0.953 using FDG-PET images. The same were also able to differentiate MCI from HC patients with an accuracy of 78.9%, a sensitivity of 78.1%, a specificity of 80%, and an AUC of 0.839 [142]. [PERSON] et al., compared the performance of voxel-wise linear regression (GLM) and a CNN in modeling spatial dependencies between tau-PET and amyloid burden throughout the brain. They  
Figure 7: Visualization of convolutional neural network architecture specifically designed for classification based on image data. A series of 16@128 \(\times\) 128 images are input to the network. These frames are passed through a max pooling layer and a convolutional layer before being flattened into a 1D vector. Two fully connected layers of size 256 and 128 connect to a final node containing the network output. discovered that the CNN outperformed the GLM in predicting amyloid centiloid values and found previously unknown associations between tau topography and overall amyloid burden [143]. [PERSON] et al., created a network based on the Inception v3 architecture, which differentiated between AD, MCI, and non-AD/non-MCI FDG-PET images with AUCs of 0.92, 0.63, and 0.73, respectively [144]. Most importantly, this network significantly outperformed radiology readers in identifying AD and MCI subjects from FDG-PET images. [PERSON] et al., were able to develop a graph convolutional network that differentiated between AD and HC subjects with 93% accuracy and between AD, MCI, and HC groups with 77% accuracy [145]. [PERSON] and [PERSON] reported 96% in AD vs. HC classification and 84.2% in differentiating pMCI vs. sMCI by using vanilla 3D CNN architecture [146]. [PERSON] et al., used a residual neural network on FDG-PET data to differentiate between AD and HC with an accuracy of 93.5% and an AUC of 0.976. They were also able to differentiate between pMCI vs. sMCI patients with 74.7% accuracy and AUC = 0.811 [147].