## 3 Methods and Materials
### CNN Models with SVM
#### 3.3.1 Extracting Feature Maps  
In recent years, CNN techniques have been applied, which have greatly served humanity in various fields, including medical fields, such as early diagnosis of tumors and various diseases or prediction of the spread of diseases and epidemics before their outbreak. CNN technologies are distinguished from traditional networks by their superior ability to extract feature maps with promising accuracy. CNN models contain many layers interconnected by millions of weights and connections between neurons [32]. CNN models receive the optimized images and pass them to the following layers in which complex computations are performed to perform specific tasks. The most critical layers in which feature maps are extracted are convolutional layers and auxiliary layers that follow some convolutional layers.  
Convolutional layers are essential layers of CNNs, and the mission varies from layer to layer. Its performance varies based on three primary parameters: filter size for each filter convolution layer of a different size, zero-padding (P) to preserve the original image size, and p-step (S) to set the number of move (step) that the filter can move on the image. The filter size is determined, and then according to the filter size f (t), a set of pixels is selected on the image x (t) [33]. The filter moves around the image, and each time a group of image pixels is selected, the method is repeated until all pixels are processed, as in Equation (2). Each convolutional layer has an output as input to the next layer; the output of convolutional layers controls the input image size L \(\times\) W \(\times\) D, P is zero-padding, and p-step is S as in Equation (3).  
\[W(t)=(x*f)\ (t)=\int x(a)f(t-a)\ da \tag{2}\]  
\(W\) (_t_) indicates to output, _x (t)_ indicates to input and _f(t)_ indicates to filter.  
\[O\ (N)=\frac{W-K+2P}{S}+1 \tag{3}\]  
\(O\) (_N_) indicates size of output neuron.  
The pooling layers are for reducing the features of high-dimensional. CNN models produce millions of weights and parameters that require complex calculations, so the pooling layer solves these challenges and facilitates complex calculations. The pooling layers have two types, Average and Max. Each type has a specific method for reducing high dimensions [34]. The average-pooling selects a group of image pixels the same as the filter size, then calculates average values and replaces all selected values by average calculated as shown in Equation (4). The Max pooling layers select a group of image pixels the same as the filter size, take the Max value, and replace all selected values by it as in Equation (5).  
\[z(i;\ j)=\frac{1}{k^{2}}\sum_{m,n=1...k}f[(i-1)p+m;\ (\ j-1)p+n] \tag{4}\]\[z(i;\ j)=max_{m,n=1...k}f[(i-1)p+m;\ (\ j-1)p+n] \tag{5}\]  
where \(m\), \(n\) means the site in the matrix, \(p\) denotes the step, \(f\) means the filter size and \(k\) denotes the matrix size.  
In this section, feature maps of WSIs of LBC slice samples of abnormal cells in the cervical are extracted using VGG-16 [35] and GoogLeNet [36] models. The CNN produce high-dimensional feature maps, so the PCA was used to reduce the high-dimensional features and select the most important representative features for each class of abnormal cell of cervical.