# Sports Risk Prediction Model Based on Automatic Encoder and Convolutional Neural Network
## 2 Overview of Relevant Theories
### Introduction to Relevant Algorithms and Technologies
#### 2.2.4 Convolution Neural Network  
A convolutional neural network (CNN) is a kind of neural network specialized for multidimensional data processing such as images and videos that can automatically perform feature extraction and feature learning, avoiding the tedious process of manual feature extraction and improving feature representation [19]. Moreover, the convolutional and pooling layers in convolutional neural networks use parameter sharing and local connectivity, which reduces the number of parameters, reduces the risk of overfitting, and improves the generalization ability of the model. At the same time, due to the advantages of parameter sharing and local connectivity of convolutional neural networks, the network is much less computationally intensive, faster in operation, and capable of handling large-scale image data [20]. Specifically, the convolutional neural network structure consists of the following layers:  
1. Input layer The input layer accepts image data, which is usually a three-dimensional matrix, i.e., width, height, and number of channels, usually three for RGB and one for grayscale images [21].
2. Convolutional layer The convolutional layer is the core part of the CNN, which uses filters to perform convolutional operations on the input image in order to extract features. A filter can be understood as a small, learnable set of weight matrices that are used to extract image regions with specific features from the input image. Convolutional layers are characterized by parameter sharing and local connectivity, which can significantly reduce the number of parameters in the network and increase the learning efficiency and generalization ability. In convolutional neural networks, the two-dimensional convolution formula is defined as shown below: \[S(i,j)=(X\times W)(i,j)=\sum_{m}\sum_{n}x(i+m,j+n)w(m,n)\] (5) where \(X\) is the input, \(W\) is the convolution kernel, also known as the filter, whose size is \(m\times n\), and has weight. The convolution process can be understood as follows: the filter slides on the input matrix with a specific step size, its weight and the input matrix are multiplied and summed at the corresponding position, and finally the output is obtained.
3. Pooling layer The pooling layer is used to reduce the size of the output feature map of the convolutional layer, thus reducing the number of parameters and improving the generalization ability of the model. Commonly used pooling methods include maximum pooling and average pooling, which involve performing aggregation operations on local regions of the feature map to eventually obtain a feature map of smaller size [22]. The parameters of the pooling layer usually include zero padding, the size and step size of the convolution kernel, etc.
4. Fully connected layer The fully connected layer is a standard neural network structure that is usually used for the classification or regression prediction of features from the preceding convolutional and pooling layers. In the fully connected layer, each neuron is connected to all the neurons in the previous layer, so the number of fully connected layer parameters is large and prone to overfitting.
5. Activation function layer The activation function layer is used to introduce nonlinear factors to enable the model to learn more complex features. The commonly used activation functions include the sigmoid function, ReLU function, leaky ReLU function, etc.