# A Study of Breast Cancer Classification Algorithms by Fusing Machine Learning and Deep Learning
## 2 Related Work
### Deep Learning  
The convolutional neural network is a deep learning method and an important branch of machine learning algorithms. Like a multilayer perceptron of artificial neural networks, it is commonly used to analyze visual images. Convolutional neural networks have long been one of the core algorithms in the field of image recognition and have a consistent performance when learning large amounts of data. The most important features of this network model are self-learning, self-organization, and self-adaptability. For general large-scale image classification problems, convolutional neural networks can be used to build hierarchical classifiers and can also be used in fine classification recognition to extract discriminative features of images for other classifiers. Composed mainly of a convolutional layer and a subsampling layer, convolutional neural networks extract data features for classification by convolution. Specifically, it includes input layer, convolutional layer, pooling layer, nonlinear layer, fully connected layer, classification output layer, etc. Figure 2 below shows the schematic diagram of a convolutional neural network. As shown in Figure 2, in the convolutional layer of a convolutional neural network model, the input data matrix is first convolved by multiple updatable convolutional kernels, and then undergoes a nonlinear transformation by the activation function, and finally a feature layer is formed. To reduce gradient descent, the activation function of the convolutional neural network model often adopts the ReLu function. After the convolution layer,  
Figure 1: Random forest algorithm mechanism. Figure 2: Convolutional neural network model diagram. each output feature map is linked to the original image of the previous input layer by a convolution operation. The convolution process of the convolution layer is as follows. \[\mathrm{x}_{j}^{l}=f\left(\sum_{i\in M_{j}}x_{i}^{l-1}k_{ij}^{l}+b^{l}\right) \tag{1}\]  
where \(l\) is the number of layers of the neural network, \(k\) is the convolutional kernel of the network, \(Mj\) is the features of the input data, and \(b\) is the bias corresponding to the features of each output. The role of the pooling layer in a convolutional neural network is to sample the feature images and obtain their subgraphs. Therefore, it is also referred to as the subsampling layer. If there are \(m\) input feature maps after the convolution operation, the number of feature maps remains the same after sampling, which is still \(m\), but the size of the output feature map becomes smaller. The pooling layer is calculated as follows:  
\[\mathrm{x}_{j}^{1}=f\left(a_{j}^{l}\mathrm{down}\left(x_{j}^{l-1}\right)+b_{j }^{l}\right) \tag{2}\]  
where down (\(\cdot\)) is the down-sampling function, which is mainly used to find the maximum or average number in the region for a feature matrix of input size \(n\)\(\times\)\(n\). It is called maximum pooling or average pooling. From the input size, the output feature size is \(ln\) of the input data size. \(A\) and \(b\) in Equation (2) are the biases of the output features. The fully connected and output layers are consistent with the basic neural network structure and the role of the fully connected layer is to expand the feature images sequentially and input the feature information to the neurons. The learning algorithm of the neural network is used to continuously improve the parameters to achieve the best output. In this paper, we mainly adopt a convolutional neural network in data processing and attempt to improve the accuracy of breast cancer classification while optimizing the classification results by improving the classification model. Currently, automatic breast cancer classification recognition includes both traditional image recognition with manual feature extraction and deep learning-based recognition. Deep learning can automatically extract image features and exclude the human factors in the traditional recognition methods.