## 2 Methodologies
### Feature Extraction Process
#### 2.3.1 Convolutional Neural Network Layer  
Convolutional neural networks (CNNs) have been widely used in both computer vision and natural language processing fields and have become a mature feature extractor. Compared with recurrent neural networks, the sliding window operation of CNNs is order-independent, and different convolutional kernels have no influence on each other, thus exhibiting very high parallel freedom. In addition, by controlling the number of convolutional kernels, it is possible to achieve channel size scaling, thereby achieving the goal of scaling feature dimensions. To take advantage of these benefits of CNNs, we introduce a layered structure based on CNNs in the feature extraction module, mapping the original text features to different feature spaces and reducing the dimensionality of word vectors to reduce the number of parameters and computation at each layer.  
The introduction of text convolution also allows the model to better utilize the positional information of the sequence. The feature vectors output by the convolutional layer contain positional information (depending on the convolution order of the kernels). Unlike traditional convolutional structures, we do not include a Max Pooling layer after the convolutional layer (which only retains the maximum value in the feature extraction), as Max Pooling would lead to the loss of crucial positional encoding information in the feature representation. This way, our model can better capture the local features of the text, thereby improving its performance.  
In our model, the role of the convolutional layer is to perform convolutional operations on the word embedding matrix to extract corresponding local features. The process of CNN extracting local features is illustrated in Figure 3. In the model implementation, we use multiple convolutional kernels of different sizes to extract n-gram features of different lengths. By setting different kernel sizes, we can capture word combinations of different lengths and obtain richer local feature information which helps to increase the model's robustness and generalization ability. At the same time, the output dimension of the convolutional layer is reduced by adjusting the number of convolutional kernels. The specific calculation process of a CNN is as follows. For each parallel convolutional layer, we perform n-gram convolution between the input sentence word embedding matrix \(E\in\mathbb{R}^{n\times d}\) (\(n\) is the sentence length, \(d\) is the word embedding dimension) and different-sized convolutional kernels \(C=[c_{1},c_{2},\dots,c_{d/l}]\), generating local feature outputs of different layers, where \(c_{i}\in\mathbb{R}^{k\times d}\) (\(k\) is the kernel size, \(l\) is the parallel layer number). The computation process of the feature map matrix \(M_{l}\in\mathbb{R}^{n\times(d/l)}\) can be referred to as Equation (2):  
\[M_{l}=E\varocc, \tag{2}\]  
where represents the convolution operation of \(c_{i}\) on \(E\). Specifically, the calculation of values in the feature map is shown in Equation (3):  
\[m_{i}=f(c_{i}*E+b), \tag{3}\]  
where \(f\) is the nonlinear activation function of the convolution layer and \(b\) is the bias term.  
The convolution operation maps the original text sequence from the word space to a semantic feature space with higher information content. In this way, we can obtain the output matrices of the convolution layers, i.e., \([M_{1},M_{2},\ldots,M_{l}]\). These output matrices contain various local features in the input sequence, such as word combinations, phrases, and sentence structures. Through these features, we can better capture the semantic information of the text, thereby improving the performance of text classification tasks.