## 2 Research Methodology
### CNN Model  
Convolutional Neural Networks (CNNs) are deep learning models that excel at image recognition and pattern recognition. Basically, it has the ability to detect and extract local patterns from grid-like data, such as images. It is used in various fields such as image processing, computer vision, and natural language processing. The basic structures of CNN models include convolutions, pooling, activation functions, and fully connected layers [11].  
The role of convolution here is to extract local features by applying a filter (kernel) to the input data. Filters perform multiplication operations while sliding the input data through a small window. This allows for the recognition of regional features in the input data. Equation (1) represents the computation of one element of the output feature map.  
\[F(i,j)=(W\cdot X)(i,j)=\sum(W(k,l)\cdot X(i+k,j+l)) \tag{1}\]here, \(F(i,j)\) denotes the value at position \((i,j)\) of the output feature map. \(W\) is the weight matrix of the filter (kernel), \(X\) is the input data matrix, and \(k\), \(l\) are the filter indices. The role of pooling is to reduce the size of the extracted feature maps and preserve important information. In general, max pooling is the most common, and the largest value in a given area is selected and used as a representative value. Pooling can reduce the size of the space and the amount of computation. Here, Equation (2) is used in max pooling.  
\[Y(i,j)=max(X(2i,2j),X(2i,2j+1),X(2i+1,2j),X(2i+1,2j+1)) \tag{2}\]  
in this context, \(Y(i,j)\) represents the pooling result at position \((i,j)\), and \(X\) refers to the pixel at positions \(2i\), \(2j\) in the input data matrix. An activation function is used after the convolution and pooling operations to introduce nonlinearity. Typically, the Rectified Linear Unit (ReLU) function is used, which converts negative values to 0 and leaves positive values unchanged. This allows the model to learn nonlinear patterns.  
Therefore, the activation function, usually ReLU, is used as shown in Equation (3).  
\[\text{ReLU}(x)=max(0,x) \tag{3}\]  
The fully connected layer (FCL)takes the feature maps that have undergone convolution and pooling and flattens them into a one-dimensional vector. This vector is then fed into the fully connected layer to perform the final prediction. The fully connected layer is a layer where all neurons between the input and output are connected, enabling predictions for various class labels. The following Equation (4) represents the formula for the FCL, which calculates the values of the output neurons.  
\[Z=W\cdot X+b \tag{4}\]  
here, \(Z\) represents the value of the output neuron, \(W\) denotes the weight matrix, \(X\) represents the input vector, and \(b\) is the bias vector. The structure of a CNN consists of alternating convolutional layers and pooling layers. This configuration allows the network to learn abstract features at different levels. Typically, a fully connected layer is added at the end to perform the final prediction. The CNN learns and optimizes the weights of the filters through training, using the backpropagation algorithm to propagate errors and update the weights.