## 3 Methodology
### Applied Machine Learning and Deep Learning Methods for Comparison  
To evaluate the performance of our proposed DCNN model, we applied three widely used ML models--LR, RF, and GBDT--as well as several well-known DL models--VGGNet, ResNet, and EfficientNet--and compared their performance with our proposed prediction model. In the experiment, the representative VGG16, VGG19, ResNet50, ResNet101, and EfficientNetB0 were used. All applied ML and DL algorithms are introduced briefly in the following. \begin{table}
\begin{tabular}{c c} \hline \hline
**Layer** & **Detailed Parameters** \\ \hline Input layer & Size (224 \(\times\) 224) \\ C1 & 16 3 \(\times\) 3 2D convolutional layer (Relu) \\ C2 & 16 3 \(\times\) 3 2D convolutional layer (Relu) \\ P1 & Max pooling layer 2 \(\times\) 2 \\ C3 & 32 3 \(\times\) 3 2D convolutional layer (Relu) \\ C4 & 32 3 \(\times\) 3 2D convolutional layer (Relu) \\ P2 & Max pooling layer 2 \(\times\) 2 \\ C5 & 64 3 \(\times\) 3 2D convolutional layer (Relu) \\ C6 & 64 3 \(\times\) 3 2D convolutional layer (Relu) \\ P3 & Max pooling layer 2 \(\times\) 2 \\ C7 & 128 3 \(\times\) 3 2D convolutional layer (Relu) \\ C8 & 128 3 \(\times\) 3 2D convolutional layer (Relu) \\ P4 & Max pooling layer 2 \(\times\) 2 \\ C9 & 256 3 \(\times\) 3 2D convolutional layer (Relu) \\ C10 & 256 3 \(\times\) 3 2D convolutional layer (Relu) \\ P5 & Max pooling layer 2 \(\times\) 2 \\ C11 & 512 3 \(\times\) 3 2D convolutional layer (Relu) \\ C12 & 512 3 \(\times\) 3 2D convolutional layer (Relu) \\ P6 & Max pooling layer 2 \(\times\) 2 \\ \multicolumn{2}{c}{Flatten} \\ \multicolumn{2}{c}{FC1} & Fully connected layer 512 (Relu) \\ Dropout layer & Dropout (rate = 0.5) \\ FC2 & Fully connected layer 512 (Relu) \\ Output layer & Output layer 8 (Softmax) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The configuration parameters of the proposed DCNN-based prediction model. Figure 3: The architecture of the proposed DCNN-based prediction model for wafer map failure recognition. Note: C denotes the convolutional layer, P the pooling layer, and FC the fully connected layer. LR [19] is a popularly used statistical model in ML, and uses a logistic function to compress the output of linear equations in the classification problem to values between 0 and 1. The logistic function is used to describe the probabilities of possible outcomes. RF [20] is an ensemble learning approach for classification, regression, and other tasks. It constructs multiple decision trees that are then applied to different sub-samples of the original dataset during training, and then it selects the class with the maximum votes of the decision trees as the result during testing. Therefore, RF is able to deal with overfitting, improving the final performance. GBDT [21] is a powerful ML algorithm for building prediction models for both classification and regression problems. The models in GBDT are built sequentially, and each subsequent model tries to reduce the error obtained by the previous model. Finally, a strong model is produced that combines multiple decision tree-based weak prediction models and maximizes the prediction accuracy. VGG16 and VGG19 [22] are well-known VGGNet models, consisting of 16 and 19 weighted layers in the architectures. They were proposed by the Visual Geometry Group of Oxford University in 2015 and were able to obtain accurate classification performance on a very large image dataset. There are 13 convolution layers, 3 fully connected layers, 5 max-pooling layers, and 1 Softmax layer in VGG16, and 16 convolution layers, 3 fully connected layers, 5 max-pooling layers, and 1 Softmax layer in VGG19. In the VGG16 and VGG19 models, the number of filters increases with the increasing depth of convolution layers, which starts from 64 to 512 feature maps during training and includes two fully connected layers with 4096 neurons in each layer after the convolutional and max-pooling layers, and one output layer with the Softmax activation function and 8 neurons.