## 4 Experimental Results and Comparisons
### Experiments on the Benchmark Dataset NEU
#### 4.1.1 The Performance of Progressive Learning in Clean Dataset  
In this experiment, the NEU dataset was divided into a training set and a test set. The training set contained 1500 samples, and each defect retained 50 samples with truth labels, and the remaining labels were removed. The NEU dataset is a benchmark dataset; therefore, we assumed that all the samples are truth labels. All the hyperparameters were selected by cross-validation, and a summary of the Inception_v2 network is presented in Table 1. During the network training, the learning rate was set to 0.01, the batch_size was set to 36, and the max_step was set to 1000. Figure 2: Examples of defect images in NEU: (**a**) crazing (Cr), (**b**) inclusion (In), (**c**) patches (Pa), (**d**) pitted surface (PS), (**e**) rolled-in scale (RS), and (**f**) scratches (Sc). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Type** & **Patch Size/Stride** & **Input Size** \\ \hline Conv & \(3\times 3/2\) & \(299\times 299\times 3\) \\ Conv & \(3\times 3/1\) & \(149\times 149\times 32\) \\ conv padded & \(3\times 3/1\) & \(147\times 147\times 32\) \\ Pool & \(3\times 3/2\) & \(147\times 147\times 64\) \\ Conv & \(3\times 3/1\) & \(73\times 73\times 64\) \\ Conv & \(3\times 3/2\) & \(71\times 71\times 80\) \\ Conv & \(3\times 3/1\) & \(35\times 35\times 192\) \\ \(3\times Inception\) & As in Figure 3 & \(35\times 35\times 288\) \\ \(5\times Inception\) & As in Figure 4 & \(17\times 17\times 768\) \\ \(2\times Inception\) & As in Figure 5 & \(8\times 8\times 1280\) \\ Pool & \(8\times 8\) & \(8\times 8\times 2048\) \\ Linear & Logits & \(1\times 1\times 2048\) \\ Softmax & Classifier & \(1\times 1\times 1000\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Details of Inception_v2. Figure 4: The \(5\times Inception\) module. Figure 3: The \(3\times Inception\) module. This experiment compared the performance of the standard Inception_v2 and the proposed progressive learning method on a clean dataset. The results are presented in Table 2. Before the comparison, the confusion matrix was introduced. A confusion matrix is a matrix used for assessing the performance of classifiers. The general idea of a confusion matrix is to compute the number of instances of Class A which are classified as Class B. A confusion matrix produces a lot of information, which can be summarized as follows:  
* False negative (FN) is the outcome where the model incorrectly predicts the negative class. * True negative (TN) is the outcome the model correctly predicts the negative class. * False positive (FP) is the outcome where the model incorrectly predicts the positive class. * True positive (TP) is the outcome where the model correctly predicts positive class. Accuracy is the most common metric used to evaluate the performance of a classification model. The recognition accuracy is calculated as follows:  
\[A\text{accuracy}=\frac{\text{TN}+\text{TP}}{\text{TN}+\text{TP}+\text{FN}+ \text{FP}} \tag{6}\]  
It can be seen from Table 2 that the average classification accuracies of the standard Inception_v2 and proposed method are 86.55% and 83.79%, respectively. Although the proposed method can still obtain high classification accuracy, compared with the standard Inception_v2, the accuracy is not significantly improved. One possible explanation is that labels in the original NEU dataset are clean labels, and a standard Inception_v2 is sufficient to improve the defect classification accuracy through simple network training when the dataset is relatively small. Meanwhile, PCA for the proposed method for dimensionality reduction may lose some information, even though it will speed up network training. \begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**Original NEU Dataset**} \\ \hline Accuracy (\%) &
\begin{tabular}{c} Standard Inception\_v2 \\ Proposed method \\ \end{tabular} & 86.55 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The average classification accuracies of standard Inception_v2 and the proposed method with the original NEU dataset.