## 3 Results and Discussion
### All Convolutional Layers Are Frozen  
In the model-training phase, only the fully connected layers of the pre-trained VGG13 network were released, so the weights of fully connected layers were updated. Since all the convolutional layers were frozen, all the weights of convolutional layers were applied to hotspot detection. After 10 epochs of training, the model was evaluated.  
As shown in Table 2 and Figure 9, the results of the proposed method were compared with the results of references. Since only the recall, precision, and F1 score are given in the references, there is only the accuracy obtained by the proposed method in Figure 9a. Additionally, there are only the average performance of recall, precision, and F1 score in Ref. [25]. The proposed method shows good performance in accuracy; the accuracy is in the range of 96.1% to 99.3%. For the recall performance, the proposed method is not the best, but it is comparable to the results of references; the average recall of the proposed method reaches 97%. Compared with the results of references, there is significant improvement in the precision and F1 score of the proposed method. In the test results of five benchmarks, the precision performance of the proposed method is in the range of 72.4% to 96.8%. The average precision of the proposed method reaches 88.4%, while the results of all references are less than 48%. For the F1 score performance, the F1 score of the proposed method is in the range of 84% to 97.7%, and the average F1 score reaches 91.9%. Compared with the results of references, the proposed method obtains the much better F1 score performance. The proposed method obtains the best F1 score performance, which indicates that the proposed method has the best comprehensive performance in recall and precision. The improvement of precision and F1 score indicates that the proposed hotspot-detection method has low false-alarm rate. A low false-alarm rate will decrease the post-processing steps and decrease the turn-around time of IC manufacturing.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Benchmarks** & **Methods** & **Accuracy** & **Recall** & **Precision** & **F1 Score** \\ \hline \multirow{3}{*}{Benchmark 1} & Ref. [16] & - & 0.951 & 0.358 & 0.520 \\  & Ref. [26] & - & 0.995 & 0.324 & 0.489 \\  & The proposed method & 0.961 & 0.938 & 0.968 & 0.952 \\ \hline \multirow{3}{*}{Benchmark 2} & Ref. [16] & - & 0.988 & 0.216 & 0.354 \\  & Ref. [26] & - & 0.986 & 0.702 & 0.820 \\  & The proposed method & 0.979 & 0.988 & 0.843 & 0.901 \\ \hline \multirow{3}{*}{Benchmark 3} & Ref. [16] & - & 0.975 & 0.199 & 0.331 \\  & Ref. [26] & - & 0.982 & 0.443 & 0.640 \\  & The proposed method & 0.984 & 0.988 & 0.966 & 0.977 \\ \hline \multirow{3}{*}{Benchmark 4} & Ref. [16] & - & 0.938 & 0.157 & 0.269 \\  & Ref. [26] & - & 0.972 & 0.355 & 0.520 \\  & The proposed method & 0.992 & 0.932 & 0.918 & 0.925 \\ \hline \multirow{3}{*}{Benchmark 5} & Ref. [16] & - & 0.927 & 0.181 & 0.303 \\  & Ref. [26] & - & 0.980 & 0.549 & 0.635 \\ \cline{1-1}  & The proposed method & 0.993 & 1.000 & 0.724 & 0.840 \\ \hline \multirow{3}{*}{Average} & Ref. [16] & - & 0.955 & 0.222 & 0.355 \\ \cline{1-1}  & Ref. [26] & - & 0.983 & 0.475 & 0.635 \\ \cline{1-1}  & Ref. [25] & - & 0.980 & 0.300 & 0.458 \\ \cline{1-1}  & The proposed method & 0.982 & 0.970 & 0.884 & 0.919 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The results of the proposed method and the references.