# Automatic Breast Tumor Screening of Mammographic Images with Optimal Convolutional Neural Network
## 3 Experimental Results
### Multilayer CNN-Based Classifier Testing and Validation  
This study uses Model #1, as shown in Table 5, which adopts three convolutional layers, and the same completely connected classification layer to develop four models, as shown in Table 6. The convolutional window sizes of the second and third layers are combinations of (\(3\times 3\), \(3\times 3\)), (\(3\times 3\), \(5\times 5\)), (\(5\times 5\), \(3\times 3\)), and (\(5\times 5\), \(5\times 5\)) [51]. The image dataset is divided into two groups of equal size. The four models use 466 trained and 466 untrained feature patterns to test and confirm the performance of the classifier. A total of 1000 epochs are set for the training classifier, with the trained and untrained feature patterns. Figure 7 shows (a) the training performance of the classifier and (b) the training history curve of the classification performance validation; in (b), the solid blue line represents the results of the training performance test and the solid orange line indicates the results of classification performance validation. As the number of epoch training increases, the classifier's output accuracy (%) gradually increases. The four classifier models require an average of lower than 240 s (lower than 4 min) CPU time to complete the training and testing tasks, as seen in Table 6. Then, the trained and untrained feature patterns are randomly selected, and the accuracy (%) of the four classifier models is tested by performing 10-fold cross-validation (\(K_{f}\) = 10). Table 7 shows the overall cross-validation results. Figure 7a indicates that the accuracy (%) of Models #2 and #3 can be improved over 600 epochs of training. By comparison, the accuracy of Models #1 and #4 can be improved over 200-400 epochs,  
Figure 6: (**a**) The original image (malignant tumor) and the enhanced image of the three convolutions, (**b**) The original image and the pixel greyscale distribution map after image enhancement. after which it converges, and the accuracy (%) of classification approaches the maximum. The training convergence curve of the classifier is shown in Figure 7b. The accuracy (%) of the four models may reach larger than 95%. To shorten the classifier's design cycle and reduce the memory requirements for storing classifier parameters, we recommend using the architectures of Models #1 and #4 to establish and implement the multilayer CNN-based classifiers. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Model** & **1 st** & **2 nd** & **2 nd** & **3 rd** & **3 rd** & **Classification** & **Average** \\
**Convolutional** & **Layer** & **Convolutional** & **Pooling** & **Convolutional** & **Layer** & **Pooling** & **Layer** \\ \hline
1 & & \(3\times 3,16\) & & \(3\times 3,16\) & & \(625\) input nodes, & \(<\)280 \\ \hline
2 & & \(3\times 3,16\) & & \(2\times 2,16\) & \(2\times 2,16\) & \(2\times 2,16\) & \(168\) 1 st hidden nodes, & \(<\)220 \\ \hline
3 & & \(5\times 5,16\) & & \(3\times 3,16\) & \(3\times 3,16\) & \(3\times 3,16\) & \(64\) 2 nd hidden nodes, & \(<\)240 \\ \hline
4 & & \(5\times 5,16\) & & \(5\times 5,16\) & & \(2\) output nodes & \(<\)330 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparisons of the training CPU time for different models of multilayer CNN-based classifier. Figure 7: Training history curves of the multilayer CNN-based classifier. (**a**) Training performance test and classification performance validation as seen classification accuracy versus the training epoch and (**b**) classifier training convergence curve as a loss function versus the training epoch. Considering the experimental results listed in Table 6, the architecture of Model #1 is selected to establish the screening classifier. After training is completed, 466 untrained feature patterns, including 184 abnormal and 282 normal patterns, are randomly selected from the dataset to validate the performance of the classifier. The experimental results of the classifier produce a visual confusion matrix.